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1// boost atanh.hpp header file2 3// (C) Copyright Hubert Holin 2001.4// (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_ATANH_HPP12#define BOOST_ATANH_HPP13 14#ifdef _MSC_VER15#pragma once16#endif17 18#include <boost/math/tools/config.hpp>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/special_functions/fpclassify.hpp>24 25// This is the inverse of the hyperbolic tangent function.26 27namespace boost28{29 namespace math30 {31 namespace detail32 {33 // This is the main fare34 35 template<typename T, typename Policy>36 BOOST_MATH_GPU_ENABLED inline T atanh_imp(const T x, const Policy& pol)37 {38 BOOST_MATH_STD_USING39 constexpr auto function = "boost::math::atanh<%1%>(%1%)";40 41 if(x < -1)42 {43 return policies::raise_domain_error<T>(function, "atanh requires x >= -1, but got x = %1%.", x, pol);44 }45 else if(x > 1)46 {47 return policies::raise_domain_error<T>(function, "atanh requires x <= 1, but got x = %1%.", x, pol);48 }49 else if((boost::math::isnan)(x))50 {51 return policies::raise_domain_error<T>(function, "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);52 }53 else if(x < -1 + tools::epsilon<T>())54 {55 // -Infinity:56 return -policies::raise_overflow_error<T>(function, nullptr, pol);57 }58 else if(x > 1 - tools::epsilon<T>())59 {60 // Infinity:61 return policies::raise_overflow_error<T>(function, nullptr, pol);62 }63 else if(abs(x) >= tools::forth_root_epsilon<T>())64 {65 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/66 if(abs(x) < 0.5f)67 return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;68 return(log( (1 + x) / (1 - x) ) / 2);69 }70 else71 {72 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/73 // approximation by taylor series in x at 0 up to order 274 T result = x;75 76 if (abs(x) >= tools::root_epsilon<T>())77 {78 T x3 = x*x*x;79 80 // approximation by taylor series in x at 0 up to order 481 result += x3/static_cast<T>(3);82 }83 84 return(result);85 }86 }87 }88 89 template<typename T, typename Policy>90 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type atanh(T x, const Policy&)91 {92 typedef typename tools::promote_args<T>::type result_type;93 typedef typename policies::evaluation<result_type, Policy>::type value_type;94 typedef typename policies::normalise<95 Policy,96 policies::promote_float<false>,97 policies::promote_double<false>,98 policies::discrete_quantile<>,99 policies::assert_undefined<> >::type forwarding_policy;100 return policies::checked_narrowing_cast<result_type, forwarding_policy>(101 detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),102 "boost::math::atanh<%1%>(%1%)");103 }104 template<typename T>105 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type atanh(T x)106 {107 return boost::math::atanh(x, policies::policy<>());108 }109 110 }111}112 113#endif /* BOOST_ATANH_HPP */114 115 116 117