11.2.0/tr1/beta_function.tcc

// 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
Revision:	1166
Committed:	Tue Oct 26 14:22:36 2021 UTC (4 years ago) by rossy
File size:	5995 byte(s)
Log Message:	Daodan: Replace MinGW build env with an up-to-date MSYS2 env
#	Content
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