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

// Copyright (C) 2006, 2007, 2008, 2009, 2010

// 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

// .

/** @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)

{

namespace tr1

{

  // [5.2] Special functions

  // Implementation-space details.

  namespace __detail

  {

  _GLIBCXX_BEGIN_NAMESPACE_VERSION

    /**

     *   @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

    _Tp

    __beta_gamma(_Tp __x, _Tp __y)

    {

      _Tp __bet;

#if _GLIBCXX_USE_C99_MATH_TR1

      if (__x > __y)

        {

          __bet = std::tr1::tgamma(__x)

                / std::tr1::tgamma(__x + __y);

          __bet *= std::tr1::tgamma(__y);

        }

      else

        {

          __bet = std::tr1::tgamma(__y)

                / std::tr1::tgamma(__x + __y);

          __bet *= std::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

    _Tp

    __beta_lgamma(_Tp __x, _Tp __y)

    {

#if _GLIBCXX_USE_C99_MATH_TR1

      _Tp __bet = std::tr1::lgamma(__x)

                + std::tr1::lgamma(__y)

                - std::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

    _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

    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);

    }

  _GLIBCXX_END_NAMESPACE_VERSION

  } // namespace std::tr1::__detail

}

}

#endif // __GLIBCXX_TR1_BETA_FUNCTION_TCC