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>(
0044                   function,
0045                   "atanh requires x >= -1, but got x = %1%.", x, pol);
0046             }
0047             else if(x > 1)
0048             {
0049                return policies::raise_domain_error<T>(
0050                   function,
0051                   "atanh requires x <= 1, but got x = %1%.", x, pol);
0052             }
0053             else if((boost::math::isnan)(x))
0054             {
0055                return policies::raise_domain_error<T>(
0056                   function,
0057                   "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
0058             }
0059             else if(x < -1 + tools::epsilon<T>())
0060             {
0061                // -Infinity:
0062                return -policies::raise_overflow_error<T>(function, nullptr, pol);
0063             }
0064             else if(x > 1 - tools::epsilon<T>())
0065             {
0066                // Infinity:
0067                return policies::raise_overflow_error<T>(function, nullptr, pol);
0068             }
0069             else if(abs(x) >= tools::forth_root_epsilon<T>())
0070             {
0071                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
0072                 if(abs(x) < 0.5f)
0073                    return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
0074                 return(log( (1 + x) / (1 - x) ) / 2);
0075             }
0076             else
0077             {
0078                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
0079                 // approximation by taylor series in x at 0 up to order 2
0080                 T    result = x;
0081
0082                 if    (abs(x) >= tools::root_epsilon<T>())
0083                 {
0084                     T    x3 = x*x*x;
0085
0086                     // approximation by taylor series in x at 0 up to order 4
0087                     result += x3/static_cast<T>(3);
0088                 }
0089
0090                 return(result);
0091             }
0092         }
0093        }
0094
0095         template<typename T, typename Policy>
0096         inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
0097         {
0098             typedef typename tools::promote_args<T>::type result_type;
0099             typedef typename policies::evaluation<result_type, Policy>::type value_type;
0100             typedef typename policies::normalise<
0101                Policy,
0102                policies::promote_float<false>,
0103                policies::promote_double<false>,
0104                policies::discrete_quantile<>,
0105                policies::assert_undefined<> >::type forwarding_policy;
0106            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
0107               detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
0108               "boost::math::atanh<%1%>(%1%)");
0109         }
0110         template<typename T>
0111         inline typename tools::promote_args<T>::type atanh(T x)
0112         {
0113            return boost::math::atanh(x, policies::policy<>());
0114         }
0115
0116     }
0117 }
0118
0119 #endif /* BOOST_ATANH_HPP */
0120
0121
0122