（cmath）关于头文件cmath

关于头文件cmath

// -*- C++ -*- C forwarding header.

// Copyright (C) 1997-2014 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/c++config.h>
#include <bits/cpp_type_traits.h>
#include <ext/type_traits.h>
#include <math.h>

#ifndef _GLIBCXX_CMATH
#define _GLIBCXX_CMATH 1

// Get rid of those macros defined in <math.h> in lieu of real functions.
#undef abs
#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

namespace std _GLIBCXX_VISIBILITY(default) {
    _GLIBCXX_BEGIN_NAMESPACE_VERSION

#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
    inline _GLIBCXX_CONSTEXPR double
    abs(double __x) {
        return __builtin_fabs(__x);
    }
#endif

#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
    inline _GLIBCXX_CONSTEXPR float
    abs(float __x) {
        return __builtin_fabsf(__x);
    }

    inline _GLIBCXX_CONSTEXPR long double
    abs(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
    abs(_Tp __x) {
        return __builtin_fabs(__x);
    }

    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

    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));
    }

    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

    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));
    }

    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

    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));
    }

    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);
    }

    _GLIBCXX_END_NAMESPACE_VERSION
} // namespace

#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

namespace std _GLIBCXX_VISIBILITY(default) {
    _GLIBCXX_BEGIN_NAMESPACE_VERSION

#if __cplusplus >= 201103L
    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);
    }

    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;
    }

    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);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              bool>::__type
    isfinite(_Tp __x) {
        return true;
    }

    constexpr bool
    isinf(float __x) {
        return __builtin_isinf(__x);
    }

    constexpr bool
    isinf(double __x) {
        return __builtin_isinf(__x);
    }

    constexpr bool
    isinf(long double __x) {
        return __builtin_isinf(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              bool>::__type
    isinf(_Tp __x) {
        return false;
    }

    constexpr bool
    isnan(float __x) {
        return __builtin_isnan(__x);
    }

    constexpr bool
    isnan(double __x) {
        return __builtin_isnan(__x);
    }

    constexpr bool
    isnan(long double __x) {
        return __builtin_isnan(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              bool>::__type
    isnan(_Tp __x) {
        return false;
    }

    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);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              bool>::__type
    isnormal(_Tp __x) {
        return __x != 0 ? true : false;
    }

    // The front-end doesn't provide a type generic builtin (libstdc++/58625).
    constexpr bool
    signbit(float __x) {
        return __builtin_signbitf(__x);
    }

    constexpr bool
    signbit(double __x) {
        return __builtin_signbit(__x);
    }

    constexpr bool
    signbit(long double __x) {
        return __builtin_signbitl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              bool>::__type
    signbit(_Tp __x) {
        return __x < 0 ? true : false;
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

#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

    _GLIBCXX_END_NAMESPACE_VERSION
} // namespace

#endif /* _GLIBCXX_USE_C99_FP_MACROS_DYNAMIC */
#endif

#if __cplusplus >= 201103L

#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

namespace std _GLIBCXX_VISIBILITY(default) {
    _GLIBCXX_BEGIN_NAMESPACE_VERSION

    // 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;

    /// Additional overloads.
    constexpr float
    acosh(float __x) {
        return __builtin_acoshf(__x);
    }

    constexpr long double
    acosh(long double __x) {
        return __builtin_acoshl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    acosh(_Tp __x) {
        return __builtin_acosh(__x);
    }

    constexpr float
    asinh(float __x) {
        return __builtin_asinhf(__x);
    }

    constexpr long double
    asinh(long double __x) {
        return __builtin_asinhl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    asinh(_Tp __x) {
        return __builtin_asinh(__x);
    }

    constexpr float
    atanh(float __x) {
        return __builtin_atanhf(__x);
    }

    constexpr long double
    atanh(long double __x) {
        return __builtin_atanhl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    atanh(_Tp __x) {
        return __builtin_atanh(__x);
    }

    constexpr float
    cbrt(float __x) {
        return __builtin_cbrtf(__x);
    }

    constexpr long double
    cbrt(long double __x) {
        return __builtin_cbrtl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    cbrt(_Tp __x) {
        return __builtin_cbrt(__x);
    }

    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);
    }

    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));
    }

    constexpr float
    erf(float __x) {
        return __builtin_erff(__x);
    }

    constexpr long double
    erf(long double __x) {
        return __builtin_erfl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    erf(_Tp __x) {
        return __builtin_erf(__x);
    }

    constexpr float
    erfc(float __x) {
        return __builtin_erfcf(__x);
    }

    constexpr long double
    erfc(long double __x) {
        return __builtin_erfcl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    erfc(_Tp __x) {
        return __builtin_erfc(__x);
    }

    constexpr float
    exp2(float __x) {
        return __builtin_exp2f(__x);
    }

    constexpr long double
    exp2(long double __x) {
        return __builtin_exp2l(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    exp2(_Tp __x) {
        return __builtin_exp2(__x);
    }

    constexpr float
    expm1(float __x) {
        return __builtin_expm1f(__x);
    }

    constexpr long double
    expm1(long double __x) {
        return __builtin_expm1l(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    expm1(_Tp __x) {
        return __builtin_expm1(__x);
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    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);
    }

    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));
    }

    constexpr int
    ilogb(float __x) {
        return __builtin_ilogbf(__x);
    }

    constexpr int
    ilogb(long double __x) {
        return __builtin_ilogbl(__x);
    }

    template<typename _Tp>
    constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
             int>::__type
    ilogb(_Tp __x) {
        return __builtin_ilogb(__x);
    }

    constexpr float
    lgamma(float __x) {
        return __builtin_lgammaf(__x);
    }

    constexpr long double
    lgamma(long double __x) {
        return __builtin_lgammal(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    lgamma(_Tp __x) {
        return __builtin_lgamma(__x);
    }

    constexpr long long
    llrint(float __x) {
        return __builtin_llrintf(__x);
    }

    constexpr long long
    llrint(long double __x) {
        return __builtin_llrintl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              long long>::__type
    llrint(_Tp __x) {
        return __builtin_llrint(__x);
    }

    constexpr long long
    llround(float __x) {
        return __builtin_llroundf(__x);
    }

    constexpr long long
    llround(long double __x) {
        return __builtin_llroundl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              long long>::__type
    llround(_Tp __x) {
        return __builtin_llround(__x);
    }

    constexpr float
    log1p(float __x) {
        return __builtin_log1pf(__x);
    }

    constexpr long double
    log1p(long double __x) {
        return __builtin_log1pl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    log1p(_Tp __x) {
        return __builtin_log1p(__x);
    }

    // DR 568.
    constexpr float
    log2(float __x) {
        return __builtin_log2f(__x);
    }

    constexpr long double
    log2(long double __x) {
        return __builtin_log2l(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    log2(_Tp __x) {
        return __builtin_log2(__x);
    }

    constexpr float
    logb(float __x) {
        return __builtin_logbf(__x);
    }

    constexpr long double
    logb(long double __x) {
        return __builtin_logbl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    logb(_Tp __x) {
        return __builtin_logb(__x);
    }

    constexpr long
    lrint(float __x) {
        return __builtin_lrintf(__x);
    }

    constexpr long
    lrint(long double __x) {
        return __builtin_lrintl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              long>::__type
    lrint(_Tp __x) {
        return __builtin_lrint(__x);
    }

    constexpr long
    lround(float __x) {
        return __builtin_lroundf(__x);
    }

    constexpr long
    lround(long double __x) {
        return __builtin_lroundl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              long>::__type
    lround(_Tp __x) {
        return __builtin_lround(__x);
    }

    constexpr float
    nearbyint(float __x) {
        return __builtin_nearbyintf(__x);
    }

    constexpr long double
    nearbyint(long double __x) {
        return __builtin_nearbyintl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    nearbyint(_Tp __x) {
        return __builtin_nearbyint(__x);
    }

    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);
    }

    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));
    }

    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);
    }

    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);
    }

    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);
    }

    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));
    }

    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);
    }

    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);
    }

    constexpr float
    rint(float __x) {
        return __builtin_rintf(__x);
    }

    constexpr long double
    rint(long double __x) {
        return __builtin_rintl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    rint(_Tp __x) {
        return __builtin_rint(__x);
    }

    constexpr float
    round(float __x) {
        return __builtin_roundf(__x);
    }

    constexpr long double
    round(long double __x) {
        return __builtin_roundl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    round(_Tp __x) {
        return __builtin_round(__x);
    }

    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);
    }

    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);
    }

    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);
    }

    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);
    }

    constexpr float
    tgamma(float __x) {
        return __builtin_tgammaf(__x);
    }

    constexpr long double
    tgamma(long double __x) {
        return __builtin_tgammal(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    tgamma(_Tp __x) {
        return __builtin_tgamma(__x);
    }

    constexpr float
    trunc(float __x) {
        return __builtin_truncf(__x);
    }

    constexpr long double
    trunc(long double __x) {
        return __builtin_truncl(__x);
    }

    template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
              double>::__type
    trunc(_Tp __x) {
        return __builtin_trunc(__x);
    }

    _GLIBCXX_END_NAMESPACE_VERSION
} // namespace

#endif // _GLIBCXX_USE_C99_MATH_TR1

#endif // C++11

#endif