1 | // Special functions -*- C++ -*- |
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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 |