text: // -*- C++ -*-
  //===---------------------------- math.h ----------------------------------===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is dual licensed under the MIT and the University of Illinois Open
  // Source Licenses. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  
  #ifndef _LIBCPP_MATH_H
  #define _LIBCPP_MATH_H
  
  /*
      math.h synopsis
  
  Macros:
  
      HUGE_VAL
      HUGE_VALF               // C99
      HUGE_VALL               // C99
      INFINITY                // C99
      NAN                     // C99
      FP_INFINITE             // C99
      FP_NAN                  // C99
      FP_NORMAL               // C99
      FP_SUBNORMAL            // C99
      FP_ZERO                 // C99
      FP_FAST_FMA             // C99
      FP_FAST_FMAF            // C99
      FP_FAST_FMAL            // C99
      FP_ILOGB0               // C99
      FP_ILOGBNAN             // C99
      MATH_ERRNO              // C99
      MATH_ERREXCEPT          // C99
      math_errhandling        // C99
  
  Types:
  
      float_t                 // C99
      double_t                // C99
  
  // C90
  
  floating_point abs(floating_point x);
  
  floating_point acos (arithmetic x);
  float          acosf(float x);
  long double    acosl(long double x);
  
  floating_point asin (arithmetic x);
  float          asinf(float x);
  long double    asinl(long double x);
  
  floating_point atan (arithmetic x);
  float          atanf(float x);
  long double    atanl(long double x);
  
  floating_point atan2 (arithmetic y, arithmetic x);
  float          atan2f(float y, float x);
  long double    atan2l(long double y, long double x);
  
  floating_point ceil (arithmetic x);
  float          ceilf(float x);
  long double    ceill(long double x);
  
  floating_point cos (arithmetic x);
  float          cosf(float x);
  long double    cosl(long double x);
  
  floating_point cosh (arithmetic x);
  float          coshf(float x);
  long double    coshl(long double x);
  
  floating_point exp (arithmetic x);
  float          expf(float x);
  long double    expl(long double x);
  
  floating_point fabs (arithmetic x);
  float          fabsf(float x);
  long double    fabsl(long double x);
  
  floating_point floor (arithmetic x);
  float          floorf(float x);
  long double    floorl(long double x);
  
  floating_point fmod (arithmetic x, arithmetic y);
  float          fmodf(float x, float y);
  long double    fmodl(long double x, long double y);
  
  floating_point frexp (arithmetic value, int* exp);
  float          frexpf(float value, int* exp);
  long double    frexpl(long double value, int* exp);
  
  floating_point ldexp (arithmetic value, int exp);
  float          ldexpf(float value, int exp);
  long double    ldexpl(long double value, int exp);
  
  floating_point log (arithmetic x);
  float          logf(float x);
  long double    logl(long double x);
  
  floating_point log10 (arithmetic x);
  float          log10f(float x);
  long double    log10l(long double x);
  
  floating_point modf (floating_point value, floating_point* iptr);
  float          modff(float value, float* iptr);
  long double    modfl(long double value, long double* iptr);
  
  floating_point pow (arithmetic x, arithmetic y);
  float          powf(float x, float y);
  long double    powl(long double x, long double y);
  
  floating_point sin (arithmetic x);
  float          sinf(float x);
  long double    sinl(long double x);
  
  floating_point sinh (arithmetic x);
  float          sinhf(float x);
  long double    sinhl(long double x);
  
  floating_point sqrt (arithmetic x);
  float          sqrtf(float x);
  long double    sqrtl(long double x);
  
  floating_point tan (arithmetic x);
  float          tanf(float x);
  long double    tanl(long double x);
  
  floating_point tanh (arithmetic x);
  float          tanhf(float x);
  long double    tanhl(long double x);
  
  //  C99
  
  bool signbit(arithmetic x);
  
  int fpclassify(arithmetic x);
  
  bool isfinite(arithmetic x);
  bool isinf(arithmetic x);
  bool isnan(arithmetic x);
  bool isnormal(arithmetic x);
  
  bool isgreater(arithmetic x, arithmetic y);
  bool isgreaterequal(arithmetic x, arithmetic y);
  bool isless(arithmetic x, arithmetic y);
  bool islessequal(arithmetic x, arithmetic y);
  bool islessgreater(arithmetic x, arithmetic y);
  bool isunordered(arithmetic x, arithmetic y);
  
  floating_point acosh (arithmetic x);
  float          acoshf(float x);
  long double    acoshl(long double x);
  
  floating_point asinh (arithmetic x);
  float          asinhf(float x);
  long double    asinhl(long double x);
  
  floating_point atanh (arithmetic x);
  float          atanhf(float x);
  long double    atanhl(long double x);
  
  floating_point cbrt (arithmetic x);
  float          cbrtf(float x);
  long double    cbrtl(long double x);
  
  floating_point copysign (arithmetic x, arithmetic y);
  float          copysignf(float x, float y);
  long double    copysignl(long double x, long double y);
  
  floating_point erf (arithmetic x);
  float          erff(float x);
  long double    erfl(long double x);
  
  floating_point erfc (arithmetic x);
  float          erfcf(float x);
  long double    erfcl(long double x);
  
  floating_point exp2 (arithmetic x);
  float          exp2f(float x);
  long double    exp2l(long double x);
  
  floating_point expm1 (arithmetic x);
  float          expm1f(float x);
  long double    expm1l(long double x);
  
  floating_point fdim (arithmetic x, arithmetic y);
  float          fdimf(float x, float y);
  long double    fdiml(long double x, long double y);
  
  floating_point fma (arithmetic x, arithmetic y, arithmetic z);
  float          fmaf(float x, float y, float z);
  long double    fmal(long double x, long double y, long double z);
  
  floating_point fmax (arithmetic x, arithmetic y);
  float          fmaxf(float x, float y);
  long double    fmaxl(long double x, long double y);
  
  floating_point fmin (arithmetic x, arithmetic y);
  float          fminf(float x, float y);
  long double    fminl(long double x, long double y);
  
  floating_point hypot (arithmetic x, arithmetic y);
  float          hypotf(float x, float y);
  long double    hypotl(long double x, long double y);
  
  int ilogb (arithmetic x);
  int ilogbf(float x);
  int ilogbl(long double x);
  
  floating_point lgamma (arithmetic x);
  float          lgammaf(float x);
  long double    lgammal(long double x);
  
  long long llrint (arithmetic x);
  long long llrintf(float x);
  long long llrintl(long double x);
  
  long long llround (arithmetic x);
  long long llroundf(float x);
  long long llroundl(long double x);
  
  floating_point log1p (arithmetic x);
  float          log1pf(float x);
  long double    log1pl(long double x);
  
  floating_point log2 (arithmetic x);
  float          log2f(float x);
  long double    log2l(long double x);
  
  floating_point logb (arithmetic x);
  float          logbf(float x);
  long double    logbl(long double x);
  
  long lrint (arithmetic x);
  long lrintf(float x);
  long lrintl(long double x);
  
  long lround (arithmetic x);
  long lroundf(float x);
  long lroundl(long double x);
  
  double      nan (const char* str);
  float       nanf(const char* str);
  long double nanl(const char* str);
  
  floating_point nearbyint (arithmetic x);
  float          nearbyintf(float x);
  long double    nearbyintl(long double x);
  
  floating_point nextafter (arithmetic x, arithmetic y);
  float          nextafterf(float x, float y);
  long double    nextafterl(long double x, long double y);
  
  floating_point nexttoward (arithmetic x, long double y);
  float          nexttowardf(float x, long double y);
  long double    nexttowardl(long double x, long double y);
  
  floating_point remainder (arithmetic x, arithmetic y);
  float          remainderf(float x, float y);
  long double    remainderl(long double x, long double y);
  
  floating_point remquo (arithmetic x, arithmetic y, int* pquo);
  float          remquof(float x, float y, int* pquo);
  long double    remquol(long double x, long double y, int* pquo);
  
  floating_point rint (arithmetic x);
  float          rintf(float x);
  long double    rintl(long double x);
  
  floating_point round (arithmetic x);
  float          roundf(float x);
  long double    roundl(long double x);
  
  floating_point scalbln (arithmetic x, long ex);
  float          scalblnf(float x, long ex);
  long double    scalblnl(long double x, long ex);
  
  floating_point scalbn (arithmetic x, int ex);
  float          scalbnf(float x, int ex);
  long double    scalbnl(long double x, int ex);
  
  floating_point tgamma (arithmetic x);
  float          tgammaf(float x);
  long double    tgammal(long double x);
  
  floating_point trunc (arithmetic x);
  float          truncf(float x);
  long double    truncl(long double x);
  
  */
  
  #include <__config>
  #if defined(_LIBCPP_MSVCRT)
  #include <crtversion.h>
  #endif
  
  #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
  #pragma GCC system_header
  #endif
  
  #include_next <math.h>
  
  #ifdef __cplusplus
  
  // We support including .h headers inside 'extern "C"' contexts, so switch
  // back to C++ linkage before including these C++ headers.
  extern "C++" {
  
  #include <type_traits>
  
  // signbit
  
  #ifdef signbit
  
  template <class _A1>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_signbit(_A1 __lcpp_x) _NOEXCEPT
  {
      return signbit(__lcpp_x);
  }
  
  #undef signbit
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, bool>::type
  signbit(_A1 __lcpp_x) _NOEXCEPT
  {
      return __libcpp_signbit((typename std::__promote<_A1>::type)__lcpp_x);
  }
  
  #elif defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) >= 14)
  
  template <typename _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, bool>::type
  signbit(_A1 __lcpp_x) _NOEXCEPT
  {
    return ::signbit(static_cast<typename std::__promote<_A1>::type>(__lcpp_x));
  }
  
  #endif  // signbit
  
  // fpclassify
  
  #ifdef fpclassify
  
  template <class _A1>
  _LIBCPP_ALWAYS_INLINE
  int
  __libcpp_fpclassify(_A1 __lcpp_x) _NOEXCEPT
  {
      return fpclassify(__lcpp_x);
  }
  
  #undef fpclassify
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, int>::type
  fpclassify(_A1 __lcpp_x) _NOEXCEPT
  {
      return __libcpp_fpclassify((typename std::__promote<_A1>::type)__lcpp_x);
  }
  
  #elif defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) >= 14)
  
  template <typename _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, int>::type
  fpclassify(_A1 __lcpp_x) _NOEXCEPT
  {
    return ::fpclassify(static_cast<typename std::__promote<_A1>::type>(__lcpp_x));
  }
  
  #endif  // fpclassify
  
  // isfinite
  
  #ifdef isfinite
  
  template <class _A1>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isfinite(_A1 __lcpp_x) _NOEXCEPT
  {
      return isfinite(__lcpp_x);
  }
  
  #undef isfinite
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, bool>::type
  isfinite(_A1 __lcpp_x) _NOEXCEPT
  {
      return __libcpp_isfinite((typename std::__promote<_A1>::type)__lcpp_x);
  }
  
  #endif  // isfinite
  
  // isinf
  
  #ifdef isinf
  
  template <class _A1>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isinf(_A1 __lcpp_x) _NOEXCEPT
  {
      return isinf(__lcpp_x);
  }
  
  #undef isinf
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, bool>::type
  isinf(_A1 __lcpp_x) _NOEXCEPT
  {
      return __libcpp_isinf((typename std::__promote<_A1>::type)__lcpp_x);
  }
  
  #endif  // isinf
  
  // isnan
  
  #ifdef isnan
  
  template <class _A1>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isnan(_A1 __lcpp_x) _NOEXCEPT
  {
      return isnan(__lcpp_x);
  }
  
  #undef isnan
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, bool>::type
  isnan(_A1 __lcpp_x) _NOEXCEPT
  {
      return __libcpp_isnan((typename std::__promote<_A1>::type)__lcpp_x);
  }
  
  #endif  // isnan
  
  // isnormal
  
  #ifdef isnormal
  
  template <class _A1>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isnormal(_A1 __lcpp_x) _NOEXCEPT
  {
      return isnormal(__lcpp_x);
  }
  
  #undef isnormal
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_arithmetic<_A1>::value, bool>::type
  isnormal(_A1 __lcpp_x) _NOEXCEPT
  {
      return __libcpp_isnormal((typename std::__promote<_A1>::type)__lcpp_x);
  }
  
  #endif  // isnormal
  
  // isgreater
  
  #ifdef isgreater
  
  template <class _A1, class _A2>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isgreater(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      return isgreater(__lcpp_x, __lcpp_y);
  }
  
  #undef isgreater
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      bool
  >::type
  isgreater(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type type;
      return __libcpp_isgreater((type)__lcpp_x, (type)__lcpp_y);
  }
  
  #endif  // isgreater
  
  // isgreaterequal
  
  #ifdef isgreaterequal
  
  template <class _A1, class _A2>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isgreaterequal(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      return isgreaterequal(__lcpp_x, __lcpp_y);
  }
  
  #undef isgreaterequal
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      bool
  >::type
  isgreaterequal(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type type;
      return __libcpp_isgreaterequal((type)__lcpp_x, (type)__lcpp_y);
  }
  
  #endif  // isgreaterequal
  
  // isless
  
  #ifdef isless
  
  template <class _A1, class _A2>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isless(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      return isless(__lcpp_x, __lcpp_y);
  }
  
  #undef isless
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      bool
  >::type
  isless(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type type;
      return __libcpp_isless((type)__lcpp_x, (type)__lcpp_y);
  }
  
  #endif  // isless
  
  // islessequal
  
  #ifdef islessequal
  
  template <class _A1, class _A2>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_islessequal(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      return islessequal(__lcpp_x, __lcpp_y);
  }
  
  #undef islessequal
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      bool
  >::type
  islessequal(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type type;
      return __libcpp_islessequal((type)__lcpp_x, (type)__lcpp_y);
  }
  
  #endif  // islessequal
  
  // islessgreater
  
  #ifdef islessgreater
  
  template <class _A1, class _A2>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_islessgreater(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      return islessgreater(__lcpp_x, __lcpp_y);
  }
  
  #undef islessgreater
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      bool
  >::type
  islessgreater(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type type;
      return __libcpp_islessgreater((type)__lcpp_x, (type)__lcpp_y);
  }
  
  #endif  // islessgreater
  
  // isunordered
  
  #ifdef isunordered
  
  template <class _A1, class _A2>
  _LIBCPP_ALWAYS_INLINE
  bool
  __libcpp_isunordered(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      return isunordered(__lcpp_x, __lcpp_y);
  }
  
  #undef isunordered
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      bool
  >::type
  isunordered(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type type;
      return __libcpp_isunordered((type)__lcpp_x, (type)__lcpp_y);
  }
  
  #endif  // isunordered
  
  // abs
  
  #if !(defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY
  float
  abs(float __lcpp_x) _NOEXCEPT {return ::fabsf(__lcpp_x);}
  
  inline _LIBCPP_INLINE_VISIBILITY
  double
  abs(double __lcpp_x) _NOEXCEPT {return ::fabs(__lcpp_x);}
  
  inline _LIBCPP_INLINE_VISIBILITY
  long double
  abs(long double __lcpp_x) _NOEXCEPT {return ::fabsl(__lcpp_x);}
  #endif // !(defined(_AIX) || defined(__sun__))
  
  // acos
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       acos(float __lcpp_x) _NOEXCEPT       {return ::acosf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double acos(long double __lcpp_x) _NOEXCEPT {return ::acosl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  acos(_A1 __lcpp_x) _NOEXCEPT {return ::acos((double)__lcpp_x);}
  
  // asin
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       asin(float __lcpp_x) _NOEXCEPT       {return ::asinf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double asin(long double __lcpp_x) _NOEXCEPT {return ::asinl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  asin(_A1 __lcpp_x) _NOEXCEPT {return ::asin((double)__lcpp_x);}
  
  // atan
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       atan(float __lcpp_x) _NOEXCEPT       {return ::atanf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double atan(long double __lcpp_x) _NOEXCEPT {return ::atanl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  atan(_A1 __lcpp_x) _NOEXCEPT {return ::atan((double)__lcpp_x);}
  
  // atan2
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       atan2(float __lcpp_y, float __lcpp_x) _NOEXCEPT             {return ::atan2f(__lcpp_y, __lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double atan2(long double __lcpp_y, long double __lcpp_x) _NOEXCEPT {return ::atan2l(__lcpp_y, __lcpp_x);}
  #endif
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  atan2(_A1 __lcpp_y, _A2 __lcpp_x) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::atan2((__result_type)__lcpp_y, (__result_type)__lcpp_x);
  }
  
  // ceil
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       ceil(float __lcpp_x) _NOEXCEPT       {return ::ceilf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double ceil(long double __lcpp_x) _NOEXCEPT {return ::ceill(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  ceil(_A1 __lcpp_x) _NOEXCEPT {return ::ceil((double)__lcpp_x);}
  
  // cos
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       cos(float __lcpp_x) _NOEXCEPT       {return ::cosf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double cos(long double __lcpp_x) _NOEXCEPT {return ::cosl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  cos(_A1 __lcpp_x) _NOEXCEPT {return ::cos((double)__lcpp_x);}
  
  // cosh
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       cosh(float __lcpp_x) _NOEXCEPT       {return ::coshf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double cosh(long double __lcpp_x) _NOEXCEPT {return ::coshl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  cosh(_A1 __lcpp_x) _NOEXCEPT {return ::cosh((double)__lcpp_x);}
  
  // exp
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       exp(float __lcpp_x) _NOEXCEPT       {return ::expf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double exp(long double __lcpp_x) _NOEXCEPT {return ::expl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  exp(_A1 __lcpp_x) _NOEXCEPT {return ::exp((double)__lcpp_x);}
  
  // fabs
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       fabs(float __lcpp_x) _NOEXCEPT       {return ::fabsf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double fabs(long double __lcpp_x) _NOEXCEPT {return ::fabsl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  fabs(_A1 __lcpp_x) _NOEXCEPT {return ::fabs((double)__lcpp_x);}
  
  // floor
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       floor(float __lcpp_x) _NOEXCEPT       {return ::floorf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double floor(long double __lcpp_x) _NOEXCEPT {return ::floorl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  floor(_A1 __lcpp_x) _NOEXCEPT {return ::floor((double)__lcpp_x);}
  
  // fmod
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       fmod(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::fmodf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double fmod(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::fmodl(__lcpp_x, __lcpp_y);}
  #endif
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  fmod(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::fmod((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // frexp
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       frexp(float __lcpp_x, int* __lcpp_e) _NOEXCEPT       {return ::frexpf(__lcpp_x, __lcpp_e);}
  inline _LIBCPP_INLINE_VISIBILITY long double frexp(long double __lcpp_x, int* __lcpp_e) _NOEXCEPT {return ::frexpl(__lcpp_x, __lcpp_e);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  frexp(_A1 __lcpp_x, int* __lcpp_e) _NOEXCEPT {return ::frexp((double)__lcpp_x, __lcpp_e);}
  
  // ldexp
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       ldexp(float __lcpp_x, int __lcpp_e) _NOEXCEPT       {return ::ldexpf(__lcpp_x, __lcpp_e);}
  inline _LIBCPP_INLINE_VISIBILITY long double ldexp(long double __lcpp_x, int __lcpp_e) _NOEXCEPT {return ::ldexpl(__lcpp_x, __lcpp_e);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  ldexp(_A1 __lcpp_x, int __lcpp_e) _NOEXCEPT {return ::ldexp((double)__lcpp_x, __lcpp_e);}
  
  // log
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       log(float __lcpp_x) _NOEXCEPT       {return ::logf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double log(long double __lcpp_x) _NOEXCEPT {return ::logl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  log(_A1 __lcpp_x) _NOEXCEPT {return ::log((double)__lcpp_x);}
  
  // log10
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       log10(float __lcpp_x) _NOEXCEPT       {return ::log10f(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double log10(long double __lcpp_x) _NOEXCEPT {return ::log10l(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  log10(_A1 __lcpp_x) _NOEXCEPT {return ::log10((double)__lcpp_x);}
  
  // modf
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       modf(float __lcpp_x, float* __lcpp_y) _NOEXCEPT             {return ::modff(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double modf(long double __lcpp_x, long double* __lcpp_y) _NOEXCEPT {return ::modfl(__lcpp_x, __lcpp_y);}
  #endif
  
  // pow
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       pow(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::powf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double pow(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::powl(__lcpp_x, __lcpp_y);}
  #endif
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  pow(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::pow((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // sin
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       sin(float __lcpp_x) _NOEXCEPT       {return ::sinf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double sin(long double __lcpp_x) _NOEXCEPT {return ::sinl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  sin(_A1 __lcpp_x) _NOEXCEPT {return ::sin((double)__lcpp_x);}
  
  // sinh
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       sinh(float __lcpp_x) _NOEXCEPT       {return ::sinhf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double sinh(long double __lcpp_x) _NOEXCEPT {return ::sinhl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  sinh(_A1 __lcpp_x) _NOEXCEPT {return ::sinh((double)__lcpp_x);}
  
  // sqrt
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       sqrt(float __lcpp_x) _NOEXCEPT       {return ::sqrtf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double sqrt(long double __lcpp_x) _NOEXCEPT {return ::sqrtl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  sqrt(_A1 __lcpp_x) _NOEXCEPT {return ::sqrt((double)__lcpp_x);}
  
  // tan
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       tan(float __lcpp_x) _NOEXCEPT       {return ::tanf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double tan(long double __lcpp_x) _NOEXCEPT {return ::tanl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  tan(_A1 __lcpp_x) _NOEXCEPT {return ::tan((double)__lcpp_x);}
  
  // tanh
  
  #if !((defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14) || defined(_AIX) || defined(__sun__))
  inline _LIBCPP_INLINE_VISIBILITY float       tanh(float __lcpp_x) _NOEXCEPT       {return ::tanhf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double tanh(long double __lcpp_x) _NOEXCEPT {return ::tanhl(__lcpp_x);}
  #endif
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  tanh(_A1 __lcpp_x) _NOEXCEPT {return ::tanh((double)__lcpp_x);}
  
  // acosh
  
  #if !(defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14)
  inline _LIBCPP_INLINE_VISIBILITY float       acosh(float __lcpp_x) _NOEXCEPT       {return ::acoshf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double acosh(long double __lcpp_x) _NOEXCEPT {return ::acoshl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  acosh(_A1 __lcpp_x) _NOEXCEPT {return ::acosh((double)__lcpp_x);}
  #endif
  
  // asinh
  
  #if !(defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14)
  inline _LIBCPP_INLINE_VISIBILITY float       asinh(float __lcpp_x) _NOEXCEPT       {return ::asinhf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double asinh(long double __lcpp_x) _NOEXCEPT {return ::asinhl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  asinh(_A1 __lcpp_x) _NOEXCEPT {return ::asinh((double)__lcpp_x);}
  #endif
  
  // atanh
  
  #if !(defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14)
  inline _LIBCPP_INLINE_VISIBILITY float       atanh(float __lcpp_x) _NOEXCEPT       {return ::atanhf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double atanh(long double __lcpp_x) _NOEXCEPT {return ::atanhl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  atanh(_A1 __lcpp_x) _NOEXCEPT {return ::atanh((double)__lcpp_x);}
  #endif
  
  // cbrt
  
  #if !(defined(_LIBCPP_MSVCRT) && (_VC_CRT_MAJOR_VERSION-0) < 14)
  inline _LIBCPP_INLINE_VISIBILITY float       cbrt(float __lcpp_x) _NOEXCEPT       {return ::cbrtf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double cbrt(long double __lcpp_x) _NOEXCEPT {return ::cbrtl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  cbrt(_A1 __lcpp_x) _NOEXCEPT {return ::cbrt((double)__lcpp_x);}
  #endif
  
  // copysign
  
  #if !defined(_VC_CRT_MAJOR_VERSION) || (_VC_CRT_MAJOR_VERSION < 12)
  inline _LIBCPP_INLINE_VISIBILITY float copysign(float __lcpp_x,
                                                  float __lcpp_y) _NOEXCEPT {
    return ::copysignf(__lcpp_x, __lcpp_y);
  }
  inline _LIBCPP_INLINE_VISIBILITY long double
  copysign(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {
    return ::copysignl(__lcpp_x, __lcpp_y);
  }
  #endif
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  copysign(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::copysign((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  #if !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14))
  
  // erf
  
  inline _LIBCPP_INLINE_VISIBILITY float       erf(float __lcpp_x) _NOEXCEPT       {return ::erff(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double erf(long double __lcpp_x) _NOEXCEPT {return ::erfl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  erf(_A1 __lcpp_x) _NOEXCEPT {return ::erf((double)__lcpp_x);}
  
  // erfc
  
  inline _LIBCPP_INLINE_VISIBILITY float       erfc(float __lcpp_x) _NOEXCEPT       {return ::erfcf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double erfc(long double __lcpp_x) _NOEXCEPT {return ::erfcl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  erfc(_A1 __lcpp_x) _NOEXCEPT {return ::erfc((double)__lcpp_x);}
  
  // exp2
  
  inline _LIBCPP_INLINE_VISIBILITY float       exp2(float __lcpp_x) _NOEXCEPT       {return ::exp2f(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double exp2(long double __lcpp_x) _NOEXCEPT {return ::exp2l(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  exp2(_A1 __lcpp_x) _NOEXCEPT {return ::exp2((double)__lcpp_x);}
  
  // expm1
  
  inline _LIBCPP_INLINE_VISIBILITY float       expm1(float __lcpp_x) _NOEXCEPT       {return ::expm1f(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double expm1(long double __lcpp_x) _NOEXCEPT {return ::expm1l(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  expm1(_A1 __lcpp_x) _NOEXCEPT {return ::expm1((double)__lcpp_x);}
  
  // fdim
  
  inline _LIBCPP_INLINE_VISIBILITY float       fdim(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::fdimf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double fdim(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::fdiml(__lcpp_x, __lcpp_y);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  fdim(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::fdim((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // fma
  
  inline _LIBCPP_INLINE_VISIBILITY float       fma(float __lcpp_x, float __lcpp_y, float __lcpp_z) _NOEXCEPT                   {return ::fmaf(__lcpp_x, __lcpp_y, __lcpp_z);}
  inline _LIBCPP_INLINE_VISIBILITY long double fma(long double __lcpp_x, long double __lcpp_y, long double __lcpp_z) _NOEXCEPT {return ::fmal(__lcpp_x, __lcpp_y, __lcpp_z);}
  
  template <class _A1, class _A2, class _A3>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value &&
      std::is_arithmetic<_A3>::value,
      std::__promote<_A1, _A2, _A3>
  >::type
  fma(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2, _A3>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value &&
                       std::is_same<_A3, __result_type>::value)), "");
      return ::fma((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
  }
  
  // fmax
  
  inline _LIBCPP_INLINE_VISIBILITY float       fmax(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::fmaxf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double fmax(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::fmaxl(__lcpp_x, __lcpp_y);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  fmax(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::fmax((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // fmin
  
  inline _LIBCPP_INLINE_VISIBILITY float       fmin(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::fminf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double fmin(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::fminl(__lcpp_x, __lcpp_y);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  fmin(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::fmin((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // hypot
  
  inline _LIBCPP_INLINE_VISIBILITY float       hypot(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::hypotf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double hypot(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::hypotl(__lcpp_x, __lcpp_y);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  hypot(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // ilogb
  
  inline _LIBCPP_INLINE_VISIBILITY int ilogb(float __lcpp_x) _NOEXCEPT       {return ::ilogbf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY int ilogb(long double __lcpp_x) _NOEXCEPT {return ::ilogbl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, int>::type
  ilogb(_A1 __lcpp_x) _NOEXCEPT {return ::ilogb((double)__lcpp_x);}
  
  // lgamma
  
  inline _LIBCPP_INLINE_VISIBILITY float       lgamma(float __lcpp_x) _NOEXCEPT       {return ::lgammaf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double lgamma(long double __lcpp_x) _NOEXCEPT {return ::lgammal(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  lgamma(_A1 __lcpp_x) _NOEXCEPT {return ::lgamma((double)__lcpp_x);}
  
  // llrint
  
  inline _LIBCPP_INLINE_VISIBILITY long long llrint(float __lcpp_x) _NOEXCEPT       {return ::llrintf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long long llrint(long double __lcpp_x) _NOEXCEPT {return ::llrintl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, long long>::type
  llrint(_A1 __lcpp_x) _NOEXCEPT {return ::llrint((double)__lcpp_x);}
  
  // llround
  
  inline _LIBCPP_INLINE_VISIBILITY long long llround(float __lcpp_x) _NOEXCEPT       {return ::llroundf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long long llround(long double __lcpp_x) _NOEXCEPT {return ::llroundl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, long long>::type
  llround(_A1 __lcpp_x) _NOEXCEPT {return ::llround((double)__lcpp_x);}
  
  // log1p
  
  inline _LIBCPP_INLINE_VISIBILITY float       log1p(float __lcpp_x) _NOEXCEPT       {return ::log1pf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double log1p(long double __lcpp_x) _NOEXCEPT {return ::log1pl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  log1p(_A1 __lcpp_x) _NOEXCEPT {return ::log1p((double)__lcpp_x);}
  
  // log2
  
  inline _LIBCPP_INLINE_VISIBILITY float       log2(float __lcpp_x) _NOEXCEPT       {return ::log2f(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double log2(long double __lcpp_x) _NOEXCEPT {return ::log2l(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  log2(_A1 __lcpp_x) _NOEXCEPT {return ::log2((double)__lcpp_x);}
  
  // logb
  
  inline _LIBCPP_INLINE_VISIBILITY float       logb(float __lcpp_x) _NOEXCEPT       {return ::logbf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double logb(long double __lcpp_x) _NOEXCEPT {return ::logbl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  logb(_A1 __lcpp_x) _NOEXCEPT {return ::logb((double)__lcpp_x);}
  
  // lrint
  
  inline _LIBCPP_INLINE_VISIBILITY long lrint(float __lcpp_x) _NOEXCEPT       {return ::lrintf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long lrint(long double __lcpp_x) _NOEXCEPT {return ::lrintl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, long>::type
  lrint(_A1 __lcpp_x) _NOEXCEPT {return ::lrint((double)__lcpp_x);}
  
  // lround
  
  inline _LIBCPP_INLINE_VISIBILITY long lround(float __lcpp_x) _NOEXCEPT       {return ::lroundf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long lround(long double __lcpp_x) _NOEXCEPT {return ::lroundl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, long>::type
  lround(_A1 __lcpp_x) _NOEXCEPT {return ::lround((double)__lcpp_x);}
  
  // nan
  
  // nearbyint
  
  inline _LIBCPP_INLINE_VISIBILITY float       nearbyint(float __lcpp_x) _NOEXCEPT       {return ::nearbyintf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double nearbyint(long double __lcpp_x) _NOEXCEPT {return ::nearbyintl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  nearbyint(_A1 __lcpp_x) _NOEXCEPT {return ::nearbyint((double)__lcpp_x);}
  
  // nextafter
  
  inline _LIBCPP_INLINE_VISIBILITY float       nextafter(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::nextafterf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double nextafter(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::nextafterl(__lcpp_x, __lcpp_y);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  nextafter(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::nextafter((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // nexttoward
  
  inline _LIBCPP_INLINE_VISIBILITY float       nexttoward(float __lcpp_x, long double __lcpp_y) _NOEXCEPT       {return ::nexttowardf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double nexttoward(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::nexttowardl(__lcpp_x, __lcpp_y);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  nexttoward(_A1 __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::nexttoward((double)__lcpp_x, __lcpp_y);}
  
  // remainder
  
  inline _LIBCPP_INLINE_VISIBILITY float       remainder(float __lcpp_x, float __lcpp_y) _NOEXCEPT             {return ::remainderf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double remainder(long double __lcpp_x, long double __lcpp_y) _NOEXCEPT {return ::remainderl(__lcpp_x, __lcpp_y);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  remainder(_A1 __lcpp_x, _A2 __lcpp_y) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::remainder((__result_type)__lcpp_x, (__result_type)__lcpp_y);
  }
  
  // remquo
  
  inline _LIBCPP_INLINE_VISIBILITY float       remquo(float __lcpp_x, float __lcpp_y, int* __lcpp_z) _NOEXCEPT             {return ::remquof(__lcpp_x, __lcpp_y, __lcpp_z);}
  inline _LIBCPP_INLINE_VISIBILITY long double remquo(long double __lcpp_x, long double __lcpp_y, int* __lcpp_z) _NOEXCEPT {return ::remquol(__lcpp_x, __lcpp_y, __lcpp_z);}
  
  template <class _A1, class _A2>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::__lazy_enable_if
  <
      std::is_arithmetic<_A1>::value &&
      std::is_arithmetic<_A2>::value,
      std::__promote<_A1, _A2>
  >::type
  remquo(_A1 __lcpp_x, _A2 __lcpp_y, int* __lcpp_z) _NOEXCEPT
  {
      typedef typename std::__promote<_A1, _A2>::type __result_type;
      static_assert((!(std::is_same<_A1, __result_type>::value &&
                       std::is_same<_A2, __result_type>::value)), "");
      return ::remquo((__result_type)__lcpp_x, (__result_type)__lcpp_y, __lcpp_z);
  }
  
  // rint
  
  inline _LIBCPP_INLINE_VISIBILITY float       rint(float __lcpp_x) _NOEXCEPT       {return ::rintf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double rint(long double __lcpp_x) _NOEXCEPT {return ::rintl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  rint(_A1 __lcpp_x) _NOEXCEPT {return ::rint((double)__lcpp_x);}
  
  // round
  
  inline _LIBCPP_INLINE_VISIBILITY float       round(float __lcpp_x) _NOEXCEPT       {return ::roundf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double round(long double __lcpp_x) _NOEXCEPT {return ::roundl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  round(_A1 __lcpp_x) _NOEXCEPT {return ::round((double)__lcpp_x);}
  
  // scalbln
  
  inline _LIBCPP_INLINE_VISIBILITY float       scalbln(float __lcpp_x, long __lcpp_y) _NOEXCEPT       {return ::scalblnf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double scalbln(long double __lcpp_x, long __lcpp_y) _NOEXCEPT {return ::scalblnl(__lcpp_x, __lcpp_y);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  scalbln(_A1 __lcpp_x, long __lcpp_y) _NOEXCEPT {return ::scalbln((double)__lcpp_x, __lcpp_y);}
  
  // scalbn
  
  inline _LIBCPP_INLINE_VISIBILITY float       scalbn(float __lcpp_x, int __lcpp_y) _NOEXCEPT       {return ::scalbnf(__lcpp_x, __lcpp_y);}
  inline _LIBCPP_INLINE_VISIBILITY long double scalbn(long double __lcpp_x, int __lcpp_y) _NOEXCEPT {return ::scalbnl(__lcpp_x, __lcpp_y);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  scalbn(_A1 __lcpp_x, int __lcpp_y) _NOEXCEPT {return ::scalbn((double)__lcpp_x, __lcpp_y);}
  
  // tgamma
  
  inline _LIBCPP_INLINE_VISIBILITY float       tgamma(float __lcpp_x) _NOEXCEPT       {return ::tgammaf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double tgamma(long double __lcpp_x) _NOEXCEPT {return ::tgammal(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  tgamma(_A1 __lcpp_x) _NOEXCEPT {return ::tgamma((double)__lcpp_x);}
  
  // trunc
  
  inline _LIBCPP_INLINE_VISIBILITY float       trunc(float __lcpp_x) _NOEXCEPT       {return ::truncf(__lcpp_x);}
  inline _LIBCPP_INLINE_VISIBILITY long double trunc(long double __lcpp_x) _NOEXCEPT {return ::truncl(__lcpp_x);}
  
  template <class _A1>
  inline _LIBCPP_INLINE_VISIBILITY
  typename std::enable_if<std::is_integral<_A1>::value, double>::type
  trunc(_A1 __lcpp_x) _NOEXCEPT {return ::trunc((double)__lcpp_x);}
  
  #endif // !(defined(_LIBCPP_MSVCRT) && ((_VC_CRT_MAJOR_VERSION-0) < 14))
  
  } // extern "C++"
  
  #endif // __cplusplus
  
  #endif  // _LIBCPP_MATH_H
  