117 lines
3.5 KiB
C++
Executable File
117 lines
3.5 KiB
C++
Executable File
// boost asinh.hpp header file
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// (C) Copyright Eric Ford 2001 & Hubert Holin.
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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 <cmath>
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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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// 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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#if defined(__GNUC__) && (__GNUC__ < 3)
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// gcc 2.x ignores function scope using declarations,
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// put them in the scope of the enclosing namespace instead:
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using ::std::abs;
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using ::std::sqrt;
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using ::std::log;
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using ::std::numeric_limits;
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#endif
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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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using ::std::abs;
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using ::std::sqrt;
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using ::std::log;
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T const one = static_cast<T>(1);
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T const two = static_cast<T>(2);
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static T const taylor_2_bound = sqrt(tools::epsilon<T>());
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static T const taylor_n_bound = sqrt(taylor_2_bound);
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static T const upper_taylor_2_bound = one/taylor_2_bound;
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if(x < one)
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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 >= taylor_n_bound)
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{
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if (x > upper_taylor_2_bound)
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{
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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*two) );
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}
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else
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{
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return( log( x + sqrt(x*x-one) ) );
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}
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}
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else
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{
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T y = sqrt(x-one);
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// approximation by taylor series in y at 0 up to order 2
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T result = y;
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if (y >= taylor_2_bound)
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{
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T y3 = y*y*y;
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// approximation by taylor series in y at 0 up to order 4
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result -= y3/static_cast<T>(12);
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}
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return(sqrt(static_cast<T>(2))*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(const T x, const Policy& pol)
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{
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typedef typename tools::promote_args<T>::type result_type;
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return detail::acosh_imp(
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static_cast<result_type>(x), pol);
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}
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template<typename T>
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inline typename tools::promote_args<T>::type acosh(const T x)
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{
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typedef typename tools::promote_args<T>::type result_type;
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return detail::acosh_imp(
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static_cast<result_type>(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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