508 lines
16 KiB
C++
508 lines
16 KiB
C++
// TR1 cmath -*- C++ -*-
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// Copyright (C) 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 3, or (at your option)
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// any later version.
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// Under Section 7 of GPL version 3, you are granted additional
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// permissions described in the GCC Runtime Library Exception, version
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// 3.1, as published by the Free Software Foundation.
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// You should have received a copy of the GNU General Public License and
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// a copy of the GCC Runtime Library Exception along with this program;
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// <http://www.gnu.org/licenses/>.
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/** @file tr1/cmath
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* This is a TR1 C++ Library header.
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*/
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#ifndef _GLIBCXX_TR1_CMATH
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#define _GLIBCXX_TR1_CMATH 1
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#pragma GCC system_header
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#if defined(_GLIBCXX_INCLUDE_AS_CXX0X)
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# error TR1 header cannot be included from C++0x header
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#endif
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#include <cmath>
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#if defined(_GLIBCXX_INCLUDE_AS_TR1)
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# include <tr1_impl/cmath>
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#else
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# define _GLIBCXX_INCLUDE_AS_TR1
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# define _GLIBCXX_BEGIN_NAMESPACE_TR1 namespace tr1 {
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# define _GLIBCXX_END_NAMESPACE_TR1 }
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# define _GLIBCXX_TR1 tr1::
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# include <tr1_impl/cmath>
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# undef _GLIBCXX_TR1
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# undef _GLIBCXX_END_NAMESPACE_TR1
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# undef _GLIBCXX_BEGIN_NAMESPACE_TR1
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# undef _GLIBCXX_INCLUDE_AS_TR1
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#endif
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namespace std
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{
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namespace tr1
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{
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// DR 550. What should the return type of pow(float,int) be?
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// NB: C++0x and TR1 != C++03.
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inline double
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pow(double __x, double __y)
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{ return std::pow(__x, __y); }
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inline float
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pow(float __x, float __y)
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{ return std::pow(__x, __y); }
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inline long double
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pow(long double __x, long double __y)
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{ return std::pow(__x, __y); }
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template<typename _Tp, typename _Up>
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inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
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pow(_Tp __x, _Up __y)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
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return std::pow(__type(__x), __type(__y));
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}
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}
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}
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#include <bits/stl_algobase.h>
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#include <limits>
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#include <tr1/type_traits>
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#include <tr1/gamma.tcc>
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#include <tr1/bessel_function.tcc>
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#include <tr1/beta_function.tcc>
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#include <tr1/ell_integral.tcc>
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#include <tr1/exp_integral.tcc>
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#include <tr1/hypergeometric.tcc>
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#include <tr1/legendre_function.tcc>
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#include <tr1/modified_bessel_func.tcc>
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#include <tr1/poly_hermite.tcc>
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#include <tr1/poly_laguerre.tcc>
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#include <tr1/riemann_zeta.tcc>
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namespace std
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{
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namespace tr1
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{
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/**
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* @defgroup tr1_math_spec_func Mathematical Special Functions
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* @ingroup numerics
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*
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* A collection of advanced mathematical special functions.
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* @{
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*/
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inline float
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assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
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{ return __detail::__assoc_laguerre<float>(__n, __m, __x); }
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inline long double
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assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
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{
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return __detail::__assoc_laguerre<long double>(__n, __m, __x);
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}
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/// 5.2.1.1 Associated Laguerre polynomials.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__assoc_laguerre<__type>(__n, __m, __x);
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}
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inline float
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assoc_legendref(unsigned int __l, unsigned int __m, float __x)
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{ return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
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inline long double
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assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
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{ return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
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/// 5.2.1.2 Associated Legendre functions.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
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}
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inline float
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betaf(float __x, float __y)
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{ return __detail::__beta<float>(__x, __y); }
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inline long double
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betal(long double __x, long double __y)
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{ return __detail::__beta<long double>(__x, __y); }
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/// 5.2.1.3 Beta functions.
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template<typename _Tpx, typename _Tpy>
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inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
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beta(_Tpx __x, _Tpy __y)
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{
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typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
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return __detail::__beta<__type>(__x, __y);
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}
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inline float
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comp_ellint_1f(float __k)
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{ return __detail::__comp_ellint_1<float>(__k); }
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inline long double
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comp_ellint_1l(long double __k)
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{ return __detail::__comp_ellint_1<long double>(__k); }
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/// 5.2.1.4 Complete elliptic integrals of the first kind.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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comp_ellint_1(_Tp __k)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__comp_ellint_1<__type>(__k);
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}
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inline float
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comp_ellint_2f(float __k)
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{ return __detail::__comp_ellint_2<float>(__k); }
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inline long double
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comp_ellint_2l(long double __k)
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{ return __detail::__comp_ellint_2<long double>(__k); }
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/// 5.2.1.5 Complete elliptic integrals of the second kind.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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comp_ellint_2(_Tp __k)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__comp_ellint_2<__type>(__k);
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}
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inline float
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comp_ellint_3f(float __k, float __nu)
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{ return __detail::__comp_ellint_3<float>(__k, __nu); }
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inline long double
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comp_ellint_3l(long double __k, long double __nu)
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{ return __detail::__comp_ellint_3<long double>(__k, __nu); }
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/// 5.2.1.6 Complete elliptic integrals of the third kind.
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template<typename _Tp, typename _Tpn>
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inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
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comp_ellint_3(_Tp __k, _Tpn __nu)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
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return __detail::__comp_ellint_3<__type>(__k, __nu);
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}
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inline float
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conf_hypergf(float __a, float __c, float __x)
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{ return __detail::__conf_hyperg<float>(__a, __c, __x); }
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inline long double
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conf_hypergl(long double __a, long double __c, long double __x)
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{ return __detail::__conf_hyperg<long double>(__a, __c, __x); }
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/// 5.2.1.7 Confluent hypergeometric functions.
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template<typename _Tpa, typename _Tpc, typename _Tp>
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inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
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conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
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return __detail::__conf_hyperg<__type>(__a, __c, __x);
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}
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inline float
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cyl_bessel_if(float __nu, float __x)
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{ return __detail::__cyl_bessel_i<float>(__nu, __x); }
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inline long double
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cyl_bessel_il(long double __nu, long double __x)
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{ return __detail::__cyl_bessel_i<long double>(__nu, __x); }
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/// 5.2.1.8 Regular modified cylindrical Bessel functions.
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template<typename _Tpnu, typename _Tp>
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inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
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cyl_bessel_i(_Tpnu __nu, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
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return __detail::__cyl_bessel_i<__type>(__nu, __x);
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}
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inline float
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cyl_bessel_jf(float __nu, float __x)
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{ return __detail::__cyl_bessel_j<float>(__nu, __x); }
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inline long double
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cyl_bessel_jl(long double __nu, long double __x)
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{ return __detail::__cyl_bessel_j<long double>(__nu, __x); }
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/// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
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template<typename _Tpnu, typename _Tp>
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inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
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cyl_bessel_j(_Tpnu __nu, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
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return __detail::__cyl_bessel_j<__type>(__nu, __x);
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}
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inline float
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cyl_bessel_kf(float __nu, float __x)
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{ return __detail::__cyl_bessel_k<float>(__nu, __x); }
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inline long double
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cyl_bessel_kl(long double __nu, long double __x)
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{ return __detail::__cyl_bessel_k<long double>(__nu, __x); }
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/// 5.2.1.10 Irregular modified cylindrical Bessel functions.
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template<typename _Tpnu, typename _Tp>
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inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
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cyl_bessel_k(_Tpnu __nu, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
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return __detail::__cyl_bessel_k<__type>(__nu, __x);
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}
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inline float
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cyl_neumannf(float __nu, float __x)
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{ return __detail::__cyl_neumann_n<float>(__nu, __x); }
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inline long double
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cyl_neumannl(long double __nu, long double __x)
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{ return __detail::__cyl_neumann_n<long double>(__nu, __x); }
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/// 5.2.1.11 Cylindrical Neumann functions.
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template<typename _Tpnu, typename _Tp>
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inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
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cyl_neumann(_Tpnu __nu, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
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return __detail::__cyl_neumann_n<__type>(__nu, __x);
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}
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inline float
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ellint_1f(float __k, float __phi)
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{ return __detail::__ellint_1<float>(__k, __phi); }
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inline long double
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ellint_1l(long double __k, long double __phi)
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{ return __detail::__ellint_1<long double>(__k, __phi); }
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/// 5.2.1.12 Incomplete elliptic integrals of the first kind.
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template<typename _Tp, typename _Tpp>
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inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
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ellint_1(_Tp __k, _Tpp __phi)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
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return __detail::__ellint_1<__type>(__k, __phi);
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}
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inline float
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ellint_2f(float __k, float __phi)
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{ return __detail::__ellint_2<float>(__k, __phi); }
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inline long double
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ellint_2l(long double __k, long double __phi)
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{ return __detail::__ellint_2<long double>(__k, __phi); }
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/// 5.2.1.13 Incomplete elliptic integrals of the second kind.
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template<typename _Tp, typename _Tpp>
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inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
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ellint_2(_Tp __k, _Tpp __phi)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
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return __detail::__ellint_2<__type>(__k, __phi);
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}
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inline float
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ellint_3f(float __k, float __nu, float __phi)
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{ return __detail::__ellint_3<float>(__k, __nu, __phi); }
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inline long double
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ellint_3l(long double __k, long double __nu, long double __phi)
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{ return __detail::__ellint_3<long double>(__k, __nu, __phi); }
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/// 5.2.1.14 Incomplete elliptic integrals of the third kind.
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template<typename _Tp, typename _Tpn, typename _Tpp>
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inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
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ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
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{
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typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
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return __detail::__ellint_3<__type>(__k, __nu, __phi);
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}
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inline float
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expintf(float __x)
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{ return __detail::__expint<float>(__x); }
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inline long double
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expintl(long double __x)
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{ return __detail::__expint<long double>(__x); }
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/// 5.2.1.15 Exponential integrals.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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expint(_Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__expint<__type>(__x);
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}
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inline float
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hermitef(unsigned int __n, float __x)
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{ return __detail::__poly_hermite<float>(__n, __x); }
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inline long double
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hermitel(unsigned int __n, long double __x)
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{ return __detail::__poly_hermite<long double>(__n, __x); }
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/// 5.2.1.16 Hermite polynomials.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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hermite(unsigned int __n, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__poly_hermite<__type>(__n, __x);
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}
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inline float
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hypergf(float __a, float __b, float __c, float __x)
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{ return __detail::__hyperg<float>(__a, __b, __c, __x); }
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inline long double
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hypergl(long double __a, long double __b, long double __c, long double __x)
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{ return __detail::__hyperg<long double>(__a, __b, __c, __x); }
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/// 5.2.1.17 Hypergeometric functions.
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template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
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inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
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hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
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return __detail::__hyperg<__type>(__a, __b, __c, __x);
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}
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inline float
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laguerref(unsigned int __n, float __x)
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{ return __detail::__laguerre<float>(__n, __x); }
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inline long double
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laguerrel(unsigned int __n, long double __x)
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{ return __detail::__laguerre<long double>(__n, __x); }
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/// 5.2.1.18 Laguerre polynomials.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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laguerre(unsigned int __n, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__laguerre<__type>(__n, __x);
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}
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inline float
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legendref(unsigned int __n, float __x)
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{ return __detail::__poly_legendre_p<float>(__n, __x); }
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inline long double
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legendrel(unsigned int __n, long double __x)
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{ return __detail::__poly_legendre_p<long double>(__n, __x); }
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/// 5.2.1.19 Legendre polynomials.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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legendre(unsigned int __n, _Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__poly_legendre_p<__type>(__n, __x);
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}
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inline float
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riemann_zetaf(float __x)
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{ return __detail::__riemann_zeta<float>(__x); }
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inline long double
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riemann_zetal(long double __x)
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{ return __detail::__riemann_zeta<long double>(__x); }
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/// 5.2.1.20 Riemann zeta function.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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riemann_zeta(_Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__riemann_zeta<__type>(__x);
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}
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inline float
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sph_besself(unsigned int __n, float __x)
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{ return __detail::__sph_bessel<float>(__n, __x); }
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inline long double
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sph_bessell(unsigned int __n, long double __x)
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{ return __detail::__sph_bessel<long double>(__n, __x); }
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/// 5.2.1.21 Spherical Bessel functions.
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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sph_bessel(unsigned int __n, _Tp __x)
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|
{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __detail::__sph_bessel<__type>(__n, __x);
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|
}
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|
inline float
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sph_legendref(unsigned int __l, unsigned int __m, float __theta)
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{ return __detail::__sph_legendre<float>(__l, __m, __theta); }
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|
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inline long double
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sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
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|
{ return __detail::__sph_legendre<long double>(__l, __m, __theta); }
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|
|
|
/// 5.2.1.22 Spherical associated Legendre functions.
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|
template<typename _Tp>
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|
inline typename __gnu_cxx::__promote<_Tp>::__type
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|
sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
|
|
{
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|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
return __detail::__sph_legendre<__type>(__l, __m, __theta);
|
|
}
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|
|
|
inline float
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|
sph_neumannf(unsigned int __n, float __x)
|
|
{ return __detail::__sph_neumann<float>(__n, __x); }
|
|
|
|
inline long double
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|
sph_neumannl(unsigned int __n, long double __x)
|
|
{ return __detail::__sph_neumann<long double>(__n, __x); }
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|
|
|
/// 5.2.1.23 Spherical Neumann functions.
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
sph_neumann(unsigned int __n, _Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
return __detail::__sph_neumann<__type>(__n, __x);
|
|
}
|
|
|
|
/* @} */ // tr1_math_spec_func
|
|
}
|
|
}
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|
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|
#endif // _GLIBCXX_TR1_CMATH
|