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-// Special functions -*- C++ -*-
-
-// Copyright (C) 2006, 2007, 2008, 2009
-// 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.
- * 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 _GLIBCXX_TR1_BETA_FUNCTION_TCC
-#define _GLIBCXX_TR1_BETA_FUNCTION_TCC 1
-
-namespace std
-{
-namespace tr1
-{
-
- // [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 = 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<typename _Tp>
- _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<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
-}
-}
-
-#endif // __GLIBCXX_TR1_BETA_FUNCTION_TCC