105 lines
3.7 KiB
C++
105 lines
3.7 KiB
C++
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// boost asinh.hpp header file
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// (C) Copyright Eric Ford 2001 & Hubert Holin.
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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_ACOSH_HPP
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#define BOOST_ACOSH_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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#include <boost/math/constants/constants.hpp>
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// This is the inverse of the hyperbolic cosine 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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template<typename T, typename Policy>
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inline T acosh_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 < 1)
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{
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return policies::raise_domain_error<T>(
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"boost::math::acosh<%1%>(%1%)",
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"acosh requires x >= 1, but got x = %1%.", x, pol);
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}
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else if ((x - 1) >= tools::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/ArcCosh/06/01/06/01/0001/
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// approximation by laurent series in 1/x at 0+ order from -1 to 0
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return log(x) + constants::ln_two<T>();
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}
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else if(x < 1.5f)
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{
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// This is just a rearrangement of the standard form below
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// devised to minimse loss of precision when x ~ 1:
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T y = x - 1;
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return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
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}
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else
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcCosh/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
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{
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// see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
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T y = x - 1;
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// approximation by taylor series in y at 0 up to order 2
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T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
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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 acosh(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::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
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"boost::math::acosh<%1%>(%1%)");
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}
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template<typename T>
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inline typename tools::promote_args<T>::type acosh(T x)
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{
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return boost::math::acosh(x, policies::policy<>());
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}
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}
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}
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#endif /* BOOST_ACOSH_HPP */
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