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1// boost asinh.hpp header file2 3// (C) Copyright Eric Ford 2001 & Hubert Holin.4// (C) Copyright John Maddock 2008.5// Distributed under the Boost Software License, Version 1.0. (See6// accompanying file LICENSE_1_0.txt or copy at7// http://www.boost.org/LICENSE_1_0.txt)8 9// See http://www.boost.org for updates, documentation, and revision history.10 11#ifndef BOOST_ACOSH_HPP12#define BOOST_ACOSH_HPP13 14#ifdef _MSC_VER15#pragma once16#endif17 18#include <cmath>19#include <boost/math/tools/precision.hpp>20#include <boost/math/policies/error_handling.hpp>21#include <boost/math/special_functions/math_fwd.hpp>22#include <boost/math/special_functions/log1p.hpp>23#include <boost/math/constants/constants.hpp>24#include <boost/math/special_functions/fpclassify.hpp>25 26// This is the inverse of the hyperbolic cosine function.27 28namespace boost29{30 namespace math31 {32 namespace detail33 {34 template<typename T, typename Policy>35 inline T acosh_imp(const T x, const Policy& pol)36 {37 BOOST_MATH_STD_USING38 39 if((x < 1) || (boost::math::isnan)(x))40 {41 return policies::raise_domain_error<T>("boost::math::acosh<%1%>(%1%)", "acosh requires x >= 1, but got x = %1%.", x, pol);42 }43 else if ((x - 1) >= tools::root_epsilon<T>())44 {45 if (x > 1 / tools::root_epsilon<T>())46 {47 // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/48 // approximation by laurent series in 1/x at 0+ order from -1 to 049 return log(x) + constants::ln_two<T>();50 }51 else if(x < 1.5f)52 {53 // This is just a rearrangement of the standard form below54 // devised to minimise loss of precision when x ~ 1:55 T y = x - 1;56 return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);57 }58 else59 {60 // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/61 return( log( x + sqrt(x * x - 1) ) );62 }63 }64 else65 {66 // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/67 T y = x - 1;68 69 // approximation by taylor series in y at 0 up to order 270 T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);71 return result;72 }73 }74 }75 76 template<typename T, typename Policy>77 inline typename tools::promote_args<T>::type acosh(T x, const Policy&)78 {79 typedef typename tools::promote_args<T>::type result_type;80 typedef typename policies::evaluation<result_type, Policy>::type value_type;81 typedef typename policies::normalise<82 Policy, 83 policies::promote_float<false>, 84 policies::promote_double<false>, 85 policies::discrete_quantile<>,86 policies::assert_undefined<> >::type forwarding_policy;87 return policies::checked_narrowing_cast<result_type, forwarding_policy>(88 detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()),89 "boost::math::acosh<%1%>(%1%)");90 }91 template<typename T>92 inline typename tools::promote_args<T>::type acosh(T x)93 {94 return boost::math::acosh(x, policies::policy<>());95 }96 97 }98}99 100#endif /* BOOST_ACOSH_HPP */101 102 103