| // -*- 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 | 
 |  | 
 | */ | 
 |  | 
 | #if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) | 
 | #  include <__cxx03/cmath> | 
 | #else | 
 | #  include <__config> | 
 | #  include <__math/hypot.h> | 
 | #  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; | 
 |  | 
 | 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); | 
 | } | 
 |  | 
 | #  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> | 
 |   requires(is_arithmetic_v<_A1> && is_arithmetic_v<_A2> && is_arithmetic_v<_A3>) | 
 | _LIBCPP_HIDE_FROM_ABI inline constexpr __promote_t<_A1, _A2, _A3> lerp(_A1 __a, _A2 __b, _A3 __t) noexcept { | 
 |   using __result_type = __promote_t<_A1, _A2, _A3>; | 
 |   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 // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) | 
 |  | 
 | #endif // _LIBCPP_CMATH |