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// Special functions -*- C++ -*-
// Copyright (C) 2006-2007
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2, or (at your option)
// any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING. If not, write to the Free
// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// USA.
//
// As a special exception, you may use this file as part of a free software
// library without restriction. Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License. This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.
/** @file tr1/beta_function.tcc
* This is an internal header file, included by other library headers.
* You should not attempt to use it directly.
*/
//
// ISO C++ 14882 TR1: 5.2 Special functions
//
// Written by Edward Smith-Rowland based on:
// (1) Handbook of Mathematical Functions,
// ed. Milton Abramowitz and Irene A. Stegun,
// Dover Publications,
// Section 6, pp. 253-266
// (2) The Gnu Scientific Library, http://www.gnu.org/software/gsl
// (3) Numerical Recipes in C, by W. H. Press, S. A. Teukolsky,
// W. T. Vetterling, B. P. Flannery, Cambridge University Press (1992),
// 2nd ed, pp. 213-216
// (4) Gamma, Exploring Euler's Constant, Julian Havil,
// Princeton, 2003.
#ifndef _TR1_BETA_FUNCTION_TCC
#define _TR1_BETA_FUNCTION_TCC 1
namespace std
{
_GLIBCXX_BEGIN_NAMESPACE(_GLIBCXX_TR1)
// [5.2] Special functions
/**
* @ingroup tr1_math_spec_func
* @{
*/
//
// Implementation-space details.
//
namespace __detail
{
/**
* @brief Return the beta function: \f$B(x,y)\f$.
*
* The beta function is defined by
* @f[
* B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}
* @f]
*
* @param __x The first argument of the beta function.
* @param __y The second argument of the beta function.
* @return The beta function.
*/
template<typename _Tp>
_Tp
__beta_gamma(_Tp __x, _Tp __y)
{
_Tp __bet;
#if _GLIBCXX_USE_C99_MATH_TR1
if (__x > __y)
{
__bet = std::_GLIBCXX_TR1::tgamma(__x)
/ std::_GLIBCXX_TR1::tgamma(__x + __y);
__bet *= std::_GLIBCXX_TR1::tgamma(__y);
}
else
{
__bet = std::_GLIBCXX_TR1::tgamma(__y)
/ std::_GLIBCXX_TR1::tgamma(__x + __y);
__bet *= std::_GLIBCXX_TR1::tgamma(__x);
}
#else
if (__x > __y)
{
__bet = __gamma(__x) / __gamma(__x + __y);
__bet *= __gamma(__y);
}
else
{
__bet = __gamma(__y) / __gamma(__x + __y);
__bet *= __gamma(__x);
}
#endif
return __bet;
}
/**
* @brief Return the beta function \f$B(x,y)\f$ using
* the log gamma functions.
*
* The beta function is defined by
* @f[
* B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}
* @f]
*
* @param __x The first argument of the beta function.
* @param __y The second argument of the beta function.
* @return The beta function.
*/
template<typename _Tp>
_Tp
__beta_lgamma(_Tp __x, _Tp __y)
{
#if _GLIBCXX_USE_C99_MATH_TR1
_Tp __bet = std::_GLIBCXX_TR1::lgamma(__x)
+ std::_GLIBCXX_TR1::lgamma(__y)
- std::_GLIBCXX_TR1::lgamma(__x + __y);
#else
_Tp __bet = __log_gamma(__x)
+ __log_gamma(__y)
- __log_gamma(__x + __y);
#endif
__bet = std::exp(__bet);
return __bet;
}
/**
* @brief Return the beta function \f$B(x,y)\f$ using
* the product form.
*
* The beta function is defined by
* @f[
* B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}
* @f]
*
* @param __x The first argument of the beta function.
* @param __y The second argument of the beta function.
* @return The beta function.
*/
template<typename _Tp>
_Tp
__beta_product(_Tp __x, _Tp __y)
{
_Tp __bet = (__x + __y) / (__x * __y);
unsigned int __max_iter = 1000000;
for (unsigned int __k = 1; __k < __max_iter; ++__k)
{
_Tp __term = (_Tp(1) + (__x + __y) / __k)
/ ((_Tp(1) + __x / __k) * (_Tp(1) + __y / __k));
__bet *= __term;
}
return __bet;
}
/**
* @brief Return the beta function \f$ B(x,y) \f$.
*
* The beta function is defined by
* @f[
* B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}
* @f]
*
* @param __x The first argument of the beta function.
* @param __y The second argument of the beta function.
* @return The beta function.
*/
template<typename _Tp>
inline _Tp
__beta(_Tp __x, _Tp __y)
{
if (__isnan(__x) || __isnan(__y))
return std::numeric_limits<_Tp>::quiet_NaN();
else
return __beta_lgamma(__x, __y);
}
} // namespace std::tr1::__detail
/* @} */ // group tr1_math_spec_func
_GLIBCXX_END_NAMESPACE
}
#endif // _TR1_BETA_FUNCTION_TCC
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