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jeremybenn |
// 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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// .
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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
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#if defined(_GLIBCXX_INCLUDE_AS_TR1)
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# include
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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
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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
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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
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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#include
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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(__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(__n, __m, __x);
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}
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/// 5.2.1.1 Associated Laguerre polynomials.
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template
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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(__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(__l, __m, __x); }
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/// 5.2.1.2 Associated Legendre functions.
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template
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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(__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(__x, __y); }
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/// 5.2.1.3 Beta functions.
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template
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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(__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(__k); }
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/// 5.2.1.4 Complete elliptic integrals of the first kind.
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template
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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(__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(__k); }
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/// 5.2.1.5 Complete elliptic integrals of the second kind.
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template
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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(__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(__k, __nu); }
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/// 5.2.1.6 Complete elliptic integrals of the third kind.
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template
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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(__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(__a, __c, __x); }
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/// 5.2.1.7 Confluent hypergeometric functions.
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template
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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(__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(__nu, __x); }
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/// 5.2.1.8 Regular modified cylindrical Bessel functions.
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template
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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(__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(__nu, __x); }
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/// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
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template
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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(__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(__nu, __x); }
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| 273 |
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/// 5.2.1.10 Irregular modified cylindrical Bessel functions.
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template
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| 275 |
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inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
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| 276 |
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cyl_bessel_k(_Tpnu __nu, _Tp __x)
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{
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| 278 |
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typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
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| 279 |
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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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| 283 |
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cyl_neumannf(float __nu, float __x)
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{ return __detail::__cyl_neumann_n(__nu, __x); }
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| 285 |
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| 286 |
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inline long double
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| 287 |
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cyl_neumannl(long double __nu, long double __x)
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{ return __detail::__cyl_neumann_n(__nu, __x); }
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| 289 |
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| 290 |
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/// 5.2.1.11 Cylindrical Neumann functions.
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| 291 |
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template
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| 292 |
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inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
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| 293 |
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cyl_neumann(_Tpnu __nu, _Tp __x)
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| 294 |
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{
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| 295 |
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typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
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| 296 |
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return __detail::__cyl_neumann_n<__type>(__nu, __x);
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| 297 |
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}
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| 298 |
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| 299 |
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inline float
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| 300 |
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ellint_1f(float __k, float __phi)
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| 301 |
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{ return __detail::__ellint_1(__k, __phi); }
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| 302 |
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| 303 |
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inline long double
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| 304 |
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ellint_1l(long double __k, long double __phi)
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| 305 |
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{ return __detail::__ellint_1(__k, __phi); }
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| 306 |
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| 307 |
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/// 5.2.1.12 Incomplete elliptic integrals of the first kind.
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| 308 |
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template
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| 309 |
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inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
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| 310 |
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ellint_1(_Tp __k, _Tpp __phi)
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| 311 |
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{
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| 312 |
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typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
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| 313 |
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return __detail::__ellint_1<__type>(__k, __phi);
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| 314 |
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}
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| 315 |
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| 316 |
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inline float
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| 317 |
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ellint_2f(float __k, float __phi)
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| 318 |
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{ return __detail::__ellint_2(__k, __phi); }
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| 319 |
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| 320 |
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inline long double
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| 321 |
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ellint_2l(long double __k, long double __phi)
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| 322 |
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{ return __detail::__ellint_2(__k, __phi); }
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| 323 |
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| 324 |
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/// 5.2.1.13 Incomplete elliptic integrals of the second kind.
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| 325 |
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template
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| 326 |
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inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
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| 327 |
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ellint_2(_Tp __k, _Tpp __phi)
|
| 328 |
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{
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| 329 |
|
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typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
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| 330 |
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return __detail::__ellint_2<__type>(__k, __phi);
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| 331 |
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}
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| 332 |
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| 333 |
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inline float
|
| 334 |
|
|
ellint_3f(float __k, float __nu, float __phi)
|
| 335 |
|
|
{ return __detail::__ellint_3(__k, __nu, __phi); }
|
| 336 |
|
|
|
| 337 |
|
|
inline long double
|
| 338 |
|
|
ellint_3l(long double __k, long double __nu, long double __phi)
|
| 339 |
|
|
{ return __detail::__ellint_3(__k, __nu, __phi); }
|
| 340 |
|
|
|
| 341 |
|
|
/// 5.2.1.14 Incomplete elliptic integrals of the third kind.
|
| 342 |
|
|
template
|
| 343 |
|
|
inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
|
| 344 |
|
|
ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
|
| 345 |
|
|
{
|
| 346 |
|
|
typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
|
| 347 |
|
|
return __detail::__ellint_3<__type>(__k, __nu, __phi);
|
| 348 |
|
|
}
|
| 349 |
|
|
|
| 350 |
|
|
inline float
|
| 351 |
|
|
expintf(float __x)
|
| 352 |
|
|
{ return __detail::__expint(__x); }
|
| 353 |
|
|
|
| 354 |
|
|
inline long double
|
| 355 |
|
|
expintl(long double __x)
|
| 356 |
|
|
{ return __detail::__expint(__x); }
|
| 357 |
|
|
|
| 358 |
|
|
/// 5.2.1.15 Exponential integrals.
|
| 359 |
|
|
template
|
| 360 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 361 |
|
|
expint(_Tp __x)
|
| 362 |
|
|
{
|
| 363 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 364 |
|
|
return __detail::__expint<__type>(__x);
|
| 365 |
|
|
}
|
| 366 |
|
|
|
| 367 |
|
|
inline float
|
| 368 |
|
|
hermitef(unsigned int __n, float __x)
|
| 369 |
|
|
{ return __detail::__poly_hermite(__n, __x); }
|
| 370 |
|
|
|
| 371 |
|
|
inline long double
|
| 372 |
|
|
hermitel(unsigned int __n, long double __x)
|
| 373 |
|
|
{ return __detail::__poly_hermite(__n, __x); }
|
| 374 |
|
|
|
| 375 |
|
|
/// 5.2.1.16 Hermite polynomials.
|
| 376 |
|
|
template
|
| 377 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 378 |
|
|
hermite(unsigned int __n, _Tp __x)
|
| 379 |
|
|
{
|
| 380 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 381 |
|
|
return __detail::__poly_hermite<__type>(__n, __x);
|
| 382 |
|
|
}
|
| 383 |
|
|
|
| 384 |
|
|
inline float
|
| 385 |
|
|
hypergf(float __a, float __b, float __c, float __x)
|
| 386 |
|
|
{ return __detail::__hyperg(__a, __b, __c, __x); }
|
| 387 |
|
|
|
| 388 |
|
|
inline long double
|
| 389 |
|
|
hypergl(long double __a, long double __b, long double __c, long double __x)
|
| 390 |
|
|
{ return __detail::__hyperg(__a, __b, __c, __x); }
|
| 391 |
|
|
|
| 392 |
|
|
/// 5.2.1.17 Hypergeometric functions.
|
| 393 |
|
|
template
|
| 394 |
|
|
inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
|
| 395 |
|
|
hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
|
| 396 |
|
|
{
|
| 397 |
|
|
typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
|
| 398 |
|
|
return __detail::__hyperg<__type>(__a, __b, __c, __x);
|
| 399 |
|
|
}
|
| 400 |
|
|
|
| 401 |
|
|
inline float
|
| 402 |
|
|
laguerref(unsigned int __n, float __x)
|
| 403 |
|
|
{ return __detail::__laguerre(__n, __x); }
|
| 404 |
|
|
|
| 405 |
|
|
inline long double
|
| 406 |
|
|
laguerrel(unsigned int __n, long double __x)
|
| 407 |
|
|
{ return __detail::__laguerre(__n, __x); }
|
| 408 |
|
|
|
| 409 |
|
|
/// 5.2.1.18 Laguerre polynomials.
|
| 410 |
|
|
template
|
| 411 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 412 |
|
|
laguerre(unsigned int __n, _Tp __x)
|
| 413 |
|
|
{
|
| 414 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 415 |
|
|
return __detail::__laguerre<__type>(__n, __x);
|
| 416 |
|
|
}
|
| 417 |
|
|
|
| 418 |
|
|
inline float
|
| 419 |
|
|
legendref(unsigned int __n, float __x)
|
| 420 |
|
|
{ return __detail::__poly_legendre_p(__n, __x); }
|
| 421 |
|
|
|
| 422 |
|
|
inline long double
|
| 423 |
|
|
legendrel(unsigned int __n, long double __x)
|
| 424 |
|
|
{ return __detail::__poly_legendre_p(__n, __x); }
|
| 425 |
|
|
|
| 426 |
|
|
/// 5.2.1.19 Legendre polynomials.
|
| 427 |
|
|
template
|
| 428 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 429 |
|
|
legendre(unsigned int __n, _Tp __x)
|
| 430 |
|
|
{
|
| 431 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 432 |
|
|
return __detail::__poly_legendre_p<__type>(__n, __x);
|
| 433 |
|
|
}
|
| 434 |
|
|
|
| 435 |
|
|
inline float
|
| 436 |
|
|
riemann_zetaf(float __x)
|
| 437 |
|
|
{ return __detail::__riemann_zeta(__x); }
|
| 438 |
|
|
|
| 439 |
|
|
inline long double
|
| 440 |
|
|
riemann_zetal(long double __x)
|
| 441 |
|
|
{ return __detail::__riemann_zeta(__x); }
|
| 442 |
|
|
|
| 443 |
|
|
/// 5.2.1.20 Riemann zeta function.
|
| 444 |
|
|
template
|
| 445 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 446 |
|
|
riemann_zeta(_Tp __x)
|
| 447 |
|
|
{
|
| 448 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 449 |
|
|
return __detail::__riemann_zeta<__type>(__x);
|
| 450 |
|
|
}
|
| 451 |
|
|
|
| 452 |
|
|
inline float
|
| 453 |
|
|
sph_besself(unsigned int __n, float __x)
|
| 454 |
|
|
{ return __detail::__sph_bessel(__n, __x); }
|
| 455 |
|
|
|
| 456 |
|
|
inline long double
|
| 457 |
|
|
sph_bessell(unsigned int __n, long double __x)
|
| 458 |
|
|
{ return __detail::__sph_bessel(__n, __x); }
|
| 459 |
|
|
|
| 460 |
|
|
/// 5.2.1.21 Spherical Bessel functions.
|
| 461 |
|
|
template
|
| 462 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 463 |
|
|
sph_bessel(unsigned int __n, _Tp __x)
|
| 464 |
|
|
{
|
| 465 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 466 |
|
|
return __detail::__sph_bessel<__type>(__n, __x);
|
| 467 |
|
|
}
|
| 468 |
|
|
|
| 469 |
|
|
inline float
|
| 470 |
|
|
sph_legendref(unsigned int __l, unsigned int __m, float __theta)
|
| 471 |
|
|
{ return __detail::__sph_legendre(__l, __m, __theta); }
|
| 472 |
|
|
|
| 473 |
|
|
inline long double
|
| 474 |
|
|
sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
|
| 475 |
|
|
{ return __detail::__sph_legendre(__l, __m, __theta); }
|
| 476 |
|
|
|
| 477 |
|
|
/// 5.2.1.22 Spherical associated Legendre functions.
|
| 478 |
|
|
template
|
| 479 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 480 |
|
|
sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
|
| 481 |
|
|
{
|
| 482 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 483 |
|
|
return __detail::__sph_legendre<__type>(__l, __m, __theta);
|
| 484 |
|
|
}
|
| 485 |
|
|
|
| 486 |
|
|
inline float
|
| 487 |
|
|
sph_neumannf(unsigned int __n, float __x)
|
| 488 |
|
|
{ return __detail::__sph_neumann(__n, __x); }
|
| 489 |
|
|
|
| 490 |
|
|
inline long double
|
| 491 |
|
|
sph_neumannl(unsigned int __n, long double __x)
|
| 492 |
|
|
{ return __detail::__sph_neumann(__n, __x); }
|
| 493 |
|
|
|
| 494 |
|
|
/// 5.2.1.23 Spherical Neumann functions.
|
| 495 |
|
|
template
|
| 496 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 497 |
|
|
sph_neumann(unsigned int __n, _Tp __x)
|
| 498 |
|
|
{
|
| 499 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 500 |
|
|
return __detail::__sph_neumann<__type>(__n, __x);
|
| 501 |
|
|
}
|
| 502 |
|
|
|
| 503 |
|
|
/* @} */ // tr1_math_spec_func
|
| 504 |
|
|
}
|
| 505 |
|
|
}
|
| 506 |
|
|
|
| 507 |
|
|
#endif // _GLIBCXX_TR1_CMATH
|
