118 lines
3.9 KiB
Plaintext
118 lines
3.9 KiB
Plaintext
// boost atanh.hpp header file
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// (C) Copyright Hubert Holin 2001.
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// (C) Copyright John Maddock 2008.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_ATANH_HPP
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#define BOOST_ATANH_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/config/no_tr1/cmath.hpp>
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#include <boost/config.hpp>
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#include <boost/math/tools/precision.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/log1p.hpp>
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// This is the inverse of the hyperbolic tangent function.
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namespace boost
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{
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namespace math
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{
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namespace detail
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{
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// This is the main fare
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template<typename T, typename Policy>
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inline T atanh_imp(const T x, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::atanh<%1%>(%1%)";
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if(x < -1)
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{
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return policies::raise_domain_error<T>(
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function,
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"atanh requires x >= -1, but got x = %1%.", x, pol);
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}
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else if(x > 1)
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{
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return policies::raise_domain_error<T>(
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function,
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"atanh requires x <= 1, but got x = %1%.", x, pol);
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}
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else if(x < -1 + tools::epsilon<T>())
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{
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// -Infinity:
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return -policies::raise_overflow_error<T>(function, 0, pol);
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}
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else if(x > 1 - tools::epsilon<T>())
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{
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// Infinity:
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return policies::raise_overflow_error<T>(function, 0, pol);
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}
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else if(abs(x) >= tools::forth_root_epsilon<T>())
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
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if(abs(x) < 0.5f)
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return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
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return(log( (1 + x) / (1 - x) ) / 2);
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}
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else
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
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// approximation by taylor series in x at 0 up to order 2
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T result = x;
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if (abs(x) >= tools::root_epsilon<T>())
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{
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T x3 = x*x*x;
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// approximation by taylor series in x at 0 up to order 4
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result += x3/static_cast<T>(3);
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}
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return(result);
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}
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}
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}
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template<typename T, typename Policy>
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inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
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{
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typedef typename tools::promote_args<T>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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typedef typename policies::normalise<
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Policy,
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policies::promote_float<false>,
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policies::promote_double<false>,
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policies::discrete_quantile<>,
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policies::assert_undefined<> >::type forwarding_policy;
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return policies::checked_narrowing_cast<result_type, forwarding_policy>(
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detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
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"boost::math::atanh<%1%>(%1%)");
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}
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template<typename T>
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inline typename tools::promote_args<T>::type atanh(T x)
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{
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return boost::math::atanh(x, policies::policy<>());
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}
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}
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}
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#endif /* BOOST_ATANH_HPP */
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