// Special functions -*- C++ -*- // Copyright (C) 2006-2021 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 SIMPAN PERUBAHAN