| // Special functions -*- C++ -*- |
| |
| // Copyright (C) 2006, 2007, 2008 |
| // 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 _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 |