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File beta_function.tcc

// Special functions -*- C++ -*-

// Copyright (C) 2006-2018 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 3, 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.
//
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file tr1/beta_function.tcc
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{tr1/cmath}
 */

//
// 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 _GLIBCXX_TR1_BETA_FUNCTION_TCC
#define _GLIBCXX_TR1_BETA_FUNCTION_TCC 1

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

#if _GLIBCXX_USE_STD_SPEC_FUNCS
# define _GLIBCXX_MATH_NS ::std
#elif defined(_GLIBCXX_TR1_CMATH)
namespace tr1
{
# define _GLIBCXX_MATH_NS ::std::tr1
#else
# error do not include this header directly, use <cmath> or <tr1/cmath>
#endif
  // [5.2] Special functions

// 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 = _GLIBCXX_MATH_NS::tgamma(__x)
                / _GLIBCXX_MATH_NS::tgamma(__x + __y);
          __bet *= _GLIBCXX_MATH_NS::tgamma(__y);
        }
      else
        {
          __bet = _GLIBCXX_MATH_NS::tgamma(__y)
                / _GLIBCXX_MATH_NS::tgamma(__x + __y);
          __bet *= _GLIBCXX_MATH_NS::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 = _GLIBCXX_MATH_NS::lgamma(__x)
                + _GLIBCXX_MATH_NS::lgamma(__y)
                - _GLIBCXX_MATH_NS::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 __detail
#undef _GLIBCXX_MATH_NS
#if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH)
} // namespace tr1
#endif

_GLIBCXX_END_NAMESPACE_VERSION
}

#endif // _GLIBCXX_TR1_BETA_FUNCTION_TCC

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array	text/x-c	6.8 KB	-rw-r--r--	2025-08-26 09:45:04
bessel_function.tcc	text/x-c	21.95 KB	-rw-r--r--	2025-08-26 09:45:04
beta_function.tcc	text/plain	5.85 KB	-rw-r--r--	2025-08-26 09:45:04
ccomplex	text/x-c	1.23 KB	-rw-r--r--	2025-08-26 09:45:04
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complex	text/x-c	12.09 KB	-rw-r--r--	2025-08-26 09:45:04
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cstdarg	text/x-c	1.22 KB	-rw-r--r--	2025-08-26 09:45:04
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cwctype	text/x-c	1.42 KB	-rw-r--r--	2025-08-26 09:45:04
ell_integral.tcc	text/plain	27.07 KB	-rw-r--r--	2025-08-26 09:45:04
exp_integral.tcc	text/x-c	15.63 KB	-rw-r--r--	2025-08-26 09:45:04
fenv.h	text/x-c	1.18 KB	-rw-r--r--	2025-08-26 09:45:04
float.h	text/x-c	1.18 KB	-rw-r--r--	2025-08-26 09:45:04
functional	text/x-c	68.89 KB	-rw-r--r--	2025-08-26 09:45:04
functional_hash.h	text/plain	5.9 KB	-rw-r--r--	2025-08-26 09:45:04
gamma.tcc	text/x-c	14.34 KB	-rw-r--r--	2025-08-26 09:45:04
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hashtable_policy.h	text/plain	24.5 KB	-rw-r--r--	2025-08-26 09:45:04
hypergeometric.tcc	text/plain	27.41 KB	-rw-r--r--	2025-08-26 09:45:04
inttypes.h	text/x-c	1.24 KB	-rw-r--r--	2025-08-26 09:45:04
legendre_function.tcc	text/x-c	10.65 KB	-rw-r--r--	2025-08-26 09:45:04
limits.h	text/x-c	1.19 KB	-rw-r--r--	2025-08-26 09:45:04
math.h	text/x-c	4.45 KB	-rw-r--r--	2025-08-26 09:45:04
memory	text/x-c	1.75 KB	-rw-r--r--	2025-08-26 09:45:04
modified_bessel_func.tcc	text/x-c	15.94 KB	-rw-r--r--	2025-08-26 09:45:04
poly_hermite.tcc	text/plain	3.83 KB	-rw-r--r--	2025-08-26 09:45:04
poly_laguerre.tcc	text/plain	11.4 KB	-rw-r--r--	2025-08-26 09:45:04
random	text/x-c	1.55 KB	-rw-r--r--	2025-08-26 09:45:04
random.h	text/plain	71.41 KB	-rw-r--r--	2025-08-26 09:45:04
random.tcc	text/plain	52.66 KB	-rw-r--r--	2025-08-26 09:45:04
regex	text/x-c	90.7 KB	-rw-r--r--	2025-08-26 09:45:04
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shared_ptr.h	text/plain	31.84 KB	-rw-r--r--	2025-08-26 09:45:04
special_function_util.h	text/plain	4.94 KB	-rw-r--r--	2025-08-26 09:45:04
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