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// Special functions -*- C++ -*-// 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 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.* Do not attempt to use it directly. @headername{tr1/cmath}*///// 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 1namespace 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* 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$.** @todo Handle b == nonpositive integer blowup - return NaN.** @param __a The @a numerator parameter.* @param __c The @a denominator parameter.* @param __x The argument of the confluent hypergeometric function.* @return The confluent hypergeometric function.*/template<typename _Tp>inline _Tp__conf_hyperg(const _Tp __a, const _Tp __c, const _Tp __x){#if _GLIBCXX_USE_C99_MATH_TR1const _Tp __c_nint = std::tr1::nearbyint(__c);#elseconst _Tp __c_nint = static_cast<int>(__c + _Tp(0.5L));#endifif (__isnan(__a) || __isnan(__c) || __isnan(__x))return std::numeric_limits<_Tp>::quiet_NaN();else if (__c_nint == __c && __c_nint <= 0)return std::numeric_limits<_Tp>::infinity();else if (__a == _Tp(0))return _Tp(1);else if (__c == __a)return std::exp(__x);else if (__x < _Tp(0))return __conf_hyperg_luke(__a, __c, __x);elsereturn __conf_hyperg_series(__a, __c, __x);}/*** @brief Return the hypogeometric function @f$ _2F_1(a,b;c;x) @f$* by series expansion.** The hypogeometric function is defined by* @f[* _2F_1(a,b;c;x) = \frac{\Gamma(c)}{\Gamma(a)\Gamma(b)}* \sum_{n=0}^{\infty}* \frac{\Gamma(a+n)\Gamma(b+n)}{\Gamma(c+n)}* \frac{x^n}{n!}* @f]** This works and it's pretty fast.** @param __a The first @a numerator parameter.* @param __a The second @a numerator parameter.* @param __c The @a denominator parameter.* @param __x The argument of the confluent hypergeometric function.* @return The confluent hypergeometric function.*/template<typename _Tp>_Tp__hyperg_series(const _Tp __a, const _Tp __b,const _Tp __c, const _Tp __x){const _Tp __eps = std::numeric_limits<_Tp>::epsilon();_Tp __term = _Tp(1);_Tp __Fabc = _Tp(1);const unsigned int __max_iter = 100000;unsigned int __i;for (__i = 0; __i < __max_iter; ++__i){__term *= (__a + _Tp(__i)) * (__b + _Tp(__i)) * __x/ ((__c + _Tp(__i)) * _Tp(1 + __i));if (std::abs(__term) < __eps){break;}__Fabc += __term;}if (__i == __max_iter)std::__throw_runtime_error(__N("Series failed to converge ""in __hyperg_series."));return __Fabc;}/*** @brief Return the hypogeometric function @f$ _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 6.3.5const _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 evaluationconst _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 @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.*/template<typename _Tp>inline _Tp__hyperg(const _Tp __a, const _Tp __b, const _Tp __c, const _Tp __x){#if _GLIBCXX_USE_C99_MATH_TR1const _Tp __a_nint = std::tr1::nearbyint(__a);const _Tp __b_nint = std::tr1::nearbyint(__b);const _Tp __c_nint = std::tr1::nearbyint(__c);#elseconst _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));#endifconst _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);elseif (std::abs(__c) > _Tp(10))return __hyperg_series(__a, __b, __c, __x);elsereturn __hyperg_reflect(__a, __b, __c, __x);}elsereturn __hyperg_luke(__a, __b, __c, __x);}_GLIBCXX_END_NAMESPACE_VERSION} // namespace std::tr1::__detail}}#endif // _GLIBCXX_TR1_HYPERGEOMETRIC_TCC
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