cmath
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// -*- C++ -*- C forwarding header.
// Copyright (C) 1997-2024 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 include/cmath
* This is a Standard C++ Library file. You should @c \#include this file
* in your programs, rather than any of the @a *.h implementation files.
*
* This is the C++ version of the Standard C Library header @c math.h,
* and its contents are (mostly) the same as that header, but are all
* contained in the namespace @c std (except for names which are defined
* as macros in C).
*/
//
// ISO C++ 14882: 26.5 C library
//
#pragma GCC system_header
#include <bits/requires_hosted.h>
#include <bits/c++config.h>
#include <bits/cpp_type_traits.h>
#include <ext/type_traits.h>
#define _GLIBCXX_INCLUDE_NEXT_C_HEADERS
#include_next <math.h>
#undef _GLIBCXX_INCLUDE_NEXT_C_HEADERS
#include <bits/std_abs.h>
#ifndef _GLIBCXX_CMATH
#define _GLIBCXX_CMATH 1
#define __glibcxx_want_hypot
#define __glibcxx_want_interpolate
#include <bits/version.h>
// Get rid of those macros defined in <math.h> in lieu of real functions.
#undef div
#undef acos
#undef asin
#undef atan
#undef atan2
#undef ceil
#undef cos
#undef cosh
#undef exp
#undef fabs
#undef floor
#undef fmod
#undef frexp
#undef ldexp
#undef log
#undef log10
#undef modf
#undef pow
#undef sin
#undef sinh
#undef sqrt
#undef tan
#undef tanh
extern "C++"
{
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
using ::acos;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
acos(float __x)
{ return __builtin_acosf(__x); }
inline _GLIBCXX_CONSTEXPR long double
acos(long double __x)
{ return __builtin_acosl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
acos(_Tp __x)
{ return __builtin_acos(__x); }
using ::asin;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
asin(float __x)
{ return __builtin_asinf(__x); }
inline _GLIBCXX_CONSTEXPR long double
asin(long double __x)
{ return __builtin_asinl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
asin(_Tp __x)
{ return __builtin_asin(__x); }
using ::atan;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
atan(float __x)
{ return __builtin_atanf(__x); }
inline _GLIBCXX_CONSTEXPR long double
atan(long double __x)
{ return __builtin_atanl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
atan(_Tp __x)
{ return __builtin_atan(__x); }
using ::atan2;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
atan2(float __y, float __x)
{ return __builtin_atan2f(__y, __x); }
inline _GLIBCXX_CONSTEXPR long double
atan2(long double __y, long double __x)
{ return __builtin_atan2l(__y, __x); }
#endif
using ::ceil;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
ceil(float __x)
{ return __builtin_ceilf(__x); }
inline _GLIBCXX_CONSTEXPR long double
ceil(long double __x)
{ return __builtin_ceill(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
ceil(_Tp __x)
{ return __builtin_ceil(__x); }
using ::cos;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
cos(float __x)
{ return __builtin_cosf(__x); }
inline _GLIBCXX_CONSTEXPR long double
cos(long double __x)
{ return __builtin_cosl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
cos(_Tp __x)
{ return __builtin_cos(__x); }
using ::cosh;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
cosh(float __x)
{ return __builtin_coshf(__x); }
inline _GLIBCXX_CONSTEXPR long double
cosh(long double __x)
{ return __builtin_coshl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
cosh(_Tp __x)
{ return __builtin_cosh(__x); }
using ::exp;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
exp(float __x)
{ return __builtin_expf(__x); }
inline _GLIBCXX_CONSTEXPR long double
exp(long double __x)
{ return __builtin_expl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
exp(_Tp __x)
{ return __builtin_exp(__x); }
using ::fabs;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
fabs(float __x)
{ return __builtin_fabsf(__x); }
inline _GLIBCXX_CONSTEXPR long double
fabs(long double __x)
{ return __builtin_fabsl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
fabs(_Tp __x)
{ return __builtin_fabs(__x); }
using ::floor;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
floor(float __x)
{ return __builtin_floorf(__x); }
inline _GLIBCXX_CONSTEXPR long double
floor(long double __x)
{ return __builtin_floorl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
floor(_Tp __x)
{ return __builtin_floor(__x); }
using ::fmod;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
fmod(float __x, float __y)
{ return __builtin_fmodf(__x, __y); }
inline _GLIBCXX_CONSTEXPR long double
fmod(long double __x, long double __y)
{ return __builtin_fmodl(__x, __y); }
#endif
using ::frexp;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline float
frexp(float __x, int* __exp)
{ return __builtin_frexpf(__x, __exp); }
inline long double
frexp(long double __x, int* __exp)
{ return __builtin_frexpl(__x, __exp); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
frexp(_Tp __x, int* __exp)
{ return __builtin_frexp(__x, __exp); }
using ::ldexp;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
ldexp(float __x, int __exp)
{ return __builtin_ldexpf(__x, __exp); }
inline _GLIBCXX_CONSTEXPR long double
ldexp(long double __x, int __exp)
{ return __builtin_ldexpl(__x, __exp); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
ldexp(_Tp __x, int __exp)
{ return __builtin_ldexp(__x, __exp); }
using ::log;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
log(float __x)
{ return __builtin_logf(__x); }
inline _GLIBCXX_CONSTEXPR long double
log(long double __x)
{ return __builtin_logl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
log(_Tp __x)
{ return __builtin_log(__x); }
using ::log10;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
log10(float __x)
{ return __builtin_log10f(__x); }
inline _GLIBCXX_CONSTEXPR long double
log10(long double __x)
{ return __builtin_log10l(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
log10(_Tp __x)
{ return __builtin_log10(__x); }
using ::modf;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline float
modf(float __x, float* __iptr)
{ return __builtin_modff(__x, __iptr); }
inline long double
modf(long double __x, long double* __iptr)
{ return __builtin_modfl(__x, __iptr); }
#endif
using ::pow;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
pow(float __x, float __y)
{ return __builtin_powf(__x, __y); }
inline _GLIBCXX_CONSTEXPR long double
pow(long double __x, long double __y)
{ return __builtin_powl(__x, __y); }
#if __cplusplus < 201103L
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 550. What should the return type of pow(float,int) be?
inline double
pow(double __x, int __i)
{ return __builtin_powi(__x, __i); }
inline float
pow(float __x, int __n)
{ return __builtin_powif(__x, __n); }
inline long double
pow(long double __x, int __n)
{ return __builtin_powil(__x, __n); }
#endif
#endif
using ::sin;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
sin(float __x)
{ return __builtin_sinf(__x); }
inline _GLIBCXX_CONSTEXPR long double
sin(long double __x)
{ return __builtin_sinl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
sin(_Tp __x)
{ return __builtin_sin(__x); }
using ::sinh;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
sinh(float __x)
{ return __builtin_sinhf(__x); }
inline _GLIBCXX_CONSTEXPR long double
sinh(long double __x)
{ return __builtin_sinhl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
sinh(_Tp __x)
{ return __builtin_sinh(__x); }
using ::sqrt;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
sqrt(float __x)
{ return __builtin_sqrtf(__x); }
inline _GLIBCXX_CONSTEXPR long double
sqrt(long double __x)
{ return __builtin_sqrtl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
sqrt(_Tp __x)
{ return __builtin_sqrt(__x); }
using ::tan;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
tan(float __x)
{ return __builtin_tanf(__x); }
inline _GLIBCXX_CONSTEXPR long double
tan(long double __x)
{ return __builtin_tanl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
tan(_Tp __x)
{ return __builtin_tan(__x); }
using ::tanh;
#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
inline _GLIBCXX_CONSTEXPR float
tanh(float __x)
{ return __builtin_tanhf(__x); }
inline _GLIBCXX_CONSTEXPR long double
tanh(long double __x)
{ return __builtin_tanhl(__x); }
#endif
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
tanh(_Tp __x)
{ return __builtin_tanh(__x); }
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
constexpr _Float16
acos(_Float16 __x)
{ return _Float16(__builtin_acosf(__x)); }
constexpr _Float16
asin(_Float16 __x)
{ return _Float16(__builtin_asinf(__x)); }
constexpr _Float16
atan(_Float16 __x)
{ return _Float16(__builtin_atanf(__x)); }
constexpr _Float16
atan2(_Float16 __y, _Float16 __x)
{ return _Float16(__builtin_atan2f(__y, __x)); }
constexpr _Float16
ceil(_Float16 __x)
{ return _Float16(__builtin_ceilf(__x)); }
constexpr _Float16
cos(_Float16 __x)
{ return _Float16(__builtin_cosf(__x)); }
constexpr _Float16
cosh(_Float16 __x)
{ return _Float16(__builtin_coshf(__x)); }
constexpr _Float16
exp(_Float16 __x)
{ return _Float16(__builtin_expf(__x)); }
constexpr _Float16
fabs(_Float16 __x)
{ return _Float16(__builtin_fabsf(__x)); }
constexpr _Float16
floor(_Float16 __x)
{ return _Float16(__builtin_floorf(__x)); }
constexpr _Float16
fmod(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_fmodf(__x, __y)); }
inline _Float16
frexp(_Float16 __x, int* __exp)
{ return _Float16(__builtin_frexpf(__x, __exp)); }
constexpr _Float16
ldexp(_Float16 __x, int __exp)
{ return _Float16(__builtin_ldexpf(__x, __exp)); }
constexpr _Float16
log(_Float16 __x)
{ return _Float16(__builtin_logf(__x)); }
constexpr _Float16
log10(_Float16 __x)
{ return _Float16(__builtin_log10f(__x)); }
inline _Float16
modf(_Float16 __x, _Float16* __iptr)
{
float __i, __ret = __builtin_modff(__x, &__i);
*__iptr = _Float16(__i);
return _Float16(__ret);
}
constexpr _Float16
pow(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_powf(__x, __y)); }
constexpr _Float16
sin(_Float16 __x)
{ return _Float16(__builtin_sinf(__x)); }
constexpr _Float16
sinh(_Float16 __x)
{ return _Float16(__builtin_sinhf(__x)); }
constexpr _Float16
sqrt(_Float16 __x)
{ return _Float16(__builtin_sqrtf(__x)); }
constexpr _Float16
tan(_Float16 __x)
{ return _Float16(__builtin_tanf(__x)); }
constexpr _Float16
tanh(_Float16 __x)
{ return _Float16(__builtin_tanhf(__x)); }
#endif
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
constexpr _Float32
acos(_Float32 __x)
{ return __builtin_acosf(__x); }
constexpr _Float32
asin(_Float32 __x)
{ return __builtin_asinf(__x); }
constexpr _Float32
atan(_Float32 __x)
{ return __builtin_atanf(__x); }
constexpr _Float32
atan2(_Float32 __y, _Float32 __x)
{ return __builtin_atan2f(__y, __x); }
constexpr _Float32
ceil(_Float32 __x)
{ return __builtin_ceilf(__x); }
constexpr _Float32
cos(_Float32 __x)
{ return __builtin_cosf(__x); }
constexpr _Float32
cosh(_Float32 __x)
{ return __builtin_coshf(__x); }
constexpr _Float32
exp(_Float32 __x)
{ return __builtin_expf(__x); }
constexpr _Float32
fabs(_Float32 __x)
{ return __builtin_fabsf(__x); }
constexpr _Float32
floor(_Float32 __x)
{ return __builtin_floorf(__x); }
constexpr _Float32
fmod(_Float32 __x, _Float32 __y)
{ return __builtin_fmodf(__x, __y); }
inline _Float32
frexp(_Float32 __x, int* __exp)
{ return __builtin_frexpf(__x, __exp); }
constexpr _Float32
ldexp(_Float32 __x, int __exp)
{ return __builtin_ldexpf(__x, __exp); }
constexpr _Float32
log(_Float32 __x)
{ return __builtin_logf(__x); }
constexpr _Float32
log10(_Float32 __x)
{ return __builtin_log10f(__x); }
inline _Float32
modf(_Float32 __x, _Float32* __iptr)
{
float __i, __ret = __builtin_modff(__x, &__i);
*__iptr = __i;
return __ret;
}
constexpr _Float32
pow(_Float32 __x, _Float32 __y)
{ return __builtin_powf(__x, __y); }
constexpr _Float32
sin(_Float32 __x)
{ return __builtin_sinf(__x); }
constexpr _Float32
sinh(_Float32 __x)
{ return __builtin_sinhf(__x); }
constexpr _Float32
sqrt(_Float32 __x)
{ return __builtin_sqrtf(__x); }
constexpr _Float32
tan(_Float32 __x)
{ return __builtin_tanf(__x); }
constexpr _Float32
tanh(_Float32 __x)
{ return __builtin_tanhf(__x); }
#endif
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
constexpr _Float64
acos(_Float64 __x)
{ return __builtin_acos(__x); }
constexpr _Float64
asin(_Float64 __x)
{ return __builtin_asin(__x); }
constexpr _Float64
atan(_Float64 __x)
{ return __builtin_atan(__x); }
constexpr _Float64
atan2(_Float64 __y, _Float64 __x)
{ return __builtin_atan2(__y, __x); }
constexpr _Float64
ceil(_Float64 __x)
{ return __builtin_ceil(__x); }
constexpr _Float64
cos(_Float64 __x)
{ return __builtin_cos(__x); }
constexpr _Float64
cosh(_Float64 __x)
{ return __builtin_cosh(__x); }
constexpr _Float64
exp(_Float64 __x)
{ return __builtin_exp(__x); }
constexpr _Float64
fabs(_Float64 __x)
{ return __builtin_fabs(__x); }
constexpr _Float64
floor(_Float64 __x)
{ return __builtin_floor(__x); }
constexpr _Float64
fmod(_Float64 __x, _Float64 __y)
{ return __builtin_fmod(__x, __y); }
inline _Float64
frexp(_Float64 __x, int* __exp)
{ return __builtin_frexp(__x, __exp); }
constexpr _Float64
ldexp(_Float64 __x, int __exp)
{ return __builtin_ldexp(__x, __exp); }
constexpr _Float64
log(_Float64 __x)
{ return __builtin_log(__x); }
constexpr _Float64
log10(_Float64 __x)
{ return __builtin_log10(__x); }
inline _Float64
modf(_Float64 __x, _Float64* __iptr)
{
double __i, __ret = __builtin_modf(__x, &__i);
*__iptr = __i;
return __ret;
}
constexpr _Float64
pow(_Float64 __x, _Float64 __y)
{ return __builtin_pow(__x, __y); }
constexpr _Float64
sin(_Float64 __x)
{ return __builtin_sin(__x); }
constexpr _Float64
sinh(_Float64 __x)
{ return __builtin_sinh(__x); }
constexpr _Float64
sqrt(_Float64 __x)
{ return __builtin_sqrt(__x); }
constexpr _Float64
tan(_Float64 __x)
{ return __builtin_tan(__x); }
constexpr _Float64
tanh(_Float64 __x)
{ return __builtin_tanh(__x); }
#endif
#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
constexpr _Float128
acos(_Float128 __x)
{ return __builtin_acosl(__x); }
constexpr _Float128
asin(_Float128 __x)
{ return __builtin_asinl(__x); }
constexpr _Float128
atan(_Float128 __x)
{ return __builtin_atanl(__x); }
constexpr _Float128
atan2(_Float128 __y, _Float128 __x)
{ return __builtin_atan2l(__y, __x); }
constexpr _Float128
ceil(_Float128 __x)
{ return __builtin_ceill(__x); }
constexpr _Float128
cos(_Float128 __x)
{ return __builtin_cosl(__x); }
constexpr _Float128
cosh(_Float128 __x)
{ return __builtin_coshl(__x); }
constexpr _Float128
exp(_Float128 __x)
{ return __builtin_expl(__x); }
constexpr _Float128
fabs(_Float128 __x)
{ return __builtin_fabsl(__x); }
constexpr _Float128
floor(_Float128 __x)
{ return __builtin_floorl(__x); }
constexpr _Float128
fmod(_Float128 __x, _Float128 __y)
{ return __builtin_fmodl(__x, __y); }
inline _Float128
frexp(_Float128 __x, int* __exp)
{ return __builtin_frexpl(__x, __exp); }
constexpr _Float128
ldexp(_Float128 __x, int __exp)
{ return __builtin_ldexpl(__x, __exp); }
constexpr _Float128
log(_Float128 __x)
{ return __builtin_logl(__x); }
constexpr _Float128
log10(_Float128 __x)
{ return __builtin_log10l(__x); }
inline _Float128
modf(_Float128 __x, _Float128* __iptr)
{
long double __i, __ret = __builtin_modfl(__x, &__i);
*__iptr = __i;
return __ret;
}
constexpr _Float128
pow(_Float128 __x, _Float128 __y)
{ return __builtin_powl(__x, __y); }
constexpr _Float128
sin(_Float128 __x)
{ return __builtin_sinl(__x); }
constexpr _Float128
sinh(_Float128 __x)
{ return __builtin_sinhl(__x); }
constexpr _Float128
sqrt(_Float128 __x)
{ return __builtin_sqrtl(__x); }
constexpr _Float128
tan(_Float128 __x)
{ return __builtin_tanl(__x); }
constexpr _Float128
tanh(_Float128 __x)
{ return __builtin_tanhl(__x); }
#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
constexpr _Float128
acos(_Float128 __x)
{ return __builtin_acosf128(__x); }
constexpr _Float128
asin(_Float128 __x)
{ return __builtin_asinf128(__x); }
constexpr _Float128
atan(_Float128 __x)
{ return __builtin_atanf128(__x); }
constexpr _Float128
atan2(_Float128 __y, _Float128 __x)
{ return __builtin_atan2f128(__y, __x); }
constexpr _Float128
ceil(_Float128 __x)
{ return __builtin_ceilf128(__x); }
constexpr _Float128
cos(_Float128 __x)
{ return __builtin_cosf128(__x); }
constexpr _Float128
cosh(_Float128 __x)
{ return __builtin_coshf128(__x); }
constexpr _Float128
exp(_Float128 __x)
{ return __builtin_expf128(__x); }
constexpr _Float128
fabs(_Float128 __x)
{ return __builtin_fabsf128(__x); }
constexpr _Float128
floor(_Float128 __x)
{ return __builtin_floorf128(__x); }
constexpr _Float128
fmod(_Float128 __x, _Float128 __y)
{ return __builtin_fmodf128(__x, __y); }
inline _Float128
frexp(_Float128 __x, int* __exp)
{ return __builtin_frexpf128(__x, __exp); }
constexpr _Float128
ldexp(_Float128 __x, int __exp)
{ return __builtin_ldexpf128(__x, __exp); }
constexpr _Float128
log(_Float128 __x)
{ return __builtin_logf128(__x); }
constexpr _Float128
log10(_Float128 __x)
{ return __builtin_log10f128(__x); }
inline _Float128
modf(_Float128 __x, _Float128* __iptr)
{ return __builtin_modff128(__x, __iptr); }
constexpr _Float128
pow(_Float128 __x, _Float128 __y)
{ return __builtin_powf128(__x, __y); }
constexpr _Float128
sin(_Float128 __x)
{ return __builtin_sinf128(__x); }
constexpr _Float128
sinh(_Float128 __x)
{ return __builtin_sinhf128(__x); }
constexpr _Float128
sqrt(_Float128 __x)
{ return __builtin_sqrtf128(__x); }
constexpr _Float128
tan(_Float128 __x)
{ return __builtin_tanf128(__x); }
constexpr _Float128
tanh(_Float128 __x)
{ return __builtin_tanhf128(__x); }
#endif
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
constexpr __gnu_cxx::__bfloat16_t
acos(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_acosf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
asin(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_asinf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
atan(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_atanf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
atan2(__gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_atan2f(__y, __x)); }
constexpr __gnu_cxx::__bfloat16_t
ceil(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_ceilf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
cos(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_cosf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
cosh(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_coshf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
exp(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_expf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
fabs(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_fabsf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
floor(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_floorf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
fmod(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_fmodf(__x, __y)); }
inline __gnu_cxx::__bfloat16_t
frexp(__gnu_cxx::__bfloat16_t __x, int* __exp)
{ return __gnu_cxx::__bfloat16_t(__builtin_frexpf(__x, __exp)); }
constexpr __gnu_cxx::__bfloat16_t
ldexp(__gnu_cxx::__bfloat16_t __x, int __exp)
{ return __gnu_cxx::__bfloat16_t(__builtin_ldexpf(__x, __exp)); }
constexpr __gnu_cxx::__bfloat16_t
log(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_logf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
log10(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_log10f(__x)); }
inline __gnu_cxx::__bfloat16_t
modf(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t* __iptr)
{
float __i, __ret = __builtin_modff(__x, &__i);
*__iptr = __gnu_cxx::__bfloat16_t(__i);
return __gnu_cxx::__bfloat16_t(__ret);
}
constexpr __gnu_cxx::__bfloat16_t
pow(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_powf(__x, __y)); }
constexpr __gnu_cxx::__bfloat16_t
sin(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_sinf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
sinh(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_sinhf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
sqrt(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_sqrtf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
tan(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_tanf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
tanh(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_tanhf(__x)); }
#endif
template<typename _Tp, typename _Up>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
atan2(_Tp __y, _Up __x)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return atan2(__type(__y), __type(__x));
}
template<typename _Tp, typename _Up>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
fmod(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return fmod(__type(__x), __type(__y));
}
template<typename _Tp, typename _Up>
inline _GLIBCXX_CONSTEXPR
typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
pow(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return pow(__type(__x), __type(__y));
}
#if _GLIBCXX_USE_C99_MATH
#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
// These are possible macros imported from C99-land.
#undef fpclassify
#undef isfinite
#undef isinf
#undef isnan
#undef isnormal
#undef signbit
#undef isgreater
#undef isgreaterequal
#undef isless
#undef islessequal
#undef islessgreater
#undef isunordered
#if __cplusplus >= 201103L
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr int
fpclassify(float __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr int
fpclassify(double __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr int
fpclassify(long double __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
int>::__type
fpclassify(_Tp __x)
{ return __x != 0 ? FP_NORMAL : FP_ZERO; }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isfinite(float __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isfinite(double __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isfinite(long double __x)
{ return __builtin_isfinite(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
bool>::__type
isfinite(_Tp)
{ return true; }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isinf(float __x)
{ return __builtin_isinf(__x); }
#if _GLIBCXX_HAVE_OBSOLETE_ISINF \
&& !_GLIBCXX_NO_OBSOLETE_ISINF_ISNAN_DYNAMIC
using ::isinf;
#else
constexpr bool
isinf(double __x)
{ return __builtin_isinf(__x); }
#endif
constexpr bool
isinf(long double __x)
{ return __builtin_isinf(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
bool>::__type
isinf(_Tp)
{ return false; }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isnan(float __x)
{ return __builtin_isnan(__x); }
#if _GLIBCXX_HAVE_OBSOLETE_ISNAN \
&& !_GLIBCXX_NO_OBSOLETE_ISINF_ISNAN_DYNAMIC
using ::isnan;
#else
constexpr bool
isnan(double __x)
{ return __builtin_isnan(__x); }
#endif
constexpr bool
isnan(long double __x)
{ return __builtin_isnan(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
bool>::__type
isnan(_Tp)
{ return false; }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isnormal(float __x)
{ return __builtin_isnormal(__x); }
constexpr bool
isnormal(double __x)
{ return __builtin_isnormal(__x); }
constexpr bool
isnormal(long double __x)
{ return __builtin_isnormal(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
bool>::__type
isnormal(_Tp __x)
{ return __x != 0 ? true : false; }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
// Note: middle-end/36757 is fixed, __builtin_signbit is type-generic.
constexpr bool
signbit(float __x)
{ return __builtin_signbit(__x); }
constexpr bool
signbit(double __x)
{ return __builtin_signbit(__x); }
constexpr bool
signbit(long double __x)
{ return __builtin_signbit(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
bool>::__type
signbit(_Tp __x)
{ return __x < 0 ? true : false; }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isgreater(float __x, float __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreater(double __x, double __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreater(long double __x, long double __y)
{ return __builtin_isgreater(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr typename
__gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
&& __is_arithmetic<_Up>::__value), bool>::__type
isgreater(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return __builtin_isgreater(__type(__x), __type(__y));
}
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isgreaterequal(float __x, float __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isgreaterequal(double __x, double __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isgreaterequal(long double __x, long double __y)
{ return __builtin_isgreaterequal(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr typename
__gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
&& __is_arithmetic<_Up>::__value), bool>::__type
isgreaterequal(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return __builtin_isgreaterequal(__type(__x), __type(__y));
}
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isless(float __x, float __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
isless(double __x, double __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
isless(long double __x, long double __y)
{ return __builtin_isless(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr typename
__gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
&& __is_arithmetic<_Up>::__value), bool>::__type
isless(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return __builtin_isless(__type(__x), __type(__y));
}
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
islessequal(float __x, float __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessequal(double __x, double __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessequal(long double __x, long double __y)
{ return __builtin_islessequal(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr typename
__gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
&& __is_arithmetic<_Up>::__value), bool>::__type
islessequal(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return __builtin_islessequal(__type(__x), __type(__y));
}
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
islessgreater(float __x, float __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
islessgreater(double __x, double __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
islessgreater(long double __x, long double __y)
{ return __builtin_islessgreater(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr typename
__gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
&& __is_arithmetic<_Up>::__value), bool>::__type
islessgreater(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return __builtin_islessgreater(__type(__x), __type(__y));
}
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr bool
isunordered(float __x, float __y)
{ return __builtin_isunordered(__x, __y); }
constexpr bool
isunordered(double __x, double __y)
{ return __builtin_isunordered(__x, __y); }
constexpr bool
isunordered(long double __x, long double __y)
{ return __builtin_isunordered(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr typename
__gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
&& __is_arithmetic<_Up>::__value), bool>::__type
isunordered(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return __builtin_isunordered(__type(__x), __type(__y));
}
#endif
#else
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 // C++11
#ifdef __STDCPP_FLOAT16_T__
constexpr int
fpclassify(_Float16 __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr bool
isfinite(_Float16 __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isinf(_Float16 __x)
{ return __builtin_isinf(__x); }
constexpr bool
isnan(_Float16 __x)
{ return __builtin_isnan(__x); }
constexpr bool
isnormal(_Float16 __x)
{ return __builtin_isnormal(__x); }
constexpr bool
signbit(_Float16 __x)
{ return __builtin_signbit(__x); }
constexpr bool
isgreater(_Float16 __x, _Float16 __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreaterequal(_Float16 __x, _Float16 __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isless(_Float16 __x, _Float16 __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
islessequal(_Float16 __x, _Float16 __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessgreater(_Float16 __x, _Float16 __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
isunordered(_Float16 __x, _Float16 __y)
{ return __builtin_isunordered(__x, __y); }
#endif
#ifdef __STDCPP_FLOAT32_T__
constexpr int
fpclassify(_Float32 __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr bool
isfinite(_Float32 __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isinf(_Float32 __x)
{ return __builtin_isinf(__x); }
constexpr bool
isnan(_Float32 __x)
{ return __builtin_isnan(__x); }
constexpr bool
isnormal(_Float32 __x)
{ return __builtin_isnormal(__x); }
constexpr bool
signbit(_Float32 __x)
{ return __builtin_signbit(__x); }
constexpr bool
isgreater(_Float32 __x, _Float32 __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreaterequal(_Float32 __x, _Float32 __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isless(_Float32 __x, _Float32 __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
islessequal(_Float32 __x, _Float32 __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessgreater(_Float32 __x, _Float32 __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
isunordered(_Float32 __x, _Float32 __y)
{ return __builtin_isunordered(__x, __y); }
#endif
#ifdef __STDCPP_FLOAT64_T__
constexpr int
fpclassify(_Float64 __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr bool
isfinite(_Float64 __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isinf(_Float64 __x)
{ return __builtin_isinf(__x); }
constexpr bool
isnan(_Float64 __x)
{ return __builtin_isnan(__x); }
constexpr bool
isnormal(_Float64 __x)
{ return __builtin_isnormal(__x); }
constexpr bool
signbit(_Float64 __x)
{ return __builtin_signbit(__x); }
constexpr bool
isgreater(_Float64 __x, _Float64 __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreaterequal(_Float64 __x, _Float64 __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isless(_Float64 __x, _Float64 __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
islessequal(_Float64 __x, _Float64 __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessgreater(_Float64 __x, _Float64 __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
isunordered(_Float64 __x, _Float64 __y)
{ return __builtin_isunordered(__x, __y); }
#endif
#ifdef __STDCPP_FLOAT128_T__
constexpr int
fpclassify(_Float128 __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr bool
isfinite(_Float128 __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isinf(_Float128 __x)
{ return __builtin_isinf(__x); }
constexpr bool
isnan(_Float128 __x)
{ return __builtin_isnan(__x); }
constexpr bool
isnormal(_Float128 __x)
{ return __builtin_isnormal(__x); }
constexpr bool
signbit(_Float128 __x)
{ return __builtin_signbit(__x); }
constexpr bool
isgreater(_Float128 __x, _Float128 __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreaterequal(_Float128 __x, _Float128 __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isless(_Float128 __x, _Float128 __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
islessequal(_Float128 __x, _Float128 __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessgreater(_Float128 __x, _Float128 __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
isunordered(_Float128 __x, _Float128 __y)
{ return __builtin_isunordered(__x, __y); }
#endif
#ifdef __STDCPP_BFLOAT16_T__
constexpr int
fpclassify(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
FP_SUBNORMAL, FP_ZERO, __x); }
constexpr bool
isfinite(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_isfinite(__x); }
constexpr bool
isinf(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_isinf(__x); }
constexpr bool
isnan(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_isnan(__x); }
constexpr bool
isnormal(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_isnormal(__x); }
constexpr bool
signbit(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_signbit(__x); }
constexpr bool
isgreater(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __builtin_isgreater(__x, __y); }
constexpr bool
isgreaterequal(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __builtin_isgreaterequal(__x, __y); }
constexpr bool
isless(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __builtin_isless(__x, __y); }
constexpr bool
islessequal(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __builtin_islessequal(__x, __y); }
constexpr bool
islessgreater(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __builtin_islessgreater(__x, __y); }
constexpr bool
isunordered(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __builtin_isunordered(__x, __y); }
#endif
#endif /* _GLIBCXX_USE_C99_FP_MACROS_DYNAMIC */
#endif /* _GLIBCXX_USE_C99_MATH */
#if __cplusplus >= 201103L
#undef acosf
#undef acosl
#undef asinf
#undef asinl
#undef atanf
#undef atanl
#undef atan2f
#undef atan2l
#undef ceilf
#undef ceill
#undef cosf
#undef cosl
#undef coshf
#undef coshl
#undef expf
#undef expl
#undef fabsf
#undef fabsl
#undef floorf
#undef floorl
#undef fmodf
#undef fmodl
#undef frexpf
#undef frexpl
#undef ldexpf
#undef ldexpl
#undef logf
#undef logl
#undef log10f
#undef log10l
#undef modff
#undef modfl
#undef powf
#undef powl
#undef sinf
#undef sinl
#undef sinhf
#undef sinhl
#undef sqrtf
#undef sqrtl
#undef tanf
#undef tanl
#undef tanhf
#undef tanhl
#ifdef _GLIBCXX_HAVE_ACOSF
using ::acosf;
#endif
#ifdef _GLIBCXX_HAVE_ACOSL
using ::acosl;
#endif
#ifdef _GLIBCXX_HAVE_ASINF
using ::asinf;
#endif
#ifdef _GLIBCXX_HAVE_ASINL
using ::asinl;
#endif
#ifdef _GLIBCXX_HAVE_ATANF
using ::atanf;
#endif
#ifdef _GLIBCXX_HAVE_ATANL
using ::atanl;
#endif
#ifdef _GLIBCXX_HAVE_ATAN2F
using ::atan2f;
#endif
#ifdef _GLIBCXX_HAVE_ATAN2L
using ::atan2l;
#endif
#ifdef _GLIBCXX_HAVE_CEILF
using ::ceilf;
#endif
#ifdef _GLIBCXX_HAVE_CEILL
using ::ceill;
#endif
#ifdef _GLIBCXX_HAVE_COSF
using ::cosf;
#endif
#ifdef _GLIBCXX_HAVE_COSL
using ::cosl;
#endif
#ifdef _GLIBCXX_HAVE_COSHF
using ::coshf;
#endif
#ifdef _GLIBCXX_HAVE_COSHL
using ::coshl;
#endif
#ifdef _GLIBCXX_HAVE_EXPF
using ::expf;
#endif
#ifdef _GLIBCXX_HAVE_EXPL
using ::expl;
#endif
#ifdef _GLIBCXX_HAVE_FABSF
using ::fabsf;
#endif
#ifdef _GLIBCXX_HAVE_FABSL
using ::fabsl;
#endif
#ifdef _GLIBCXX_HAVE_FLOORF
using ::floorf;
#endif
#ifdef _GLIBCXX_HAVE_FLOORL
using ::floorl;
#endif
#ifdef _GLIBCXX_HAVE_FMODF
using ::fmodf;
#endif
#ifdef _GLIBCXX_HAVE_FMODL
using ::fmodl;
#endif
#ifdef _GLIBCXX_HAVE_FREXPF
using ::frexpf;
#endif
#ifdef _GLIBCXX_HAVE_FREXPL
using ::frexpl;
#endif
#ifdef _GLIBCXX_HAVE_LDEXPF
using ::ldexpf;
#endif
#ifdef _GLIBCXX_HAVE_LDEXPL
using ::ldexpl;
#endif
#ifdef _GLIBCXX_HAVE_LOGF
using ::logf;
#endif
#ifdef _GLIBCXX_HAVE_LOGL
using ::logl;
#endif
#ifdef _GLIBCXX_HAVE_LOG10F
using ::log10f;
#endif
#ifdef _GLIBCXX_HAVE_LOG10L
using ::log10l;
#endif
#ifdef _GLIBCXX_HAVE_MODFF
using ::modff;
#endif
#ifdef _GLIBCXX_HAVE_MODFL
using ::modfl;
#endif
#ifdef _GLIBCXX_HAVE_POWF
using ::powf;
#endif
#ifdef _GLIBCXX_HAVE_POWL
using ::powl;
#endif
#ifdef _GLIBCXX_HAVE_SINF
using ::sinf;
#endif
#ifdef _GLIBCXX_HAVE_SINL
using ::sinl;
#endif
#ifdef _GLIBCXX_HAVE_SINHF
using ::sinhf;
#endif
#ifdef _GLIBCXX_HAVE_SINHL
using ::sinhl;
#endif
#ifdef _GLIBCXX_HAVE_SQRTF
using ::sqrtf;
#endif
#ifdef _GLIBCXX_HAVE_SQRTL
using ::sqrtl;
#endif
#ifdef _GLIBCXX_HAVE_TANF
using ::tanf;
#endif
#ifdef _GLIBCXX_HAVE_TANL
using ::tanl;
#endif
#ifdef _GLIBCXX_HAVE_TANHF
using ::tanhf;
#endif
#ifdef _GLIBCXX_HAVE_TANHL
using ::tanhl;
#endif
#ifdef _GLIBCXX_USE_C99_MATH_FUNCS
#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
#ifndef _GLIBCXX_NO_C99_ROUNDING_FUNCS
#undef llrint
#undef llrintf
#undef llrintl
#undef llround
#undef llroundf
#undef llroundl
#endif
#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
#ifdef _GLIBCXX_HAVE_C99_FLT_EVAL_TYPES
// types
using ::double_t;
using ::float_t;
#endif
// 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;
#ifndef _GLIBCXX_NO_C99_ROUNDING_FUNCS
using ::llrint;
using ::llrintf;
using ::llrintl;
using ::llround;
using ::llroundf;
using ::llroundl;
#endif
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;
/// Additional overloads.
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
acosh(float __x)
{ return __builtin_acoshf(__x); }
constexpr long double
acosh(long double __x)
{ return __builtin_acoshl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
acosh(_Tp __x)
{ return __builtin_acosh(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
asinh(float __x)
{ return __builtin_asinhf(__x); }
constexpr long double
asinh(long double __x)
{ return __builtin_asinhl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
asinh(_Tp __x)
{ return __builtin_asinh(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
atanh(float __x)
{ return __builtin_atanhf(__x); }
constexpr long double
atanh(long double __x)
{ return __builtin_atanhl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
atanh(_Tp __x)
{ return __builtin_atanh(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
cbrt(float __x)
{ return __builtin_cbrtf(__x); }
constexpr long double
cbrt(long double __x)
{ return __builtin_cbrtl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
cbrt(_Tp __x)
{ return __builtin_cbrt(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
copysign(float __x, float __y)
{ return __builtin_copysignf(__x, __y); }
constexpr long double
copysign(long double __x, long double __y)
{ return __builtin_copysignl(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
erf(float __x)
{ return __builtin_erff(__x); }
constexpr long double
erf(long double __x)
{ return __builtin_erfl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
erf(_Tp __x)
{ return __builtin_erf(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
erfc(float __x)
{ return __builtin_erfcf(__x); }
constexpr long double
erfc(long double __x)
{ return __builtin_erfcl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
erfc(_Tp __x)
{ return __builtin_erfc(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
exp2(float __x)
{ return __builtin_exp2f(__x); }
constexpr long double
exp2(long double __x)
{ return __builtin_exp2l(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
exp2(_Tp __x)
{ return __builtin_exp2(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
expm1(float __x)
{ return __builtin_expm1f(__x); }
constexpr long double
expm1(long double __x)
{ return __builtin_expm1l(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
expm1(_Tp __x)
{ return __builtin_expm1(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
fdim(float __x, float __y)
{ return __builtin_fdimf(__x, __y); }
constexpr long double
fdim(long double __x, long double __y)
{ return __builtin_fdiml(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
fma(float __x, float __y, float __z)
{ return __builtin_fmaf(__x, __y, __z); }
constexpr long double
fma(long double __x, long double __y, long double __z)
{ return __builtin_fmal(__x, __y, __z); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
fmax(float __x, float __y)
{ return __builtin_fmaxf(__x, __y); }
constexpr long double
fmax(long double __x, long double __y)
{ return __builtin_fmaxl(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
fmin(float __x, float __y)
{ return __builtin_fminf(__x, __y); }
constexpr long double
fmin(long double __x, long double __y)
{ return __builtin_fminl(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
hypot(float __x, float __y)
{ return __builtin_hypotf(__x, __y); }
constexpr long double
hypot(long double __x, long double __y)
{ return __builtin_hypotl(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr int
ilogb(float __x)
{ return __builtin_ilogbf(__x); }
constexpr int
ilogb(long double __x)
{ return __builtin_ilogbl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr
typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
int>::__type
ilogb(_Tp __x)
{ return __builtin_ilogb(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
lgamma(float __x)
{ return __builtin_lgammaf(__x); }
constexpr long double
lgamma(long double __x)
{ return __builtin_lgammal(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
lgamma(_Tp __x)
{ return __builtin_lgamma(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr long long
llrint(float __x)
{ return __builtin_llrintf(__x); }
constexpr long long
llrint(long double __x)
{ return __builtin_llrintl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long long>::__type
llrint(_Tp __x)
{ return __builtin_llrint(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr long long
llround(float __x)
{ return __builtin_llroundf(__x); }
constexpr long long
llround(long double __x)
{ return __builtin_llroundl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long long>::__type
llround(_Tp __x)
{ return __builtin_llround(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
log1p(float __x)
{ return __builtin_log1pf(__x); }
constexpr long double
log1p(long double __x)
{ return __builtin_log1pl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
log1p(_Tp __x)
{ return __builtin_log1p(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
// DR 568.
constexpr float
log2(float __x)
{ return __builtin_log2f(__x); }
constexpr long double
log2(long double __x)
{ return __builtin_log2l(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
log2(_Tp __x)
{ return __builtin_log2(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
logb(float __x)
{ return __builtin_logbf(__x); }
constexpr long double
logb(long double __x)
{ return __builtin_logbl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
logb(_Tp __x)
{ return __builtin_logb(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr long
lrint(float __x)
{ return __builtin_lrintf(__x); }
constexpr long
lrint(long double __x)
{ return __builtin_lrintl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long>::__type
lrint(_Tp __x)
{ return __builtin_lrint(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr long
lround(float __x)
{ return __builtin_lroundf(__x); }
constexpr long
lround(long double __x)
{ return __builtin_lroundl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
long>::__type
lround(_Tp __x)
{ return __builtin_lround(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
nearbyint(float __x)
{ return __builtin_nearbyintf(__x); }
constexpr long double
nearbyint(long double __x)
{ return __builtin_nearbyintl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
nearbyint(_Tp __x)
{ return __builtin_nearbyint(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
nextafter(float __x, float __y)
{ return __builtin_nextafterf(__x, __y); }
constexpr long double
nextafter(long double __x, long double __y)
{ return __builtin_nextafterl(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
nexttoward(float __x, long double __y)
{ return __builtin_nexttowardf(__x, __y); }
constexpr long double
nexttoward(long double __x, long double __y)
{ return __builtin_nexttowardl(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
nexttoward(_Tp __x, long double __y)
{ return __builtin_nexttoward(__x, __y); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
remainder(float __x, float __y)
{ return __builtin_remainderf(__x, __y); }
constexpr long double
remainder(long double __x, long double __y)
{ return __builtin_remainderl(__x, __y); }
#endif
#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
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
rint(float __x)
{ return __builtin_rintf(__x); }
constexpr long double
rint(long double __x)
{ return __builtin_rintl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
rint(_Tp __x)
{ return __builtin_rint(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
round(float __x)
{ return __builtin_roundf(__x); }
constexpr long double
round(long double __x)
{ return __builtin_roundl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
round(_Tp __x)
{ return __builtin_round(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
scalbln(float __x, long __ex)
{ return __builtin_scalblnf(__x, __ex); }
constexpr long double
scalbln(long double __x, long __ex)
{ return __builtin_scalblnl(__x, __ex); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
scalbln(_Tp __x, long __ex)
{ return __builtin_scalbln(__x, __ex); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
scalbn(float __x, int __ex)
{ return __builtin_scalbnf(__x, __ex); }
constexpr long double
scalbn(long double __x, int __ex)
{ return __builtin_scalbnl(__x, __ex); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
scalbn(_Tp __x, int __ex)
{ return __builtin_scalbn(__x, __ex); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
tgamma(float __x)
{ return __builtin_tgammaf(__x); }
constexpr long double
tgamma(long double __x)
{ return __builtin_tgammal(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
tgamma(_Tp __x)
{ return __builtin_tgamma(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
constexpr float
trunc(float __x)
{ return __builtin_truncf(__x); }
constexpr long double
trunc(long double __x)
{ return __builtin_truncl(__x); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp>
constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
double>::__type
trunc(_Tp __x)
{ return __builtin_trunc(__x); }
#endif
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
constexpr _Float16
acosh(_Float16 __x)
{ return _Float16(__builtin_acoshf(__x)); }
constexpr _Float16
asinh(_Float16 __x)
{ return _Float16(__builtin_asinhf(__x)); }
constexpr _Float16
atanh(_Float16 __x)
{ return _Float16(__builtin_atanhf(__x)); }
constexpr _Float16
cbrt(_Float16 __x)
{ return _Float16(__builtin_cbrtf(__x)); }
constexpr _Float16
copysign(_Float16 __x, _Float16 __y)
{ return __builtin_copysignf16(__x, __y); }
constexpr _Float16
erf(_Float16 __x)
{ return _Float16(__builtin_erff(__x)); }
constexpr _Float16
erfc(_Float16 __x)
{ return _Float16(__builtin_erfcf(__x)); }
constexpr _Float16
exp2(_Float16 __x)
{ return _Float16(__builtin_exp2f(__x)); }
constexpr _Float16
expm1(_Float16 __x)
{ return _Float16(__builtin_expm1f(__x)); }
constexpr _Float16
fdim(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_fdimf(__x, __y)); }
constexpr _Float16
fma(_Float16 __x, _Float16 __y, _Float16 __z)
{ return _Float16(__builtin_fmaf(__x, __y, __z)); }
constexpr _Float16
fmax(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_fmaxf(__x, __y)); }
constexpr _Float16
fmin(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_fminf(__x, __y)); }
constexpr _Float16
hypot(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_hypotf(__x, __y)); }
constexpr int
ilogb(_Float16 __x)
{ return __builtin_ilogbf(__x); }
constexpr _Float16
lgamma(_Float16 __x)
{ return _Float16(__builtin_lgammaf(__x)); }
constexpr long long
llrint(_Float16 __x)
{ return __builtin_llrintf(__x); }
constexpr long long
llround(_Float16 __x)
{ return __builtin_llroundf(__x); }
constexpr _Float16
log1p(_Float16 __x)
{ return _Float16(__builtin_log1pf(__x)); }
// DR 568.
constexpr _Float16
log2(_Float16 __x)
{ return _Float16(__builtin_log2f(__x)); }
constexpr _Float16
logb(_Float16 __x)
{ return _Float16(__builtin_logbf(__x)); }
constexpr long
lrint(_Float16 __x)
{ return __builtin_lrintf(__x); }
constexpr long
lround(_Float16 __x)
{ return __builtin_lroundf(__x); }
constexpr _Float16
nearbyint(_Float16 __x)
{ return _Float16(__builtin_nearbyintf(__x)); }
constexpr _Float16
nextafter(_Float16 __x, _Float16 __y)
{
#if __cpp_if_consteval >= 202106L
// Can't use if (std::__is_constant_evaluated()) here, as it
// doesn't guarantee optimizing the body away at -O0 and
// nothing defines nextafterf16.
if consteval { return __builtin_nextafterf16(__x, __y); }
#endif
#ifdef __INT16_TYPE__
using __float16_int_type = __INT16_TYPE__;
#else
using __float16_int_type = short int;
#endif
__float16_int_type __hx, __hy, __ix, __iy;
__builtin_memcpy(&__hx, &__x, sizeof(__x));
__builtin_memcpy(&__hy, &__y, sizeof(__x));
__ix = __hx & 0x7fff; // |x|
__iy = __hy & 0x7fff; // |y|
if (__ix > 0x7c00 || __iy > 0x7c00) // x or y is NaN
return __x + __y;
if (__x == __y)
return __y; // x == y, return y
if (__ix == 0) // x == 0
{
__hy = (__hy & 0x8000) | 1; // return +-__FLT16_DENORM_MIN__
__builtin_memcpy(&__x, &__hy, sizeof(__x));
__builtin_nextafterf(0.0f, 1.0f); // raise underflow
return __x;
}
if (__hx >= 0) // x > 0
{
if (__hx > __hy) // x > y, x -= ulp
--__hx;
else // x < y, x += ulp
++__hx;
}
else // x < 0
{
if (__hy >= 0 || __hx > __hy) // x < y, x -= ulp
--__hx;
else // x > y, x += ulp
++__hx;
}
__hy = __hx & 0x7c00;
if (__hy >= 0x7c00)
__builtin_nextafterf(__FLT_MAX__, __builtin_inff()); // overflow
else if (__hy < 0x0400)
__builtin_nextafterf(__FLT_MIN__, 0.0f); // underflow
__builtin_memcpy(&__x, &__hx, sizeof(__x));
return __x;
}
constexpr _Float16
remainder(_Float16 __x, _Float16 __y)
{ return _Float16(__builtin_remainderf(__x, __y)); }
inline _Float16
remquo(_Float16 __x, _Float16 __y, int* __pquo)
{ return _Float16(__builtin_remquof(__x, __y, __pquo)); }
constexpr _Float16
rint(_Float16 __x)
{ return _Float16(__builtin_rintf(__x)); }
constexpr _Float16
round(_Float16 __x)
{ return _Float16(__builtin_roundf(__x)); }
constexpr _Float16
scalbln(_Float16 __x, long __ex)
{ return _Float16(__builtin_scalblnf(__x, __ex)); }
constexpr _Float16
scalbn(_Float16 __x, int __ex)
{ return _Float16(__builtin_scalbnf(__x, __ex)); }
constexpr _Float16
tgamma(_Float16 __x)
{ return _Float16(__builtin_tgammaf(__x)); }
constexpr _Float16
trunc(_Float16 __x)
{ return _Float16(__builtin_truncf(__x)); }
#endif
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
constexpr _Float32
acosh(_Float32 __x)
{ return __builtin_acoshf(__x); }
constexpr _Float32
asinh(_Float32 __x)
{ return __builtin_asinhf(__x); }
constexpr _Float32
atanh(_Float32 __x)
{ return __builtin_atanhf(__x); }
constexpr _Float32
cbrt(_Float32 __x)
{ return __builtin_cbrtf(__x); }
constexpr _Float32
copysign(_Float32 __x, _Float32 __y)
{ return __builtin_copysignf(__x, __y); }
constexpr _Float32
erf(_Float32 __x)
{ return __builtin_erff(__x); }
constexpr _Float32
erfc(_Float32 __x)
{ return __builtin_erfcf(__x); }
constexpr _Float32
exp2(_Float32 __x)
{ return __builtin_exp2f(__x); }
constexpr _Float32
expm1(_Float32 __x)
{ return __builtin_expm1f(__x); }
constexpr _Float32
fdim(_Float32 __x, _Float32 __y)
{ return __builtin_fdimf(__x, __y); }
constexpr _Float32
fma(_Float32 __x, _Float32 __y, _Float32 __z)
{ return __builtin_fmaf(__x, __y, __z); }
constexpr _Float32
fmax(_Float32 __x, _Float32 __y)
{ return __builtin_fmaxf(__x, __y); }
constexpr _Float32
fmin(_Float32 __x, _Float32 __y)
{ return __builtin_fminf(__x, __y); }
constexpr _Float32
hypot(_Float32 __x, _Float32 __y)
{ return __builtin_hypotf(__x, __y); }
constexpr int
ilogb(_Float32 __x)
{ return __builtin_ilogbf(__x); }
constexpr _Float32
lgamma(_Float32 __x)
{ return __builtin_lgammaf(__x); }
constexpr long long
llrint(_Float32 __x)
{ return __builtin_llrintf(__x); }
constexpr long long
llround(_Float32 __x)
{ return __builtin_llroundf(__x); }
constexpr _Float32
log1p(_Float32 __x)
{ return __builtin_log1pf(__x); }
// DR 568.
constexpr _Float32
log2(_Float32 __x)
{ return __builtin_log2f(__x); }
constexpr _Float32
logb(_Float32 __x)
{ return __builtin_logbf(__x); }
constexpr long
lrint(_Float32 __x)
{ return __builtin_lrintf(__x); }
constexpr long
lround(_Float32 __x)
{ return __builtin_lroundf(__x); }
constexpr _Float32
nearbyint(_Float32 __x)
{ return __builtin_nearbyintf(__x); }
constexpr _Float32
nextafter(_Float32 __x, _Float32 __y)
{ return __builtin_nextafterf(__x, __y); }
constexpr _Float32
remainder(_Float32 __x, _Float32 __y)
{ return __builtin_remainderf(__x, __y); }
inline _Float32
remquo(_Float32 __x, _Float32 __y, int* __pquo)
{ return __builtin_remquof(__x, __y, __pquo); }
constexpr _Float32
rint(_Float32 __x)
{ return __builtin_rintf(__x); }
constexpr _Float32
round(_Float32 __x)
{ return __builtin_roundf(__x); }
constexpr _Float32
scalbln(_Float32 __x, long __ex)
{ return __builtin_scalblnf(__x, __ex); }
constexpr _Float32
scalbn(_Float32 __x, int __ex)
{ return __builtin_scalbnf(__x, __ex); }
constexpr _Float32
tgamma(_Float32 __x)
{ return __builtin_tgammaf(__x); }
constexpr _Float32
trunc(_Float32 __x)
{ return __builtin_truncf(__x); }
#endif
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
constexpr _Float64
acosh(_Float64 __x)
{ return __builtin_acosh(__x); }
constexpr _Float64
asinh(_Float64 __x)
{ return __builtin_asinh(__x); }
constexpr _Float64
atanh(_Float64 __x)
{ return __builtin_atanh(__x); }
constexpr _Float64
cbrt(_Float64 __x)
{ return __builtin_cbrt(__x); }
constexpr _Float64
copysign(_Float64 __x, _Float64 __y)
{ return __builtin_copysign(__x, __y); }
constexpr _Float64
erf(_Float64 __x)
{ return __builtin_erf(__x); }
constexpr _Float64
erfc(_Float64 __x)
{ return __builtin_erfc(__x); }
constexpr _Float64
exp2(_Float64 __x)
{ return __builtin_exp2(__x); }
constexpr _Float64
expm1(_Float64 __x)
{ return __builtin_expm1(__x); }
constexpr _Float64
fdim(_Float64 __x, _Float64 __y)
{ return __builtin_fdim(__x, __y); }
constexpr _Float64
fma(_Float64 __x, _Float64 __y, _Float64 __z)
{ return __builtin_fma(__x, __y, __z); }
constexpr _Float64
fmax(_Float64 __x, _Float64 __y)
{ return __builtin_fmax(__x, __y); }
constexpr _Float64
fmin(_Float64 __x, _Float64 __y)
{ return __builtin_fmin(__x, __y); }
constexpr _Float64
hypot(_Float64 __x, _Float64 __y)
{ return __builtin_hypot(__x, __y); }
constexpr int
ilogb(_Float64 __x)
{ return __builtin_ilogb(__x); }
constexpr _Float64
lgamma(_Float64 __x)
{ return __builtin_lgamma(__x); }
constexpr long long
llrint(_Float64 __x)
{ return __builtin_llrint(__x); }
constexpr long long
llround(_Float64 __x)
{ return __builtin_llround(__x); }
constexpr _Float64
log1p(_Float64 __x)
{ return __builtin_log1p(__x); }
// DR 568.
constexpr _Float64
log2(_Float64 __x)
{ return __builtin_log2(__x); }
constexpr _Float64
logb(_Float64 __x)
{ return __builtin_logb(__x); }
constexpr long
lrint(_Float64 __x)
{ return __builtin_lrint(__x); }
constexpr long
lround(_Float64 __x)
{ return __builtin_lround(__x); }
constexpr _Float64
nearbyint(_Float64 __x)
{ return __builtin_nearbyint(__x); }
constexpr _Float64
nextafter(_Float64 __x, _Float64 __y)
{ return __builtin_nextafter(__x, __y); }
constexpr _Float64
remainder(_Float64 __x, _Float64 __y)
{ return __builtin_remainder(__x, __y); }
inline _Float64
remquo(_Float64 __x, _Float64 __y, int* __pquo)
{ return __builtin_remquo(__x, __y, __pquo); }
constexpr _Float64
rint(_Float64 __x)
{ return __builtin_rint(__x); }
constexpr _Float64
round(_Float64 __x)
{ return __builtin_round(__x); }
constexpr _Float64
scalbln(_Float64 __x, long __ex)
{ return __builtin_scalbln(__x, __ex); }
constexpr _Float64
scalbn(_Float64 __x, int __ex)
{ return __builtin_scalbn(__x, __ex); }
constexpr _Float64
tgamma(_Float64 __x)
{ return __builtin_tgamma(__x); }
constexpr _Float64
trunc(_Float64 __x)
{ return __builtin_trunc(__x); }
#endif
#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
constexpr _Float128
acosh(_Float128 __x)
{ return __builtin_acoshl(__x); }
constexpr _Float128
asinh(_Float128 __x)
{ return __builtin_asinhl(__x); }
constexpr _Float128
atanh(_Float128 __x)
{ return __builtin_atanhl(__x); }
constexpr _Float128
cbrt(_Float128 __x)
{ return __builtin_cbrtl(__x); }
constexpr _Float128
copysign(_Float128 __x, _Float128 __y)
{ return __builtin_copysignl(__x, __y); }
constexpr _Float128
erf(_Float128 __x)
{ return __builtin_erfl(__x); }
constexpr _Float128
erfc(_Float128 __x)
{ return __builtin_erfcl(__x); }
constexpr _Float128
exp2(_Float128 __x)
{ return __builtin_exp2l(__x); }
constexpr _Float128
expm1(_Float128 __x)
{ return __builtin_expm1l(__x); }
constexpr _Float128
fdim(_Float128 __x, _Float128 __y)
{ return __builtin_fdiml(__x, __y); }
constexpr _Float128
fma(_Float128 __x, _Float128 __y, _Float128 __z)
{ return __builtin_fmal(__x, __y, __z); }
constexpr _Float128
fmax(_Float128 __x, _Float128 __y)
{ return __builtin_fmaxl(__x, __y); }
constexpr _Float128
fmin(_Float128 __x, _Float128 __y)
{ return __builtin_fminl(__x, __y); }
constexpr _Float128
hypot(_Float128 __x, _Float128 __y)
{ return __builtin_hypotl(__x, __y); }
constexpr int
ilogb(_Float128 __x)
{ return __builtin_ilogbl(__x); }
constexpr _Float128
lgamma(_Float128 __x)
{ return __builtin_lgammal(__x); }
constexpr long long
llrint(_Float128 __x)
{ return __builtin_llrintl(__x); }
constexpr long long
llround(_Float128 __x)
{ return __builtin_llroundl(__x); }
constexpr _Float128
log1p(_Float128 __x)
{ return __builtin_log1pl(__x); }
// DR 568.
constexpr _Float128
log2(_Float128 __x)
{ return __builtin_log2l(__x); }
constexpr _Float128
logb(_Float128 __x)
{ return __builtin_logbl(__x); }
constexpr long
lrint(_Float128 __x)
{ return __builtin_lrintl(__x); }
constexpr long
lround(_Float128 __x)
{ return __builtin_lroundl(__x); }
constexpr _Float128
nearbyint(_Float128 __x)
{ return __builtin_nearbyintl(__x); }
constexpr _Float128
nextafter(_Float128 __x, _Float128 __y)
{ return __builtin_nextafterl(__x, __y); }
constexpr _Float128
remainder(_Float128 __x, _Float128 __y)
{ return __builtin_remainderl(__x, __y); }
inline _Float128
remquo(_Float128 __x, _Float128 __y, int* __pquo)
{ return __builtin_remquol(__x, __y, __pquo); }
constexpr _Float128
rint(_Float128 __x)
{ return __builtin_rintl(__x); }
constexpr _Float128
round(_Float128 __x)
{ return __builtin_roundl(__x); }
constexpr _Float128
scalbln(_Float128 __x, long __ex)
{ return __builtin_scalblnl(__x, __ex); }
constexpr _Float128
scalbn(_Float128 __x, int __ex)
{ return __builtin_scalbnl(__x, __ex); }
constexpr _Float128
tgamma(_Float128 __x)
{ return __builtin_tgammal(__x); }
constexpr _Float128
trunc(_Float128 __x)
{ return __builtin_truncl(__x); }
#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
constexpr _Float128
acosh(_Float128 __x)
{ return __builtin_acoshf128(__x); }
constexpr _Float128
asinh(_Float128 __x)
{ return __builtin_asinhf128(__x); }
constexpr _Float128
atanh(_Float128 __x)
{ return __builtin_atanhf128(__x); }
constexpr _Float128
cbrt(_Float128 __x)
{ return __builtin_cbrtf128(__x); }
constexpr _Float128
copysign(_Float128 __x, _Float128 __y)
{ return __builtin_copysignf128(__x, __y); }
constexpr _Float128
erf(_Float128 __x)
{ return __builtin_erff128(__x); }
constexpr _Float128
erfc(_Float128 __x)
{ return __builtin_erfcf128(__x); }
constexpr _Float128
exp2(_Float128 __x)
{ return __builtin_exp2f128(__x); }
constexpr _Float128
expm1(_Float128 __x)
{ return __builtin_expm1f128(__x); }
constexpr _Float128
fdim(_Float128 __x, _Float128 __y)
{ return __builtin_fdimf128(__x, __y); }
constexpr _Float128
fma(_Float128 __x, _Float128 __y, _Float128 __z)
{ return __builtin_fmaf128(__x, __y, __z); }
constexpr _Float128
fmax(_Float128 __x, _Float128 __y)
{ return __builtin_fmaxf128(__x, __y); }
constexpr _Float128
fmin(_Float128 __x, _Float128 __y)
{ return __builtin_fminf128(__x, __y); }
constexpr _Float128
hypot(_Float128 __x, _Float128 __y)
{ return __builtin_hypotf128(__x, __y); }
constexpr int
ilogb(_Float128 __x)
{ return __builtin_ilogbf128(__x); }
constexpr _Float128
lgamma(_Float128 __x)
{ return __builtin_lgammaf128(__x); }
constexpr long long
llrint(_Float128 __x)
{ return __builtin_llrintf128(__x); }
constexpr long long
llround(_Float128 __x)
{ return __builtin_llroundf128(__x); }
constexpr _Float128
log1p(_Float128 __x)
{ return __builtin_log1pf128(__x); }
// DR 568.
constexpr _Float128
log2(_Float128 __x)
{ return __builtin_log2f128(__x); }
constexpr _Float128
logb(_Float128 __x)
{ return __builtin_logbf128(__x); }
constexpr long
lrint(_Float128 __x)
{ return __builtin_lrintf128(__x); }
constexpr long
lround(_Float128 __x)
{ return __builtin_lroundf128(__x); }
constexpr _Float128
nearbyint(_Float128 __x)
{ return __builtin_nearbyintf128(__x); }
constexpr _Float128
nextafter(_Float128 __x, _Float128 __y)
{ return __builtin_nextafterf128(__x, __y); }
constexpr _Float128
remainder(_Float128 __x, _Float128 __y)
{ return __builtin_remainderf128(__x, __y); }
inline _Float128
remquo(_Float128 __x, _Float128 __y, int* __pquo)
{ return __builtin_remquof128(__x, __y, __pquo); }
constexpr _Float128
rint(_Float128 __x)
{ return __builtin_rintf128(__x); }
constexpr _Float128
round(_Float128 __x)
{ return __builtin_roundf128(__x); }
constexpr _Float128
scalbln(_Float128 __x, long __ex)
{ return __builtin_scalblnf128(__x, __ex); }
constexpr _Float128
scalbn(_Float128 __x, int __ex)
{ return __builtin_scalbnf128(__x, __ex); }
constexpr _Float128
tgamma(_Float128 __x)
{ return __builtin_tgammaf128(__x); }
constexpr _Float128
trunc(_Float128 __x)
{ return __builtin_truncf128(__x); }
#endif
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
constexpr __gnu_cxx::__bfloat16_t
acosh(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_acoshf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
asinh(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_asinhf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
atanh(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_atanhf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
cbrt(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_cbrtf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
copysign(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_copysignf(__x, __y)); }
constexpr __gnu_cxx::__bfloat16_t
erf(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_erff(__x)); }
constexpr __gnu_cxx::__bfloat16_t
erfc(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_erfcf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
exp2(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_exp2f(__x)); }
constexpr __gnu_cxx::__bfloat16_t
expm1(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_expm1f(__x)); }
constexpr __gnu_cxx::__bfloat16_t
fdim(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_fdimf(__x, __y)); }
constexpr __gnu_cxx::__bfloat16_t
fma(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __z)
{ return __gnu_cxx::__bfloat16_t(__builtin_fmaf(__x, __y, __z)); }
constexpr __gnu_cxx::__bfloat16_t
fmax(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_fmaxf(__x, __y)); }
constexpr __gnu_cxx::__bfloat16_t
fmin(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_fminf(__x, __y)); }
constexpr __gnu_cxx::__bfloat16_t
hypot(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_hypotf(__x, __y)); }
constexpr int
ilogb(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_ilogbf(__x); }
constexpr __gnu_cxx::__bfloat16_t
lgamma(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_lgammaf(__x)); }
constexpr long long
llrint(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_llrintf(__x); }
constexpr long long
llround(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_llroundf(__x); }
constexpr __gnu_cxx::__bfloat16_t
log1p(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_log1pf(__x)); }
// DR 568.
constexpr __gnu_cxx::__bfloat16_t
log2(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_log2f(__x)); }
constexpr __gnu_cxx::__bfloat16_t
logb(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_logbf(__x)); }
constexpr long
lrint(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_lrintf(__x); }
constexpr long
lround(__gnu_cxx::__bfloat16_t __x)
{ return __builtin_lroundf(__x); }
constexpr __gnu_cxx::__bfloat16_t
nearbyint(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_nearbyintf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
nextafter(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{
#if __cpp_if_consteval >= 202106L
// Can't use if (std::__is_constant_evaluated()) here, as it
// doesn't guarantee optimizing the body away at -O0 and
// nothing defines nextafterf16b.
if consteval { return __builtin_nextafterf16b(__x, __y); }
#endif
#ifdef __INT16_TYPE__
using __bfloat16_int_type = __INT16_TYPE__;
#else
using __bfloat16_int_type = short int;
#endif
__bfloat16_int_type __hx, __hy, __ix, __iy;
__builtin_memcpy(&__hx, &__x, sizeof(__x));
__builtin_memcpy(&__hy, &__y, sizeof(__x));
__ix = __hx & 0x7fff; // |x|
__iy = __hy & 0x7fff; // |y|
if (__ix > 0x7f80 || __iy > 0x7f80) // x or y is NaN
return __x + __y;
if (__x == __y)
return __y; // x == y, return y
if (__ix == 0) // x == 0
{
__hy = (__hy & 0x8000) | 1; // return +-__BFLT16_DENORM_MIN__
__builtin_memcpy(&__x, &__hy, sizeof(__x));
__builtin_nextafterf(0.0f, 1.0f); // raise underflow
return __x;
}
if (__hx >= 0) // x > 0
{
if (__hx > __hy) // x > y, x -= ulp
--__hx;
else // x < y, x += ulp
++__hx;
}
else // x < 0
{
if (__hy >= 0 || __hx > __hy) // x < y, x -= ulp
--__hx;
else // x > y, x += ulp
++__hx;
}
__hy = __hx & 0x7f80;
if (__hy >= 0x7f80)
__builtin_nextafterf(__FLT_MAX__, __builtin_inff()); // overflow
else if (__hy < 0x0080)
__builtin_nextafterf(__FLT_MIN__, 0.0f); // underflow
__builtin_memcpy(&__x, &__hx, sizeof(__x));
return __x;
}
constexpr __gnu_cxx::__bfloat16_t
remainder(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
{ return __gnu_cxx::__bfloat16_t(__builtin_remainderf(__x, __y)); }
inline __gnu_cxx::__bfloat16_t
remquo(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, int* __pquo)
{ return __gnu_cxx::__bfloat16_t(__builtin_remquof(__x, __y, __pquo)); }
constexpr __gnu_cxx::__bfloat16_t
rint(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_rintf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
round(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_roundf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
scalbln(__gnu_cxx::__bfloat16_t __x, long __ex)
{ return __gnu_cxx::__bfloat16_t(__builtin_scalblnf(__x, __ex)); }
constexpr __gnu_cxx::__bfloat16_t
scalbn(__gnu_cxx::__bfloat16_t __x, int __ex)
{ return __gnu_cxx::__bfloat16_t(__builtin_scalbnf(__x, __ex)); }
constexpr __gnu_cxx::__bfloat16_t
tgamma(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_tgammaf(__x)); }
constexpr __gnu_cxx::__bfloat16_t
trunc(__gnu_cxx::__bfloat16_t __x)
{ return __gnu_cxx::__bfloat16_t(__builtin_truncf(__x)); }
#endif
#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
template<typename _Tp, typename _Up>
constexpr 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));
}
template<typename _Tp, typename _Up>
constexpr 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));
}
template<typename _Tp, typename _Up>
constexpr 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));
}
template<typename _Tp, typename _Up>
constexpr 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));
}
template<typename _Tp, typename _Up>
constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
hypot(_Tp __x, _Up __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return hypot(__type(__x), __type(__y));
}
template<typename _Tp, typename _Up>
constexpr 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));
}
template<typename _Tp, typename _Up>
constexpr 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));
}
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);
}
template<typename _Tp, typename _Up, typename _Vp>
constexpr 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));
}
#endif
#endif // _GLIBCXX_USE_C99_MATH_FUNCS
#endif // C++11
#ifdef __cpp_lib_hypot // C++ >= 17 && HOSTED
// [c.math.hypot3], three-dimensional hypotenuse
template<typename _Tp>
inline _Tp
__hypot3(_Tp __x, _Tp __y, _Tp __z)
{
__x = std::abs(__x);
__y = std::abs(__y);
__z = std::abs(__z);
if (_Tp __a = __x < __y ? __y < __z ? __z : __y : __x < __z ? __z : __x)
return __a * std::sqrt((__x / __a) * (__x / __a)
+ (__y / __a) * (__y / __a)
+ (__z / __a) * (__z / __a));
else
return {};
}
inline float
hypot(float __x, float __y, float __z)
{ return std::__hypot3<float>(__x, __y, __z); }
inline double
hypot(double __x, double __y, double __z)
{ return std::__hypot3<double>(__x, __y, __z); }
inline long double
hypot(long double __x, long double __y, long double __z)
{ return std::__hypot3<long double>(__x, __y, __z); }
template<typename _Tp, typename _Up, typename _Vp>
typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
hypot(_Tp __x, _Up __y, _Vp __z)
{
using __type = typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type;
return std::__hypot3<__type>(__x, __y, __z);
}
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
inline _Float16
hypot(_Float16 __x, _Float16 __y, _Float16 __z)
{ return std::__hypot3<_Float16>(__x, __y, __z); }
#endif
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
inline _Float32
hypot(_Float32 __x, _Float32 __y, _Float32 __z)
{ return std::__hypot3<_Float32>(__x, __y, __z); }
#endif
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
inline _Float64
hypot(_Float64 __x, _Float64 __y, _Float64 __z)
{ return std::__hypot3<_Float64>(__x, __y, __z); }
#endif
#if defined(__STDCPP_FLOAT128_T__) \
&& (defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128) \
|| defined(_GLIBCXX_HAVE_FLOAT128_MATH))
inline _Float128
hypot(_Float128 __x, _Float128 __y, _Float128 __z)
{ return std::__hypot3<_Float128>(__x, __y, __z); }
#endif
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
inline __gnu_cxx::__bfloat16_t
hypot(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __z)
{ return std::__hypot3<__gnu_cxx::__bfloat16_t>(__x, __y, __z); }
#endif
#endif // __cpp_lib_hypot
#ifdef __cpp_lib_interpolate // C++ >= 20
// linear interpolation
template<typename _Fp>
constexpr _Fp
__lerp(_Fp __a, _Fp __b, _Fp __t) noexcept
{
if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
return __t * __b + (1 - __t) * __a;
if (__t == 1)
return __b; // exact
// Exact at __t=0, monotonic except near __t=1,
// bounded, determinate, and consistent:
const _Fp __x = __a + __t * (__b - __a);
return (__t > 1) == (__b > __a)
? (__b < __x ? __x : __b)
: (__b > __x ? __x : __b); // monotonic near __t=1
}
constexpr float
lerp(float __a, float __b, float __t) noexcept
{ return std::__lerp(__a, __b, __t); }
constexpr double
lerp(double __a, double __b, double __t) noexcept
{ return std::__lerp(__a, __b, __t); }
constexpr long double
lerp(long double __a, long double __b, long double __t) noexcept
{ return std::__lerp(__a, __b, __t); }
template<typename _Tp, typename _Up, typename _Vp>
constexpr __gnu_cxx::__promoted_t<_Tp, _Up, _Vp>
lerp(_Tp __x, _Up __y, _Vp __z) noexcept
{
using __type = __gnu_cxx::__promoted_t<_Tp, _Up, _Vp>;
return std::__lerp<__type>(__x, __y, __z);
}
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
inline _Float16
lerp(_Float16 __x, _Float16 __y, _Float16 __z) noexcept
{ return std::__lerp<_Float16>(__x, __y, __z); }
#endif
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
inline _Float32
lerp(_Float32 __x, _Float32 __y, _Float32 __z) noexcept
{ return std::__lerp<_Float32>(__x, __y, __z); }
#endif
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
inline _Float64
lerp(_Float64 __x, _Float64 __y, _Float64 __z) noexcept
{ return std::__lerp<_Float64>(__x, __y, __z); }
#endif
#if defined(__STDCPP_FLOAT128_T__) \
&& (defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128) \
|| defined(_GLIBCXX_HAVE_FLOAT128_MATH))
inline _Float128
lerp(_Float128 __x, _Float128 __y, _Float128 __z) noexcept
{ return std::__lerp<_Float128>(__x, __y, __z); }
#endif
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
inline __gnu_cxx::__bfloat16_t
lerp(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __z) noexcept
{ return std::__lerp<__gnu_cxx::__bfloat16_t>(__x, __y, __z); }
#endif
#endif // __cpp_lib_interpolate
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
#if _GLIBCXX_USE_STD_SPEC_FUNCS
# include <bits/specfun.h>
#endif
} // extern "C++"
#endif
requires_hosted.h
specfun.h
std_abs.h
version.h
cpp_type_traits.h
c++config.h
type_traits.h
std::log10
complex< _Tp > log10(const complex< _Tp > &)
Return complex base 10 logarithm of z.
Definition complex:1095
std::sin
complex< _Tp > sin(const complex< _Tp > &)
Return complex sine of z.
Definition complex:1121
std::log
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition complex:1086
std::tan
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition complex:1222
std::abs
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition complex:892
std::exp
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition complex:1059
std::cosh
complex< _Tp > cosh(const complex< _Tp > &)
Return complex hyperbolic cosine of z.
Definition complex:1033
std::tanh
complex< _Tp > tanh(const complex< _Tp > &)
Return complex hyperbolic tangent of z.
Definition complex:1250
std::pow
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
Definition complex:1285
std::sinh
complex< _Tp > sinh(const complex< _Tp > &)
Return complex hyperbolic sine of z.
Definition complex:1151
std::cos
complex< _Tp > cos(const complex< _Tp > &)
Return complex cosine of z.
Definition complex:1003
std::sqrt
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition complex:1195
std
ISO C++ entities toplevel namespace is std.
std::fabs
_Tp fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
Definition complex:2429