FM / tr1

/usr/include/c++/8/tr1

Name	Size	Mode	Actions
array	6964	0644	edit dl rm
bessel_function.tcc	22473	0644	edit dl rm
beta_function.tcc	5995	0644	edit dl rm
ccomplex	1255	0644	edit dl rm
cctype	1412	0644	edit dl rm
cfenv	2004	0644	edit dl rm
cfloat	1380	0644	edit dl rm
cinttypes	2256	0644	edit dl rm
climits	1454	0644	edit dl rm
cmath	43806	0644	edit dl rm
complex	12384	0644	edit dl rm
complex.h	1261	0644	edit dl rm
cstdarg	1246	0644	edit dl rm
cstdbool	1344	0644	edit dl rm
cstdint	2623	0644	edit dl rm
cstdio	1482	0644	edit dl rm
cstdlib	1796	0644	edit dl rm
ctgmath	1248	0644	edit dl rm
ctime	1234	0644	edit dl rm
ctype.h	1209	0644	edit dl rm
cwchar	1718	0644	edit dl rm
cwctype	1459	0644	edit dl rm
ell_integral.tcc	27724	0644	edit dl rm
exp_integral.tcc	16009	0644	edit dl rm
fenv.h	1204	0644	edit dl rm
float.h	1209	0644	edit dl rm
functional	70545	0644	edit dl rm
functional_hash.h	6043	0644	edit dl rm
gamma.tcc	14682	0644	edit dl rm
hashtable.h	41537	0644	edit dl rm
hashtable_policy.h	25086	0644	edit dl rm
hypergeometric.tcc	28066	0644	edit dl rm
inttypes.h	1267	0644	edit dl rm
legendre_function.tcc	10909	0644	edit dl rm
limits.h	1214	0644	edit dl rm
math.h	4553	0644	edit dl rm
memory	1791	0644	edit dl rm
modified_bessel_func.tcc	16320	0644	edit dl rm
poly_hermite.tcc	3925	0644	edit dl rm
poly_laguerre.tcc	11676	0644	edit dl rm
random	1589	0644	edit dl rm
random.h	73123	0644	edit dl rm
random.tcc	53927	0644	edit dl rm
regex	92880	0644	edit dl rm
riemann_zeta.tcc	14063	0644	edit dl rm
shared_ptr.h	32608	0644	edit dl rm
special_function_util.h	5055	0644	edit dl rm
stdarg.h	1214	0644	edit dl rm
stdbool.h	1219	0644	edit dl rm
stdint.h	1214	0644	edit dl rm
stdio.h	1209	0644	edit dl rm
stdlib.h	1487	0644	edit dl rm
tgmath.h	1255	0644	edit dl rm
tuple	12119	0644	edit dl rm
type_traits	19019	0644	edit dl rm
unordered_map	1574	0644	edit dl rm
unordered_map.h	10216	0644	edit dl rm
unordered_set	1574	0644	edit dl rm
unordered_set.h	9540	0644	edit dl rm
utility	3225	0644	edit dl rm
wchar.h	1249	0644	edit dl rm
wctype.h	1255	0644	edit dl rm

Edit: /usr/include/c++/8/tr1/beta_function.tcc (5995B)

// Special functions -*- C++ -*-

// Copyright (C) 2006-2018 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

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