1 // Special functions -*- C++ -*- 2 3 // Copyright (C) 2006-2013 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 // 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 // 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file tr1/beta_function.tcc 26 * This is an internal header file, included by other library headers. 27 * Do not attempt to use it directly. @headername{tr1/cmath} 28 */ 29 30 // 31 // ISO C++ 14882 TR1: 5.2 Special functions 32 // 33 34 // Written by Edward Smith-Rowland based on: 35 // (1) Handbook of Mathematical Functions, 36 // ed. Milton Abramowitz and Irene A. Stegun, 37 // Dover Publications, 38 // Section 6, pp. 253-266 39 // (2) The Gnu Scientific Library, http://www.gnu.org/software/gsl 40 // (3) Numerical Recipes in C, by W. H. Press, S. A. Teukolsky, 41 // W. T. Vetterling, B. P. Flannery, Cambridge University Press (1992), 42 // 2nd ed, pp. 213-216 43 // (4) Gamma, Exploring Euler's Constant, Julian Havil, 44 // Princeton, 2003. 45 46 #ifndef _GLIBCXX_TR1_BETA_FUNCTION_TCC 47 #define _GLIBCXX_TR1_BETA_FUNCTION_TCC 1 48 49 namespace std _GLIBCXX_VISIBILITY(default) 50 { 51 namespace tr1 52 { 53 // [5.2] Special functions 54 55 // Implementation-space details. 56 namespace __detail 57 { 58 _GLIBCXX_BEGIN_NAMESPACE_VERSION 59 60 /** 61 * @brief Return the beta function: \f$B(x,y)\f$. 62 * 63 * The beta function is defined by 64 * @f[ 65 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 66 * @f] 67 * 68 * @param __x The first argument of the beta function. 69 * @param __y The second argument of the beta function. 70 * @return The beta function. 71 */ 72 template<typename _Tp> 73 _Tp 74 __beta_gamma(_Tp __x, _Tp __y) 75 { 76 77 _Tp __bet; 78 #if _GLIBCXX_USE_C99_MATH_TR1 79 if (__x > __y) 80 { 81 __bet = std::tr1::tgamma(__x) 82 / std::tr1::tgamma(__x + __y); 83 __bet *= std::tr1::tgamma(__y); 84 } 85 else 86 { 87 __bet = std::tr1::tgamma(__y) 88 / std::tr1::tgamma(__x + __y); 89 __bet *= std::tr1::tgamma(__x); 90 } 91 #else 92 if (__x > __y) 93 { 94 __bet = __gamma(__x) / __gamma(__x + __y); 95 __bet *= __gamma(__y); 96 } 97 else 98 { 99 __bet = __gamma(__y) / __gamma(__x + __y); 100 __bet *= __gamma(__x); 101 } 102 #endif 103 104 return __bet; 105 } 106 107 /** 108 * @brief Return the beta function \f$B(x,y)\f$ using 109 * the log gamma functions. 110 * 111 * The beta function is defined by 112 * @f[ 113 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 114 * @f] 115 * 116 * @param __x The first argument of the beta function. 117 * @param __y The second argument of the beta function. 118 * @return The beta function. 119 */ 120 template<typename _Tp> 121 _Tp 122 __beta_lgamma(_Tp __x, _Tp __y) 123 { 124 #if _GLIBCXX_USE_C99_MATH_TR1 125 _Tp __bet = std::tr1::lgamma(__x) 126 + std::tr1::lgamma(__y) 127 - std::tr1::lgamma(__x + __y); 128 #else 129 _Tp __bet = __log_gamma(__x) 130 + __log_gamma(__y) 131 - __log_gamma(__x + __y); 132 #endif 133 __bet = std::exp(__bet); 134 return __bet; 135 } 136 137 138 /** 139 * @brief Return the beta function \f$B(x,y)\f$ using 140 * the product form. 141 * 142 * The beta function is defined by 143 * @f[ 144 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 145 * @f] 146 * 147 * @param __x The first argument of the beta function. 148 * @param __y The second argument of the beta function. 149 * @return The beta function. 150 */ 151 template<typename _Tp> 152 _Tp 153 __beta_product(_Tp __x, _Tp __y) 154 { 155 156 _Tp __bet = (__x + __y) / (__x * __y); 157 158 unsigned int __max_iter = 1000000; 159 for (unsigned int __k = 1; __k < __max_iter; ++__k) 160 { 161 _Tp __term = (_Tp(1) + (__x + __y) / __k) 162 / ((_Tp(1) + __x / __k) * (_Tp(1) + __y / __k)); 163 __bet *= __term; 164 } 165 166 return __bet; 167 } 168 169 170 /** 171 * @brief Return the beta function \f$ B(x,y) \f$. 172 * 173 * The beta function is defined by 174 * @f[ 175 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 176 * @f] 177 * 178 * @param __x The first argument of the beta function. 179 * @param __y The second argument of the beta function. 180 * @return The beta function. 181 */ 182 template<typename _Tp> 183 inline _Tp 184 __beta(_Tp __x, _Tp __y) 185 { 186 if (__isnan(__x) || __isnan(__y)) 187 return std::numeric_limits<_Tp>::quiet_NaN(); 188 else 189 return __beta_lgamma(__x, __y); 190 } 191 192 _GLIBCXX_END_NAMESPACE_VERSION 193 } // namespace std::tr1::__detail 194 } 195 } 196 197 #endif // __GLIBCXX_TR1_BETA_FUNCTION_TCC 198
