using Base.MPFR, Base.GMP, Base.GMP.MPZ _widen(x::UInt64) = UInt128(x) _widen(x::Int64) = Int128(x) _unwiden(x::UInt128) = x % UInt64 _unwiden(x::Int128) = x % Int64 _unwiden(x::BigInt) = x % Int128 const BIGINT = BigInt[] function access_threaded(f, v::Vector) tid = Threads.threadid() 0 < tid <= length(v) || _length_assert() if @inbounds isassigned(v, tid) @inbounds x = v[tid] else x = f() @inbounds v[tid] = x end return x end @noinline _length_assert() = @assert false "0 < tid <= v" function _widen(v::T) where {T <: Union{Int128, UInt128}} x = access_threaded(() -> (@static VERSION > v"1.5" ? BigInt(; nbits=256) : BigInt()), BIGINT) ccall((:__gmpz_import, :libgmp), Int32, (Ref{BigInt}, Csize_t, Cint, Csize_t, Cint, Csize_t, Ref{T}), x, 1, 1, 16, 0, 0, v) return x end # Base.exponent_max(T) + Base.significand_bits(T) + 3 # "-0." maxdigits(::Type{Float64}) = 1079 maxdigits(::Type{Float32}) = 154 maxdigits(::Type{Float16}) = 29 maxdigits(T) = typemax(Int64) ten(::Type{T}) where {T} = T(10) const TEN = BigInt(10) ten(::Type{BigInt}) = TEN _muladd(ten, digits, b) = ten * digits + b function _muladd(ten, digits::BigInt, b) Base.GMP.MPZ.mul!(digits, ten) Base.GMP.MPZ.add_ui!(digits, b) return digits end @enum FloatType FLOAT16 FLOAT32 FLOAT64 BIGFLOAT # for non SupportedFloat Reals, parse as Float64, then convert @inline function typeparser(conf::AbstractConf{T}, source, pos, len, b, code, pl, options) where {T <: Real} pos, code, pl, x = typeparser(DefaultConf{Float64}(), source, pos, len, b, code, pl, options) return pos, code, pl, T(x) end function typeparser(::AbstractConf{BigFloat}, source, pos, len, b, code, pl, options) base = 0 rounding = Base.MPFR.ROUNDING_MODE[] z = BigFloat(precision=Base.MPFR.DEFAULT_PRECISION[]) if source isa AbstractVector{UInt8} || source isa String str = source strpos = pos else _, _, _pl, _ = typeparser(String, source, pos, len, b, code, pl, options) _pos = position(source) vpos, vlen = _pl.pos, _pl.len fastseek!(source, vpos - 1) str = Base.StringVector(vlen) strpos = 1 readbytes!(source, str, vlen) fastseek!(source, _pos) # reset IO to earlier position end GC.@preserve str begin ptr = pointer(str, strpos) endptr = Ref{Ptr{UInt8}}() err = ccall((:mpfr_strtofr, :libmpfr), Int32, (Ref{BigFloat}, Ptr{UInt8}, Ref{Ptr{UInt8}}, Int32, Base.MPFR.MPFRRoundingMode), z, ptr, endptr, base, rounding) code |= endptr[] == ptr ? INVALID : OK pos += Int(endptr[] - ptr) return pos, code, PosLen(pl.pos, max(0, pos - pl.pos)), z end end @inline function typeparser(conf::AbstractConf{T}, source, pos, len, b, code, pl, options) where {T <: SupportedFloats} # keep track of starting pos in case of invalid, we can rewind to start of parsing startpos = pos x = zero(T) neg = b == UInt8('-') if neg || b == UInt8('+') pos += 1 incr!(source) end if eof(source, pos, len) # invalid because input is empty or contained only '-' or '+' code |= INVALID | EOF @goto done end b = peekbyte(source, pos) if b != options.decimal && (b - UInt8('0')) > 0x09 # character isn't a digit or decimal point, check for special values, otherwise INVALID if b == UInt8('n') || b == UInt8('N') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto invalid end b = peekbyte(source, pos) if b == UInt8('a') || b == UInt8('A') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto invalid end b = peekbyte(source, pos) if b == UInt8('n') || b == UInt8('N') x = T(NaN) pos += 1 incr!(source) if eof(source, pos, len) code |= EOF end code |= OK | SPECIAL_VALUE @goto done end end elseif b == UInt8('i') || b == UInt8('I') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto invalid end b = peekbyte(source, pos) if b == UInt8('n') || b == UInt8('N') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto invalid end b = peekbyte(source, pos) if b == UInt8('f') || b == UInt8('F') x = ifelse(neg, T(-Inf), T(Inf)) code |= OK | SPECIAL_VALUE pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto done end b = peekbyte(source, pos) if b == UInt8('i') || b == UInt8('I') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto done end b = peekbyte(source, pos) if b == UInt8('n') || b == UInt8('N') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto done end b = peekbyte(source, pos) if b == UInt8('i') || b == UInt8('I') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto done end b = peekbyte(source, pos) if b == UInt8('t') || b == UInt8('T') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF @goto done end b = peekbyte(source, pos) if b == UInt8('y') || b == UInt8('Y') pos += 1 incr!(source) if eof(source, pos, len) code |= EOF end @goto done end end end end end @goto done end end else end @label invalid fastseek!(source, startpos - 1) pos = startpos code |= INVALID @goto done end # start parsing digits or decimal point; we start digits as UInt64(0) and can _widen type if needed x, code, pos = parsedigits(conf, source, pos, len, b, code, options, UInt64(0), neg, startpos) @label done return pos, code, PosLen(pl.pos, pos - pl.pos), x end @inline function handlef(x::T, f::F) where {T, F} if f === nothing return x else f(x) return nothing end end rettype(::Type{T}) where {T} = T === Number ? Nothing : T # when a function is passed to apply to the parsed value, we have to be really careful that the `x` # returned from parsedigits is `Nothing`, otherwise we end up with an overall return type like # `Tuple{Union{Nothing, T}, ReturnCode, Int}`, which can cause dynamic dispatches/inlining issues # for callers. The rule to follow is that before any call to `@goto done`, we need to ensure `x` # has been "handled" properly: either applied or in error cases, set to `nothing` getx(x, f) = f === nothing ? x : nothing # if we need to _widen the type due to `digits` overflow, we want a non-inlined version so base case compilation doesn't get out of control @noinline _parsedigits(conf::AbstractConf{T}, source, pos, len, b, code, options, digits::IntType, neg::Bool, startpos, overflow_invalid::Bool, ndigits::Int, f::F) where {T, IntType, F} = parsedigits(conf, source, pos, len, b, code, options, digits, neg, startpos, overflow_invalid, ndigits, f)::Tuple{rettype(T), ReturnCode, Int} @inline function parsedigits(conf::AbstractConf{T}, source, pos, len, b, code, options, digits::IntType, neg::Bool, startpos, overflow_invalid::Bool=false, ndigits::Int=0, f::F=nothing) where {T, IntType, F} x = zero(T) anydigits = false has_groupmark = _has_groupmark(options, code) groupmark0 = something(options.groupmark, 0xff) - UInt8('0') # we already previously checked if `b` was decimal or a digit, so don't need to check explicitly again if b != options.decimal b -= UInt8('0') prev_b0 = b anydigits = b <= 0x09 while true if b <= 0x09 if overflows(IntType) && digits > overflowval(IntType) return _parsedigits(conf, source, pos, len, b + UInt8('0'), code, options, _widen(digits), neg, startpos, overflow_invalid, ndigits, f) elseif ndigits > maxdigits(T) # if input is way too big, just bail fastseek!(source, startpos - 1) pos = startpos code |= INVALID x = getx(x, f) @goto done end digits = _muladd(ten(IntType), digits, b) pos += 1 incr!(source) ndigits += (!iszero(ndigits) || !iszero(b)) # only accumulate digits without leading zeros if eof(source, pos, len) # input is integer, like "1" if T === Number && IntType != Int64 && digits <= _unwiden(digits) # if T is Number, let's do a quick check if we tripped the # overflow and can actually unwiden y = _unwiden(digits) x = handlef(ifelse(neg, -y, y), f) else x, code = noscale(conf, digits, neg, code, ndigits, f, options) end code |= OK | EOF @goto done end elseif has_groupmark && b == groupmark0 prev_b0 == groupmark0 && (code |= INVALID; x = getx(x, f); @goto done) # two groupmarks in a row pos += 1 Parsers.incr!(source) Parsers.eof(source, pos, len) && (code |= INVALID | EOF; x = getx(x, f); @goto done) # groupmark at end of input else # if `b` isn't a digit or a groupmark, time to break out of digit parsing while loop ((has_groupmark && prev_b0 == groupmark0) || !anydigits) && (code |= INVALID; x = getx(x, f); @goto done) # ended with groupmark break end prev_b0 = b b = peekbyte(source, pos) - UInt8('0') end # b wasn't a digit, so add back '0' to recover original Char value b += UInt8('0') end if b == options.decimal pos += 1 incr!(source) if eof(source, pos, len) # if input is "." then invalid, otherwise ok, like "1." if T === Number x = handlef(ifelse(neg, -Float64(digits), Float64(digits)), f) else x, code = noscale(conf, digits, neg, code, ndigits, f, options) end code |= ((startpos + 1) == pos ? INVALID : OK) | EOF @goto done end b = peekbyte(source, pos) if b - UInt8('0') > 0x09 && !(b == UInt8('e') || b == UInt8('E') || b == UInt8('f') || b == UInt8('F')) # if the next byte after decimal point isn't a digit or exponent char ('e', 'E', 'f', 'F') # and we haven't parsed any digits, like ".a", then invalid # otherwise ok, like "1.a" (only "1." is parsed) if !anydigits code |= INVALID x = getx(x, f) @goto done else if T === Number x = handlef(ifelse(neg, -Float64(digits), Float64(digits)), f) else x, code = noscale(conf, digits, neg, code, ndigits, f, options) end code |= OK @goto done end end end # we've parsed any digits preceding decimal point and consumed decimal point if any # now we parse any digits following decimal point (if any); start `frac` at UInt64(0) # `digits` still receives any fractional digits, `frac` just keeps track of how many digits # were parsed to combine with any "e123" exponent numbers to determine final exponent value (overflows(IntType) && digits > overflowval(IntType)) && (digits = _widen(digits)) x, code, pos = parsefrac(conf, source, pos, len, b, code, options, digits, neg, startpos, UInt64(0), overflow_invalid, ndigits, f) @label done return x, code, pos end # same as above; if digits overflows, we want a non-inlined version to call with a wider type # note that we never expect `frac` to overflow, since it's just keep track of the # of digits # we parse post-decimal point @noinline _parsefrac(conf::AbstractConf{T}, source, pos, len, b, code, options, digits::IntType, neg::Bool, startpos, frac, overflow_invalid, ndigits, f::F) where {T, IntType, F} = parsefrac(conf, source, pos, len, b, code, options, digits, neg, startpos, frac, overflow_invalid, ndigits, f)::Tuple{rettype(T), ReturnCode, Int} @inline function parsefrac(conf::AbstractConf{T}, source, pos, len, b, code, options, digits::IntType, neg::Bool, startpos, frac, overflow_invalid, ndigits, f::F) where {T, IntType, F} x = zero(T) parsedanyfrac = false FT = FLOAT64 # check if `b` is a digit if b - UInt8('0') < 0x0a b -= UInt8('0') parsedanyfrac = true # if so, parse fractional digits while true digits = _muladd(ten(IntType), digits, b) ndigits += (!iszero(ndigits) || !iszero(b)) # only accumulate digits without leading zeros pos += 1 incr!(source) frac += UInt64(1) if eof(source, pos, len) # input is simple non-scientific-notation floating number, like "1.1" if overflow_invalid && -signed(frac) > 308 code |= INVALID x = getx(x, f) else x, code = scale(conf, FT, digits, -signed(frac), neg, code, ndigits, f, options) code |= OK | EOF end @goto done end b = peekbyte(source, pos) - UInt8('0') b > 0x09 && break if overflows(IntType) && digits > overflowval(IntType) return _parsefrac(conf, source, pos, len, b + UInt8('0'), code, options, _widen(digits), neg, startpos, frac, overflow_invalid, ndigits, f) end end b += UInt8('0') end # check for exponent notation if b == UInt8('e') || b == UInt8('E') || b == UInt8('f') || b == UInt8('F') if b == UInt8('f') || b == UInt8('F') FT = FLOAT32 end pos += 1 incr!(source) if eof(source, pos, len) # it's an error to have a "dangling" 'e', so input was something like "1.1e" code |= INVALID | EOF x = getx(x, f) @goto done end b = peekbyte(source, pos) # check for plus or minus sign for exponent number negexp = b == UInt8('-') if negexp || b == UInt8('+') pos += 1 incr!(source) if eof(source, pos, len) # it's an error to have a "dangling" '-' or '+', so input was something like "1.1e-" code |= INVALID | EOF x = getx(x, f) @goto done end b = peekbyte(source, pos) end b -= UInt8('0') if b > 0x09 # invalid to have a "dangling" 'e' code |= INVALID x = getx(x, f) @goto done end # at this point, we've parsed X and Y in "X.YeZ", but not Z in a scientific notation exponent number # we start our exponent number at UInt64(0) return parseexp(conf, source, pos, len, b, code, options, digits, neg, startpos, frac, UInt64(0), negexp, FT, overflow_invalid, ndigits, f) else # if no scientific notation, we're done, so scale digits + frac and return if parsedanyfrac if overflow_invalid && -signed(frac) > 308 code |= INVALID x = getx(x, f) @goto done else x, code = scale(conf, FT, digits, -signed(frac), neg, code, ndigits, f, options) end else x, code = noscale(conf, digits, neg, code, ndigits, f, options) end code |= OK end @label done return x, code, pos end # same no-inline story, but this time for exponent number; probably even more rare to overflow the exponent number # compared to pre/post decimal digits, but we account for it all the same (a lot of float parsers don't account for this) @noinline _parseexp(conf::AbstractConf{T}, source, pos, len, b, code, options, digits, neg::Bool, startpos, frac, exp::ExpType, negexp, FT, overflow_invalid, ndigits, f::F) where {T, ExpType, F} = parseexp(conf, source, pos, len, b, code, options, digits, neg, startpos, frac, exp, negexp, FT, overflow_invalid, ndigits, f)::Tuple{rettype(T), ReturnCode, Int} @inline function parseexp(conf::AbstractConf{T}, source, pos, len, b, code, options, digits, neg::Bool, startpos, frac, exp::ExpType, negexp, FT, overflow_invalid, ndigits, f::F) where {T, ExpType, F} x = zero(T) # note that `b` has already had `b - UInt8('0')` applied to it for parseexp while true exp = ExpType(10) * exp + b pos += 1 incr!(source) if eof(source, pos, len) # we finished parsing input like "1.1e1" ee = ifelse(negexp, -signed(exp), signed(exp)) - signed(frac) if overflow_invalid && ee > 308 code |= INVALID x = getx(x, f) else x, code = scale(conf, FT, digits, ee, neg, code, ndigits, f, options) code |= OK | EOF end @goto done end b = peekbyte(source, pos) - UInt8('0') # if we encounter a non-digit, that must mean we're done if b > 0x09 ee = ifelse(negexp, -signed(exp), signed(exp)) - signed(frac) if overflow_invalid && ee > 308 code |= INVALID x = getx(x, f) else x, code = scale(conf, FT, digits, ifelse(negexp, -signed(exp), signed(exp)) - signed(frac), neg, code, ndigits, f, options) code |= OK end @goto done end if overflows(ExpType) && exp > overflowval(ExpType) return _parseexp(conf, source, pos, len, b, code, options, digits, neg, startpos, frac, _widen(exp), negexp, FT, overflow_invalid, ndigits, f) end end @label done return x, code, pos end # utilities for calculating final float value maxsig(::Type{Float16}) = 2048 maxsig(::Type{Float32}) = 16777216 maxsig(::Type{Float64}) = 9007199254740992 maxsig(::Type{BigFloat}) = 9007199254740992 ceillog5(::Type{Float16}) = 5 ceillog5(::Type{Float32}) = 11 ceillog5(::Type{Float64}) = 23 ceillog5(::Type{BigFloat}) = 23 const F16_SHORT_POWERS = [exp10(Float16(x)) for x = 0:ceillog5(Float16)-1] const F32_SHORT_POWERS = [exp10(Float32(x)) for x = 0:ceillog5(Float32)-1] const F64_SHORT_POWERS = [exp10(Float64(x)) for x = 0:ceillog5(Float64)-1] pow10(::Type{Float16}, e) = (@inbounds v = F16_SHORT_POWERS[e+1]; return v) pow10(::Type{Float32}, e) = (@inbounds v = F32_SHORT_POWERS[e+1]; return v) pow10(::Type{Float64}, e) = (@inbounds v = F64_SHORT_POWERS[e+1]; return v) pow10(::Type{BigFloat}, e) = (@inbounds v = F64_SHORT_POWERS[e+1]; return v) _unsigned(x::BigInt) = x _unsigned(x) = unsigned(x) # No fractional part or exponent, digits in `v` are already scaled @inline function noscale(::AbstractConf{T}, v::Integer, neg::Bool, code, ndigits, f::F, ::Options) where {T, F} return handlef(ifelse(neg, -T(v), T(v)), f), code end # Digits in `v` need to be scaled by `exp` @inline function scale(::AbstractConf{T}, FT::FloatType, v, exp, neg, code, ndigits, f::F, ::Options) where {T, F} if T === Float64 return handlef(__scale(Float64, _unsigned(v), exp, neg), f), code elseif T === Float32 return handlef(__scale(Float32, _unsigned(v), exp, neg), f), code elseif T === Float16 return handlef(__scale(Float16, _unsigned(v), exp, neg), f), code elseif FT == FLOAT64 f64 = __scale(Float64, _unsigned(v), exp, neg) if isfinite(f64) return handlef(f64, f), code else code |= INVALID return nothing, code end elseif FT == FLOAT32 f32 = __scale(Float32, _unsigned(v), exp, neg) if isfinite(f32) return handlef(f32, f), code else code |= INVALID return nothing, code end elseif FT == FLOAT16 f16 = __scale(Float16, _unsigned(v), exp, neg) if isfinite(f16) return handlef(f16, f), code else code |= INVALID return nothing, code end else error("invalid float type for scale: `$T`") end end function __scale(::Type{T}, v, exp, neg) where {T} ms = maxsig(T) cl = ceillog5(T) if v < ms # fastest path if 0 <= exp < cl x = T(v) * pow10(T, exp) return ifelse(neg, -x, x) elseif -cl < exp < 0 x = T(v) / pow10(T, -exp) return ifelse(neg, -x, x) end end v == 0 && return zero(T) if exp > 308 && T != BigFloat return T(neg ? -Inf : Inf) elseif exp < -326 # https://github.com/JuliaData/Parsers.jl/issues/83 return _scale(T, UInt128(v), exp, neg) end return _scale(T, v, exp, neg) end function _scale(::Type{T}, v::UInt64, exp, neg) where {T} mant, pow = pow10spl(exp + 326) lz = leading_zeros(v) newv = v << lz upper, lower = two_prod(newv, mant) if upper & 0x1FF == 0x1FF && (lower + newv < lower) mant_low = mant128(exp + 325) product_middle2, product_low = two_prod(newv, mant_low) product_middle1 = lower product_high = upper product_middle = product_middle1 + product_middle2 if product_middle < product_middle1 product_high += 1 # overflow carry end if (product_middle + 1 == 0) && (product_high & 0x1FF == 0x1FF) && (product_low + v < product_low) return _scale(T, UInt128(v), exp, neg) end upper = product_high lower = product_middle end upperbit = upper >> 63 mantissa = upper >> (upperbit + 9) lz += xor(1, upperbit) if (lower == 0) && upper & 0x1FF == 0 && mantissa & 3 == 1 return _scale(T, UInt128(v), exp, neg) end mantissa += mantissa & 1 mantissa >>= 1 if mantissa >= UInt64(1) << 53 mantissa = UInt64(1) << 52 lz -= 1 end mantissa &= ~(UInt64(1) << 52) real_exponent = pow - lz if real_exponent < 1 || real_exponent > 2046 return _scale(T, UInt128(v), exp, neg) end mantissa |= real_exponent << 52 mantissa |= (UInt64(neg) << 63) return T(Core.bitcast(Float64, mantissa)) end convert_and_apply_neg(::Type{T}, x, neg) where {T} = neg ? T(-x) : T(x) # Copied from https://github.com/JuliaLang/julia/blob/c054dbc6d4e03d7168864fed018e3635b546d251/base/mpfr.jl#L1029-L1031 function unalias_bigfloat(x::BigFloat) d = x._d d′ = GC.@preserve d unsafe_string(pointer(d), sizeof(d)) # creates a definitely-new String return Base.MPFR._BigFloat(x.prec, x.sign, x.exp, d′) end # need to special-case here because `x` came from thread-local BIGFLOATS array # so we need to make a copy to get a fresh BigFloat # # See https://github.com/JuliaData/CSV.jl/issues/938 function convert_and_apply_neg(::Type{BigFloat}, x::BigFloat, neg) y = unalias_bigfloat(x) if neg ccall((:mpfr_neg, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), y, y, MPFR.ROUNDING_MODE[]) end return y end function _scale(::Type{T}, v::V, exp, neg) where {T, V <: UInt128} if exp == 23 # special-case concluded from https://github.com/JuliaLang/julia/issues/38509 x = v * V(1e23) elseif 0 <= exp < 290 x = v * exp10(exp) elseif exp < -308 || exp > 308 || v > maxsig(T) # if v is too large, we lose precision by just doing # v / exp10(-exp) since that only promotes to Float64 # so detect and re-route to this branch where we widen v y = _widen(v) return _scale(T, y, exp, neg) else x = v / exp10(-exp) end return convert_and_apply_neg(T, x, neg) end const BIGEXP10 = [1 / exp10(BigInt(e)) for e = 309:327] const BIGFLOATS = BigFloat[] const BIGFLOATEXP10 = [exp10(BigFloat(i; precision=256)) for i = 1:308] function _scale(::Type{T}, v::V, exp, neg) where {T, V <: BigInt} x = access_threaded(BigFloat, BIGFLOATS) ccall((:mpfr_set_z, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}, Int32), x, v, MPFR.ROUNDING_MODE[]) if exp < -308 # v * (1 / exp10(-exp)) if exp < -327 y = 1 / exp10(BigInt(-exp)) else y = BIGEXP10[-exp - 308] end ccall((:mpfr_mul, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), x, x, y, MPFR.ROUNDING_MODE[]) elseif exp < 0 # v / exp10(-exp) y = BIGFLOATEXP10[-exp] ccall((:mpfr_div, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), x, x, y, MPFR.ROUNDING_MODE[]) else # v * exp10(V(exp)) if exp <= 308 y = BIGFLOATEXP10[exp] else y = exp10(BigFloat(exp; precision=256)) end ccall((:mpfr_mul, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), x, x, y, MPFR.ROUNDING_MODE[]) end return convert_and_apply_neg(T, x, neg) end @inline function two_prod(a, b) x = UInt128(a) * b return UInt64(x >> 64), x % UInt64 end pow10spl(i) = (@inbounds x = POW10SPL[i + 1]; return x) mant128(i) = (@inbounds x = MANTISSA128[i + 1]; return x) const POW10SPL = [ (0xa5ced43b7e3e9188, 7), (0xa5ced43b7e3e9188, 7), (0xcf42894a5dce35ea, 10), (0x818995ce7aa0e1b2, 14), (0xa1ebfb4219491a1f, 17), (0xca66fa129f9b60a6, 20), (0xfd00b897478238d0, 23), (0x9e20735e8cb16382, 27), (0xc5a890362fddbc62, 30), (0xf712b443bbd52b7b, 33), (0x9a6bb0aa55653b2d, 37), (0xc1069cd4eabe89f8, 40), (0xf148440a256e2c76, 43), (0x96cd2a865764dbca, 47), (0xbc807527ed3e12bc, 50), (0xeba09271e88d976b, 53), (0x93445b8731587ea3, 57), (0xb8157268fdae9e4c, 60), (0xe61acf033d1a45df, 63), (0x8fd0c16206306bab, 67), (0xb3c4f1ba87bc8696, 70), (0xe0b62e2929aba83c, 73), (0x8c71dcd9ba0b4925, 77), (0xaf8e5410288e1b6f, 80), (0xdb71e91432b1a24a, 83), (0x892731ac9faf056e, 87), (0xab70fe17c79ac6ca, 90), (0xd64d3d9db981787d, 93), (0x85f0468293f0eb4e, 97), (0xa76c582338ed2621, 100), (0xd1476e2c07286faa, 103), (0x82cca4db847945ca, 107), (0xa37fce126597973c, 110), (0xcc5fc196fefd7d0c, 113), (0xff77b1fcbebcdc4f, 116), (0x9faacf3df73609b1, 120), (0xc795830d75038c1d, 123), (0xf97ae3d0d2446f25, 126), (0x9becce62836ac577, 130), (0xc2e801fb244576d5, 133), (0xf3a20279ed56d48a, 136), (0x9845418c345644d6, 140), (0xbe5691ef416bd60c, 143), (0xedec366b11c6cb8f, 146), (0x94b3a202eb1c3f39, 150), (0xb9e08a83a5e34f07, 153), (0xe858ad248f5c22c9, 156), (0x91376c36d99995be, 160), (0xb58547448ffffb2d, 163), (0xe2e69915b3fff9f9, 166), (0x8dd01fad907ffc3b, 170), (0xb1442798f49ffb4a, 173), (0xdd95317f31c7fa1d, 176), (0x8a7d3eef7f1cfc52, 180), (0xad1c8eab5ee43b66, 183), (0xd863b256369d4a40, 186), (0x873e4f75e2224e68, 190), (0xa90de3535aaae202, 193), (0xd3515c2831559a83, 196), (0x8412d9991ed58091, 200), (0xa5178fff668ae0b6, 203), (0xce5d73ff402d98e3, 206), (0x80fa687f881c7f8e, 210), (0xa139029f6a239f72, 213), (0xc987434744ac874e, 216), (0xfbe9141915d7a922, 219), (0x9d71ac8fada6c9b5, 223), (0xc4ce17b399107c22, 226), (0xf6019da07f549b2b, 229), (0x99c102844f94e0fb, 233), (0xc0314325637a1939, 236), (0xf03d93eebc589f88, 239), (0x96267c7535b763b5, 243), (0xbbb01b9283253ca2, 246), (0xea9c227723ee8bcb, 249), (0x92a1958a7675175f, 253), (0xb749faed14125d36, 256), (0xe51c79a85916f484, 259), (0x8f31cc0937ae58d2, 263), (0xb2fe3f0b8599ef07, 266), (0xdfbdcece67006ac9, 269), (0x8bd6a141006042bd, 273), (0xaecc49914078536d, 276), (0xda7f5bf590966848, 279), (0x888f99797a5e012d, 283), (0xaab37fd7d8f58178, 286), (0xd5605fcdcf32e1d6, 289), (0x855c3be0a17fcd26, 293), (0xa6b34ad8c9dfc06f, 296), (0xd0601d8efc57b08b, 299), (0x823c12795db6ce57, 303), (0xa2cb1717b52481ed, 306), (0xcb7ddcdda26da268, 309), (0xfe5d54150b090b02, 312), (0x9efa548d26e5a6e1, 316), (0xc6b8e9b0709f109a, 319), (0xf867241c8cc6d4c0, 322), (0x9b407691d7fc44f8, 326), (0xc21094364dfb5636, 329), (0xf294b943e17a2bc4, 332), (0x979cf3ca6cec5b5a, 336), (0xbd8430bd08277231, 339), (0xece53cec4a314ebd, 342), (0x940f4613ae5ed136, 346), (0xb913179899f68584, 349), (0xe757dd7ec07426e5, 352), (0x9096ea6f3848984f, 356), (0xb4bca50b065abe63, 359), (0xe1ebce4dc7f16dfb, 362), (0x8d3360f09cf6e4bd, 366), (0xb080392cc4349dec, 369), (0xdca04777f541c567, 372), (0x89e42caaf9491b60, 376), (0xac5d37d5b79b6239, 379), (0xd77485cb25823ac7, 382), (0x86a8d39ef77164bc, 386), (0xa8530886b54dbdeb, 389), (0xd267caa862a12d66, 392), (0x8380dea93da4bc60, 396), (0xa46116538d0deb78, 399), (0xcd795be870516656, 402), (0x806bd9714632dff6, 406), (0xa086cfcd97bf97f3, 409), (0xc8a883c0fdaf7df0, 412), (0xfad2a4b13d1b5d6c, 415), (0x9cc3a6eec6311a63, 419), (0xc3f490aa77bd60fc, 422), (0xf4f1b4d515acb93b, 425), (0x991711052d8bf3c5, 429), (0xbf5cd54678eef0b6, 432), (0xef340a98172aace4, 435), (0x9580869f0e7aac0e, 439), (0xbae0a846d2195712, 442), (0xe998d258869facd7, 445), (0x91ff83775423cc06, 449), (0xb67f6455292cbf08, 452), (0xe41f3d6a7377eeca, 455), (0x8e938662882af53e, 459), (0xb23867fb2a35b28d, 462), (0xdec681f9f4c31f31, 465), (0x8b3c113c38f9f37e, 469), (0xae0b158b4738705e, 472), (0xd98ddaee19068c76, 475), (0x87f8a8d4cfa417c9, 479), (0xa9f6d30a038d1dbc, 482), (0xd47487cc8470652b, 485), (0x84c8d4dfd2c63f3b, 489), (0xa5fb0a17c777cf09, 492), (0xcf79cc9db955c2cc, 495), (0x81ac1fe293d599bf, 499), (0xa21727db38cb002f, 502), (0xca9cf1d206fdc03b, 505), (0xfd442e4688bd304a, 508), (0x9e4a9cec15763e2e, 512), (0xc5dd44271ad3cdba, 515), (0xf7549530e188c128, 518), (0x9a94dd3e8cf578b9, 522), (0xc13a148e3032d6e7, 525), (0xf18899b1bc3f8ca1, 528), (0x96f5600f15a7b7e5, 532), (0xbcb2b812db11a5de, 535), (0xebdf661791d60f56, 538), (0x936b9fcebb25c995, 542), (0xb84687c269ef3bfb, 545), (0xe65829b3046b0afa, 548), (0x8ff71a0fe2c2e6dc, 552), (0xb3f4e093db73a093, 555), (0xe0f218b8d25088b8, 558), (0x8c974f7383725573, 562), (0xafbd2350644eeacf, 565), (0xdbac6c247d62a583, 568), (0x894bc396ce5da772, 572), (0xab9eb47c81f5114f, 575), (0xd686619ba27255a2, 578), (0x8613fd0145877585, 582), (0xa798fc4196e952e7, 585), (0xd17f3b51fca3a7a0, 588), (0x82ef85133de648c4, 592), (0xa3ab66580d5fdaf5, 595), (0xcc963fee10b7d1b3, 598), (0xffbbcfe994e5c61f, 601), (0x9fd561f1fd0f9bd3, 605), (0xc7caba6e7c5382c8, 608), (0xf9bd690a1b68637b, 611), (0x9c1661a651213e2d, 615), (0xc31bfa0fe5698db8, 618), (0xf3e2f893dec3f126, 621), (0x986ddb5c6b3a76b7, 625), (0xbe89523386091465, 628), (0xee2ba6c0678b597f, 631), (0x94db483840b717ef, 635), (0xba121a4650e4ddeb, 638), (0xe896a0d7e51e1566, 641), (0x915e2486ef32cd60, 645), (0xb5b5ada8aaff80b8, 648), (0xe3231912d5bf60e6, 651), (0x8df5efabc5979c8f, 655), (0xb1736b96b6fd83b3, 658), (0xddd0467c64bce4a0, 661), (0x8aa22c0dbef60ee4, 665), (0xad4ab7112eb3929d, 668), (0xd89d64d57a607744, 671), (0x87625f056c7c4a8b, 675), (0xa93af6c6c79b5d2d, 678), (0xd389b47879823479, 681), (0x843610cb4bf160cb, 685), (0xa54394fe1eedb8fe, 688), (0xce947a3da6a9273e, 691), (0x811ccc668829b887, 695), (0xa163ff802a3426a8, 698), (0xc9bcff6034c13052, 701), (0xfc2c3f3841f17c67, 704), (0x9d9ba7832936edc0, 708), (0xc5029163f384a931, 711), (0xf64335bcf065d37d, 714), (0x99ea0196163fa42e, 718), (0xc06481fb9bcf8d39, 721), (0xf07da27a82c37088, 724), (0x964e858c91ba2655, 728), (0xbbe226efb628afea, 731), (0xeadab0aba3b2dbe5, 734), (0x92c8ae6b464fc96f, 738), (0xb77ada0617e3bbcb, 741), (0xe55990879ddcaabd, 744), (0x8f57fa54c2a9eab6, 748), (0xb32df8e9f3546564, 751), (0xdff9772470297ebd, 754), (0x8bfbea76c619ef36, 758), (0xaefae51477a06b03, 761), (0xdab99e59958885c4, 764), (0x88b402f7fd75539b, 768), (0xaae103b5fcd2a881, 771), (0xd59944a37c0752a2, 774), (0x857fcae62d8493a5, 778), (0xa6dfbd9fb8e5b88e, 781), (0xd097ad07a71f26b2, 784), (0x825ecc24c873782f, 788), (0xa2f67f2dfa90563b, 791), (0xcbb41ef979346bca, 794), (0xfea126b7d78186bc, 797), (0x9f24b832e6b0f436, 801), (0xc6ede63fa05d3143, 804), (0xf8a95fcf88747d94, 807), (0x9b69dbe1b548ce7c, 811), (0xc24452da229b021b, 814), (0xf2d56790ab41c2a2, 817), (0x97c560ba6b0919a5, 821), (0xbdb6b8e905cb600f, 824), (0xed246723473e3813, 827), (0x9436c0760c86e30b, 831), (0xb94470938fa89bce, 834), (0xe7958cb87392c2c2, 837), (0x90bd77f3483bb9b9, 841), (0xb4ecd5f01a4aa828, 844), (0xe2280b6c20dd5232, 847), (0x8d590723948a535f, 851), (0xb0af48ec79ace837, 854), (0xdcdb1b2798182244, 857), (0x8a08f0f8bf0f156b, 861), (0xac8b2d36eed2dac5, 864), (0xd7adf884aa879177, 867), (0x86ccbb52ea94baea, 871), (0xa87fea27a539e9a5, 874), (0xd29fe4b18e88640e, 877), (0x83a3eeeef9153e89, 881), (0xa48ceaaab75a8e2b, 884), (0xcdb02555653131b6, 887), (0x808e17555f3ebf11, 891), (0xa0b19d2ab70e6ed6, 894), (0xc8de047564d20a8b, 897), (0xfb158592be068d2e, 900), (0x9ced737bb6c4183d, 904), (0xc428d05aa4751e4c, 907), (0xf53304714d9265df, 910), (0x993fe2c6d07b7fab, 914), (0xbf8fdb78849a5f96, 917), (0xef73d256a5c0f77c, 920), (0x95a8637627989aad, 924), (0xbb127c53b17ec159, 927), (0xe9d71b689dde71af, 930), (0x9226712162ab070d, 934), (0xb6b00d69bb55c8d1, 937), (0xe45c10c42a2b3b05, 940), (0x8eb98a7a9a5b04e3, 944), (0xb267ed1940f1c61c, 947), (0xdf01e85f912e37a3, 950), (0x8b61313bbabce2c6, 954), (0xae397d8aa96c1b77, 957), (0xd9c7dced53c72255, 960), (0x881cea14545c7575, 964), (0xaa242499697392d2, 967), (0xd4ad2dbfc3d07787, 970), (0x84ec3c97da624ab4, 974), (0xa6274bbdd0fadd61, 977), (0xcfb11ead453994ba, 980), (0x81ceb32c4b43fcf4, 984), (0xa2425ff75e14fc31, 987), (0xcad2f7f5359a3b3e, 990), (0xfd87b5f28300ca0d, 993), (0x9e74d1b791e07e48, 997), (0xc612062576589dda, 1000), (0xf79687aed3eec551, 1003), (0x9abe14cd44753b52, 1007), (0xc16d9a0095928a27, 1010), (0xf1c90080baf72cb1, 1013), (0x971da05074da7bee, 1017), (0xbce5086492111aea, 1020), (0xec1e4a7db69561a5, 1023), (0x9392ee8e921d5d07, 1027), (0xb877aa3236a4b449, 1030), (0xe69594bec44de15b, 1033), (0x901d7cf73ab0acd9, 1037), (0xb424dc35095cd80f, 1040), (0xe12e13424bb40e13, 1043), (0x8cbccc096f5088cb, 1047), (0xafebff0bcb24aafe, 1050), (0xdbe6fecebdedd5be, 1053), (0x89705f4136b4a597, 1057), (0xabcc77118461cefc, 1060), (0xd6bf94d5e57a42bc, 1063), (0x8637bd05af6c69b5, 1067), (0xa7c5ac471b478423, 1070), (0xd1b71758e219652b, 1073), (0x83126e978d4fdf3b, 1077), (0xa3d70a3d70a3d70a, 1080), (0xcccccccccccccccc, 1083), (0x8000000000000000, 1087), (0xa000000000000000, 1090), (0xc800000000000000, 1093), (0xfa00000000000000, 1096), (0x9c40000000000000, 1100), (0xc350000000000000, 1103), (0xf424000000000000, 1106), (0x9896800000000000, 1110), (0xbebc200000000000, 1113), (0xee6b280000000000, 1116), (0x9502f90000000000, 1120), (0xba43b74000000000, 1123), (0xe8d4a51000000000, 1126), (0x9184e72a00000000, 1130), (0xb5e620f480000000, 1133), (0xe35fa931a0000000, 1136), (0x8e1bc9bf04000000, 1140), (0xb1a2bc2ec5000000, 1143), (0xde0b6b3a76400000, 1146), (0x8ac7230489e80000, 1150), (0xad78ebc5ac620000, 1153), (0xd8d726b7177a8000, 1156), (0x878678326eac9000, 1160), (0xa968163f0a57b400, 1163), (0xd3c21bcecceda100, 1166), (0x84595161401484a0, 1170), (0xa56fa5b99019a5c8, 1173), (0xcecb8f27f4200f3a, 1176), (0x813f3978f8940984, 1180), (0xa18f07d736b90be5, 1183), (0xc9f2c9cd04674ede, 1186), (0xfc6f7c4045812296, 1189), (0x9dc5ada82b70b59d, 1193), (0xc5371912364ce305, 1196), (0xf684df56c3e01bc6, 1199), (0x9a130b963a6c115c, 1203), (0xc097ce7bc90715b3, 1206), (0xf0bdc21abb48db20, 1209), (0x96769950b50d88f4, 1213), (0xbc143fa4e250eb31, 1216), (0xeb194f8e1ae525fd, 1219), (0x92efd1b8d0cf37be, 1223), (0xb7abc627050305ad, 1226), (0xe596b7b0c643c719, 1229), (0x8f7e32ce7bea5c6f, 1233), (0xb35dbf821ae4f38b, 1236), (0xe0352f62a19e306e, 1239), (0x8c213d9da502de45, 1243), (0xaf298d050e4395d6, 1246), (0xdaf3f04651d47b4c, 1249), (0x88d8762bf324cd0f, 1253), (0xab0e93b6efee0053, 1256), (0xd5d238a4abe98068, 1259), (0x85a36366eb71f041, 1263), (0xa70c3c40a64e6c51, 1266), (0xd0cf4b50cfe20765, 1269), (0x82818f1281ed449f, 1273), (0xa321f2d7226895c7, 1276), (0xcbea6f8ceb02bb39, 1279), (0xfee50b7025c36a08, 1282), (0x9f4f2726179a2245, 1286), (0xc722f0ef9d80aad6, 1289), (0xf8ebad2b84e0d58b, 1292), (0x9b934c3b330c8577, 1296), (0xc2781f49ffcfa6d5, 1299), (0xf316271c7fc3908a, 1302), (0x97edd871cfda3a56, 1306), (0xbde94e8e43d0c8ec, 1309), (0xed63a231d4c4fb27, 1312), (0x945e455f24fb1cf8, 1316), (0xb975d6b6ee39e436, 1319), (0xe7d34c64a9c85d44, 1322), (0x90e40fbeea1d3a4a, 1326), (0xb51d13aea4a488dd, 1329), (0xe264589a4dcdab14, 1332), (0x8d7eb76070a08aec, 1336), (0xb0de65388cc8ada8, 1339), (0xdd15fe86affad912, 1342), (0x8a2dbf142dfcc7ab, 1346), (0xacb92ed9397bf996, 1349), (0xd7e77a8f87daf7fb, 1352), (0x86f0ac99b4e8dafd, 1356), (0xa8acd7c0222311bc, 1359), (0xd2d80db02aabd62b, 1362), (0x83c7088e1aab65db, 1366), (0xa4b8cab1a1563f52, 1369), (0xcde6fd5e09abcf26, 1372), (0x80b05e5ac60b6178, 1376), (0xa0dc75f1778e39d6, 1379), (0xc913936dd571c84c, 1382), (0xfb5878494ace3a5f, 1385), (0x9d174b2dcec0e47b, 1389), (0xc45d1df942711d9a, 1392), (0xf5746577930d6500, 1395), (0x9968bf6abbe85f20, 1399), (0xbfc2ef456ae276e8, 1402), (0xefb3ab16c59b14a2, 1405), (0x95d04aee3b80ece5, 1409), (0xbb445da9ca61281f, 1412), (0xea1575143cf97226, 1415), (0x924d692ca61be758, 1419), (0xb6e0c377cfa2e12e, 1422), (0xe498f455c38b997a, 1425), (0x8edf98b59a373fec, 1429), (0xb2977ee300c50fe7, 1432), (0xdf3d5e9bc0f653e1, 1435), (0x8b865b215899f46c, 1439), (0xae67f1e9aec07187, 1442), (0xda01ee641a708de9, 1445), (0x884134fe908658b2, 1449), (0xaa51823e34a7eede, 1452), (0xd4e5e2cdc1d1ea96, 1455), (0x850fadc09923329e, 1459), (0xa6539930bf6bff45, 1462), (0xcfe87f7cef46ff16, 1465), (0x81f14fae158c5f6e, 1469), (0xa26da3999aef7749, 1472), (0xcb090c8001ab551c, 1475), (0xfdcb4fa002162a63, 1478), (0x9e9f11c4014dda7e, 1482), (0xc646d63501a1511d, 1485), (0xf7d88bc24209a565, 1488), (0x9ae757596946075f, 1492), (0xc1a12d2fc3978937, 1495), (0xf209787bb47d6b84, 1498), (0x9745eb4d50ce6332, 1502), (0xbd176620a501fbff, 1505), (0xec5d3fa8ce427aff, 1508), (0x93ba47c980e98cdf, 1512), (0xb8a8d9bbe123f017, 1515), (0xe6d3102ad96cec1d, 1518), (0x9043ea1ac7e41392, 1522), (0xb454e4a179dd1877, 1525), (0xe16a1dc9d8545e94, 1528), (0x8ce2529e2734bb1d, 1532), (0xb01ae745b101e9e4, 1535), (0xdc21a1171d42645d, 1538), (0x899504ae72497eba, 1542), (0xabfa45da0edbde69, 1545), (0xd6f8d7509292d603, 1548), (0x865b86925b9bc5c2, 1552), (0xa7f26836f282b732, 1555), (0xd1ef0244af2364ff, 1558), (0x8335616aed761f1f, 1562), (0xa402b9c5a8d3a6e7, 1565), (0xcd036837130890a1, 1568), (0x802221226be55a64, 1572), (0xa02aa96b06deb0fd, 1575), (0xc83553c5c8965d3d, 1578), (0xfa42a8b73abbf48c, 1581), (0x9c69a97284b578d7, 1585), (0xc38413cf25e2d70d, 1588), (0xf46518c2ef5b8cd1, 1591), (0x98bf2f79d5993802, 1595), (0xbeeefb584aff8603, 1598), (0xeeaaba2e5dbf6784, 1601), (0x952ab45cfa97a0b2, 1605), (0xba756174393d88df, 1608), (0xe912b9d1478ceb17, 1611), (0x91abb422ccb812ee, 1615), (0xb616a12b7fe617aa, 1618), (0xe39c49765fdf9d94, 1621), (0x8e41ade9fbebc27d, 1625), (0xb1d219647ae6b31c, 1628), (0xde469fbd99a05fe3, 1631), (0x8aec23d680043bee, 1635), (0xada72ccc20054ae9, 1638), (0xd910f7ff28069da4, 1641), (0x87aa9aff79042286, 1645), (0xa99541bf57452b28, 1648), (0xd3fa922f2d1675f2, 1651), (0x847c9b5d7c2e09b7, 1655), (0xa59bc234db398c25, 1658), (0xcf02b2c21207ef2e, 1661), (0x8161afb94b44f57d, 1665), (0xa1ba1ba79e1632dc, 1668), (0xca28a291859bbf93, 1671), (0xfcb2cb35e702af78, 1674), (0x9defbf01b061adab, 1678), (0xc56baec21c7a1916, 1681), (0xf6c69a72a3989f5b, 1684), (0x9a3c2087a63f6399, 1688), (0xc0cb28a98fcf3c7f, 1691), (0xf0fdf2d3f3c30b9f, 1694), (0x969eb7c47859e743, 1698), (0xbc4665b596706114, 1701), (0xeb57ff22fc0c7959, 1704), (0x9316ff75dd87cbd8, 1708), (0xb7dcbf5354e9bece, 1711), (0xe5d3ef282a242e81, 1714), (0x8fa475791a569d10, 1718), (0xb38d92d760ec4455, 1721), (0xe070f78d3927556a, 1724), (0x8c469ab843b89562, 1728), (0xaf58416654a6babb, 1731), (0xdb2e51bfe9d0696a, 1734), (0x88fcf317f22241e2, 1738), (0xab3c2fddeeaad25a, 1741), (0xd60b3bd56a5586f1, 1744), (0x85c7056562757456, 1748), (0xa738c6bebb12d16c, 1751), (0xd106f86e69d785c7, 1754), (0x82a45b450226b39c, 1758), (0xa34d721642b06084, 1761), (0xcc20ce9bd35c78a5, 1764), (0xff290242c83396ce, 1767), (0x9f79a169bd203e41, 1771), (0xc75809c42c684dd1, 1774), (0xf92e0c3537826145, 1777), (0x9bbcc7a142b17ccb, 1781), (0xc2abf989935ddbfe, 1784), (0xf356f7ebf83552fe, 1787), (0x98165af37b2153de, 1791), (0xbe1bf1b059e9a8d6, 1794), (0xeda2ee1c7064130c, 1797), (0x9485d4d1c63e8be7, 1801), (0xb9a74a0637ce2ee1, 1804), (0xe8111c87c5c1ba99, 1807), (0x910ab1d4db9914a0, 1811), (0xb54d5e4a127f59c8, 1814), (0xe2a0b5dc971f303a, 1817), (0x8da471a9de737e24, 1821), (0xb10d8e1456105dad, 1824), (0xdd50f1996b947518, 1827), (0x8a5296ffe33cc92f, 1831), (0xace73cbfdc0bfb7b, 1834), (0xd8210befd30efa5a, 1837), (0x8714a775e3e95c78, 1841), (0xa8d9d1535ce3b396, 1844), (0xd31045a8341ca07c, 1847), (0x83ea2b892091e44d, 1851), (0xa4e4b66b68b65d60, 1854), (0xce1de40642e3f4b9, 1857), (0x80d2ae83e9ce78f3, 1861), (0xa1075a24e4421730, 1864), (0xc94930ae1d529cfc, 1867), (0xfb9b7cd9a4a7443c, 1870), (0x9d412e0806e88aa5, 1874), (0xc491798a08a2ad4e, 1877), (0xf5b5d7ec8acb58a2, 1880), (0x9991a6f3d6bf1765, 1884), (0xbff610b0cc6edd3f, 1887), (0xeff394dcff8a948e, 1890), (0x95f83d0a1fb69cd9, 1894), (0xbb764c4ca7a4440f, 1897), (0xea53df5fd18d5513, 1900), (0x92746b9be2f8552c, 1904), (0xb7118682dbb66a77, 1907), (0xe4d5e82392a40515, 1910), (0x8f05b1163ba6832d, 1914), (0xb2c71d5bca9023f8, 1917), (0xdf78e4b2bd342cf6, 1920), (0x8bab8eefb6409c1a, 1924), (0xae9672aba3d0c320, 1927), (0xda3c0f568cc4f3e8, 1930), (0x8865899617fb1871, 1934), (0xaa7eebfb9df9de8d, 1937), (0xd51ea6fa85785631, 1940), (0x8533285c936b35de, 1944), (0xa67ff273b8460356, 1947), (0xd01fef10a657842c, 1950), (0x8213f56a67f6b29b, 1954), (0xa298f2c501f45f42, 1957), (0xcb3f2f7642717713, 1960), (0xfe0efb53d30dd4d7, 1963), (0x9ec95d1463e8a506, 1967), (0xc67bb4597ce2ce48, 1970), (0xf81aa16fdc1b81da, 1973), (0x9b10a4e5e9913128, 1977), (0xc1d4ce1f63f57d72, 1980), (0xf24a01a73cf2dccf, 1983), (0x976e41088617ca01, 1987), (0xbd49d14aa79dbc82, 1990), (0xec9c459d51852ba2, 1993), (0x93e1ab8252f33b45, 1997), (0xb8da1662e7b00a17, 2000), (0xe7109bfba19c0c9d, 2003), (0x906a617d450187e2, 2007), (0xb484f9dc9641e9da, 2010), (0xe1a63853bbd26451, 2013), (0x8d07e33455637eb2, 2017), (0xb049dc016abc5e5f, 2020), (0xdc5c5301c56b75f7, 2023), (0x89b9b3e11b6329ba, 2027), (0xac2820d9623bf429, 2030), (0xd732290fbacaf133, 2033), (0x867f59a9d4bed6c0, 2037), (0xa81f301449ee8c70, 2040), (0xd226fc195c6a2f8c, 2043), (0x83585d8fd9c25db7, 2047), (0xa42e74f3d032f525, 2050), (0xcd3a1230c43fb26f, 2053), (0x80444b5e7aa7cf85, 2057), (0xa0555e361951c366, 2060), (0xc86ab5c39fa63440, 2063), (0xfa856334878fc150, 2066), (0x9c935e00d4b9d8d2, 2070), (0xc3b8358109e84f07, 2073), (0xf4a642e14c6262c8, 2076), (0x98e7e9cccfbd7dbd, 2080), (0xbf21e44003acdd2c, 2083), (0xeeea5d5004981478, 2086), (0x95527a5202df0ccb, 2090), (0xbaa718e68396cffd, 2093), (0xe950df20247c83fd, 2096), (0x91d28b7416cdd27e, 2100), (0xb6472e511c81471d, 2103), (0xe3d8f9e563a198e5, 2106), (0x8e679c2f5e44ff8f, 2110)] const MANTISSA128 = [0x419ea3bd35385e2d, 0x52064cac828675b9, 0x7343efebd1940993, 0x1014ebe6c5f90bf8, 0xd41a26e077774ef6, 0x8920b098955522b4, 0x55b46e5f5d5535b0, 0xeb2189f734aa831d, 0xa5e9ec7501d523e4, 0x47b233c92125366e, 0x999ec0bb696e840a, 0xc00670ea43ca250d, 0x380406926a5e5728, 0xc605083704f5ecf2, 0xf7864a44c633682e, 0x7ab3ee6afbe0211d, 0x5960ea05bad82964, 0x6fb92487298e33bd, 0xa5d3b6d479f8e056, 0x8f48a4899877186c, 0x331acdabfe94de87, 0x9ff0c08b7f1d0b14, 0x7ecf0ae5ee44dd9, 0xc9e82cd9f69d6150, 0xbe311c083a225cd2, 0x6dbd630a48aaf406, 0x92cbbccdad5b108, 0x25bbf56008c58ea5, 0xaf2af2b80af6f24e, 0x1af5af660db4aee1, 0x50d98d9fc890ed4d, 0xe50ff107bab528a0, 0x1e53ed49a96272c8, 0x25e8e89c13bb0f7a, 0x77b191618c54e9ac, 0xd59df5b9ef6a2417, 0x4b0573286b44ad1d, 0x4ee367f9430aec32, 0x229c41f793cda73f, 0x6b43527578c1110f, 0x830a13896b78aaa9, 0x23cc986bc656d553, 0x2cbfbe86b7ec8aa8, 0x7bf7d71432f3d6a9, 0xdaf5ccd93fb0cc53, 0xd1b3400f8f9cff68, 0x23100809b9c21fa1, 0xabd40a0c2832a78a, 0x16c90c8f323f516c, 0xae3da7d97f6792e3, 0x99cd11cfdf41779c, 0x40405643d711d583, 0x482835ea666b2572, 0xda3243650005eecf, 0x90bed43e40076a82, 0x5a7744a6e804a291, 0x711515d0a205cb36, 0xd5a5b44ca873e03, 0xe858790afe9486c2, 0x626e974dbe39a872, 0xfb0a3d212dc8128f, 0x7ce66634bc9d0b99, 0x1c1fffc1ebc44e80, 0xa327ffb266b56220, 0x4bf1ff9f0062baa8, 0x6f773fc3603db4a9, 0xcb550fb4384d21d3, 0x7e2a53a146606a48, 0x2eda7444cbfc426d, 0xfa911155fefb5308, 0x793555ab7eba27ca, 0x4bc1558b2f3458de, 0x9eb1aaedfb016f16, 0x465e15a979c1cadc, 0xbfacd89ec191ec9, 0xcef980ec671f667b, 0x82b7e12780e7401a, 0xd1b2ecb8b0908810, 0x861fa7e6dcb4aa15, 0x67a791e093e1d49a, 0xe0c8bb2c5c6d24e0, 0x58fae9f773886e18, 0xaf39a475506a899e, 0x6d8406c952429603, 0xc8e5087ba6d33b83, 0xfb1e4a9a90880a64, 0x5cf2eea09a55067f, 0xf42faa48c0ea481e, 0xf13b94daf124da26, 0x76c53d08d6b70858, 0x54768c4b0c64ca6e, 0xa9942f5dcf7dfd09, 0xd3f93b35435d7c4c, 0xc47bc5014a1a6daf, 0x359ab6419ca1091b, 0xc30163d203c94b62, 0x79e0de63425dcf1d, 0x985915fc12f542e4, 0x3e6f5b7b17b2939d, 0xa705992ceecf9c42, 0x50c6ff782a838353, 0xa4f8bf5635246428, 0x871b7795e136be99, 0x28e2557b59846e3f, 0x331aeada2fe589cf, 0x3ff0d2c85def7621, 0xfed077a756b53a9, 0xd3e8495912c62894, 0x64712dd7abbbd95c, 0xbd8d794d96aacfb3, 0xecf0d7a0fc5583a0, 0xf41686c49db57244, 0x311c2875c522ced5, 0x7d633293366b828b, 0xae5dff9c02033197, 0xd9f57f830283fdfc, 0xd072df63c324fd7b, 0x4247cb9e59f71e6d, 0x52d9be85f074e608, 0x67902e276c921f8b, 0xba1cd8a3db53b6, 0x80e8a40eccd228a4, 0x6122cd128006b2cd, 0x796b805720085f81, 0xcbe3303674053bb0, 0xbedbfc4411068a9c, 0xee92fb5515482d44, 0x751bdd152d4d1c4a, 0xd262d45a78a0635d, 0x86fb897116c87c34, 0xd45d35e6ae3d4da0, 0x8974836059cca109, 0x2bd1a438703fc94b, 0x7b6306a34627ddcf, 0x1a3bc84c17b1d542, 0x20caba5f1d9e4a93, 0x547eb47b7282ee9c, 0xe99e619a4f23aa43, 0x6405fa00e2ec94d4, 0xde83bc408dd3dd04, 0x9624ab50b148d445, 0x3badd624dd9b0957, 0xe54ca5d70a80e5d6, 0x5e9fcf4ccd211f4c, 0x7647c3200069671f, 0x29ecd9f40041e073, 0xf468107100525890, 0x7182148d4066eeb4, 0xc6f14cd848405530, 0xb8ada00e5a506a7c, 0xa6d90811f0e4851c, 0x908f4a166d1da663, 0x9a598e4e043287fe, 0x40eff1e1853f29fd, 0xd12bee59e68ef47c, 0x82bb74f8301958ce, 0xe36a52363c1faf01, 0xdc44e6c3cb279ac1, 0x29ab103a5ef8c0b9, 0x7415d448f6b6f0e7, 0x111b495b3464ad21, 0xcab10dd900beec34, 0x3d5d514f40eea742, 0xcb4a5a3112a5112, 0x47f0e785eaba72ab, 0x59ed216765690f56, 0x306869c13ec3532c, 0x1e414218c73a13fb, 0xe5d1929ef90898fa, 0xdf45f746b74abf39, 0x6b8bba8c328eb783, 0x66ea92f3f326564, 0xc80a537b0efefebd, 0xbd06742ce95f5f36, 0x2c48113823b73704, 0xf75a15862ca504c5, 0x9a984d73dbe722fb, 0xc13e60d0d2e0ebba, 0x318df905079926a8, 0xfdf17746497f7052, 0xfeb6ea8bedefa633, 0xfe64a52ee96b8fc0, 0x3dfdce7aa3c673b0, 0x6bea10ca65c084e, 0x486e494fcff30a62, 0x5a89dba3c3efccfa, 0xf89629465a75e01c, 0xf6bbb397f1135823, 0x746aa07ded582e2c, 0xa8c2a44eb4571cdc, 0x92f34d62616ce413, 0x77b020baf9c81d17, 0xace1474dc1d122e, 0xd819992132456ba, 0x10e1fff697ed6c69, 0xca8d3ffa1ef463c1, 0xbd308ff8a6b17cb2, 0xac7cb3f6d05ddbde, 0x6bcdf07a423aa96b, 0x86c16c98d2c953c6, 0xe871c7bf077ba8b7, 0x11471cd764ad4972, 0xd598e40d3dd89bcf, 0x4aff1d108d4ec2c3, 0xcedf722a585139ba, 0xc2974eb4ee658828, 0x733d226229feea32, 0x806357d5a3f525f, 0xca07c2dcb0cf26f7, 0xfc89b393dd02f0b5, 0xbbac2078d443ace2, 0xd54b944b84aa4c0d, 0xa9e795e65d4df11, 0x4d4617b5ff4a16d5, 0x504bced1bf8e4e45, 0xe45ec2862f71e1d6, 0x5d767327bb4e5a4c, 0x3a6a07f8d510f86f, 0x890489f70a55368b, 0x2b45ac74ccea842e, 0x3b0b8bc90012929d, 0x9ce6ebb40173744, 0xcc420a6a101d0515, 0x9fa946824a12232d, 0x47939822dc96abf9, 0x59787e2b93bc56f7, 0x57eb4edb3c55b65a, 0xede622920b6b23f1, 0xe95fab368e45eced, 0x11dbcb0218ebb414, 0xd652bdc29f26a119, 0x4be76d3346f0495f, 0x6f70a4400c562ddb, 0xcb4ccd500f6bb952, 0x7e2000a41346a7a7, 0x8ed400668c0c28c8, 0x728900802f0f32fa, 0x4f2b40a03ad2ffb9, 0xe2f610c84987bfa8, 0xdd9ca7d2df4d7c9, 0x91503d1c79720dbb, 0x75a44c6397ce912a, 0xc986afbe3ee11aba, 0xfbe85badce996168, 0xfae27299423fb9c3, 0xdccd879fc967d41a, 0x5400e987bbc1c920, 0x290123e9aab23b68, 0xf9a0b6720aaf6521, 0xf808e40e8d5b3e69, 0xb60b1d1230b20e04, 0xb1c6f22b5e6f48c2, 0x1e38aeb6360b1af3, 0x25c6da63c38de1b0, 0x579c487e5a38ad0e, 0x2d835a9df0c6d851, 0xf8e431456cf88e65, 0x1b8e9ecb641b58ff, 0xe272467e3d222f3f, 0x5b0ed81dcc6abb0f, 0x98e947129fc2b4e9, 0x3f2398d747b36224, 0x8eec7f0d19a03aad, 0x1953cf68300424ac, 0x5fa8c3423c052dd7, 0x3792f412cb06794d, 0xe2bbd88bbee40bd0, 0x5b6aceaeae9d0ec4, 0xf245825a5a445275, 0xeed6e2f0f0d56712, 0x55464dd69685606b, 0xaa97e14c3c26b886, 0xd53dd99f4b3066a8, 0xe546a8038efe4029, 0xde98520472bdd033, 0x963e66858f6d4440, 0xdde7001379a44aa8, 0x5560c018580d5d52, 0xaab8f01e6e10b4a6, 0xcab3961304ca70e8, 0x3d607b97c5fd0d22, 0x8cb89a7db77c506a, 0x77f3608e92adb242, 0x55f038b237591ed3, 0x6b6c46dec52f6688, 0x2323ac4b3b3da015, 0xabec975e0a0d081a, 0x96e7bd358c904a21, 0x7e50d64177da2e54, 0xdde50bd1d5d0b9e9, 0x955e4ec64b44e864, 0xbd5af13bef0b113e, 0xecb1ad8aeacdd58e, 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