#$@%#$%!

Ngiler SH3LL 360
: / proc / thread-self / root / usr / include / c++ / 8 / tr1 /

Information Server
MySQL : OFF Perl : OFF CURL : ON WGET : OFF PKEXEC : OFF

Directive	Local Value
IP Address	162.0.209.101
System	Linux premium169.web-hosting.com 4.18.0-553.50.1.lve.el8.x86_64 #1 SMP Thu Apr 17 19:10:24 UTC 2025 x86_64
User	luxeelil
PHP Version	8.0.30
Software	LiteSpeed
Doc root	Writable

Edit File : beta_function.tcc \| Size : 5.85 KB
// 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 Back

Edit File : beta_function.tcc | Size : 5.85 KB

// 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

Back