gcc/libstdc++-v3/include/tr1/hypergeometric.tcc - Issue 3050029: [gcc] GCC 4.5.0=>4.5.1

Unified Diff: gcc/libstdc++-v3/include/tr1/hypergeometric.tcc

Issue 3050029: [gcc] GCC 4.5.0=>4.5.1 (Closed) Base URL: ssh://git@gitrw.chromium.org:9222/nacl-toolchain.git

Patch Set: Created 10 years, 5 months ago

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Index: gcc/libstdc++-v3/include/tr1/hypergeometric.tcc

diff --git a/gcc/libstdc++-v3/include/tr1/hypergeometric.tcc b/gcc/libstdc++-v3/include/tr1/hypergeometric.tcc

deleted file mode 100644

index c975afa598f773f1266cd8b017783e8bbe4d3923..0000000000000000000000000000000000000000

--- a/gcc/libstdc++-v3/include/tr1/hypergeometric.tcc

+++ /dev/null

@@ -1,774 +0,0 @@

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

-// 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/hypergeometric.tcc

- * This is an internal header file, included by other library headers.

- * You should not attempt to use it directly.

- */

-//

-// ISO C++ 14882 TR1: 5.2 Special functions

-//

-// Written by Edward Smith-Rowland based:

-// (1) Handbook of Mathematical Functions,

-// ed. Milton Abramowitz and Irene A. Stegun,

-// Dover Publications,

-// Section 6, pp. 555-566

-// (2) The Gnu Scientific Library, http://www.gnu.org/software/gsl

-#ifndef _GLIBCXX_TR1_HYPERGEOMETRIC_TCC

-#define _GLIBCXX_TR1_HYPERGEOMETRIC_TCC 1

-namespace std

-namespace tr1

- // [5.2] Special functions

- // Implementation-space details.

- namespace __detail

- {

- /**

- * @brief This routine returns the confluent hypergeometric function

- * by series expansion.

- *

- * @f[

- * _1F_1(a;c;x) = \frac{\Gamma(c)}{\Gamma(a)}

- * \sum_{n=0}^{\infty}

- * \frac{\Gamma(a+n)}{\Gamma(c+n)}

- * \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.

- *

- * @param __a The "numerator" parameter.

- * @param __c The "denominator" parameter.

- * @param __x The argument of the confluent hypergeometric function.

- * @return The confluent hypergeometric function.

- */

- template<typename _Tp>

- _Tp

- __conf_hyperg_series(const _Tp __a, const _Tp __c, const _Tp __x)

- {

- const _Tp __eps = std::numeric_limits<_Tp>::epsilon();

- _Tp __term = _Tp(1);

- _Tp __Fac = _Tp(1);

- const unsigned int __max_iter = 100000;

- unsigned int __i;

- for (__i = 0; __i < __max_iter; ++__i)

- {

- __term *= (__a + _Tp(__i)) * __x

- / ((__c + _Tp(__i)) * _Tp(1 + __i));

- if (std::abs(__term) < __eps)

- {

- break;

- }

- __Fac += __term;

- }

- if (__i == __max_iter)

- std::__throw_runtime_error(__N("Series failed to converge "

- "in __conf_hyperg_series."));

- return __Fac;

- }

- /**

- * @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$

- * by an iterative procedure described in

- * Luke, Algorithms for the Computation of Mathematical Functions.

- *

- * Like the case of the 2F1 rational approximations, these are

- * probably guaranteed to converge for x < 0, barring gross

- * numerical instability in the pre-asymptotic regime.

- */

- template<typename _Tp>

- _Tp

- __conf_hyperg_luke(const _Tp __a, const _Tp __c, const _Tp __xin)

- {

- const _Tp __big = std::pow(std::numeric_limits<_Tp>::max(), _Tp(0.16L));

- const int __nmax = 20000;

- const _Tp __eps = std::numeric_limits<_Tp>::epsilon();

- const _Tp __x = -__xin;

- const _Tp __x3 = __x * __x * __x;

- const _Tp __t0 = __a / __c;

- const _Tp __t1 = (__a + _Tp(1)) / (_Tp(2) * __c);

- const _Tp __t2 = (__a + _Tp(2)) / (_Tp(2) * (__c + _Tp(1)));

- _Tp __F = _Tp(1);

- _Tp __prec;

- _Tp __Bnm3 = _Tp(1);

- _Tp __Bnm2 = _Tp(1) + __t1 * __x;

- _Tp __Bnm1 = _Tp(1) + __t2 * __x * (_Tp(1) + __t1 / _Tp(3) * __x);

- _Tp __Anm3 = _Tp(1);

- _Tp __Anm2 = __Bnm2 - __t0 * __x;

- _Tp __Anm1 = __Bnm1 - __t0 * (_Tp(1) + __t2 * __x) * __x

- + __t0 * __t1 * (__c / (__c + _Tp(1))) * __x * __x;

- int __n = 3;

- while(1)

- {

- _Tp __npam1 = _Tp(__n - 1) + __a;

- _Tp __npcm1 = _Tp(__n - 1) + __c;

- _Tp __npam2 = _Tp(__n - 2) + __a;

- _Tp __npcm2 = _Tp(__n - 2) + __c;

- _Tp __tnm1 = _Tp(2 * __n - 1);

- _Tp __tnm3 = _Tp(2 * __n - 3);

- _Tp __tnm5 = _Tp(2 * __n - 5);

- _Tp __F1 = (_Tp(__n - 2) - __a) / (_Tp(2) * __tnm3 * __npcm1);

- _Tp __F2 = (_Tp(__n) + __a) * __npam1

- / (_Tp(4) * __tnm1 * __tnm3 * __npcm2 * __npcm1);

- _Tp __F3 = -__npam2 * __npam1 * (_Tp(__n - 2) - __a)

- / (_Tp(8) * __tnm3 * __tnm3 * __tnm5

- * (_Tp(__n - 3) + __c) * __npcm2 * __npcm1);

- _Tp __E = -__npam1 * (_Tp(__n - 1) - __c)

- / (_Tp(2) * __tnm3 * __npcm2 * __npcm1);

- _Tp __An = (_Tp(1) + __F1 * __x) * __Anm1

- + (__E + __F2 * __x) * __x * __Anm2 + __F3 * __x3 * __Anm3;

- _Tp __Bn = (_Tp(1) + __F1 * __x) * __Bnm1

- + (__E + __F2 * __x) * __x * __Bnm2 + __F3 * __x3 * __Bnm3;

- _Tp __r = __An / __Bn;

- __prec = std::abs((__F - __r) / __F);

- __F = __r;

- if (__prec < __eps || __n > __nmax)

- break;

- if (std::abs(__An) > __big || std::abs(__Bn) > __big)

- {

- __An /= __big;

- __Bn /= __big;

- __Anm1 /= __big;

- __Bnm1 /= __big;

- __Anm2 /= __big;

- __Bnm2 /= __big;

- __Anm3 /= __big;

- __Bnm3 /= __big;

- }

- else if (std::abs(__An) < _Tp(1) / __big

- || std::abs(__Bn) < _Tp(1) / __big)

- {

- __An *= __big;

- __Bn *= __big;

- __Anm1 *= __big;

- __Bnm1 *= __big;

- __Anm2 *= __big;

- __Bnm2 *= __big;

- __Anm3 *= __big;

- __Bnm3 *= __big;

- }

- ++__n;

- __Bnm3 = __Bnm2;

- __Bnm2 = __Bnm1;

- __Bnm1 = __Bn;

- __Anm3 = __Anm2;

- __Anm2 = __Anm1;

- __Anm1 = __An;

- }

- if (__n >= __nmax)

- std::__throw_runtime_error(__N("Iteration failed to converge "

- "in __conf_hyperg_luke."));

- return __F;

- }

- /**

- * @brief Return the confluent hypogeometric function

- * @f$ _1F_1(a;c;x) @f$.

- *

- * @todo Handle b == nonpositive integer blowup - return NaN.

- *

- * @param __a The "numerator" parameter.

- * @param __c The "denominator" parameter.

- * @param __x The argument of the confluent hypergeometric function.

- * @return The confluent hypergeometric function.

- */

- template<typename _Tp>

- inline _Tp

- __conf_hyperg(const _Tp __a, const _Tp __c, const _Tp __x)

- {

-#if _GLIBCXX_USE_C99_MATH_TR1

- const _Tp __c_nint = std::tr1::nearbyint(__c);

-#else

- const _Tp __c_nint = static_cast<int>(__c + _Tp(0.5L));

-#endif

- if (__isnan(__a) || __isnan(__c) || __isnan(__x))

- return std::numeric_limits<_Tp>::quiet_NaN();

- else if (__c_nint == __c && __c_nint <= 0)

- return std::numeric_limits<_Tp>::infinity();

- else if (__a == _Tp(0))

- return _Tp(1);

- else if (__c == __a)

- return std::exp(__x);

- else if (__x < _Tp(0))

- return __conf_hyperg_luke(__a, __c, __x);

- else

- return __conf_hyperg_series(__a, __c, __x);

- }

- /**

- * @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$

- * by series expansion.

- *

- * The hypogeometric function is defined by

- * @f[

- * _2F_1(a,b;c;x) = \frac{\Gamma(c)}{\Gamma(a)\Gamma(b)}

- * \sum_{n=0}^{\infty}

- * \frac{\Gamma(a+n)\Gamma(b+n)}{\Gamma(c+n)}

- * \frac{x^n}{n!}

- * @f]

- *

- * 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 __x The argument of the confluent hypergeometric function.

- * @return The confluent hypergeometric function.

- */

- template<typename _Tp>

- _Tp

- __hyperg_series(const _Tp __a, const _Tp __b,

- const _Tp __c, const _Tp __x)

- {

- const _Tp __eps = std::numeric_limits<_Tp>::epsilon();

- _Tp __term = _Tp(1);

- _Tp __Fabc = _Tp(1);

- const unsigned int __max_iter = 100000;

- unsigned int __i;

- for (__i = 0; __i < __max_iter; ++__i)

- {

- __term *= (__a + _Tp(__i)) * (__b + _Tp(__i)) * __x

- / ((__c + _Tp(__i)) * _Tp(1 + __i));

- if (std::abs(__term) < __eps)

- {

- break;

- }

- __Fabc += __term;

- }

- if (__i == __max_iter)

- std::__throw_runtime_error(__N("Series failed to converge "

- "in __hyperg_series."));

- return __Fabc;

- }

- /**

- * @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$

- * by an iterative procedure described in

- * Luke, Algorithms for the Computation of Mathematical Functions.

- */

- template<typename _Tp>

- _Tp

- __hyperg_luke(const _Tp __a, const _Tp __b, const _Tp __c,

- const _Tp __xin)

- {

- const _Tp __big = std::pow(std::numeric_limits<_Tp>::max(), _Tp(0.16L));

- const int __nmax = 20000;

- const _Tp __eps = std::numeric_limits<_Tp>::epsilon();

- const _Tp __x = -__xin;

- const _Tp __x3 = __x * __x * __x;

- const _Tp __t0 = __a * __b / __c;

- const _Tp __t1 = (__a + _Tp(1)) * (__b + _Tp(1)) / (_Tp(2) * __c);

- const _Tp __t2 = (__a + _Tp(2)) * (__b + _Tp(2))

- / (_Tp(2) * (__c + _Tp(1)));

- _Tp __F = _Tp(1);

- _Tp __Bnm3 = _Tp(1);

- _Tp __Bnm2 = _Tp(1) + __t1 * __x;

- _Tp __Bnm1 = _Tp(1) + __t2 * __x * (_Tp(1) + __t1 / _Tp(3) * __x);

- _Tp __Anm3 = _Tp(1);

- _Tp __Anm2 = __Bnm2 - __t0 * __x;

- _Tp __Anm1 = __Bnm1 - __t0 * (_Tp(1) + __t2 * __x) * __x

- + __t0 * __t1 * (__c / (__c + _Tp(1))) * __x * __x;

- int __n = 3;

- while (1)

- {

- const _Tp __npam1 = _Tp(__n - 1) + __a;

- const _Tp __npbm1 = _Tp(__n - 1) + __b;

- const _Tp __npcm1 = _Tp(__n - 1) + __c;

- const _Tp __npam2 = _Tp(__n - 2) + __a;

- const _Tp __npbm2 = _Tp(__n - 2) + __b;

- const _Tp __npcm2 = _Tp(__n - 2) + __c;

- const _Tp __tnm1 = _Tp(2 * __n - 1);

- const _Tp __tnm3 = _Tp(2 * __n - 3);

- const _Tp __tnm5 = _Tp(2 * __n - 5);

- const _Tp __n2 = __n * __n;

- const _Tp __F1 = (_Tp(3) * __n2 + (__a + __b - _Tp(6)) * __n

- + _Tp(2) - __a * __b - _Tp(2) * (__a + __b))

- / (_Tp(2) * __tnm3 * __npcm1);

- const _Tp __F2 = -(_Tp(3) * __n2 - (__a + __b + _Tp(6)) * __n

- + _Tp(2) - __a * __b) * __npam1 * __npbm1

- / (_Tp(4) * __tnm1 * __tnm3 * __npcm2 * __npcm1);

- const _Tp __F3 = (__npam2 * __npam1 * __npbm2 * __npbm1

- * (_Tp(__n - 2) - __a) * (_Tp(__n - 2) - __b))

- / (_Tp(8) * __tnm3 * __tnm3 * __tnm5

- * (_Tp(__n - 3) + __c) * __npcm2 * __npcm1);

- const _Tp __E = -__npam1 * __npbm1 * (_Tp(__n - 1) - __c)

- / (_Tp(2) * __tnm3 * __npcm2 * __npcm1);

- _Tp __An = (_Tp(1) + __F1 * __x) * __Anm1

- + (__E + __F2 * __x) * __x * __Anm2 + __F3 * __x3 * __Anm3;

- _Tp __Bn = (_Tp(1) + __F1 * __x) * __Bnm1

- + (__E + __F2 * __x) * __x * __Bnm2 + __F3 * __x3 * __Bnm3;

- const _Tp __r = __An / __Bn;

- const _Tp __prec = std::abs((__F - __r) / __F);

- __F = __r;

- if (__prec < __eps || __n > __nmax)

- break;

- if (std::abs(__An) > __big || std::abs(__Bn) > __big)

- {

- __An /= __big;

- __Bn /= __big;

- __Anm1 /= __big;

- __Bnm1 /= __big;

- __Anm2 /= __big;

- __Bnm2 /= __big;

- __Anm3 /= __big;

- __Bnm3 /= __big;

- }

- else if (std::abs(__An) < _Tp(1) / __big

- || std::abs(__Bn) < _Tp(1) / __big)

- {

- __An *= __big;

- __Bn *= __big;

- __Anm1 *= __big;

- __Bnm1 *= __big;

- __Anm2 *= __big;

- __Bnm2 *= __big;

- __Anm3 *= __big;

- __Bnm3 *= __big;

- }

- ++__n;

- __Bnm3 = __Bnm2;

- __Bnm2 = __Bnm1;

- __Bnm1 = __Bn;

- __Anm3 = __Anm2;

- __Anm2 = __Anm1;

- __Anm1 = __An;

- }

- if (__n >= __nmax)

- std::__throw_runtime_error(__N("Iteration failed to converge "

- "in __hyperg_luke."));

- return __F;

- }

- /**

- * @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[

- * _2F_1(a,b;c;x) = \frac{\Gamma(c)}{\Gamma(a)\Gamma(b)}

- * \sum_{n=0}^{\infty}

- * \frac{\Gamma(a+n)\Gamma(b+n)}{\Gamma(c+n)}

- * \frac{x^n}{n!}

- * @f]

- *

- * The reflection formula for nonintegral @f$ d = c - a - b @f$ is:

- * @f[

- * _2F_1(a,b;c;x) = \frac{\Gamma(c)\Gamma(d)}{\Gamma(c-a)\Gamma(c-b)}

- * _2F_1(a,b;1-d;1-x)

- * + \frac{\Gamma(c)\Gamma(-d)}{\Gamma(a)\Gamma(b)}

- * _2F_1(c-a,c-b;1+d;1-x)

- * @f]

- *

- * The reflection formula for integral @f$ m = c - a - b @f$ is:

- * @f[

- * _2F_1(a,b;a+b+m;x) = \frac{\Gamma(m)\Gamma(a+b+m)}{\Gamma(a+m)\Gamma(b+m)}

- * \sum_{k=0}^{m-1} \frac{(m+a)_k(m+b)_k}{k!(1-m)_k}

- * -

- * @f]

- */

- template<typename _Tp>

- _Tp

- __hyperg_reflect(const _Tp __a, const _Tp __b, const _Tp __c,

- const _Tp __x)

- {

- const _Tp __d = __c - __a - __b;

- const int __intd = std::floor(__d + _Tp(0.5L));

- const _Tp __eps = std::numeric_limits<_Tp>::epsilon();

- const _Tp __toler = _Tp(1000) * __eps;

- const _Tp __log_max = std::log(std::numeric_limits<_Tp>::max());

- const bool __d_integer = (std::abs(__d - __intd) < __toler);

- if (__d_integer)

- {

- const _Tp __ln_omx = std::log(_Tp(1) - __x);

- const _Tp __ad = std::abs(__d);

- _Tp __F1, __F2;

- _Tp __d1, __d2;

- if (__d >= _Tp(0))

- {

- __d1 = __d;

- __d2 = _Tp(0);

- }

- else

- {

- __d1 = _Tp(0);

- __d2 = __d;

- }

- const _Tp __lng_c = __log_gamma(__c);

- // Evaluate F1.

- if (__ad < __eps)

- {

- // d = c - a - b = 0.

- __F1 = _Tp(0);

- }

- else

- {

- bool __ok_d1 = true;

- _Tp __lng_ad, __lng_ad1, __lng_bd1;

- __try

- {

- __lng_ad = __log_gamma(__ad);

- __lng_ad1 = __log_gamma(__a + __d1);

- __lng_bd1 = __log_gamma(__b + __d1);

- }

- __catch(...)

- {

- __ok_d1 = false;

- }

- if (__ok_d1)

- {

- /* Gamma functions in the denominator are ok.

- * Proceed with evaluation.

- */

- _Tp __sum1 = _Tp(1);

- _Tp __term = _Tp(1);

- _Tp __ln_pre1 = __lng_ad + __lng_c + __d2 * __ln_omx

- - __lng_ad1 - __lng_bd1;

- /* Do F1 sum.

- */

- for (int __i = 1; __i < __ad; ++__i)

- {

- const int __j = __i - 1;

- __term *= (__a + __d2 + __j) * (__b + __d2 + __j)

- / (_Tp(1) + __d2 + __j) / __i * (_Tp(1) - __x);

- __sum1 += __term;

- }

- if (__ln_pre1 > __log_max)

- std::__throw_runtime_error(__N("Overflow of gamma functions "

- "in __hyperg_luke."));

- else

- __F1 = std::exp(__ln_pre1) * __sum1;

- }

- else

- {

- // Gamma functions in the denominator were not ok.

- // So the F1 term is zero.

- __F1 = _Tp(0);

- }

- } // end F1 evaluation

- // Evaluate F2.

- bool __ok_d2 = true;

- _Tp __lng_ad2, __lng_bd2;

- __try

- {

- __lng_ad2 = __log_gamma(__a + __d2);

- __lng_bd2 = __log_gamma(__b + __d2);

- }

- __catch(...)

- {

- __ok_d2 = false;

- }

- if (__ok_d2)

- {

- // Gamma functions in the denominator are ok.

- // Proceed with evaluation.

- const int __maxiter = 2000;

- const _Tp __psi_1 = -__numeric_constants<_Tp>::__gamma_e();

- const _Tp __psi_1pd = __psi(_Tp(1) + __ad);

- const _Tp __psi_apd1 = __psi(__a + __d1);

- const _Tp __psi_bpd1 = __psi(__b + __d1);

- _Tp __psi_term = __psi_1 + __psi_1pd - __psi_apd1

- - __psi_bpd1 - __ln_omx;

- _Tp __fact = _Tp(1);

- _Tp __sum2 = __psi_term;

- _Tp __ln_pre2 = __lng_c + __d1 * __ln_omx

- - __lng_ad2 - __lng_bd2;

- // Do F2 sum.

- int __j;

- for (__j = 1; __j < __maxiter; ++__j)

- {

- // 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))

- + _Tp(1) / (__b + __d1 + _Tp(__j - 1));

- __psi_term += __term1 - __term2;

- __fact *= (__a + __d1 + _Tp(__j - 1))

- * (__b + __d1 + _Tp(__j - 1))

- / ((__ad + __j) * __j) * (_Tp(1) - __x);

- const _Tp __delta = __fact * __psi_term;

- __sum2 += __delta;

- if (std::abs(__delta) < __eps * std::abs(__sum2))

- break;

- }

- if (__j == __maxiter)

- std::__throw_runtime_error(__N("Sum F2 failed to converge "

- "in __hyperg_reflect"));

- if (__sum2 == _Tp(0))

- __F2 = _Tp(0);

- else

- __F2 = std::exp(__ln_pre2) * __sum2;

- }

- else

- {

- // Gamma functions in the denominator not ok.

- // So the F2 term is zero.

- __F2 = _Tp(0);

- } // end F2 evaluation

- const _Tp __sgn_2 = (__intd % 2 == 1 ? -_Tp(1) : _Tp(1));

- const _Tp __F = __F1 + __sgn_2 * __F2;

- return __F;

- }

- else

- {

- // d = c - a - b not an integer.

- // These gamma functions appear in the denominator, so we

- // catch their harmless domain errors and set the terms to zero.

- bool __ok1 = true;

- _Tp __sgn_g1ca = _Tp(0), __ln_g1ca = _Tp(0);

- _Tp __sgn_g1cb = _Tp(0), __ln_g1cb = _Tp(0);

- __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(...)

- {

- __ok1 = false;

- }

- bool __ok2 = true;

- _Tp __sgn_g2a = _Tp(0), __ln_g2a = _Tp(0);

- _Tp __sgn_g2b = _Tp(0), __ln_g2b = _Tp(0);

- __try

- {

- __sgn_g2a = __log_gamma_sign(__a);

- __ln_g2a = __log_gamma(__a);

- __sgn_g2b = __log_gamma_sign(__b);

- __ln_g2b = __log_gamma(__b);

- }

- __catch(...)

- {

- __ok2 = false;

- }

- const _Tp __sgn_gc = __log_gamma_sign(__c);

- const _Tp __ln_gc = __log_gamma(__c);

- const _Tp __sgn_gd = __log_gamma_sign(__d);

- const _Tp __ln_gd = __log_gamma(__d);

- const _Tp __sgn_gmd = __log_gamma_sign(-__d);

- const _Tp __ln_gmd = __log_gamma(-__d);

- const _Tp __sgn1 = __sgn_gc * __sgn_gd * __sgn_g1ca * __sgn_g1cb;

- const _Tp __sgn2 = __sgn_gc * __sgn_gmd * __sgn_g2a * __sgn_g2b;

- _Tp __pre1, __pre2;

- if (__ok1 && __ok2)

- {

- _Tp __ln_pre1 = __ln_gc + __ln_gd - __ln_g1ca - __ln_g1cb;

- _Tp __ln_pre2 = __ln_gc + __ln_gmd - __ln_g2a - __ln_g2b

- + __d * std::log(_Tp(1) - __x);

- if (__ln_pre1 < __log_max && __ln_pre2 < __log_max)

- {

- __pre1 = std::exp(__ln_pre1);

- __pre2 = std::exp(__ln_pre2);

- __pre1 *= __sgn1;

- __pre2 *= __sgn2;

- }

- else

- {

- std::__throw_runtime_error(__N("Overflow of gamma functions "

- "in __hyperg_reflect"));

- }

- else if (__ok1 && !__ok2)

- {

- _Tp __ln_pre1 = __ln_gc + __ln_gd - __ln_g1ca - __ln_g1cb;

- if (__ln_pre1 < __log_max)

- {

- __pre1 = std::exp(__ln_pre1);

- __pre1 *= __sgn1;

- __pre2 = _Tp(0);

- }

- else

- {

- std::__throw_runtime_error(__N("Overflow of gamma functions "

- "in __hyperg_reflect"));

- }

- else if (!__ok1 && __ok2)

- {

- _Tp __ln_pre2 = __ln_gc + __ln_gmd - __ln_g2a - __ln_g2b

- + __d * std::log(_Tp(1) - __x);

- if (__ln_pre2 < __log_max)

- {

- __pre1 = _Tp(0);

- __pre2 = std::exp(__ln_pre2);

- __pre2 *= __sgn2;

- }

- else

- {

- std::__throw_runtime_error(__N("Overflow of gamma functions "

- "in __hyperg_reflect"));

- }

- else

- {

- __pre1 = _Tp(0);

- __pre2 = _Tp(0);

- std::__throw_runtime_error(__N("Underflow of gamma functions "

- "in __hyperg_reflect"));

- }

- const _Tp __F1 = __hyperg_series(__a, __b, _Tp(1) - __d,

- _Tp(1) - __x);

- const _Tp __F2 = __hyperg_series(__c - __a, __c - __b, _Tp(1) + __d,

- _Tp(1) - __x);

- const _Tp __F = __pre1 * __F1 + __pre2 * __F2;

- return __F;

- }

- /**

- * @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$.

- *

- * The hypogeometric function is defined by

- * @f[

- * _2F_1(a,b;c;x) = \frac{\Gamma(c)}{\Gamma(a)\Gamma(b)}

- * \sum_{n=0}^{\infty}

- * \frac{\Gamma(a+n)\Gamma(b+n)}{\Gamma(c+n)}

- * \frac{x^n}{n!}

- * @f]

- *

- * @param __a The first "numerator" parameter.

- * @param __a The second "numerator" parameter.

- * @param __c The "denominator" parameter.

- * @param __x The argument of the confluent hypergeometric function.

- * @return The confluent hypergeometric function.

- */

- template<typename _Tp>

- inline _Tp

- __hyperg(const _Tp __a, const _Tp __b, const _Tp __c, const _Tp __x)

- {

-#if _GLIBCXX_USE_C99_MATH_TR1

- const _Tp __a_nint = std::tr1::nearbyint(__a);

- const _Tp __b_nint = std::tr1::nearbyint(__b);

- const _Tp __c_nint = std::tr1::nearbyint(__c);

-#else

- const _Tp __a_nint = static_cast<int>(__a + _Tp(0.5L));

- const _Tp __b_nint = static_cast<int>(__b + _Tp(0.5L));

- const _Tp __c_nint = static_cast<int>(__c + _Tp(0.5L));

-#endif

- const _Tp __toler = _Tp(1000) * std::numeric_limits<_Tp>::epsilon();

- if (std::abs(__x) >= _Tp(1))

- std::__throw_domain_error(__N("Argument outside unit circle "

- "in __hyperg."));

- else if (__isnan(__a) || __isnan(__b)

- || __isnan(__c) || __isnan(__x))

- return std::numeric_limits<_Tp>::quiet_NaN();

- else if (__c_nint == __c && __c_nint <= _Tp(0))

- return std::numeric_limits<_Tp>::infinity();

- else if (std::abs(__c - __b) < __toler || std::abs(__c - __a) < __toler)

- return std::pow(_Tp(1) - __x, __c - __a - __b);

- else if (__a >= _Tp(0) && __b >= _Tp(0) && __c >= _Tp(0)

- && __x >= _Tp(0) && __x < _Tp(0.995L))

- 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.

- 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_series(__a, __b_nint, __c, __x);

- else if (__x < -_Tp(0.25L))

- return __hyperg_luke(__a, __b, __c, __x);

- else if (__x < _Tp(0.5L))

- return __hyperg_series(__a, __b, __c, __x);

- else

- if (std::abs(__c) > _Tp(10))

- return __hyperg_series(__a, __b, __c, __x);

- else

- return __hyperg_reflect(__a, __b, __c, __x);

- }

- else

- return __hyperg_luke(__a, __b, __c, __x);

- }

- } // namespace std::tr1::__detail

-#endif // _GLIBCXX_TR1_HYPERGEOMETRIC_TCC

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