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116 lines
3.8 KiB
116 lines
3.8 KiB
// 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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// 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, 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 log(x * 2) + 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)); |
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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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