include/cmath - llvm-project/libcxx - Git at Google

 // -*- 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);

 double         hermite(unsigned n, double x);                    // C++17
 float          hermite(unsigned n, float x);                     // C++17
 long double    hermite(unsigned n, long double x);               // C++17
 float          hermitef(unsigned n, float x);                    // C++17
 long double    hermitel(unsigned n, long double x);              // C++17
 template <class Integer>
 double         hermite(unsigned n, Integer x);                   // C++17

 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 <__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/promote.h>
 #include <__type_traits/remove_cv.h>
 #include <limits>
 #include <version>

 #include <__math/special_functions.h>
 #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 >= 17
 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) {
   return sqrt(__x * __x + __y * __y + __z * __z);
 }
 inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) {
   return sqrt(__x * __x + __y * __y + __z * __z);
 }
 inline _LIBCPP_HIDE_FROM_ABI 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_HIDE_FROM_ABI
 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, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __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, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT {
   return std::isnan(__lcpp_x);
 }

 template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __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, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT {
   return std::isinf(__lcpp_x);
 }

 template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __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, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT {
   return __builtin_isfinite(__lcpp_x);
 }

 #if _LIBCPP_STD_VER >= 20
 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;
 }

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

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

 _LIBCPP_HIDE_FROM_ABI inline 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 >= 20

 _LIBCPP_END_NAMESPACE_STD

 _LIBCPP_POP_MACROS

 #if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
 #  include <type_traits>
 #endif

 #endif // _LIBCPP_CMATH
	// -- 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);

	double hermite(unsigned n, double x); // C++17
	float hermite(unsigned n, float x); // C++17
	long double hermite(unsigned n, long double x); // C++17
	float hermitef(unsigned n, float x); // C++17
	long double hermitel(unsigned n, long double x); // C++17
	template <class Integer>
	double hermite(unsigned n, Integer x); // C++17

	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 <__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/promote.h>
	#include <__type_traits/remove_cv.h>
	#include <limits>
	#include <version>

	#include <__math/special_functions.h>
	#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 >= 17
	inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) {
	return sqrt(__x * __x + __y * __y + __z * __z);
	}
	inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) {
	return sqrt(__x * __x + __y * __y + __z * __z);
	}
	inline _LIBCPP_HIDE_FROM_ABI 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_HIDE_FROM_ABI
	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, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
	_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __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, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
	_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT {
	return std::isnan(__lcpp_x);
	}

	template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
	_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __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, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
	_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT {
	return std::isinf(__lcpp_x);
	}

	template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
	_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __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, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
	_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT {
	return __builtin_isfinite(__lcpp_x);
	}

	#if _LIBCPP_STD_VER >= 20
	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;
	}

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

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

	_LIBCPP_HIDE_FROM_ABI inline 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 >= 20

	_LIBCPP_END_NAMESPACE_STD

	_LIBCPP_POP_MACROS

	#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
	# include <type_traits>
	#endif

	#endif // _LIBCPP_CMATH