// boost sinc.hpp header file // (C) Copyright Hubert Holin 2001. // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // See http://www.boost.org for updates, documentation, and revision history. #ifndef BOOST_SINC_HPP #define BOOST_SINC_HPP #ifdef _MSC_VER #pragma once #endif #include <boost/math/tools/config.hpp> #include <boost/math/tools/precision.hpp> #include <boost/math/policies/policy.hpp> #include <boost/math/special_functions/math_fwd.hpp> #include <boost/config/no_tr1/cmath.hpp> #include <boost/limits.hpp> #include <string> #include <stdexcept> #include <boost/config.hpp> // These are the the "Sinus Cardinal" functions. namespace boost { namespace math { namespace detail { // This is the "Sinus Cardinal" of index Pi. template<typename T> inline T sinc_pi_imp(const T x) { BOOST_MATH_STD_USING if (abs(x) >= 3.3 * tools::forth_root_epsilon<T>()) { return(sin(x)/x); } else { // |x| < (eps*120)^(1/4) return 1 - x * x / 6; } } } // namespace detail template <class T> inline typename tools::promote_args<T>::type sinc_pi(T x) { typedef typename tools::promote_args<T>::type result_type; return detail::sinc_pi_imp(static_cast<result_type>(x)); } template <class T, class Policy> inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&) { typedef typename tools::promote_args<T>::type result_type; return detail::sinc_pi_imp(static_cast<result_type>(x)); } #ifndef BOOST_NO_TEMPLATE_TEMPLATES template<typename T, template<typename> class U> inline U<T> sinc_pi(const U<T> x) { BOOST_MATH_STD_USING using ::std::numeric_limits; T const taylor_0_bound = tools::epsilon<T>(); T const taylor_2_bound = tools::root_epsilon<T>(); T const taylor_n_bound = tools::forth_root_epsilon<T>(); if (abs(x) >= taylor_n_bound) { return(sin(x)/x); } else { // approximation by taylor series in x at 0 up to order 0 #ifdef __MWERKS__ U<T> result = static_cast<U<T> >(1); #else U<T> result = U<T>(1); #endif if (abs(x) >= taylor_0_bound) { U<T> x2 = x*x; // approximation by taylor series in x at 0 up to order 2 result -= x2/static_cast<T>(6); if (abs(x) >= taylor_2_bound) { // approximation by taylor series in x at 0 up to order 4 result += (x2*x2)/static_cast<T>(120); } } return(result); } } template<typename T, template<typename> class U, class Policy> inline U<T> sinc_pi(const U<T> x, const Policy&) { return sinc_pi(x); } #endif /* BOOST_NO_TEMPLATE_TEMPLATES */ } } #endif /* BOOST_SINC_HPP */