107 lines
3.7 KiB
Plaintext
107 lines
3.7 KiB
Plaintext
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// boost asinh.hpp header file
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// (C) Copyright Eric Ford & 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_ASINH_HPP
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#define BOOST_ASINH_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/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/sqrt1pm1.hpp>
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#include <boost/math/special_functions/log1p.hpp>
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#include <boost/math/constants/constants.hpp>
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// This is the inverse of the hyperbolic sine 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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template<typename T, class Policy>
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inline T asinh_imp(const T x, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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if (x >= tools::forth_root_epsilon<T>())
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{
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if (x > 1 / tools::root_epsilon<T>())
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
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// approximation by laurent series in 1/x at 0+ order from -1 to 1
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return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);
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}
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else if(x < 0.5f)
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{
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// As below, but rearranged to preserve digits:
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return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
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}
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else
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
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return( log( x + sqrt(x*x+1) ) );
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}
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}
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else if (x <= -tools::forth_root_epsilon<T>())
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{
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return(-asinh(-x, pol));
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}
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else
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
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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>(6);
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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>
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inline typename tools::promote_args<T>::type asinh(T x)
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{
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return boost::math::asinh(x, policies::policy<>());
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}
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template<typename T, typename Policy>
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inline typename tools::promote_args<T>::type asinh(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::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
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"boost::math::asinh<%1%>(%1%)");
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}
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}
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}
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#endif /* BOOST_ASINH_HPP */
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