X-Git-Url: https://git.donarmstrong.com/?p=rsem.git;a=blobdiff_plain;f=boost%2Fmath%2Fspecial_functions%2Fsinc.hpp;fp=boost%2Fmath%2Fspecial_functions%2Fsinc.hpp;h=84fbf0e324ace1e6602daccb674ca9adf0399e14;hp=0000000000000000000000000000000000000000;hb=2d71eb92104693ca9baa5a2e1c23eeca776d8fd3;hpb=da57529b92adbb7ae74a89861cb39fb35ac7c62d diff --git a/boost/math/special_functions/sinc.hpp b/boost/math/special_functions/sinc.hpp new file mode 100644 index 0000000..84fbf0e --- /dev/null +++ b/boost/math/special_functions/sinc.hpp @@ -0,0 +1,145 @@ +// 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 +#include +#include +#include +#include +#include +#include +#include + + +#include + + +// These are the the "Sinus Cardinal" functions. + +namespace boost +{ + namespace math + { + namespace detail + { + // This is the "Sinus Cardinal" of index Pi. + + template + inline T sinc_pi_imp(const T x) + { + BOOST_MATH_STD_USING + + T const taylor_0_bound = tools::epsilon(); + T const taylor_2_bound = tools::root_epsilon(); + T const taylor_n_bound = tools::forth_root_epsilon(); + + if (abs(x) >= taylor_n_bound) + { + return(sin(x)/x); + } + else + { + // approximation by taylor series in x at 0 up to order 0 + T result = static_cast(1); + + if (abs(x) >= taylor_0_bound) + { + T x2 = x*x; + + // approximation by taylor series in x at 0 up to order 2 + result -= x2/static_cast(6); + + if (abs(x) >= taylor_2_bound) + { + // approximation by taylor series in x at 0 up to order 4 + result += (x2*x2)/static_cast(120); + } + } + + return(result); + } + } + + } // namespace detail + + template + inline typename tools::promote_args::type sinc_pi(T x) + { + typedef typename tools::promote_args::type result_type; + return detail::sinc_pi_imp(static_cast(x)); + } + + template + inline typename tools::promote_args::type sinc_pi(T x, const Policy&) + { + typedef typename tools::promote_args::type result_type; + return detail::sinc_pi_imp(static_cast(x)); + } + +#ifndef BOOST_NO_TEMPLATE_TEMPLATES + template class U> + inline U sinc_pi(const U x) + { + BOOST_MATH_STD_USING + using ::std::numeric_limits; + + T const taylor_0_bound = tools::epsilon(); + T const taylor_2_bound = tools::root_epsilon(); + T const taylor_n_bound = tools::forth_root_epsilon(); + + 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 result = static_cast >(1); +#else + U result = U(1); +#endif + + if (abs(x) >= taylor_0_bound) + { + U x2 = x*x; + + // approximation by taylor series in x at 0 up to order 2 + result -= x2/static_cast(6); + + if (abs(x) >= taylor_2_bound) + { + // approximation by taylor series in x at 0 up to order 4 + result += (x2*x2)/static_cast(120); + } + } + + return(result); + } + } + + template class U, class Policy> + inline U sinc_pi(const U x, const Policy&) + { + return sinc_pi(x); + } +#endif /* BOOST_NO_TEMPLATE_TEMPLATES */ + } +} + +#endif /* BOOST_SINC_HPP */ +