math/special_functions/atanh.hpp

0001 //    boost atanh.hpp header file
0002
0003 //  (C) Copyright Hubert Holin 2001.
0004 //  (C) Copyright John Maddock 2008.
0005 //  Distributed under the Boost Software License, Version 1.0. (See
0006 //  accompanying file LICENSE_1_0.txt or copy at
0007 //  http://www.boost.org/LICENSE_1_0.txt)
0008
0009 // See http://www.boost.org for updates, documentation, and revision history.
0010
0011 #ifndef BOOST_ATANH_HPP
0012 #define BOOST_ATANH_HPP
0013
0014 #ifdef _MSC_VER
0015 #pragma once
0016 #endif
0017
0018 #include <cmath>
0019 #include <boost/math/tools/precision.hpp>
0020 #include <boost/math/policies/error_handling.hpp>
0021 #include <boost/math/special_functions/math_fwd.hpp>
0022 #include <boost/math/special_functions/log1p.hpp>
0023 #include <boost/math/special_functions/fpclassify.hpp>
0024
0025 // This is the inverse of the hyperbolic tangent function.
0026
0027 namespace boost
0028 {
0029     namespace math
0030     {
0031        namespace detail
0032        {
0033         // This is the main fare
0034
0035         template<typename T, typename Policy>
0036         inline T    atanh_imp(const T x, const Policy& pol)
0037         {
0038             BOOST_MATH_STD_USING
0039             static const char* function = "boost::math::atanh<%1%>(%1%)";
0040
0041             if(x < -1)
0042             {
0043                return policies::raise_domain_error<T>(function, "atanh requires x >= -1, but got x = %1%.", x, pol);
0044             }
0045             else if(x > 1)
0046             {
0047                return policies::raise_domain_error<T>(function, "atanh requires x <= 1, but got x = %1%.", x, pol);
0048             }
0049             else if((boost::math::isnan)(x))
0050             {
0051                return policies::raise_domain_error<T>(function, "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
0052             }
0053             else if(x < -1 + tools::epsilon<T>())
0054             {
0055                // -Infinity:
0056                return -policies::raise_overflow_error<T>(function, nullptr, pol);
0057             }
0058             else if(x > 1 - tools::epsilon<T>())
0059             {
0060                // Infinity:
0061                return policies::raise_overflow_error<T>(function, nullptr, pol);
0062             }
0063             else if(abs(x) >= tools::forth_root_epsilon<T>())
0064             {
0065                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
0066                 if(abs(x) < 0.5f)
0067                    return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
0068                 return(log( (1 + x) / (1 - x) ) / 2);
0069             }
0070             else
0071             {
0072                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
0073                 // approximation by taylor series in x at 0 up to order 2
0074                 T    result = x;
0075
0076                 if    (abs(x) >= tools::root_epsilon<T>())
0077                 {
0078                     T    x3 = x*x*x;
0079
0080                     // approximation by taylor series in x at 0 up to order 4
0081                     result += x3/static_cast<T>(3);
0082                 }
0083
0084                 return(result);
0085             }
0086         }
0087        }
0088
0089         template<typename T, typename Policy>
0090         inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
0091         {
0092             typedef typename tools::promote_args<T>::type result_type;
0093             typedef typename policies::evaluation<result_type, Policy>::type value_type;
0094             typedef typename policies::normalise<
0095                Policy,
0096                policies::promote_float<false>,
0097                policies::promote_double<false>,
0098                policies::discrete_quantile<>,
0099                policies::assert_undefined<> >::type forwarding_policy;
0100            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
0101               detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
0102               "boost::math::atanh<%1%>(%1%)");
0103         }
0104         template<typename T>
0105         inline typename tools::promote_args<T>::type atanh(T x)
0106         {
0107            return boost::math::atanh(x, policies::policy<>());
0108         }
0109
0110     }
0111 }
0112
0113 #endif /* BOOST_ATANH_HPP */
0114
0115
0116