author | William Roberts <williamr@symbian.org> |
Wed, 31 Mar 2010 12:27:01 +0100 | |
branch | Symbian2 |
changeset 3 | e1b950c65cb4 |
parent 2 | epoc32/include/stdapis/boost/math/special_functions/asinh.hpp@2fe1408b6811 |
child 4 | 837f303aceeb |
permissions | -rw-r--r-- |
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// 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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#include <cmath> |
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#include <limits> |
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#include <string> |
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#include <stdexcept> |
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#include <boost/config.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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#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(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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using ::std::numeric_limits; |
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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(numeric_limits<T>::epsilon()); |
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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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} |
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#endif /* BOOST_ASINH_HPP */ |