1 // boost atanh.hpp header file 2 3 // (C) Copyright Hubert Holin 2001. 4 // (C) Copyright John Maddock 2008. 5 // Distributed under the Boost Software License, Version 1.0. (See 6 // accompanying file LICENSE_1_0.txt or copy at 7 // 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_HPP 12 #define BOOST_ATANH_HPP 13 14 #ifdef _MSC_VER 15 #pragma once 16 #endif 17 18 19 #include <boost/config/no_tr1/cmath.hpp> 20 #include <boost/config.hpp> 21 #include <boost/math/tools/precision.hpp> 22 #include <boost/math/policies/error_handling.hpp> 23 #include <boost/math/special_functions/math_fwd.hpp> 24 #include <boost/math/special_functions/log1p.hpp> 25 26 // This is the inverse of the hyperbolic tangent function. 27 28 namespace boost 29 { 30 namespace math 31 { 32 namespace detail 33 { 34 // This is the main fare 35 36 template<typename T, typename Policy> atanh_imp(const T x,const Policy & pol)37 inline T atanh_imp(const T x, const Policy& pol) 38 { 39 BOOST_MATH_STD_USING 40 static const char* function = "boost::math::atanh<%1%>(%1%)"; 41 42 if(x < -1) 43 { 44 return policies::raise_domain_error<T>( 45 function, 46 "atanh requires x >= -1, but got x = %1%.", x, pol); 47 } 48 else if(x > 1) 49 { 50 return policies::raise_domain_error<T>( 51 function, 52 "atanh requires x <= 1, but got x = %1%.", x, pol); 53 } 54 else if((boost::math::isnan)(x)) 55 { 56 return policies::raise_domain_error<T>( 57 function, 58 "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol); 59 } 60 else if(x < -1 + tools::epsilon<T>()) 61 { 62 // -Infinity: 63 return -policies::raise_overflow_error<T>(function, 0, pol); 64 } 65 else if(x > 1 - tools::epsilon<T>()) 66 { 67 // Infinity: 68 return policies::raise_overflow_error<T>(function, 0, pol); 69 } 70 else if(abs(x) >= tools::forth_root_epsilon<T>()) 71 { 72 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/ 73 if(abs(x) < 0.5f) 74 return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2; 75 return(log( (1 + x) / (1 - x) ) / 2); 76 } 77 else 78 { 79 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/ 80 // approximation by taylor series in x at 0 up to order 2 81 T result = x; 82 83 if (abs(x) >= tools::root_epsilon<T>()) 84 { 85 T x3 = x*x*x; 86 87 // approximation by taylor series in x at 0 up to order 4 88 result += x3/static_cast<T>(3); 89 } 90 91 return(result); 92 } 93 } 94 } 95 96 template<typename T, typename Policy> atanh(T x,const Policy &)97 inline typename tools::promote_args<T>::type atanh(T x, const Policy&) 98 { 99 typedef typename tools::promote_args<T>::type result_type; 100 typedef typename policies::evaluation<result_type, Policy>::type value_type; 101 typedef typename policies::normalise< 102 Policy, 103 policies::promote_float<false>, 104 policies::promote_double<false>, 105 policies::discrete_quantile<>, 106 policies::assert_undefined<> >::type forwarding_policy; 107 return policies::checked_narrowing_cast<result_type, forwarding_policy>( 108 detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()), 109 "boost::math::atanh<%1%>(%1%)"); 110 } 111 template<typename T> atanh(T x)112 inline typename tools::promote_args<T>::type atanh(T x) 113 { 114 return boost::math::atanh(x, policies::policy<>()); 115 } 116 117 } 118 } 119 120 #endif /* BOOST_ATANH_HPP */ 121 122 123 124