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// boost atanh.hpp header file // (C) Copyright Hubert Holin 2001. // (C) Copyright John Maddock 2008. // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // See http://www.boost.org for updates, documentation, and revision history. #ifndef BOOST_ATANH_HPP #define BOOST_ATANH_HPP #ifdef _MSC_VER #pragma once #endif #include #include #include #include #include #include // This is the inverse of the hyperbolic tangent function. namespace boost { namespace math { namespace detail { // This is the main fare template BOOST_MATH_GPU_ENABLED inline T atanh_imp(const T x, const Policy& pol) { BOOST_MATH_STD_USING constexpr auto function = "boost::math::atanh<%1%>(%1%)"; if(x < -1) { return policies::raise_domain_error(function, "atanh requires x >= -1, but got x = %1%.", x, pol); } else if(x > 1) { return policies::raise_domain_error(function, "atanh requires x <= 1, but got x = %1%.", x, pol); } else if((boost::math::isnan)(x)) { return policies::raise_domain_error(function, "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol); } else if(x < -1 + tools::epsilon()) { // -Infinity: return -policies::raise_overflow_error(function, nullptr, pol); } else if(x > 1 - tools::epsilon()) { // Infinity: return policies::raise_overflow_error(function, nullptr, pol); } else if(abs(x) >= tools::forth_root_epsilon()) { // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/ if(abs(x) < 0.5f) return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2; return(log( (1 + x) / (1 - x) ) / 2); } else { // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/ // approximation by taylor series in x at 0 up to order 2 T result = x; if (abs(x) >= tools::root_epsilon()) { T x3 = x*x*x; // approximation by taylor series in x at 0 up to order 4 result += x3/static_cast(3); } return(result); } } } template BOOST_MATH_GPU_ENABLED inline typename tools::promote_args::type atanh(T x, const Policy&) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; typedef typename policies::normalise< Policy, policies::promote_float, policies::promote_double, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; return policies::checked_narrowing_cast( detail::atanh_imp(static_cast(x), forwarding_policy()), "boost::math::atanh<%1%>(%1%)"); } template BOOST_MATH_GPU_ENABLED inline typename tools::promote_args::type atanh(T x) { return boost::math::atanh(x, policies::policy<>()); } } } #endif /* BOOST_ATANH_HPP */