tr1/cmath
Go to the documentation of this file.
// TR1 cmath -*- C++ -*-
// Copyright (C) 2006-2018 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/cmath
* This is a TR1 C++ Library header.
*/
#ifndef _GLIBCXX_TR1_CMATH
#define _GLIBCXX_TR1_CMATH 1
#pragma GCC system_header
#include <cmath>
#ifdef _GLIBCXX_USE_C99_MATH_TR1
#undef acosh
#undef acoshf
#undef acoshl
#undef asinh
#undef asinhf
#undef asinhl
#undef atanh
#undef atanhf
#undef atanhl
#undef cbrt
#undef cbrtf
#undef cbrtl
#undef copysign
#undef copysignf
#undef copysignl
#undef erf
#undef erff
#undef erfl
#undef erfc
#undef erfcf
#undef erfcl
#undef exp2
#undef exp2f
#undef exp2l
#undef expm1
#undef expm1f
#undef expm1l
#undef fdim
#undef fdimf
#undef fdiml
#undef fma
#undef fmaf
#undef fmal
#undef fmax
#undef fmaxf
#undef fmaxl
#undef fmin
#undef fminf
#undef fminl
#undef hypot
#undef hypotf
#undef hypotl
#undef ilogb
#undef ilogbf
#undef ilogbl
#undef lgamma
#undef lgammaf
#undef lgammal
#undef llrint
#undef llrintf
#undef llrintl
#undef llround
#undef llroundf
#undef llroundl
#undef log1p
#undef log1pf
#undef log1pl
#undef log2
#undef log2f
#undef log2l
#undef logb
#undef logbf
#undef logbl
#undef lrint
#undef lrintf
#undef lrintl
#undef lround
#undef lroundf
#undef lroundl
#undef nan
#undef nanf
#undef nanl
#undef nearbyint
#undef nearbyintf
#undef nearbyintl
#undef nextafter
#undef nextafterf
#undef nextafterl
#undef nexttoward
#undef nexttowardf
#undef nexttowardl
#undef remainder
#undef remainderf
#undef remainderl
#undef remquo
#undef remquof
#undef remquol
#undef rint
#undef rintf
#undef rintl
#undef round
#undef roundf
#undef roundl
#undef scalbln
#undef scalblnf
#undef scalblnl
#undef scalbn
#undef scalbnf
#undef scalbnl
#undef tgamma
#undef tgammaf
#undef tgammal
#undef trunc
#undef truncf
#undef truncl
#endif
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
namespace tr1
{
#if _GLIBCXX_USE_C99_MATH_TR1
// Using declarations to bring names from libc's <math.h> into std::tr1.
// types
using ::double_t;
using ::float_t;
// functions
using ::acosh;
using ::acoshf;
using ::acoshl;
using ::asinh;
using ::asinhf;
using ::asinhl;
using ::atanh;
using ::atanhf;
using ::atanhl;
using ::cbrt;
using ::cbrtf;
using ::cbrtl;
using ::copysign;
using ::copysignf;
using ::copysignl;
using ::erf;
using ::erff;
using ::erfl;
using ::erfc;
using ::erfcf;
using ::erfcl;
using ::exp2;
using ::exp2f;
using ::exp2l;
using ::expm1;
using ::expm1f;
using ::expm1l;
using ::fdim;
using ::fdimf;
using ::fdiml;
using ::fma;
using ::fmaf;
using ::fmal;
using ::fmax;
using ::fmaxf;
using ::fmaxl;
using ::fmin;
using ::fminf;
using ::fminl;
using ::hypot;
using ::hypotf;
using ::hypotl;
using ::ilogb;
using ::ilogbf;
using ::ilogbl;
using ::lgamma;
using ::lgammaf;
using ::lgammal;
using ::llrint;
using ::llrintf;
using ::llrintl;
using ::llround;
using ::llroundf;
using ::llroundl;
using ::log1p;
using ::log1pf;
using ::log1pl;
using ::log2;
using ::log2f;
using ::log2l;
using ::logb;
using ::logbf;
using ::logbl;
using ::lrint;
using ::lrintf;
using ::lrintl;
using ::lround;
using ::lroundf;
using ::lroundl;
using ::nan;
using ::nanf;
using ::nanl;
using ::nearbyint;
using ::nearbyintf;
using ::nearbyintl;
using ::nextafter;
using ::nextafterf;
using ::nextafterl;
using ::nexttoward;
using ::nexttowardf;
using ::nexttowardl;
using ::remainder;
using ::remainderf;
using ::remainderl;
using ::remquo;
using ::remquof;
using ::remquol;
using ::rint;
using ::rintf;
using ::rintl;
using ::round;
using ::roundf;
using ::roundl;
using ::scalbln;
using ::scalblnf;
using ::scalblnl;
using ::scalbn;
using ::scalbnf;
using ::scalbnl;
using ::tgamma;
using ::tgammaf;
using ::tgammal;
using ::trunc;
using ::truncf;
using ::truncl;
#endif
#if _GLIBCXX_USE_C99_MATH
#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
/// Function template definitions [8.16.3].
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
fpclassify(_Tp __f)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __type(__f));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isfinite(_Tp __f)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isfinite(__type(__f));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isinf(_Tp __f)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isinf(__type(__f));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isnan(_Tp __f)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isnan(__type(__f));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isnormal(_Tp __f)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isnormal(__type(__f));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
signbit(_Tp __f)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_signbit(__type(__f));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isgreater(_Tp __f1, _Tp __f2)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isgreater(__type(__f1), __type(__f2));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isgreaterequal(_Tp __f1, _Tp __f2)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isgreaterequal(__type(__f1), __type(__f2));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isless(_Tp __f1, _Tp __f2)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isless(__type(__f1), __type(__f2));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
islessequal(_Tp __f1, _Tp __f2)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_islessequal(__type(__f1), __type(__f2));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
islessgreater(_Tp __f1, _Tp __f2)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_islessgreater(__type(__f1), __type(__f2));
}
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
int>::__type
isunordered(_Tp __f1, _Tp __f2)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __builtin_isunordered(__type(__f1), __type(__f2));
}
#endif
#endif
#if _GLIBCXX_USE_C99_MATH_TR1
/** Additional overloads [8.16.4].
* @{
*/
// For functions defined in C++03 the additional overloads are already
// declared in <cmath> so we can just re-declare them in std::tr1.
using std::acos;
using std::asin;
using std::atan;
using std::atan2;
using std::ceil;
using std::cos;
using std::cosh;
using std::exp;
using std::floor;
using std::fmod;
using std::frexp;
using std::ldexp;
using std::log;
using std::log10;
using std::sin;
using std::sinh;
using std::sqrt;
using std::tan;
using std::tanh;
#if __cplusplus >= 201103L
// Since C++11, <cmath> defines additional overloads for these functions
// in namespace std.
using std::acosh;
using std::asinh;
using std::atanh;
using std::cbrt;
using std::copysign;
using std::erf;
using std::erfc;
using std::exp2;
using std::expm1;
using std::fdim;
using std::fma;
using std::fmax;
using std::fmin;
using std::hypot;
using std::ilogb;
using std::lgamma;
using std::llrint;
using std::llround;
using std::log1p;
using std::log2;
using std::logb;
using std::lrint;
using std::lround;
using std::nan;
using std::nearbyint;
using std::nextafter;
using std::nexttoward;
using std::remainder;
using std::remquo;
using std::rint;
using std::round;
using std::scalbln;
using std::scalbn;
using std::tgamma;
using std::trunc;
#else // __cplusplus < 201103L
// In C++03 we need to provide the additional overloads.
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
acosh(float __x)
{ return __builtin_acoshf(__x); }
inline long double
acosh(long double __x)
{ return __builtin_acoshl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
acosh(_Tp __x)
{ return __builtin_acosh(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
asinh(float __x)
{ return __builtin_asinhf(__x); }
inline long double
asinh(long double __x)
{ return __builtin_asinhl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
asinh(_Tp __x)
{ return __builtin_asinh(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
atanh(float __x)
{ return __builtin_atanhf(__x); }
inline long double
atanh(long double __x)
{ return __builtin_atanhl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
atanh(_Tp __x)
{ return __builtin_atanh(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
cbrt(float __x)
{ return __builtin_cbrtf(__x); }
inline long double
cbrt(long double __x)
{ return __builtin_cbrtl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
cbrt(_Tp __x)
{ return __builtin_cbrt(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
copysign(float __x, float __y)
{ return __builtin_copysignf(__x, __y); }
inline long double
copysign(long double __x, long double __y)
{ return __builtin_copysignl(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
copysign(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return copysign(__type(__x), __type(__y));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
erf(float __x)
{ return __builtin_erff(__x); }
inline long double
erf(long double __x)
{ return __builtin_erfl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
erf(_Tp __x)
{ return __builtin_erf(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
erfc(float __x)
{ return __builtin_erfcf(__x); }
inline long double
erfc(long double __x)
{ return __builtin_erfcl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
erfc(_Tp __x)
{ return __builtin_erfc(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
exp2(float __x)
{ return __builtin_exp2f(__x); }
inline long double
exp2(long double __x)
{ return __builtin_exp2l(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
exp2(_Tp __x)
{ return __builtin_exp2(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
expm1(float __x)
{ return __builtin_expm1f(__x); }
inline long double
expm1(long double __x)
{ return __builtin_expm1l(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
expm1(_Tp __x)
{ return __builtin_expm1(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
fdim(float __x, float __y)
{ return __builtin_fdimf(__x, __y); }
inline long double
fdim(long double __x, long double __y)
{ return __builtin_fdiml(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
fdim(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return fdim(__type(__x), __type(__y));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
fma(float __x, float __y, float __z)
{ return __builtin_fmaf(__x, __y, __z); }
inline long double
fma(long double __x, long double __y, long double __z)
{ return __builtin_fmal(__x, __y, __z); }
#endif
template<typename _Tp, typename _Up, typename _Vp>
inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
fma(_Tp __x, _Up __y, _Vp __z)
{
typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
return fma(__type(__x), __type(__y), __type(__z));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
fmax(float __x, float __y)
{ return __builtin_fmaxf(__x, __y); }
inline long double
fmax(long double __x, long double __y)
{ return __builtin_fmaxl(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
fmax(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return fmax(__type(__x), __type(__y));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
fmin(float __x, float __y)
{ return __builtin_fminf(__x, __y); }
inline long double
fmin(long double __x, long double __y)
{ return __builtin_fminl(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
fmin(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return fmin(__type(__x), __type(__y));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
hypot(float __x, float __y)
{ return __builtin_hypotf(__x, __y); }
inline long double
hypot(long double __x, long double __y)
{ return __builtin_hypotl(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
hypot(_Tp __y, _Up __x)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return hypot(__type(__y), __type(__x));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline int
ilogb(float __x)
{ return __builtin_ilogbf(__x); }
inline int
ilogb(long double __x)
{ return __builtin_ilogbl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
int>::__type
ilogb(_Tp __x)
{ return __builtin_ilogb(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
lgamma(float __x)
{ return __builtin_lgammaf(__x); }
inline long double
lgamma(long double __x)
{ return __builtin_lgammal(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
lgamma(_Tp __x)
{ return __builtin_lgamma(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline long long
llrint(float __x)
{ return __builtin_llrintf(__x); }
inline long long
llrint(long double __x)
{ return __builtin_llrintl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long long>::__type
llrint(_Tp __x)
{ return __builtin_llrint(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline long long
llround(float __x)
{ return __builtin_llroundf(__x); }
inline long long
llround(long double __x)
{ return __builtin_llroundl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long long>::__type
llround(_Tp __x)
{ return __builtin_llround(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
log1p(float __x)
{ return __builtin_log1pf(__x); }
inline long double
log1p(long double __x)
{ return __builtin_log1pl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
log1p(_Tp __x)
{ return __builtin_log1p(__x); }
// DR 568.
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
log2(float __x)
{ return __builtin_log2f(__x); }
inline long double
log2(long double __x)
{ return __builtin_log2l(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
log2(_Tp __x)
{ return __builtin_log2(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
logb(float __x)
{ return __builtin_logbf(__x); }
inline long double
logb(long double __x)
{ return __builtin_logbl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
logb(_Tp __x)
{
return __builtin_logb(__x);
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline long
lrint(float __x)
{ return __builtin_lrintf(__x); }
inline long
lrint(long double __x)
{ return __builtin_lrintl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long>::__type
lrint(_Tp __x)
{ return __builtin_lrint(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline long
lround(float __x)
{ return __builtin_lroundf(__x); }
inline long
lround(long double __x)
{ return __builtin_lroundl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long>::__type
lround(_Tp __x)
{ return __builtin_lround(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
nearbyint(float __x)
{ return __builtin_nearbyintf(__x); }
inline long double
nearbyint(long double __x)
{ return __builtin_nearbyintl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
nearbyint(_Tp __x)
{ return __builtin_nearbyint(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
nextafter(float __x, float __y)
{ return __builtin_nextafterf(__x, __y); }
inline long double
nextafter(long double __x, long double __y)
{ return __builtin_nextafterl(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
nextafter(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return nextafter(__type(__x), __type(__y));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
nexttoward(float __x, long double __y)
{ return __builtin_nexttowardf(__x, __y); }
inline long double
nexttoward(long double __x, long double __y)
{ return __builtin_nexttowardl(__x, __y); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
nexttoward(_Tp __x, long double __y)
{ return __builtin_nexttoward(__x, __y); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
remainder(float __x, float __y)
{ return __builtin_remainderf(__x, __y); }
inline long double
remainder(long double __x, long double __y)
{ return __builtin_remainderl(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
remainder(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return remainder(__type(__x), __type(__y));
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
remquo(float __x, float __y, int* __pquo)
{ return __builtin_remquof(__x, __y, __pquo); }
inline long double
remquo(long double __x, long double __y, int* __pquo)
{ return __builtin_remquol(__x, __y, __pquo); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
remquo(_Tp __x, _Up __y, int* __pquo)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return remquo(__type(__x), __type(__y), __pquo);
}
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
rint(float __x)
{ return __builtin_rintf(__x); }
inline long double
rint(long double __x)
{ return __builtin_rintl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
rint(_Tp __x)
{ return __builtin_rint(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
round(float __x)
{ return __builtin_roundf(__x); }
inline long double
round(long double __x)
{ return __builtin_roundl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
round(_Tp __x)
{ return __builtin_round(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
scalbln(float __x, long __ex)
{ return __builtin_scalblnf(__x, __ex); }
inline long double
scalbln(long double __x, long __ex)
{ return __builtin_scalblnl(__x, __ex); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
scalbln(_Tp __x, long __ex)
{ return __builtin_scalbln(__x, __ex); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
scalbn(float __x, int __ex)
{ return __builtin_scalbnf(__x, __ex); }
inline long double
scalbn(long double __x, int __ex)
{ return __builtin_scalbnl(__x, __ex); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
scalbn(_Tp __x, int __ex)
{ return __builtin_scalbn(__x, __ex); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
tgamma(float __x)
{ return __builtin_tgammaf(__x); }
inline long double
tgamma(long double __x)
{ return __builtin_tgammal(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
tgamma(_Tp __x)
{ return __builtin_tgamma(__x); }
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
trunc(float __x)
{ return __builtin_truncf(__x); }
inline long double
trunc(long double __x)
{ return __builtin_truncl(__x); }
#endif
template<typename _Tp>
inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
trunc(_Tp __x)
{ return __builtin_trunc(__x); }
#endif // __cplusplus < 201103L
// @}
#endif /* _GLIBCXX_USE_C99_MATH_TR1 */
// DR 550. What should the return type of pow(float,int) be?
// NB: C++11 and TR1 != C++03.
// We cannot do "using std::pow;" because that would bring in unwanted
// pow(*, int) overloads in C++03, with the wrong return type. Instead we
// define all the necessary overloads, but the std::tr1::pow(double, double)
// overload cannot be provided here, because <tr1/math.h> would add it to
// the global namespace where it would clash with ::pow(double,double) from
// libc (revealed by the fix of PR c++/54537).
// The solution is to forward std::tr1::pow(double,double) to
// std::pow(double,double) via the function template below. See
// the discussion about this issue here:
// http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
pow(float __x, float __y)
{ return std::pow(__x, __y); }
inline long double
pow(long double __x, long double __y)
{ return std::pow(__x, __y); }
#endif
template<typename _Tp, typename _Up>
inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
pow(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(__type(__x), __type(__y));
}
#if __cplusplus >= 201103L
// We also deal with fabs in a special way, because "using std::fabs;"
// could bring in C++11's std::fabs<T>(const std::complex<T>&) with a
// different return type from std::tr1::fabs<T>(const std::complex<T>&).
// We define the necessary overloads, except std::tr1::fabs(double) which
// could clash with ::fabs(double) from libc.
// The function template handles double as well as integers, forwarding
// to std::fabs.
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
inline float
fabs(float __x)
{ return __builtin_fabsf(__x); }
inline long double
fabs(long double __x)
{ return __builtin_fabsl(__x); }
#endif
#endif
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
fabs(_Tp __x)
{ return std::fabs(__x); }
#else // ! C++11
// For C++03 just use std::fabs as there is no overload for std::complex<>.
using std::fabs;
#endif // C++11
#if _GLIBCXX_USE_STD_SPEC_FUNCS
/**
* @defgroup tr1_math_spec_func Mathematical Special Functions
* @ingroup numerics
*
* A collection of advanced mathematical special functions.
* @{
*/
using std::assoc_laguerref;
using std::assoc_laguerrel;
using std::assoc_laguerre;
using std::assoc_legendref;
using std::assoc_legendrel;
using std::assoc_legendre;
using std::betaf;
using std::betal;
using std::beta;
using std::comp_ellint_1f;
using std::comp_ellint_1l;
using std::comp_ellint_1;
using std::comp_ellint_2f;
using std::comp_ellint_2l;
using std::comp_ellint_2;
using std::comp_ellint_3f;
using std::comp_ellint_3l;
using std::comp_ellint_3;
using __gnu_cxx::conf_hypergf;
using __gnu_cxx::conf_hypergl;
using __gnu_cxx::conf_hyperg;
using std::cyl_bessel_if;
using std::cyl_bessel_il;
using std::cyl_bessel_i;
using std::cyl_bessel_jf;
using std::cyl_bessel_jl;
using std::cyl_bessel_j;
using std::cyl_bessel_kf;
using std::cyl_bessel_kl;
using std::cyl_bessel_k;
using std::cyl_neumannf;
using std::cyl_neumannl;
using std::cyl_neumann;
using std::ellint_1f;
using std::ellint_1l;
using std::ellint_1;
using std::ellint_2f;
using std::ellint_2l;
using std::ellint_2;
using std::ellint_3f;
using std::ellint_3l;
using std::ellint_3;
using std::expintf;
using std::expintl;
using std::expint;
using std::hermitef;
using std::hermitel;
using std::hermite;
using __gnu_cxx::hypergf;
using __gnu_cxx::hypergl;
using __gnu_cxx::hyperg;
using std::laguerref;
using std::laguerrel;
using std::laguerre;
using std::legendref;
using std::legendrel;
using std::legendre;
using std::riemann_zetaf;
using std::riemann_zetal;
using std::riemann_zeta;
using std::sph_besself;
using std::sph_bessell;
using std::sph_bessel;
using std::sph_legendref;
using std::sph_legendrel;
using std::sph_legendre;
using std::sph_neumannf;
using std::sph_neumannl;
using std::sph_neumann;
/* @} */ // tr1_math_spec_func
#else // ! _GLIBCXX_USE_STD_SPEC_FUNCS
} // namespace tr1
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
#include <bits/stl_algobase.h>
#include <limits>
#include <tr1/type_traits>
#include <tr1/gamma.tcc>
#include <tr1/bessel_function.tcc>
#include <tr1/beta_function.tcc>
#include <tr1/ell_integral.tcc>
#include <tr1/exp_integral.tcc>
#include <tr1/hypergeometric.tcc>
#include <tr1/legendre_function.tcc>
#include <tr1/modified_bessel_func.tcc>
#include <tr1/poly_hermite.tcc>
#include <tr1/poly_laguerre.tcc>
#include <tr1/riemann_zeta.tcc>
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
namespace tr1
{
/**
* @defgroup tr1_math_spec_func Mathematical Special Functions
* @ingroup numerics
*
* A collection of advanced mathematical special functions.
* @{
*/
inline float
assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
{ return __detail::__assoc_laguerre<float>(__n, __m, __x); }
inline long double
assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
{
return __detail::__assoc_laguerre<long double>(__n, __m, __x);
}
/// 5.2.1.1 Associated Laguerre polynomials.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__assoc_laguerre<__type>(__n, __m, __x);
}
inline float
assoc_legendref(unsigned int __l, unsigned int __m, float __x)
{ return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
inline long double
assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
{ return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
/// 5.2.1.2 Associated Legendre functions.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
}
inline float
betaf(float __x, float __y)
{ return __detail::__beta<float>(__x, __y); }
inline long double
betal(long double __x, long double __y)
{ return __detail::__beta<long double>(__x, __y); }
/// 5.2.1.3 Beta functions.
template<typename _Tpx, typename _Tpy>
inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
beta(_Tpx __x, _Tpy __y)
{
typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
return __detail::__beta<__type>(__x, __y);
}
inline float
comp_ellint_1f(float __k)
{ return __detail::__comp_ellint_1<float>(__k); }
inline long double
comp_ellint_1l(long double __k)
{ return __detail::__comp_ellint_1<long double>(__k); }
/// 5.2.1.4 Complete elliptic integrals of the first kind.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
comp_ellint_1(_Tp __k)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__comp_ellint_1<__type>(__k);
}
inline float
comp_ellint_2f(float __k)
{ return __detail::__comp_ellint_2<float>(__k); }
inline long double
comp_ellint_2l(long double __k)
{ return __detail::__comp_ellint_2<long double>(__k); }
/// 5.2.1.5 Complete elliptic integrals of the second kind.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
comp_ellint_2(_Tp __k)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__comp_ellint_2<__type>(__k);
}
inline float
comp_ellint_3f(float __k, float __nu)
{ return __detail::__comp_ellint_3<float>(__k, __nu); }
inline long double
comp_ellint_3l(long double __k, long double __nu)
{ return __detail::__comp_ellint_3<long double>(__k, __nu); }
/// 5.2.1.6 Complete elliptic integrals of the third kind.
template<typename _Tp, typename _Tpn>
inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
comp_ellint_3(_Tp __k, _Tpn __nu)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
return __detail::__comp_ellint_3<__type>(__k, __nu);
}
inline float
conf_hypergf(float __a, float __c, float __x)
{ return __detail::__conf_hyperg<float>(__a, __c, __x); }
inline long double
conf_hypergl(long double __a, long double __c, long double __x)
{ return __detail::__conf_hyperg<long double>(__a, __c, __x); }
/// 5.2.1.7 Confluent hypergeometric functions.
template<typename _Tpa, typename _Tpc, typename _Tp>
inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
{
typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
return __detail::__conf_hyperg<__type>(__a, __c, __x);
}
inline float
cyl_bessel_if(float __nu, float __x)
{ return __detail::__cyl_bessel_i<float>(__nu, __x); }
inline long double
cyl_bessel_il(long double __nu, long double __x)
{ return __detail::__cyl_bessel_i<long double>(__nu, __x); }
/// 5.2.1.8 Regular modified cylindrical Bessel functions.
template<typename _Tpnu, typename _Tp>
inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
cyl_bessel_i(_Tpnu __nu, _Tp __x)
{
typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
return __detail::__cyl_bessel_i<__type>(__nu, __x);
}
inline float
cyl_bessel_jf(float __nu, float __x)
{ return __detail::__cyl_bessel_j<float>(__nu, __x); }
inline long double
cyl_bessel_jl(long double __nu, long double __x)
{ return __detail::__cyl_bessel_j<long double>(__nu, __x); }
/// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
template<typename _Tpnu, typename _Tp>
inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
cyl_bessel_j(_Tpnu __nu, _Tp __x)
{
typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
return __detail::__cyl_bessel_j<__type>(__nu, __x);
}
inline float
cyl_bessel_kf(float __nu, float __x)
{ return __detail::__cyl_bessel_k<float>(__nu, __x); }
inline long double
cyl_bessel_kl(long double __nu, long double __x)
{ return __detail::__cyl_bessel_k<long double>(__nu, __x); }
/// 5.2.1.10 Irregular modified cylindrical Bessel functions.
template<typename _Tpnu, typename _Tp>
inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
cyl_bessel_k(_Tpnu __nu, _Tp __x)
{
typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
return __detail::__cyl_bessel_k<__type>(__nu, __x);
}
inline float
cyl_neumannf(float __nu, float __x)
{ return __detail::__cyl_neumann_n<float>(__nu, __x); }
inline long double
cyl_neumannl(long double __nu, long double __x)
{ return __detail::__cyl_neumann_n<long double>(__nu, __x); }
/// 5.2.1.11 Cylindrical Neumann functions.
template<typename _Tpnu, typename _Tp>
inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
cyl_neumann(_Tpnu __nu, _Tp __x)
{
typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
return __detail::__cyl_neumann_n<__type>(__nu, __x);
}
inline float
ellint_1f(float __k, float __phi)
{ return __detail::__ellint_1<float>(__k, __phi); }
inline long double
ellint_1l(long double __k, long double __phi)
{ return __detail::__ellint_1<long double>(__k, __phi); }
/// 5.2.1.12 Incomplete elliptic integrals of the first kind.
template<typename _Tp, typename _Tpp>
inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
ellint_1(_Tp __k, _Tpp __phi)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
return __detail::__ellint_1<__type>(__k, __phi);
}
inline float
ellint_2f(float __k, float __phi)
{ return __detail::__ellint_2<float>(__k, __phi); }
inline long double
ellint_2l(long double __k, long double __phi)
{ return __detail::__ellint_2<long double>(__k, __phi); }
/// 5.2.1.13 Incomplete elliptic integrals of the second kind.
template<typename _Tp, typename _Tpp>
inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
ellint_2(_Tp __k, _Tpp __phi)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
return __detail::__ellint_2<__type>(__k, __phi);
}
inline float
ellint_3f(float __k, float __nu, float __phi)
{ return __detail::__ellint_3<float>(__k, __nu, __phi); }
inline long double
ellint_3l(long double __k, long double __nu, long double __phi)
{ return __detail::__ellint_3<long double>(__k, __nu, __phi); }
/// 5.2.1.14 Incomplete elliptic integrals of the third kind.
template<typename _Tp, typename _Tpn, typename _Tpp>
inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
{
typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
return __detail::__ellint_3<__type>(__k, __nu, __phi);
}
inline float
expintf(float __x)
{ return __detail::__expint<float>(__x); }
inline long double
expintl(long double __x)
{ return __detail::__expint<long double>(__x); }
/// 5.2.1.15 Exponential integrals.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
expint(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__expint<__type>(__x);
}
inline float
hermitef(unsigned int __n, float __x)
{ return __detail::__poly_hermite<float>(__n, __x); }
inline long double
hermitel(unsigned int __n, long double __x)
{ return __detail::__poly_hermite<long double>(__n, __x); }
/// 5.2.1.16 Hermite polynomials.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
hermite(unsigned int __n, _Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__poly_hermite<__type>(__n, __x);
}
inline float
hypergf(float __a, float __b, float __c, float __x)
{ return __detail::__hyperg<float>(__a, __b, __c, __x); }
inline long double
hypergl(long double __a, long double __b, long double __c, long double __x)
{ return __detail::__hyperg<long double>(__a, __b, __c, __x); }
/// 5.2.1.17 Hypergeometric functions.
template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
{
typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
return __detail::__hyperg<__type>(__a, __b, __c, __x);
}
inline float
laguerref(unsigned int __n, float __x)
{ return __detail::__laguerre<float>(__n, __x); }
inline long double
laguerrel(unsigned int __n, long double __x)
{ return __detail::__laguerre<long double>(__n, __x); }
/// 5.2.1.18 Laguerre polynomials.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
laguerre(unsigned int __n, _Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__laguerre<__type>(__n, __x);
}
inline float
legendref(unsigned int __n, float __x)
{ return __detail::__poly_legendre_p<float>(__n, __x); }
inline long double
legendrel(unsigned int __n, long double __x)
{ return __detail::__poly_legendre_p<long double>(__n, __x); }
/// 5.2.1.19 Legendre polynomials.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
legendre(unsigned int __n, _Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__poly_legendre_p<__type>(__n, __x);
}
inline float
riemann_zetaf(float __x)
{ return __detail::__riemann_zeta<float>(__x); }
inline long double
riemann_zetal(long double __x)
{ return __detail::__riemann_zeta<long double>(__x); }
/// 5.2.1.20 Riemann zeta function.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
riemann_zeta(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__riemann_zeta<__type>(__x);
}
inline float
sph_besself(unsigned int __n, float __x)
{ return __detail::__sph_bessel<float>(__n, __x); }
inline long double
sph_bessell(unsigned int __n, long double __x)
{ return __detail::__sph_bessel<long double>(__n, __x); }
/// 5.2.1.21 Spherical Bessel functions.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
sph_bessel(unsigned int __n, _Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__sph_bessel<__type>(__n, __x);
}
inline float
sph_legendref(unsigned int __l, unsigned int __m, float __theta)
{ return __detail::__sph_legendre<float>(__l, __m, __theta); }
inline long double
sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
{ return __detail::__sph_legendre<long double>(__l, __m, __theta); }
/// 5.2.1.22 Spherical associated Legendre functions.
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __detail::__sph_legendre<__type>(__l, __m, __theta);
}
inline float
sph_neumannf(unsigned int __n, float __x)
{ return __detail::__sph_neumann<float>(__n, __x); }
inline long double
sph_neumannl(unsigned int __n, long double __x)
{ return __detail::__sph_neumann<long double>(__n, __x); }
/// 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
#endif // _GLIBCXX_USE_STD_SPEC_FUNCS
} // namespace tr1
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
#endif // _GLIBCXX_TR1_CMATH
std::betaf
float betaf(float __a, float __b)
Definition: specfun.h:312
std::comp_ellint_2
__gnu_cxx::__promote< _Tp >::__type comp_ellint_2(_Tp __k)
Definition: specfun.h:438
cmath
std::cyl_bessel_jl
long double cyl_bessel_jl(long double __nu, long double __x)
Definition: specfun.h:560
std::cyl_neumannl
long double cyl_neumannl(long double __nu, long double __x)
Definition: specfun.h:658
std::comp_ellint_3
__gnu_cxx::__promote_2< _Tp, _Tpn >::__type comp_ellint_3(_Tp __k, _Tpn __nu)
Definition: specfun.h:489
std::sph_legendre
__gnu_cxx::__promote< _Tp >::__type sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
Definition: specfun.h:1149
std::tr1::cyl_bessel_j
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_j(_Tpnu __nu, _Tp __x)
5.2.1.9 Cylindrical Bessel functions (of the first kind).
Definition: tr1/cmath:1419
std::legendre
__gnu_cxx::__promote< _Tp >::__type legendre(unsigned int __l, _Tp __x)
Definition: specfun.h:1007
std::cyl_bessel_k
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_k(_Tpnu __nu, _Tp __x)
Definition: specfun.h:633
std::tr1::ellint_1
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_1(_Tp __k, _Tpp __phi)
5.2.1.12 Incomplete elliptic integrals of the first kind.
Definition: tr1/cmath:1470
std::sph_neumannf
float sph_neumannf(unsigned int __n, float __x)
Definition: specfun.h:1164
std::tr1::comp_ellint_3
__gnu_cxx::__promote_2< _Tp, _Tpn >::__type comp_ellint_3(_Tp __k, _Tpn __nu)
5.2.1.6 Complete elliptic integrals of the third kind.
Definition: tr1/cmath:1368
__gnu_cxx::conf_hypergf
float conf_hypergf(float __a, float __c, float __x)
Definition: specfun.h:1291
std::assoc_laguerre
__gnu_cxx::__promote< _Tp >::__type assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
Definition: specfun.h:252
__gnu_cxx::hypergf
float hypergf(float __a, float __b, float __c, float __x)
Definition: specfun.h:1339
std::tr1::sph_bessel
__gnu_cxx::__promote< _Tp >::__type sph_bessel(unsigned int __n, _Tp __x)
5.2.1.21 Spherical Bessel functions.
Definition: tr1/cmath:1623
std::comp_ellint_3f
float comp_ellint_3f(float __k, float __nu)
Return the complete elliptic integral of the third kind for float modulus k.
Definition: specfun.h:453
std::tr1::ellint_3
__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
5.2.1.14 Incomplete elliptic integrals of the third kind.
Definition: tr1/cmath:1504
std::sph_bessell
long double sph_bessell(unsigned int __n, long double __x)
Definition: specfun.h:1083
std::cyl_bessel_jf
float cyl_bessel_jf(float __nu, float __x)
Definition: specfun.h:550
std::assoc_legendrel
long double assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
Definition: specfun.h:276
stl_algobase.h
std::tr1::sph_neumann
__gnu_cxx::__promote< _Tp >::__type sph_neumann(unsigned int __n, _Tp __x)
5.2.1.23 Spherical Neumann functions.
Definition: tr1/cmath:1657
std::laguerre
__gnu_cxx::__promote< _Tp >::__type laguerre(unsigned int __n, _Tp __x)
Definition: specfun.h:962
std::betal
long double betal(long double __a, long double __b)
Definition: specfun.h:322
std::assoc_laguerref
float assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
Definition: specfun.h:206
std::cosh
complex< _Tp > cosh(const complex< _Tp > &)
Return complex hyperbolic cosine of z.
Definition: complex:760
std::tr1::riemann_zeta
__gnu_cxx::__promote< _Tp >::__type riemann_zeta(_Tp __x)
5.2.1.20 Riemann zeta function.
Definition: tr1/cmath:1606
std::sph_besself
float sph_besself(unsigned int __n, float __x)
Definition: specfun.h:1073
std::tr1::legendre
__gnu_cxx::__promote< _Tp >::__type legendre(unsigned int __n, _Tp __x)
5.2.1.19 Legendre polynomials.
Definition: tr1/cmath:1589
std::acos
std::complex< _Tp > acos(const std::complex< _Tp > &)
acos(__z) [8.1.2].
Definition: complex:1638
std::laguerref
float laguerref(unsigned int __n, float __x)
Definition: specfun.h:933
__gnu_cxx::conf_hyperg
__gnu_cxx::__promote_3< _Tpa, _Tpc, _Tp >::__type conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
Definition: specfun.h:1323
std::sph_legendrel
long double sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
Definition: specfun.h:1128
std::tr1::cyl_bessel_i
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_i(_Tpnu __nu, _Tp __x)
5.2.1.8 Regular modified cylindrical Bessel functions.
Definition: tr1/cmath:1402
std::tr1::hermite
__gnu_cxx::__promote< _Tp >::__type hermite(unsigned int __n, _Tp __x)
5.2.1.16 Hermite polynomials.
Definition: tr1/cmath:1538
std::comp_ellint_2f
float comp_ellint_2f(float __k)
Definition: specfun.h:406
std::legendref
float legendref(unsigned int __l, float __x)
Definition: specfun.h:977
std::expintf
float expintf(float __x)
Definition: specfun.h:844
std::atanh
std::complex< _Tp > atanh(const std::complex< _Tp > &)
atanh(__z) [8.1.7].
Definition: complex:1837
std::assoc_legendre
__gnu_cxx::__promote< _Tp >::__type assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
Definition: specfun.h:298
std::tr1::comp_ellint_1
__gnu_cxx::__promote< _Tp >::__type comp_ellint_1(_Tp __k)
5.2.1.4 Complete elliptic integrals of the first kind.
Definition: tr1/cmath:1334
std::ellint_2f
float ellint_2f(float __k, float __phi)
Return the incomplete elliptic integral of the second kind for float argument.
Definition: specfun.h:744
std::expintl
long double expintl(long double __x)
Definition: specfun.h:854
std::cyl_bessel_kf
float cyl_bessel_kf(float __nu, float __x)
Definition: specfun.h:596
std::ellint_3f
float ellint_3f(float __k, float __nu, float __phi)
Return the incomplete elliptic integral of the third kind for float argument.
Definition: specfun.h:792
std::sqrt
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition: complex:922
std::comp_ellint_1l
long double comp_ellint_1l(long double __k)
Definition: specfun.h:368
std::tr1::cyl_neumann
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_neumann(_Tpnu __nu, _Tp __x)
5.2.1.11 Cylindrical Neumann functions.
Definition: tr1/cmath:1453
std::tanh
complex< _Tp > tanh(const complex< _Tp > &)
Return complex hyperbolic tangent of z.
Definition: complex:977
std::comp_ellint_2l
long double comp_ellint_2l(long double __k)
Definition: specfun.h:416
std::tan
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition: complex:949
std::riemann_zetal
long double riemann_zetal(long double __s)
Definition: specfun.h:1032
limits
std::pow
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y&#39;th power.
Definition: complex:1008
std::ellint_2
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_2(_Tp __k, _Tpp __phi)
Definition: specfun.h:777
std::tr1::laguerre
__gnu_cxx::__promote< _Tp >::__type laguerre(unsigned int __n, _Tp __x)
5.2.1.18 Laguerre polynomials.
Definition: tr1/cmath:1572
std::cos
complex< _Tp > cos(const complex< _Tp > &)
Return complex cosine of z.
Definition: complex:730
std::acosh
std::complex< _Tp > acosh(const std::complex< _Tp > &)
acosh(__z) [8.1.5].
Definition: complex:1754
std::cyl_bessel_i
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_i(_Tpnu __nu, _Tp __x)
Definition: specfun.h:535
std::tr1::cyl_bessel_k
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_k(_Tpnu __nu, _Tp __x)
5.2.1.10 Irregular modified cylindrical Bessel functions.
Definition: tr1/cmath:1436
std::ellint_3
__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
Return the incomplete elliptic integral of the third kind .
Definition: specfun.h:830
std::asinh
std::complex< _Tp > asinh(const std::complex< _Tp > &)
asinh(__z) [8.1.6].
Definition: complex:1793
std::fabs
_Tp fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
Definition: complex:1846
std
ISO C++ entities toplevel namespace is std.
std::riemann_zetaf
float riemann_zetaf(float __s)
Definition: specfun.h:1022
std::comp_ellint_1f
float comp_ellint_1f(float __k)
Definition: specfun.h:358
std::ellint_2l
long double ellint_2l(long double __k, long double __phi)
Return the incomplete elliptic integral of the second kind .
Definition: specfun.h:754
std::comp_ellint_3l
long double comp_ellint_3l(long double __k, long double __nu)
Return the complete elliptic integral of the third kind for long double modulus k.
Definition: specfun.h:463
std::cyl_bessel_j
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_j(_Tpnu __nu, _Tp __x)
Definition: specfun.h:581
std::sinh
complex< _Tp > sinh(const complex< _Tp > &)
Return complex hyperbolic sine of z.
Definition: complex:878
std::sph_neumann
__gnu_cxx::__promote< _Tp >::__type sph_neumann(unsigned int __n, _Tp __x)
Definition: specfun.h:1193
std::cyl_neumann
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_neumann(_Tpnu __nu, _Tp __x)
Definition: specfun.h:681
__gnu_cxx::hyperg
__gnu_cxx::__promote_4< _Tpa, _Tpb, _Tpc, _Tp >::__type hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
Definition: specfun.h:1372
std::sph_neumannl
long double sph_neumannl(unsigned int __n, long double __x)
Definition: specfun.h:1174
std::cyl_neumannf
float cyl_neumannf(float __nu, float __x)
Definition: specfun.h:648
std::tr1::comp_ellint_2
__gnu_cxx::__promote< _Tp >::__type comp_ellint_2(_Tp __k)
5.2.1.5 Complete elliptic integrals of the second kind.
Definition: tr1/cmath:1351
std::cyl_bessel_kl
long double cyl_bessel_kl(long double __nu, long double __x)
Definition: specfun.h:606
std::ellint_1f
float ellint_1f(float __k, float __phi)
Definition: specfun.h:696
std::sph_legendref
float sph_legendref(unsigned int __l, unsigned int __m, float __theta)
Definition: specfun.h:1117
std::atan
std::complex< _Tp > atan(const std::complex< _Tp > &)
atan(__z) [8.1.4].
Definition: complex:1718
std::tr1::expint
__gnu_cxx::__promote< _Tp >::__type expint(_Tp __x)
5.2.1.15 Exponential integrals.
Definition: tr1/cmath:1521
std::exp
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition: complex:786
__gnu_cxx::conf_hypergl
long double conf_hypergl(long double __a, long double __c, long double __x)
Definition: specfun.h:1302
std::comp_ellint_1
__gnu_cxx::__promote< _Tp >::__type comp_ellint_1(_Tp __k)
Definition: specfun.h:391
std::cyl_bessel_il
long double cyl_bessel_il(long double __nu, long double __x)
Definition: specfun.h:514
std::hermitef
float hermitef(unsigned int __n, float __x)
Definition: specfun.h:885
std::ellint_1l
long double ellint_1l(long double __k, long double __phi)
Definition: specfun.h:706
std::tr1::hyperg
__gnu_cxx::__promote_4< _Tpa, _Tpb, _Tpc, _Tp >::__type hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
5.2.1.17 Hypergeometric functions.
Definition: tr1/cmath:1555
std::tr1::assoc_laguerre
__gnu_cxx::__promote< _Tp >::__type assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
5.2.1.1 Associated Laguerre polynomials.
Definition: tr1/cmath:1283
std::sin
complex< _Tp > sin(const complex< _Tp > &)
Return complex sine of z.
Definition: complex:848
std::laguerrel
long double laguerrel(unsigned int __n, long double __x)
Definition: specfun.h:943
std::log10
complex< _Tp > log10(const complex< _Tp > &)
Return complex base 10 logarithm of z.
Definition: complex:818
std::legendrel
long double legendrel(unsigned int __l, long double __x)
Definition: specfun.h:987
std::expint
__gnu_cxx::__promote< _Tp >::__type expint(_Tp __x)
Definition: specfun.h:870
std::sph_bessel
__gnu_cxx::__promote< _Tp >::__type sph_bessel(unsigned int __n, _Tp __x)
Definition: specfun.h:1102
std::hermitel
long double hermitel(unsigned int __n, long double __x)
Definition: specfun.h:895
std::cyl_bessel_if
float cyl_bessel_if(float __nu, float __x)
Definition: specfun.h:504
std::asin
std::complex< _Tp > asin(const std::complex< _Tp > &)
asin(__z) [8.1.3].
Definition: complex:1674
std::beta
__gnu_cxx::__promote_2< _Tpa, _Tpb >::__type beta(_Tpa __a, _Tpb __b)
Definition: specfun.h:343
__gnu_cxx::hypergl
long double hypergl(long double __a, long double __b, long double __c, long double __x)
Definition: specfun.h:1350
std::riemann_zeta
__gnu_cxx::__promote< _Tp >::__type riemann_zeta(_Tp __s)
Definition: specfun.h:1058
std::tr1::sph_legendre
__gnu_cxx::__promote< _Tp >::__type sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
5.2.1.22 Spherical associated Legendre functions.
Definition: tr1/cmath:1640
std::ellint_3l
long double ellint_3l(long double __k, long double __nu, long double __phi)
Return the incomplete elliptic integral of the third kind .
Definition: specfun.h:802
std::tr1::conf_hyperg
__gnu_cxx::__promote_3< _Tpa, _Tpc, _Tp >::__type conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
5.2.1.7 Confluent hypergeometric functions.
Definition: tr1/cmath:1385
std::ellint_1
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_1(_Tp __k, _Tpp __phi)
Definition: specfun.h:729
std::hermite
__gnu_cxx::__promote< _Tp >::__type hermite(unsigned int __n, _Tp __x)
Definition: specfun.h:918
std::tr1::assoc_legendre
__gnu_cxx::__promote< _Tp >::__type assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
5.2.1.2 Associated Legendre functions.
Definition: tr1/cmath:1300
std::tr1::beta
__gnu_cxx::__promote_2< _Tpx, _Tpy >::__type beta(_Tpx __x, _Tpy __y)
5.2.1.3 Beta functions.
Definition: tr1/cmath:1317
std::log
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition: complex:813
std::tr1::ellint_2
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_2(_Tp __k, _Tpp __phi)
5.2.1.13 Incomplete elliptic integrals of the second kind.
Definition: tr1/cmath:1487
std::assoc_laguerrel
long double assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
Definition: specfun.h:216
std::assoc_legendref
float assoc_legendref(unsigned int __l, unsigned int __m, float __x)
Definition: specfun.h:267