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1// boost asinh.hpp header file2 3// (C) Copyright Eric Ford & Hubert Holin 2001.4// (C) Copyright John Maddock 2008.5// Distributed under the Boost Software License, Version 1.0. (See6// accompanying file LICENSE_1_0.txt or copy at7// 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_ASINH_HPP12#define BOOST_ASINH_HPP13 14#ifdef _MSC_VER15#pragma once16#endif17 18 19#include <cmath>20#include <boost/math/tools/precision.hpp>21#include <boost/math/special_functions/math_fwd.hpp>22#include <boost/math/special_functions/sqrt1pm1.hpp>23#include <boost/math/special_functions/log1p.hpp>24#include <boost/math/constants/constants.hpp>25#include <boost/math/special_functions/fpclassify.hpp>26 27// This is the inverse of the hyperbolic sine function.28 29namespace boost30{31 namespace math32 {33 namespace detail{34 template<typename T, class Policy>35 inline T asinh_imp(const T x, const Policy& pol)36 {37 BOOST_MATH_STD_USING38 39 if((boost::math::isnan)(x))40 {41 return policies::raise_domain_error<T>("boost::math::asinh<%1%>(%1%)", "asinh requires a finite argument, but got x = %1%.", x, pol);42 }43 if (x >= tools::forth_root_epsilon<T>())44 {45 if (x > 1 / tools::root_epsilon<T>())46 {47 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/48 // approximation by laurent series in 1/x at 0+ order from -1 to 149 return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);50 }51 else if(x < 0.5f)52 {53 // As below, but rearranged to preserve digits:54 return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);55 }56 else57 {58 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/59 return( log( x + sqrt(x*x+1) ) );60 }61 }62 else if (x <= -tools::forth_root_epsilon<T>())63 {64 return(-asinh(-x, pol));65 }66 else67 {68 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/69 // approximation by taylor series in x at 0 up to order 270 T result = x;71 72 if (abs(x) >= tools::root_epsilon<T>())73 {74 T x3 = x*x*x;75 76 // approximation by taylor series in x at 0 up to order 477 result -= x3/static_cast<T>(6);78 }79 80 return(result);81 }82 }83 }84 85 template<typename T>86 inline typename tools::promote_args<T>::type asinh(T x)87 {88 return boost::math::asinh(x, policies::policy<>());89 }90 template<typename T, typename Policy>91 inline typename tools::promote_args<T>::type asinh(T x, const Policy&)92 {93 typedef typename tools::promote_args<T>::type result_type;94 typedef typename policies::evaluation<result_type, Policy>::type value_type;95 typedef typename policies::normalise<96 Policy, 97 policies::promote_float<false>, 98 policies::promote_double<false>, 99 policies::discrete_quantile<>,100 policies::assert_undefined<> >::type forwarding_policy;101 return policies::checked_narrowing_cast<result_type, forwarding_policy>(102 detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()),103 "boost::math::asinh<%1%>(%1%)");104 }105 106 }107}108 109#endif /* BOOST_ASINH_HPP */110 111