X-Git-Url: https://git.donarmstrong.com/?p=rsem.git;a=blobdiff_plain;f=boost%2Fmath%2Fspecial_functions%2Fsinhc.hpp;fp=boost%2Fmath%2Fspecial_functions%2Fsinhc.hpp;h=d19a4b71c616104ec20e8dc5d69f17abcba6688b;hp=0000000000000000000000000000000000000000;hb=2d71eb92104693ca9baa5a2e1c23eeca776d8fd3;hpb=da57529b92adbb7ae74a89861cb39fb35ac7c62d diff --git a/boost/math/special_functions/sinhc.hpp b/boost/math/special_functions/sinhc.hpp new file mode 100644 index 0000000..d19a4b7 --- /dev/null +++ b/boost/math/special_functions/sinhc.hpp @@ -0,0 +1,167 @@ +// boost sinhc.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_SINHC_HPP +#define BOOST_SINHC_HPP + + +#ifdef _MSC_VER +#pragma once +#endif + +#include +#include +#include +#include +#include +#include +#include + +#include + + +// These are the the "Hyperbolic Sinus Cardinal" functions. + +namespace boost +{ + namespace math + { + namespace detail + { +#if defined(__GNUC__) && (__GNUC__ < 3) + // gcc 2.x ignores function scope using declarations, + // put them in the scope of the enclosing namespace instead: + + using ::std::abs; + using ::std::sqrt; + using ::std::sinh; + + using ::std::numeric_limits; +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ + + // This is the "Hyperbolic Sinus Cardinal" of index Pi. + + template + inline T sinhc_pi_imp(const T x) + { +#if defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC) + using ::abs; + using ::sinh; + using ::sqrt; +#else /* BOOST_NO_STDC_NAMESPACE */ + using ::std::abs; + using ::std::sinh; + using ::std::sqrt; +#endif /* BOOST_NO_STDC_NAMESPACE */ + + static T const taylor_0_bound = tools::epsilon(); + static T const taylor_2_bound = sqrt(taylor_0_bound); + static T const taylor_n_bound = sqrt(taylor_2_bound); + + if (abs(x) >= taylor_n_bound) + { + return(sinh(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 sinhc_pi(T x) + { + typedef typename tools::promote_args::type result_type; + return detail::sinhc_pi_imp(static_cast(x)); + } + + template + inline typename tools::promote_args::type sinhc_pi(T x, const Policy&) + { + return boost::math::sinhc_pi(x); + } + +#ifdef BOOST_NO_TEMPLATE_TEMPLATES +#else /* BOOST_NO_TEMPLATE_TEMPLATES */ + template class U> + inline U sinhc_pi(const U x) + { +#if defined(BOOST_FUNCTION_SCOPE_USING_DECLARATION_BREAKS_ADL) || defined(__GNUC__) + using namespace std; +#elif defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC) + using ::abs; + using ::sinh; + using ::sqrt; +#else /* BOOST_NO_STDC_NAMESPACE */ + using ::std::abs; + using ::std::sinh; + using ::std::sqrt; +#endif /* BOOST_NO_STDC_NAMESPACE */ + + using ::std::numeric_limits; + + static T const taylor_0_bound = tools::epsilon(); + static T const taylor_2_bound = sqrt(taylor_0_bound); + static T const taylor_n_bound = sqrt(taylor_2_bound); + + if (abs(x) >= taylor_n_bound) + { + return(sinh(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); + } + } +#endif /* BOOST_NO_TEMPLATE_TEMPLATES */ + } +} + +#endif /* BOOST_SINHC_HPP */ +