1 // Special functions -*- C++ -*- 2 3 // Copyright (C) 2006-2018 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 _GLIBCXX_BEGIN_NAMESPACE_VERSION 52 53 #if _GLIBCXX_USE_STD_SPEC_FUNCS 54 # define _GLIBCXX_MATH_NS ::std 55 #elif defined(_GLIBCXX_TR1_CMATH) 56 namespace tr1 57 { 58 # define _GLIBCXX_MATH_NS ::std::tr1 59 #else 60 # error do not include this header directly, use <cmath> or <tr1/cmath> 61 #endif 62 // [5.2] Special functions 63 64 // Implementation-space details. 65 namespace __detail 66 { 67 /** 68 * @brief Return the beta function: \f$B(x,y)\f$. 69 * 70 * The beta function is defined by 71 * @f[ 72 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 73 * @f] 74 * 75 * @param __x The first argument of the beta function. 76 * @param __y The second argument of the beta function. 77 * @return The beta function. 78 */ 79 template<typename _Tp> 80 _Tp 81 __beta_gamma(_Tp __x, _Tp __y) 82 { 83 84 _Tp __bet; 85 #if _GLIBCXX_USE_C99_MATH_TR1 86 if (__x > __y) 87 { 88 __bet = _GLIBCXX_MATH_NS::tgamma(__x) 89 / _GLIBCXX_MATH_NS::tgamma(__x + __y); 90 __bet *= _GLIBCXX_MATH_NS::tgamma(__y); 91 } 92 else 93 { 94 __bet = _GLIBCXX_MATH_NS::tgamma(__y) 95 / _GLIBCXX_MATH_NS::tgamma(__x + __y); 96 __bet *= _GLIBCXX_MATH_NS::tgamma(__x); 97 } 98 #else 99 if (__x > __y) 100 { 101 __bet = __gamma(__x) / __gamma(__x + __y); 102 __bet *= __gamma(__y); 103 } 104 else 105 { 106 __bet = __gamma(__y) / __gamma(__x + __y); 107 __bet *= __gamma(__x); 108 } 109 #endif 110 111 return __bet; 112 } 113 114 /** 115 * @brief Return the beta function \f$B(x,y)\f$ using 116 * the log gamma functions. 117 * 118 * The beta function is defined by 119 * @f[ 120 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 121 * @f] 122 * 123 * @param __x The first argument of the beta function. 124 * @param __y The second argument of the beta function. 125 * @return The beta function. 126 */ 127 template<typename _Tp> 128 _Tp 129 __beta_lgamma(_Tp __x, _Tp __y) 130 { 131 #if _GLIBCXX_USE_C99_MATH_TR1 132 _Tp __bet = _GLIBCXX_MATH_NS::lgamma(__x) 133 + _GLIBCXX_MATH_NS::lgamma(__y) 134 - _GLIBCXX_MATH_NS::lgamma(__x + __y); 135 #else 136 _Tp __bet = __log_gamma(__x) 137 + __log_gamma(__y) 138 - __log_gamma(__x + __y); 139 #endif 140 __bet = std::exp(__bet); 141 return __bet; 142 } 143 144 145 /** 146 * @brief Return the beta function \f$B(x,y)\f$ using 147 * the product form. 148 * 149 * The beta function is defined by 150 * @f[ 151 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 152 * @f] 153 * 154 * @param __x The first argument of the beta function. 155 * @param __y The second argument of the beta function. 156 * @return The beta function. 157 */ 158 template<typename _Tp> 159 _Tp 160 __beta_product(_Tp __x, _Tp __y) 161 { 162 163 _Tp __bet = (__x + __y) / (__x * __y); 164 165 unsigned int __max_iter = 1000000; 166 for (unsigned int __k = 1; __k < __max_iter; ++__k) 167 { 168 _Tp __term = (_Tp(1) + (__x + __y) / __k) 169 / ((_Tp(1) + __x / __k) * (_Tp(1) + __y / __k)); 170 __bet *= __term; 171 } 172 173 return __bet; 174 } 175 176 177 /** 178 * @brief Return the beta function \f$ B(x,y) \f$. 179 * 180 * The beta function is defined by 181 * @f[ 182 * B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} 183 * @f] 184 * 185 * @param __x The first argument of the beta function. 186 * @param __y The second argument of the beta function. 187 * @return The beta function. 188 */ 189 template<typename _Tp> 190 inline _Tp 191 __beta(_Tp __x, _Tp __y) 192 { 193 if (__isnan(__x) || __isnan(__y)) 194 return std::numeric_limits<_Tp>::quiet_NaN(); 195 else 196 return __beta_lgamma(__x, __y); 197 } 198 } // namespace __detail 199 #undef _GLIBCXX_MATH_NS 200 #if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH) 201 } // namespace tr1 202 #endif 203 204 _GLIBCXX_END_NAMESPACE_VERSION 205 } 206 207 #endif // _GLIBCXX_TR1_BETA_FUNCTION_TCC 208