// -*- C++ -*-

//===----------------------------------------------------------------------===//

//

// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.

// See https://llvm.org/LICENSE.txt for license information.

// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

//

//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_MATH_H

#define _LIBCPP_MATH_H

/*

    math.h synopsis

Macros:

    HUGE_VAL

    HUGE_VALF               // C99

    HUGE_VALL               // C99

    INFINITY                // C99

    NAN                     // C99

    FP_INFINITE             // C99

    FP_NAN                  // C99

    FP_NORMAL               // C99

    FP_SUBNORMAL            // C99

    FP_ZERO                 // C99

    FP_FAST_FMA             // C99

    FP_FAST_FMAF            // C99

    FP_FAST_FMAL            // C99

    FP_ILOGB0               // C99

    FP_ILOGBNAN             // C99

    MATH_ERRNO              // C99

    MATH_ERREXCEPT          // C99

    math_errhandling        // C99

Types:

    float_t                 // C99

    double_t                // C99

// C90

floating_point abs(floating_point x);

floating_point acos (arithmetic x);

float          acosf(float x);

long double    acosl(long double x);

floating_point asin (arithmetic x);

float          asinf(float x);

long double    asinl(long double x);

floating_point atan (arithmetic x);

float          atanf(float x);

long double    atanl(long double x);

floating_point atan2 (arithmetic y, arithmetic x);

float          atan2f(float y, float x);

long double    atan2l(long double y, long double x);

floating_point ceil (arithmetic x);

float          ceilf(float x);

long double    ceill(long double x);

floating_point cos (arithmetic x);

float          cosf(float x);

long double    cosl(long double x);

floating_point cosh (arithmetic x);

float          coshf(float x);

long double    coshl(long double x);

floating_point exp (arithmetic x);

float          expf(float x);

long double    expl(long double x);

floating_point fabs (arithmetic x);

float          fabsf(float x);

long double    fabsl(long double x);

floating_point floor (arithmetic x);

float          floorf(float x);

long double    floorl(long double x);

floating_point fmod (arithmetic x, arithmetic y);

float          fmodf(float x, float y);

long double    fmodl(long double x, long double y);

floating_point frexp (arithmetic value, int* exp);

float          frexpf(float value, int* exp);

long double    frexpl(long double value, int* exp);

floating_point ldexp (arithmetic value, int exp);

float          ldexpf(float value, int exp);

long double    ldexpl(long double value, int exp);

floating_point log (arithmetic x);

float          logf(float x);

long double    logl(long double x);

floating_point log10 (arithmetic x);

float          log10f(float x);

long double    log10l(long double x);

floating_point modf (floating_point value, floating_point* iptr);

float          modff(float value, float* iptr);

long double    modfl(long double value, long double* iptr);

floating_point pow (arithmetic x, arithmetic y);

float          powf(float x, float y);

long double    powl(long double x, long double y);

floating_point sin (arithmetic x);

float          sinf(float x);

long double    sinl(long double x);

floating_point sinh (arithmetic x);

float          sinhf(float x);

long double    sinhl(long double x);

floating_point sqrt (arithmetic x);

float          sqrtf(float x);

long double    sqrtl(long double x);

floating_point tan (arithmetic x);

float          tanf(float x);

long double    tanl(long double x);

floating_point tanh (arithmetic x);

float          tanhf(float x);

long double    tanhl(long double x);

//  C99

bool signbit(arithmetic x);

int fpclassify(arithmetic x);

bool isfinite(arithmetic x);

bool isinf(arithmetic x);

bool isnan(arithmetic x);

bool isnormal(arithmetic x);

bool isgreater(arithmetic x, arithmetic y);

bool isgreaterequal(arithmetic x, arithmetic y);

bool isless(arithmetic x, arithmetic y);

bool islessequal(arithmetic x, arithmetic y);

bool islessgreater(arithmetic x, arithmetic y);

bool isunordered(arithmetic x, arithmetic y);

floating_point acosh (arithmetic x);

float          acoshf(float x);

long double    acoshl(long double x);

floating_point asinh (arithmetic x);

float          asinhf(float x);

long double    asinhl(long double x);

floating_point atanh (arithmetic x);

float          atanhf(float x);

long double    atanhl(long double x);

floating_point cbrt (arithmetic x);

float          cbrtf(float x);

long double    cbrtl(long double x);

floating_point copysign (arithmetic x, arithmetic y);

float          copysignf(float x, float y);

long double    copysignl(long double x, long double y);

floating_point erf (arithmetic x);

float          erff(float x);

long double    erfl(long double x);

floating_point erfc (arithmetic x);

float          erfcf(float x);

long double    erfcl(long double x);

floating_point exp2 (arithmetic x);

float          exp2f(float x);

long double    exp2l(long double x);

floating_point expm1 (arithmetic x);

float          expm1f(float x);

long double    expm1l(long double x);

floating_point fdim (arithmetic x, arithmetic y);

float          fdimf(float x, float y);

long double    fdiml(long double x, long double y);

floating_point fma (arithmetic x, arithmetic y, arithmetic z);

float          fmaf(float x, float y, float z);

long double    fmal(long double x, long double y, long double z);

floating_point fmax (arithmetic x, arithmetic y);

float          fmaxf(float x, float y);

long double    fmaxl(long double x, long double y);

floating_point fmin (arithmetic x, arithmetic y);

float          fminf(float x, float y);

long double    fminl(long double x, long double y);

floating_point hypot (arithmetic x, arithmetic y);

float          hypotf(float x, float y);

long double    hypotl(long double x, long double y);

int ilogb (arithmetic x);

int ilogbf(float x);

int ilogbl(long double x);

floating_point lgamma (arithmetic x);

float          lgammaf(float x);

long double    lgammal(long double x);

long long llrint (arithmetic x);

long long llrintf(float x);

long long llrintl(long double x);

long long llround (arithmetic x);

long long llroundf(float x);

long long llroundl(long double x);

floating_point log1p (arithmetic x);

float          log1pf(float x);

long double    log1pl(long double x);

floating_point log2 (arithmetic x);

float          log2f(float x);

long double    log2l(long double x);

floating_point logb (arithmetic x);

float          logbf(float x);

long double    logbl(long double x);

long lrint (arithmetic x);

long lrintf(float x);

long lrintl(long double x);

long lround (arithmetic x);

long lroundf(float x);

long lroundl(long double x);

double      nan (const char* str);

float       nanf(const char* str);

long double nanl(const char* str);

floating_point nearbyint (arithmetic x);

float          nearbyintf(float x);

long double    nearbyintl(long double x);

floating_point nextafter (arithmetic x, arithmetic y);

float          nextafterf(float x, float y);

long double    nextafterl(long double x, long double y);

floating_point nexttoward (arithmetic x, long double y);

float          nexttowardf(float x, long double y);

long double    nexttowardl(long double x, long double y);

floating_point remainder (arithmetic x, arithmetic y);

float          remainderf(float x, float y);

long double    remainderl(long double x, long double y);

floating_point remquo (arithmetic x, arithmetic y, int* pquo);

float          remquof(float x, float y, int* pquo);

long double    remquol(long double x, long double y, int* pquo);

floating_point rint (arithmetic x);

float          rintf(float x);

long double    rintl(long double x);

floating_point round (arithmetic x);

float          roundf(float x);

long double    roundl(long double x);

floating_point scalbln (arithmetic x, long ex);

float          scalblnf(float x, long ex);

long double    scalblnl(long double x, long ex);

floating_point scalbn (arithmetic x, int ex);

float          scalbnf(float x, int ex);

long double    scalbnl(long double x, int ex);

floating_point tgamma (arithmetic x);

float          tgammaf(float x);

long double    tgammal(long double x);

floating_point trunc (arithmetic x);

float          truncf(float x);

long double    truncl(long double x);

*/

#include <__config>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

#  pragma GCC system_header

#endif

#  if __has_include_next(<math.h>)

#    include_next <math.h>

#  endif

#ifdef __cplusplus

// We support including .h headers inside 'extern "C"' contexts, so switch

// back to C++ linkage before including these C++ headers.

extern "C++" {

#include <__type_traits/enable_if.h>

#include <__type_traits/is_floating_point.h>

#include <__type_traits/is_integral.h>

#include <__type_traits/is_same.h>

#include <__type_traits/promote.h>

#include <limits>

#include <stdlib.h>

#    ifdef fpclassify

#      undef fpclassify

#    endif

#    ifdef signbit

#      undef signbit

#    endif

#    ifdef isfinite

#      undef isfinite

#    endif

#    ifdef isinf

#      undef isinf

#    endif

#    ifdef isnan

#      undef isnan

#    endif

#    ifdef isnormal

#      undef isnormal

#    endif

#    ifdef isgreater

#      undef isgreater

#    endif

#    ifdef isgreaterequal

#      undef isgreaterequal

#    endif

#    ifdef isless

#      undef isless

#    endif

#    ifdef islessequal

#      undef islessequal

#    endif

#    ifdef islessgreater

#      undef islessgreater

#    endif

#    ifdef isunordered

#      undef isunordered

#    endif

// signbit

template <class _A1, std::__enable_if_t<std::is_floating_point<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool signbit(_A1 __x) _NOEXCEPT {

  return __builtin_signbit(__x);

}

template <class _A1, std::__enable_if_t<std::is_integral<_A1>::value && std::is_signed<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool signbit(_A1 __x) _NOEXCEPT {

  return __x < 0;

}

template <class _A1, std::__enable_if_t<std::is_integral<_A1>::value && !std::is_signed<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool signbit(_A1) _NOEXCEPT {

  return false;

}

// fpclassify

template <class _A1, std::__enable_if_t<std::is_floating_point<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI int fpclassify(_A1 __x) _NOEXCEPT {

  return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, __x);

}

template <class _A1, std::__enable_if_t<std::is_integral<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI int fpclassify(_A1 __x) _NOEXCEPT {

  return __x == 0 ? FP_ZERO : FP_NORMAL;

}

// The MSVC runtime already provides these functions as templates

#ifndef _LIBCPP_MSVCRT

// isfinite

template <class _A1,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::numeric_limits<_A1>::has_infinity, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isfinite(_A1 __x) _NOEXCEPT {

  return __builtin_isfinite((typename std::__promote<_A1>::type)__x);

}

template <class _A1,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && !std::numeric_limits<_A1>::has_infinity, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isfinite(_A1) _NOEXCEPT {

  return true;

}

// isinf

template <class _A1,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::numeric_limits<_A1>::has_infinity, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isinf(_A1 __x) _NOEXCEPT {

  return __builtin_isinf((typename std::__promote<_A1>::type)__x);

}

template <class _A1>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI

    typename std::enable_if< std::is_arithmetic<_A1>::value && !std::numeric_limits<_A1>::has_infinity, bool>::type

    isinf(_A1) _NOEXCEPT {

  return false;

}

#      ifdef _LIBCPP_PREFERRED_OVERLOAD

_LIBCPP_NODISCARD_EXT inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isinf(float __x) _NOEXCEPT {

  return __builtin_isinf(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI _LIBCPP_PREFERRED_OVERLOAD bool isinf(double __x) _NOEXCEPT {

  return __builtin_isinf(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isinf(long double __x) _NOEXCEPT {

  return __builtin_isinf(__x);

}

#      endif

// isnan

template <class _A1, std::__enable_if_t<std::is_floating_point<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnan(_A1 __x) _NOEXCEPT {

  return __builtin_isnan(__x);

}

template <class _A1, std::__enable_if_t<std::is_integral<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnan(_A1) _NOEXCEPT {

  return false;

}

#      ifdef _LIBCPP_PREFERRED_OVERLOAD

_LIBCPP_NODISCARD_EXT inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnan(float __x) _NOEXCEPT {

  return __builtin_isnan(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI _LIBCPP_PREFERRED_OVERLOAD bool isnan(double __x) _NOEXCEPT {

  return __builtin_isnan(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnan(long double __x) _NOEXCEPT {

  return __builtin_isnan(__x);

}

#      endif

// isnormal

template <class _A1, std::__enable_if_t<std::is_floating_point<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(_A1 __x) _NOEXCEPT {

  return __builtin_isnormal(__x);

}

template <class _A1, std::__enable_if_t<std::is_integral<_A1>::value, int> = 0>

_LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(_A1 __x) _NOEXCEPT {

  return __x != 0;

}

// isgreater

template <class _A1,

          class _A2,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool isgreater(_A1 __x, _A2 __y) _NOEXCEPT {

  typedef typename std::__promote<_A1, _A2>::type type;

  return __builtin_isgreater((type)__x, (type)__y);

}

// isgreaterequal

template <class _A1,

          class _A2,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool isgreaterequal(_A1 __x, _A2 __y) _NOEXCEPT {

  typedef typename std::__promote<_A1, _A2>::type type;

  return __builtin_isgreaterequal((type)__x, (type)__y);

}

// isless

template <class _A1,

          class _A2,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool isless(_A1 __x, _A2 __y) _NOEXCEPT {

  typedef typename std::__promote<_A1, _A2>::type type;

  return __builtin_isless((type)__x, (type)__y);

}

// islessequal

template <class _A1,

          class _A2,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool islessequal(_A1 __x, _A2 __y) _NOEXCEPT {

  typedef typename std::__promote<_A1, _A2>::type type;

  return __builtin_islessequal((type)__x, (type)__y);

}

// islessgreater

template <class _A1,

          class _A2,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool islessgreater(_A1 __x, _A2 __y) _NOEXCEPT {

  typedef typename std::__promote<_A1, _A2>::type type;

  return __builtin_islessgreater((type)__x, (type)__y);

}

// isunordered

template <class _A1,

          class _A2,

          std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value, int> = 0>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI bool isunordered(_A1 __x, _A2 __y) _NOEXCEPT {

  typedef typename std::__promote<_A1, _A2>::type type;

  return __builtin_isunordered((type)__x, (type)__y);

}

#endif // _LIBCPP_MSVCRT

// abs

//

// handled in stdlib.h

// div

//

// handled in stdlib.h

// We have to provide double overloads for <math.h> to work on platforms that don't provide the full set of math

// functions. To make the overload set work with multiple functions that take the same arguments, we make our overloads

// templates. Functions are preferred over function templates during overload resolution, which means that our overload

// will only be selected when the C library doesn't provide one.

// acos

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       acos(float __x) _NOEXCEPT       {return __builtin_acosf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double acos(double __x) _NOEXCEPT {

  return __builtin_acos(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double acos(long double __x) _NOEXCEPT {return __builtin_acosl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

acos(_A1 __x) _NOEXCEPT {return __builtin_acos((double)__x);}

// asin

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       asin(float __x) _NOEXCEPT       {return __builtin_asinf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double asin(double __x) _NOEXCEPT {

  return __builtin_asin(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double asin(long double __x) _NOEXCEPT {return __builtin_asinl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

asin(_A1 __x) _NOEXCEPT {return __builtin_asin((double)__x);}

// atan

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       atan(float __x) _NOEXCEPT       {return __builtin_atanf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double atan(double __x) _NOEXCEPT {

  return __builtin_atan(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double atan(long double __x) _NOEXCEPT {return __builtin_atanl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

atan(_A1 __x) _NOEXCEPT {return __builtin_atan((double)__x);}

// atan2

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       atan2(float __y, float __x) _NOEXCEPT             {return __builtin_atan2f(__y, __x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double atan2(double __x, double __y) _NOEXCEPT {

  return __builtin_atan2(__x, __y);

}

inline _LIBCPP_HIDE_FROM_ABI long double atan2(long double __y, long double __x) _NOEXCEPT {return __builtin_atan2l(__y, __x);}

#    endif

template <class _A1, class _A2>

inline _LIBCPP_HIDE_FROM_ABI

typename std::__enable_if_t

<

    std::is_arithmetic<_A1>::value &&

    std::is_arithmetic<_A2>::value,

    std::__promote<_A1, _A2>

>::type

atan2(_A1 __y, _A2 __x) _NOEXCEPT

{

    typedef typename std::__promote<_A1, _A2>::type __result_type;

    static_assert((!(std::_IsSame<_A1, __result_type>::value &&

                     std::_IsSame<_A2, __result_type>::value)), "");

    return ::atan2((__result_type)__y, (__result_type)__x);

}

// ceil

#    if !defined(__sun__)

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI float       ceil(float __x) _NOEXCEPT       {return __builtin_ceilf(__x);}

template <class = int>

_LIBCPP_NODISCARD_EXT _LIBCPP_HIDE_FROM_ABI double ceil(double __x) _NOEXCEPT {

  return __builtin_ceil(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI long double ceil(long double __x) _NOEXCEPT {return __builtin_ceill(__x);}

#    endif

template <class _A1>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

ceil(_A1 __x) _NOEXCEPT {return __builtin_ceil((double)__x);}

// cos

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       cos(float __x) _NOEXCEPT       {return __builtin_cosf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double cos(double __x) _NOEXCEPT {

  return __builtin_cos(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double cos(long double __x) _NOEXCEPT {return __builtin_cosl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

cos(_A1 __x) _NOEXCEPT {return __builtin_cos((double)__x);}

// cosh

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       cosh(float __x) _NOEXCEPT       {return __builtin_coshf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double cosh(double __x) _NOEXCEPT {

  return __builtin_cosh(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double cosh(long double __x) _NOEXCEPT {return __builtin_coshl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

cosh(_A1 __x) _NOEXCEPT {return __builtin_cosh((double)__x);}

// exp

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       exp(float __x) _NOEXCEPT       {return __builtin_expf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double exp(double __x) _NOEXCEPT {

  return __builtin_exp(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double exp(long double __x) _NOEXCEPT {return __builtin_expl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

exp(_A1 __x) _NOEXCEPT {return __builtin_exp((double)__x);}

// fabs

#    if !defined(__sun__)

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI float       fabs(float __x) _NOEXCEPT       {return __builtin_fabsf(__x);}

template <class = int>

_LIBCPP_NODISCARD_EXT _LIBCPP_HIDE_FROM_ABI double fabs(double __x) _NOEXCEPT {

  return __builtin_fabs(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI long double fabs(long double __x) _NOEXCEPT {return __builtin_fabsl(__x);}

#    endif

template <class _A1>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

fabs(_A1 __x) _NOEXCEPT {return __builtin_fabs((double)__x);}

// floor

#    if !defined(__sun__)

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI float       floor(float __x) _NOEXCEPT       {return __builtin_floorf(__x);}

template <class = int>

_LIBCPP_NODISCARD_EXT _LIBCPP_HIDE_FROM_ABI double floor(double __x) _NOEXCEPT {

  return __builtin_floor(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI long double floor(long double __x) _NOEXCEPT {return __builtin_floorl(__x);}

#    endif

template <class _A1>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

floor(_A1 __x) _NOEXCEPT {return __builtin_floor((double)__x);}

// fmod

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       fmod(float __x, float __y) _NOEXCEPT             {return __builtin_fmodf(__x, __y);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double fmod(double __x, double __y) _NOEXCEPT {

  return __builtin_fmod(__x, __y);

}

inline _LIBCPP_HIDE_FROM_ABI long double fmod(long double __x, long double __y) _NOEXCEPT {return __builtin_fmodl(__x, __y);}

#    endif

template <class _A1, class _A2>

inline _LIBCPP_HIDE_FROM_ABI

typename std::__enable_if_t

<

    std::is_arithmetic<_A1>::value &&

    std::is_arithmetic<_A2>::value,

    std::__promote<_A1, _A2>

>::type

fmod(_A1 __x, _A2 __y) _NOEXCEPT

{

    typedef typename std::__promote<_A1, _A2>::type __result_type;

    static_assert((!(std::_IsSame<_A1, __result_type>::value &&

                     std::_IsSame<_A2, __result_type>::value)), "");

    return ::fmod((__result_type)__x, (__result_type)__y);

}

// frexp

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       frexp(float __x, int* __e) _NOEXCEPT       {return __builtin_frexpf(__x, __e);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double frexp(double __x, int* __e) _NOEXCEPT {

  return __builtin_frexp(__x, __e);

}

inline _LIBCPP_HIDE_FROM_ABI long double frexp(long double __x, int* __e) _NOEXCEPT {return __builtin_frexpl(__x, __e);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

frexp(_A1 __x, int* __e) _NOEXCEPT {return __builtin_frexp((double)__x, __e);}

// ldexp

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       ldexp(float __x, int __e) _NOEXCEPT       {return __builtin_ldexpf(__x, __e);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double ldexp(double __x, int __e) _NOEXCEPT {

  return __builtin_ldexp(__x, __e);

}

inline _LIBCPP_HIDE_FROM_ABI long double ldexp(long double __x, int __e) _NOEXCEPT {return __builtin_ldexpl(__x, __e);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

ldexp(_A1 __x, int __e) _NOEXCEPT {return __builtin_ldexp((double)__x, __e);}

// log

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       log(float __x) _NOEXCEPT       {return __builtin_logf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double log(double __x) _NOEXCEPT {

  return __builtin_log(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double log(long double __x) _NOEXCEPT {return __builtin_logl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

log(_A1 __x) _NOEXCEPT {return __builtin_log((double)__x);}

// log10

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       log10(float __x) _NOEXCEPT       {return __builtin_log10f(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double log10(double __x) _NOEXCEPT {

  return __builtin_log10(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double log10(long double __x) _NOEXCEPT {return __builtin_log10l(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

log10(_A1 __x) _NOEXCEPT {return __builtin_log10((double)__x);}

// modf

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       modf(float __x, float* __y) _NOEXCEPT             {return __builtin_modff(__x, __y);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double modf(double __x, double* __y) _NOEXCEPT {

  return __builtin_modf(__x, __y);

}

inline _LIBCPP_HIDE_FROM_ABI long double modf(long double __x, long double* __y) _NOEXCEPT {return __builtin_modfl(__x, __y);}

#    endif

// pow

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       pow(float __x, float __y) _NOEXCEPT             {return __builtin_powf(__x, __y);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double pow(double __x, double __y) _NOEXCEPT {

  return __builtin_pow(__x, __y);

}

inline _LIBCPP_HIDE_FROM_ABI long double pow(long double __x, long double __y) _NOEXCEPT {return __builtin_powl(__x, __y);}

#    endif

template <class _A1, class _A2>

inline _LIBCPP_HIDE_FROM_ABI

typename std::__enable_if_t

<

    std::is_arithmetic<_A1>::value &&

    std::is_arithmetic<_A2>::value,

    std::__promote<_A1, _A2>

>::type

pow(_A1 __x, _A2 __y) _NOEXCEPT

{

    typedef typename std::__promote<_A1, _A2>::type __result_type;

    static_assert((!(std::_IsSame<_A1, __result_type>::value &&

                     std::_IsSame<_A2, __result_type>::value)), "");

    return ::pow((__result_type)__x, (__result_type)__y);

}

// sin

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       sin(float __x) _NOEXCEPT       {return __builtin_sinf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double sin(double __x) _NOEXCEPT {

  return __builtin_sin(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double sin(long double __x) _NOEXCEPT {return __builtin_sinl(__x);}

#endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

sin(_A1 __x) _NOEXCEPT {return __builtin_sin((double)__x);}

// sinh

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       sinh(float __x) _NOEXCEPT       {return __builtin_sinhf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double sinh(double __x) _NOEXCEPT {

  return __builtin_sinh(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double sinh(long double __x) _NOEXCEPT {return __builtin_sinhl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

sinh(_A1 __x) _NOEXCEPT {return __builtin_sinh((double)__x);}

// sqrt

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       sqrt(float __x) _NOEXCEPT       {return __builtin_sqrtf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double sqrt(double __x) _NOEXCEPT {

  return __builtin_sqrt(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double sqrt(long double __x) _NOEXCEPT {return __builtin_sqrtl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

sqrt(_A1 __x) _NOEXCEPT {return __builtin_sqrt((double)__x);}

// tan

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       tan(float __x) _NOEXCEPT       {return __builtin_tanf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double tan(double __x) _NOEXCEPT {

  return __builtin_tan(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double tan(long double __x) _NOEXCEPT {return __builtin_tanl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

tan(_A1 __x) _NOEXCEPT {return __builtin_tan((double)__x);}

// tanh

#    if !defined(__sun__)

inline _LIBCPP_HIDE_FROM_ABI float       tanh(float __x) _NOEXCEPT       {return __builtin_tanhf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double tanh(double __x) _NOEXCEPT {

  return __builtin_tanh(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double tanh(long double __x) _NOEXCEPT {return __builtin_tanhl(__x);}

#    endif

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

tanh(_A1 __x) _NOEXCEPT {return __builtin_tanh((double)__x);}

// acosh

inline _LIBCPP_HIDE_FROM_ABI float       acosh(float __x) _NOEXCEPT       {return __builtin_acoshf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double acosh(double __x) _NOEXCEPT {

  return __builtin_acosh(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double acosh(long double __x) _NOEXCEPT {return __builtin_acoshl(__x);}

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

acosh(_A1 __x) _NOEXCEPT {return __builtin_acosh((double)__x);}

// asinh

inline _LIBCPP_HIDE_FROM_ABI float       asinh(float __x) _NOEXCEPT       {return __builtin_asinhf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double asinh(double __x) _NOEXCEPT {

  return __builtin_asinh(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double asinh(long double __x) _NOEXCEPT {return __builtin_asinhl(__x);}

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

asinh(_A1 __x) _NOEXCEPT {return __builtin_asinh((double)__x);}

// atanh

inline _LIBCPP_HIDE_FROM_ABI float       atanh(float __x) _NOEXCEPT       {return __builtin_atanhf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double atanh(double __x) _NOEXCEPT {

  return __builtin_atanh(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double atanh(long double __x) _NOEXCEPT {return __builtin_atanhl(__x);}

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

atanh(_A1 __x) _NOEXCEPT {return __builtin_atanh((double)__x);}

// cbrt

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI float       cbrt(float __x) _NOEXCEPT       {return __builtin_cbrtf(__x);}

template <class = int>

_LIBCPP_NODISCARD_EXT _LIBCPP_HIDE_FROM_ABI double cbrt(double __x) _NOEXCEPT {

  return __builtin_cbrt(__x);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI long double cbrt(long double __x) _NOEXCEPT {return __builtin_cbrtl(__x);}

template <class _A1>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

cbrt(_A1 __x) _NOEXCEPT {return __builtin_cbrt((double)__x);}

// copysign

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI float copysign(float __x, float __y) _NOEXCEPT {

  return ::__builtin_copysignf(__x, __y);

}

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI long double copysign(long double __x, long double __y) _NOEXCEPT {

  return ::__builtin_copysignl(__x, __y);

}

template <class _A1, class _A2>

_LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI

typename std::__enable_if_t

<

    std::is_arithmetic<_A1>::value &&

    std::is_arithmetic<_A2>::value,

    std::__promote<_A1, _A2>

>::type

    copysign(_A1 __x, _A2 __y) _NOEXCEPT {

  return ::__builtin_copysign(__x, __y);

}

// erf

inline _LIBCPP_HIDE_FROM_ABI float       erf(float __x) _NOEXCEPT       {return __builtin_erff(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double erf(double __x) _NOEXCEPT {

  return __builtin_erf(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double erf(long double __x) _NOEXCEPT {return __builtin_erfl(__x);}

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

erf(_A1 __x) _NOEXCEPT {return __builtin_erf((double)__x);}

// erfc

inline _LIBCPP_HIDE_FROM_ABI float       erfc(float __x) _NOEXCEPT       {return __builtin_erfcf(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double erfc(double __x) _NOEXCEPT {

  return __builtin_erfc(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double erfc(long double __x) _NOEXCEPT {return __builtin_erfcl(__x);}

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

erfc(_A1 __x) _NOEXCEPT {return __builtin_erfc((double)__x);}

// exp2

inline _LIBCPP_HIDE_FROM_ABI float       exp2(float __x) _NOEXCEPT       {return __builtin_exp2f(__x);}

template <class = int>

_LIBCPP_HIDE_FROM_ABI double exp2(double __x) _NOEXCEPT {

  return __builtin_exp2(__x);

}

inline _LIBCPP_HIDE_FROM_ABI long double exp2(long double __x) _NOEXCEPT {return __builtin_exp2l(__x);}

template <class _A1>

inline _LIBCPP_HIDE_FROM_ABI

typename std::enable_if<std::is_integral<_A1>::value, double>::type

exp2(_A1 __x) _NOEXCEPT {return __builtin_exp2((double)__x);}

// expm1

inline _LIBCPP_HIDE_FROM_ABI float       expm1(float __x) _NOEXCEPT       {return __builtin_expm1f(__x);}