1 | // Special functions -*- C++ -*- |
2 | |
3 | // Copyright (C) 2006-2021 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 | |