// -*- 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_CMATH

#define _LIBCPP_CMATH

/*

    cmath 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

namespace std

{

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);

double       hypot(double x, double y, double z);                // C++17

float        hypot(float x, float y, float z);                   // C++17

long double  hypot(long double x, long double y, long double z); // C++17

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);

constexpr float       lerp(float a, float b, float t) noexcept;                   // C++20

constexpr double      lerp(double a, double b, double t) noexcept;                // C++20

constexpr long double lerp(long double a, long double b, long double t) noexcept; // C++20

}  // std

*/

#include <__assert> // all public C++ headers provide the assertion handler

#include <__config>

#include <__type_traits/enable_if.h>

#include <__type_traits/is_arithmetic.h>

#include <__type_traits/is_constant_evaluated.h>

#include <__type_traits/is_floating_point.h>

#include <__type_traits/is_same.h>

#include <__type_traits/remove_cv.h>

#include <version>

#include <math.h>

#ifndef _LIBCPP_MATH_H

#   error <cmath> tried including <math.h> but didn't find libc++'s <math.h> header. \

          This usually means that your header search paths are not configured properly. \

          The header search paths should contain the C++ Standard Library headers before \

          any C Standard Library, and you are probably using compiler flags that make that \

          not be the case.

#endif

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

#  pragma GCC system_header

#endif

_LIBCPP_PUSH_MACROS

#include <__undef_macros>

_LIBCPP_BEGIN_NAMESPACE_STD

using ::signbit _LIBCPP_USING_IF_EXISTS;

using ::fpclassify _LIBCPP_USING_IF_EXISTS;

using ::isfinite _LIBCPP_USING_IF_EXISTS;

using ::isinf _LIBCPP_USING_IF_EXISTS;

using ::isnan _LIBCPP_USING_IF_EXISTS;

using ::isnormal _LIBCPP_USING_IF_EXISTS;

using ::isgreater _LIBCPP_USING_IF_EXISTS;

using ::isgreaterequal _LIBCPP_USING_IF_EXISTS;

using ::isless _LIBCPP_USING_IF_EXISTS;

using ::islessequal _LIBCPP_USING_IF_EXISTS;

using ::islessgreater _LIBCPP_USING_IF_EXISTS;

using ::isunordered _LIBCPP_USING_IF_EXISTS;

using ::isunordered _LIBCPP_USING_IF_EXISTS;

using ::float_t _LIBCPP_USING_IF_EXISTS;

using ::double_t _LIBCPP_USING_IF_EXISTS;

using ::abs _LIBCPP_USING_IF_EXISTS;

using ::acos _LIBCPP_USING_IF_EXISTS;

using ::acosf _LIBCPP_USING_IF_EXISTS;

using ::asin _LIBCPP_USING_IF_EXISTS;

using ::asinf _LIBCPP_USING_IF_EXISTS;

using ::atan _LIBCPP_USING_IF_EXISTS;

using ::atanf _LIBCPP_USING_IF_EXISTS;

using ::atan2 _LIBCPP_USING_IF_EXISTS;

using ::atan2f _LIBCPP_USING_IF_EXISTS;

using ::ceil _LIBCPP_USING_IF_EXISTS;

using ::ceilf _LIBCPP_USING_IF_EXISTS;

using ::cos _LIBCPP_USING_IF_EXISTS;

using ::cosf _LIBCPP_USING_IF_EXISTS;

using ::cosh _LIBCPP_USING_IF_EXISTS;

using ::coshf _LIBCPP_USING_IF_EXISTS;

using ::exp _LIBCPP_USING_IF_EXISTS;

using ::expf _LIBCPP_USING_IF_EXISTS;

using ::fabs _LIBCPP_USING_IF_EXISTS;

using ::fabsf _LIBCPP_USING_IF_EXISTS;

using ::floor _LIBCPP_USING_IF_EXISTS;

using ::floorf _LIBCPP_USING_IF_EXISTS;

using ::fmod _LIBCPP_USING_IF_EXISTS;

using ::fmodf _LIBCPP_USING_IF_EXISTS;

using ::frexp _LIBCPP_USING_IF_EXISTS;

using ::frexpf _LIBCPP_USING_IF_EXISTS;

using ::ldexp _LIBCPP_USING_IF_EXISTS;

using ::ldexpf _LIBCPP_USING_IF_EXISTS;

using ::log _LIBCPP_USING_IF_EXISTS;

using ::logf _LIBCPP_USING_IF_EXISTS;

using ::log10 _LIBCPP_USING_IF_EXISTS;

using ::log10f _LIBCPP_USING_IF_EXISTS;

using ::modf _LIBCPP_USING_IF_EXISTS;

using ::modff _LIBCPP_USING_IF_EXISTS;

using ::pow _LIBCPP_USING_IF_EXISTS;

using ::powf _LIBCPP_USING_IF_EXISTS;

using ::sin _LIBCPP_USING_IF_EXISTS;

using ::sinf _LIBCPP_USING_IF_EXISTS;

using ::sinh _LIBCPP_USING_IF_EXISTS;

using ::sinhf _LIBCPP_USING_IF_EXISTS;

using ::sqrt _LIBCPP_USING_IF_EXISTS;

using ::sqrtf _LIBCPP_USING_IF_EXISTS;

using ::tan _LIBCPP_USING_IF_EXISTS;

using ::tanf _LIBCPP_USING_IF_EXISTS;

using ::tanh _LIBCPP_USING_IF_EXISTS;

using ::tanhf _LIBCPP_USING_IF_EXISTS;

using ::acosh _LIBCPP_USING_IF_EXISTS;

using ::acoshf _LIBCPP_USING_IF_EXISTS;

using ::asinh _LIBCPP_USING_IF_EXISTS;

using ::asinhf _LIBCPP_USING_IF_EXISTS;

using ::atanh _LIBCPP_USING_IF_EXISTS;

using ::atanhf _LIBCPP_USING_IF_EXISTS;

using ::cbrt _LIBCPP_USING_IF_EXISTS;

using ::cbrtf _LIBCPP_USING_IF_EXISTS;

using ::copysign _LIBCPP_USING_IF_EXISTS;

using ::copysignf _LIBCPP_USING_IF_EXISTS;

using ::erf _LIBCPP_USING_IF_EXISTS;

using ::erff _LIBCPP_USING_IF_EXISTS;

using ::erfc _LIBCPP_USING_IF_EXISTS;

using ::erfcf _LIBCPP_USING_IF_EXISTS;

using ::exp2 _LIBCPP_USING_IF_EXISTS;

using ::exp2f _LIBCPP_USING_IF_EXISTS;

using ::expm1 _LIBCPP_USING_IF_EXISTS;

using ::expm1f _LIBCPP_USING_IF_EXISTS;

using ::fdim _LIBCPP_USING_IF_EXISTS;

using ::fdimf _LIBCPP_USING_IF_EXISTS;

using ::fmaf _LIBCPP_USING_IF_EXISTS;

using ::fma _LIBCPP_USING_IF_EXISTS;

using ::fmax _LIBCPP_USING_IF_EXISTS;

using ::fmaxf _LIBCPP_USING_IF_EXISTS;

using ::fmin _LIBCPP_USING_IF_EXISTS;

using ::fminf _LIBCPP_USING_IF_EXISTS;

using ::hypot _LIBCPP_USING_IF_EXISTS;

using ::hypotf _LIBCPP_USING_IF_EXISTS;

using ::ilogb _LIBCPP_USING_IF_EXISTS;

using ::ilogbf _LIBCPP_USING_IF_EXISTS;

using ::lgamma _LIBCPP_USING_IF_EXISTS;

using ::lgammaf _LIBCPP_USING_IF_EXISTS;

using ::llrint _LIBCPP_USING_IF_EXISTS;

using ::llrintf _LIBCPP_USING_IF_EXISTS;

using ::llround _LIBCPP_USING_IF_EXISTS;

using ::llroundf _LIBCPP_USING_IF_EXISTS;

using ::log1p _LIBCPP_USING_IF_EXISTS;

using ::log1pf _LIBCPP_USING_IF_EXISTS;

using ::log2 _LIBCPP_USING_IF_EXISTS;

using ::log2f _LIBCPP_USING_IF_EXISTS;

using ::logb _LIBCPP_USING_IF_EXISTS;

using ::logbf _LIBCPP_USING_IF_EXISTS;

using ::lrint _LIBCPP_USING_IF_EXISTS;

using ::lrintf _LIBCPP_USING_IF_EXISTS;

using ::lround _LIBCPP_USING_IF_EXISTS;

using ::lroundf _LIBCPP_USING_IF_EXISTS;

using ::nan _LIBCPP_USING_IF_EXISTS;

using ::nanf _LIBCPP_USING_IF_EXISTS;

using ::nearbyint _LIBCPP_USING_IF_EXISTS;

using ::nearbyintf _LIBCPP_USING_IF_EXISTS;

using ::nextafter _LIBCPP_USING_IF_EXISTS;

using ::nextafterf _LIBCPP_USING_IF_EXISTS;

using ::nexttoward _LIBCPP_USING_IF_EXISTS;

using ::nexttowardf _LIBCPP_USING_IF_EXISTS;

using ::remainder _LIBCPP_USING_IF_EXISTS;

using ::remainderf _LIBCPP_USING_IF_EXISTS;

using ::remquo _LIBCPP_USING_IF_EXISTS;

using ::remquof _LIBCPP_USING_IF_EXISTS;

using ::rint _LIBCPP_USING_IF_EXISTS;

using ::rintf _LIBCPP_USING_IF_EXISTS;

using ::round _LIBCPP_USING_IF_EXISTS;

using ::roundf _LIBCPP_USING_IF_EXISTS;

using ::scalbln _LIBCPP_USING_IF_EXISTS;

using ::scalblnf _LIBCPP_USING_IF_EXISTS;

using ::scalbn _LIBCPP_USING_IF_EXISTS;

using ::scalbnf _LIBCPP_USING_IF_EXISTS;

using ::tgamma _LIBCPP_USING_IF_EXISTS;

using ::tgammaf _LIBCPP_USING_IF_EXISTS;

using ::trunc _LIBCPP_USING_IF_EXISTS;

using ::truncf _LIBCPP_USING_IF_EXISTS;

using ::acosl _LIBCPP_USING_IF_EXISTS;

using ::asinl _LIBCPP_USING_IF_EXISTS;

using ::atanl _LIBCPP_USING_IF_EXISTS;

using ::atan2l _LIBCPP_USING_IF_EXISTS;

using ::ceill _LIBCPP_USING_IF_EXISTS;

using ::cosl _LIBCPP_USING_IF_EXISTS;

using ::coshl _LIBCPP_USING_IF_EXISTS;

using ::expl _LIBCPP_USING_IF_EXISTS;

using ::fabsl _LIBCPP_USING_IF_EXISTS;

using ::floorl _LIBCPP_USING_IF_EXISTS;

using ::fmodl _LIBCPP_USING_IF_EXISTS;

using ::frexpl _LIBCPP_USING_IF_EXISTS;

using ::ldexpl _LIBCPP_USING_IF_EXISTS;

using ::logl _LIBCPP_USING_IF_EXISTS;

using ::log10l _LIBCPP_USING_IF_EXISTS;

using ::modfl _LIBCPP_USING_IF_EXISTS;

using ::powl _LIBCPP_USING_IF_EXISTS;

using ::sinl _LIBCPP_USING_IF_EXISTS;

using ::sinhl _LIBCPP_USING_IF_EXISTS;

using ::sqrtl _LIBCPP_USING_IF_EXISTS;

using ::tanl _LIBCPP_USING_IF_EXISTS;

using ::tanhl _LIBCPP_USING_IF_EXISTS;

using ::acoshl _LIBCPP_USING_IF_EXISTS;

using ::asinhl _LIBCPP_USING_IF_EXISTS;

using ::atanhl _LIBCPP_USING_IF_EXISTS;

using ::cbrtl _LIBCPP_USING_IF_EXISTS;

using ::copysignl _LIBCPP_USING_IF_EXISTS;

using ::erfl _LIBCPP_USING_IF_EXISTS;

using ::erfcl _LIBCPP_USING_IF_EXISTS;

using ::exp2l _LIBCPP_USING_IF_EXISTS;

using ::expm1l _LIBCPP_USING_IF_EXISTS;

using ::fdiml _LIBCPP_USING_IF_EXISTS;

using ::fmal _LIBCPP_USING_IF_EXISTS;

using ::fmaxl _LIBCPP_USING_IF_EXISTS;

using ::fminl _LIBCPP_USING_IF_EXISTS;

using ::hypotl _LIBCPP_USING_IF_EXISTS;

using ::ilogbl _LIBCPP_USING_IF_EXISTS;

using ::lgammal _LIBCPP_USING_IF_EXISTS;

using ::llrintl _LIBCPP_USING_IF_EXISTS;

using ::llroundl _LIBCPP_USING_IF_EXISTS;

using ::log1pl _LIBCPP_USING_IF_EXISTS;

using ::log2l _LIBCPP_USING_IF_EXISTS;

using ::logbl _LIBCPP_USING_IF_EXISTS;

using ::lrintl _LIBCPP_USING_IF_EXISTS;

using ::lroundl _LIBCPP_USING_IF_EXISTS;

using ::nanl _LIBCPP_USING_IF_EXISTS;

using ::nearbyintl _LIBCPP_USING_IF_EXISTS;

using ::nextafterl _LIBCPP_USING_IF_EXISTS;

using ::nexttowardl _LIBCPP_USING_IF_EXISTS;

using ::remainderl _LIBCPP_USING_IF_EXISTS;

using ::remquol _LIBCPP_USING_IF_EXISTS;

using ::rintl _LIBCPP_USING_IF_EXISTS;

using ::roundl _LIBCPP_USING_IF_EXISTS;

using ::scalblnl _LIBCPP_USING_IF_EXISTS;

using ::scalbnl _LIBCPP_USING_IF_EXISTS;

using ::tgammal _LIBCPP_USING_IF_EXISTS;

using ::truncl _LIBCPP_USING_IF_EXISTS;

#if _LIBCPP_STD_VER > 14

inline _LIBCPP_INLINE_VISIBILITY float       hypot(       float __x,       float __y,       float __z ) { return sqrt(__x*__x + __y*__y + __z*__z); }

inline _LIBCPP_INLINE_VISIBILITY double      hypot(      double __x,      double __y,      double __z ) { return sqrt(__x*__x + __y*__y + __z*__z); }

inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double __x, long double __y, long double __z ) { return sqrt(__x*__x + __y*__y + __z*__z); }

template <class _A1, class _A2, class _A3>

inline _LIBCPP_INLINE_VISIBILITY

typename enable_if_t

<

    is_arithmetic<_A1>::value &&

    is_arithmetic<_A2>::value &&

    is_arithmetic<_A3>::value,

    __promote<_A1, _A2, _A3>

>::type

hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT

{

    typedef typename __promote<_A1, _A2, _A3>::type __result_type;

    static_assert((!(is_same<_A1, __result_type>::value &&

                     is_same<_A2, __result_type>::value &&

                     is_same<_A3, __result_type>::value)), "");

    return std::hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);

}

#endif

template <class _A1>

_LIBCPP_INLINE_VISIBILITY

_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type

__constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT

{

#if __has_builtin(__builtin_isnan)

    return __builtin_isnan(__lcpp_x);

#else

    return isnan(__lcpp_x);

#endif

}

template <class _A1>

_LIBCPP_INLINE_VISIBILITY

_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type

__constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT

{

    return std::isnan(__lcpp_x);

}

template <class _A1>

_LIBCPP_INLINE_VISIBILITY

_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type

__constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT

{

#if __has_builtin(__builtin_isinf)

    return __builtin_isinf(__lcpp_x);

#else

    return isinf(__lcpp_x);

#endif

}

template <class _A1>

_LIBCPP_INLINE_VISIBILITY

_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type

__constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT

{

    return std::isinf(__lcpp_x);

}

template <class _A1>

_LIBCPP_INLINE_VISIBILITY

_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type

__constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT

{

#if __has_builtin(__builtin_isfinite)

    return __builtin_isfinite(__lcpp_x);

#else

    return isfinite(__lcpp_x);

#endif

}

template <class _A1>

_LIBCPP_INLINE_VISIBILITY

_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type

__constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT

{

    return __builtin_isfinite(__lcpp_x);

}

_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI float __constexpr_copysign(float __x, float __y) _NOEXCEPT {

    return __builtin_copysignf(__x, __y);

}

_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI double __constexpr_copysign(double __x, double __y) _NOEXCEPT {

    return __builtin_copysign(__x, __y);

}

_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI long double

__constexpr_copysign(long double __x, long double __y) _NOEXCEPT {

    return __builtin_copysignl(__x, __y);

}

template <class _A1, class _A2>

_LIBCPP_CONSTEXPR 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

    __constexpr_copysign(_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 __builtin_copysign((__result_type)__x, (__result_type)__y);

}

inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float __constexpr_fabs(float __x) _NOEXCEPT {

    return __builtin_fabsf(__x);

}

inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double __constexpr_fabs(double __x) _NOEXCEPT {

    return __builtin_fabs(__x);

}

inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double __constexpr_fabs(long double __x) _NOEXCEPT {

    return __builtin_fabsl(__x);

}

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

_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double __constexpr_fabs(_Tp __x) _NOEXCEPT {

    return __builtin_fabs(static_cast<double>(__x));

}

inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 float __constexpr_fmax(float __x, float __y) _NOEXCEPT {

#if !__has_constexpr_builtin(__builtin_fmaxf)

  if (__libcpp_is_constant_evaluated()) {

    if (std::__constexpr_isnan(__x))

      return __y;

    if (std::__constexpr_isnan(__y))

      return __x;

    return __x < __y ? __y : __x;

  }

#endif

  return __builtin_fmaxf(__x, __y);

}

inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 double __constexpr_fmax(double __x, double __y) _NOEXCEPT {

#if !__has_constexpr_builtin(__builtin_fmax)

  if (__libcpp_is_constant_evaluated()) {

    if (std::__constexpr_isnan(__x))

      return __y;

    if (std::__constexpr_isnan(__y))

      return __x;

    return __x < __y ? __y : __x;

  }

#endif

  return __builtin_fmax(__x, __y);

}

inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 long double

__constexpr_fmax(long double __x, long double __y) _NOEXCEPT {

#if !__has_constexpr_builtin(__builtin_fmaxl)

  if (__libcpp_is_constant_evaluated()) {

    if (std::__constexpr_isnan(__x))

      return __y;

    if (std::__constexpr_isnan(__y))

      return __x;

    return __x < __y ? __y : __x;

  }

#endif

  return __builtin_fmaxl(__x, __y);

}

template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value && is_arithmetic<_Up>::value, int> = 0>

_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __promote<_Tp, _Up>::type

__constexpr_fmax(_Tp __x, _Up __y) _NOEXCEPT {

  using __result_type = typename __promote<_Tp, _Up>::type;

  return std::__constexpr_fmax(static_cast<__result_type>(__x), static_cast<__result_type>(__y));

}

template <class _Tp>

_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp __constexpr_logb(_Tp __x) {

#if !__has_constexpr_builtin(__builtin_logb)

  if (__libcpp_is_constant_evaluated()) {

    if (__x == _Tp(0)) {

      // raise FE_DIVBYZERO

      return -numeric_limits<_Tp>::infinity();

    }

    if (std::__constexpr_isinf(__x))

      return numeric_limits<_Tp>::infinity();

    if (std::__constexpr_isnan(__x))

      return numeric_limits<_Tp>::quiet_NaN();

    __x = std::__constexpr_fabs(__x);

    unsigned long long __exp = 0;

    while (__x >= numeric_limits<_Tp>::radix) {

      __x /= numeric_limits<_Tp>::radix;

      __exp += 1;

    }

    return _Tp(__exp);

  }

#endif // !__has_constexpr_builtin(__builtin_logb)

  return __builtin_logb(__x);

}

template <class _Tp>

_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Tp __constexpr_scalbn(_Tp __x, int __exp) {

#if !__has_constexpr_builtin(__builtin_scalbln)

  if (__libcpp_is_constant_evaluated()) {

    if (__x == _Tp(0))

      return __x;

    if (std::__constexpr_isinf(__x))

      return __x;

    if (__exp == _Tp(0))

      return __x;

    if (std::__constexpr_isnan(__x))

      return numeric_limits<_Tp>::quiet_NaN();

    _Tp __mult(1);

    if (__exp > 0) {

      __mult = numeric_limits<_Tp>::radix;

      --__exp;

    } else {

      ++__exp;

      __exp = -__exp;

      __mult /= numeric_limits<_Tp>::radix;

    }

    while (__exp > 0) {

      if (!(__exp & 1)) {

        __mult *= __mult;

        __exp >>= 1;

      } else {

        __x *= __mult;

        --__exp;

      }

    }

    return __x;

  }

#endif // !__has_constexpr_builtin(__builtin_scalbln)

  return __builtin_scalbn(__x, __exp);

}

#if _LIBCPP_STD_VER > 17

template <typename _Fp>

_LIBCPP_HIDE_FROM_ABI 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;

    const _Fp __x = __a + __t * (__b - __a);

    if ((__t > 1) == (__b > __a))

        return __b < __x ? __x : __b;

    else

        return __x < __b ? __x : __b;

}

Unexecuted instantiation: float std::__1::__lerp[abi:v160006]<float>(float, float, float)

Unexecuted instantiation: double std::__1::__lerp[abi:v160006]<double>(double, double, double)

Unexecuted instantiation: long double std::__1::__lerp[abi:v160006]<long double>(long double, long double, long double)

_LIBCPP_HIDE_FROM_ABI constexpr float

lerp(float __a, float __b, float __t)                   _NOEXCEPT { return __lerp(__a, __b, __t); }

_LIBCPP_HIDE_FROM_ABI constexpr double

lerp(double __a, double __b, double __t)                _NOEXCEPT { return __lerp(__a, __b, __t); }

_LIBCPP_HIDE_FROM_ABI constexpr long double

lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); }

template <class _A1, class _A2, class _A3>

inline _LIBCPP_HIDE_FROM_ABI

constexpr typename enable_if_t

<

    is_arithmetic<_A1>::value &&

    is_arithmetic<_A2>::value &&

    is_arithmetic<_A3>::value,

    __promote<_A1, _A2, _A3>

>::type

lerp(_A1 __a, _A2 __b, _A3 __t) noexcept

{

    typedef typename __promote<_A1, _A2, _A3>::type __result_type;

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

                    _IsSame<_A2, __result_type>::value &&

                    _IsSame<_A3, __result_type>::value));

    return std::__lerp((__result_type)__a, (__result_type)__b, (__result_type)__t);

}

#endif // _LIBCPP_STD_VER > 17

_LIBCPP_END_NAMESPACE_STD

_LIBCPP_POP_MACROS

#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20

#  include <type_traits>

#endif

#endif // _LIBCPP_CMATH