118 lines
3.6 KiB
C++
Executable File
118 lines
3.6 KiB
C++
Executable File
// boost asinh.hpp header file
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// (C) Copyright Eric Ford & Hubert Holin 2001.
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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 <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/special_functions/math_fwd.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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#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>
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inline T asinh_imp(const T x)
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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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static T const upper_taylor_n_bound = one/taylor_n_bound;
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if (x >= +taylor_n_bound)
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{
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if (x > upper_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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// approximation by laurent series in 1/x at 0+ order from -1 to 1
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return( log( x*two + (one/(x*two)) ) );
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}
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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 if (x <= -taylor_n_bound)
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{
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return(-asinh(-x));
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}
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else
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{
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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) >= taylor_2_bound)
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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(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::asinh_imp(
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static_cast<result_type>(x));
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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(const 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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return detail::asinh_imp(
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static_cast<result_type>(x));
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}
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}
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}
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#endif /* BOOST_ASINH_HPP */
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