// Special functions -*- C++ -*-
-// Copyright (C) 2006, 2007, 2008
+// Copyright (C) 2006, 2007, 2008, 2009, 2010
// 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 2, or (at your option)
+// 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,
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
-// You should have received a copy of the GNU General Public License along
-// with this library; see the file COPYING. If not, write to the Free
-// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
-// USA.
-//
-// As a special exception, you may use this file as part of a free software
-// library without restriction. Specifically, if other files instantiate
-// templates or use macros or inline functions from this file, or you compile
-// this file and link it with other files to produce an executable, this
-// file does not by itself cause the resulting executable to be covered by
-// the GNU General Public License. This exception does not however
-// invalidate any other reasons why the executable file might be covered by
-// the GNU General Public License.
+// 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/hypergeometric.tcc
* This is an internal header file, included by other library headers.
- * You should not attempt to use it directly.
+ * Do not attempt to use it directly. @headername{tr1/cmath}
*/
//
#ifndef _GLIBCXX_TR1_HYPERGEOMETRIC_TCC
#define _GLIBCXX_TR1_HYPERGEOMETRIC_TCC 1
-namespace std
+namespace std _GLIBCXX_VISIBILITY(default)
{
namespace tr1
{
-
// [5.2] Special functions
// Implementation-space details.
namespace __detail
{
+ _GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* @brief This routine returns the confluent hypergeometric function
* \frac{x^n}{n!}
* @f]
*
- * If a and b are integers and a < 0 and either b > 0 or b < a then the
- * series is a polynomial with a finite number of terms. If b is an integer
- * and b <= 0 the confluent hypergeometric function is undefined.
+ * If a and b are integers and a < 0 and either b > 0 or b < a
+ * then the series is a polynomial with a finite number of
+ * terms. If b is an integer and b <= 0 the confluent
+ * hypergeometric function is undefined.
*
* @param __a The "numerator" parameter.
* @param __c The "denominator" parameter.
*
* @todo Handle b == nonpositive integer blowup - return NaN.
*
- * @param __a The "numerator" parameter.
- * @param __c The "denominator" parameter.
+ * @param __a The @a numerator parameter.
+ * @param __c The @a denominator parameter.
* @param __x The argument of the confluent hypergeometric function.
* @return The confluent hypergeometric function.
*/
*
* This works and it's pretty fast.
*
- * @param __a The first "numerator" parameter.
- * @param __a The second "numerator" parameter.
- * @param __c The "denominator" parameter.
+ * @param __a The first @a numerator parameter.
+ * @param __a The second @a numerator parameter.
+ * @param __c The @a denominator parameter.
* @param __x The argument of the confluent hypergeometric function.
* @return The confluent hypergeometric function.
*/
/**
- * @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$ by the reflection
- * formulae in Abramowitz & Stegun formula 15.3.6 for d = c - a - b not integral
- * and formula 15.3.11 for d = c - a - b integral.
- * This assumes a, b, c != negative integer.
+ * @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$
+ * by the reflection formulae in Abramowitz & Stegun formula
+ * 15.3.6 for d = c - a - b not integral and formula 15.3.11 for
+ * d = c - a - b integral. This assumes a, b, c != negative
+ * integer.
*
* The hypogeometric function is defined by
* @f[
bool __ok_d1 = true;
_Tp __lng_ad, __lng_ad1, __lng_bd1;
- try
+ __try
{
__lng_ad = __log_gamma(__ad);
__lng_ad1 = __log_gamma(__a + __d1);
__lng_bd1 = __log_gamma(__b + __d1);
}
- catch(...)
+ __catch(...)
{
__ok_d1 = false;
}
}
if (__ln_pre1 > __log_max)
- std::__throw_runtime_error(__N("Overflow of gamma functions "
- "in __hyperg_luke."));
+ std::__throw_runtime_error(__N("Overflow of gamma functions"
+ " in __hyperg_luke."));
else
__F1 = std::exp(__ln_pre1) * __sum1;
}
// Evaluate F2.
bool __ok_d2 = true;
_Tp __lng_ad2, __lng_bd2;
- try
+ __try
{
__lng_ad2 = __log_gamma(__a + __d2);
__lng_bd2 = __log_gamma(__b + __d2);
}
- catch(...)
+ __catch(...)
{
__ok_d2 = false;
}
int __j;
for (__j = 1; __j < __maxiter; ++__j)
{
- // Values for psi functions use recurrence; Abramowitz & Stegun 6.3.5
+ // Values for psi functions use recurrence;
+ // Abramowitz & Stegun 6.3.5
const _Tp __term1 = _Tp(1) / _Tp(__j)
+ _Tp(1) / (__ad + __j);
const _Tp __term2 = _Tp(1) / (__a + __d1 + _Tp(__j - 1))
bool __ok1 = true;
_Tp __sgn_g1ca = _Tp(0), __ln_g1ca = _Tp(0);
_Tp __sgn_g1cb = _Tp(0), __ln_g1cb = _Tp(0);
- try
+ __try
{
__sgn_g1ca = __log_gamma_sign(__c - __a);
__ln_g1ca = __log_gamma(__c - __a);
__sgn_g1cb = __log_gamma_sign(__c - __b);
__ln_g1cb = __log_gamma(__c - __b);
}
- catch(...)
+ __catch(...)
{
__ok1 = false;
}
bool __ok2 = true;
_Tp __sgn_g2a = _Tp(0), __ln_g2a = _Tp(0);
_Tp __sgn_g2b = _Tp(0), __ln_g2b = _Tp(0);
- try
+ __try
{
__sgn_g2a = __log_gamma_sign(__a);
__ln_g2a = __log_gamma(__a);
__sgn_g2b = __log_gamma_sign(__b);
__ln_g2b = __log_gamma(__b);
}
- catch(...)
+ __catch(...)
{
__ok2 = false;
}
* \frac{x^n}{n!}
* @f]
*
- * @param __a The first "numerator" parameter.
- * @param __a The second "numerator" parameter.
- * @param __c The "denominator" parameter.
+ * @param __a The first @a numerator parameter.
+ * @param __a The second @a numerator parameter.
+ * @param __c The @a denominator parameter.
* @param __x The argument of the confluent hypergeometric function.
* @return The confluent hypergeometric function.
*/
return __hyperg_series(__a, __b, __c, __x);
else if (std::abs(__a) < _Tp(10) && std::abs(__b) < _Tp(10))
{
- // For integer a and b the hypergeometric function is a finite polynomial.
+ // For integer a and b the hypergeometric function is a
+ // finite polynomial.
if (__a < _Tp(0) && std::abs(__a - __a_nint) < __toler)
return __hyperg_series(__a_nint, __b, __c, __x);
else if (__b < _Tp(0) && std::abs(__b - __b_nint) < __toler)
return __hyperg_luke(__a, __b, __c, __x);
}
+ _GLIBCXX_END_NAMESPACE_VERSION
} // namespace std::tr1::__detail
}
}
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