649 lines
16 KiB
C++
649 lines
16 KiB
C++
// -*- C++ -*-
|
|
//===---------------------------- cmath -----------------------------------===//
|
|
//
|
|
// 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_CMATH
|
|
#define _LIBCPP_CMATH
|
|
|
|
/*
|
|
cmath synopsis
|
|
|
|
Macros:
|
|
|
|
HUGE_VAL
|
|
HUGE_VALF // C99
|
|
HUGE_VALL // C99
|
|
INFINITY // C99
|
|
NAN // C99
|
|
FP_INFINITE // C99
|
|
FP_NAN // C99
|
|
FP_NORMAL // C99
|
|
FP_SUBNORMAL // C99
|
|
FP_ZERO // C99
|
|
FP_FAST_FMA // C99
|
|
FP_FAST_FMAF // C99
|
|
FP_FAST_FMAL // C99
|
|
FP_ILOGB0 // C99
|
|
FP_ILOGBNAN // C99
|
|
MATH_ERRNO // C99
|
|
MATH_ERREXCEPT // C99
|
|
math_errhandling // C99
|
|
|
|
namespace std
|
|
{
|
|
|
|
Types:
|
|
|
|
float_t // C99
|
|
double_t // C99
|
|
|
|
// C90
|
|
|
|
floating_point abs(floating_point x);
|
|
|
|
floating_point acos (arithmetic x);
|
|
float acosf(float x);
|
|
long double acosl(long double x);
|
|
|
|
floating_point asin (arithmetic x);
|
|
float asinf(float x);
|
|
long double asinl(long double x);
|
|
|
|
floating_point atan (arithmetic x);
|
|
float atanf(float x);
|
|
long double atanl(long double x);
|
|
|
|
floating_point atan2 (arithmetic y, arithmetic x);
|
|
float atan2f(float y, float x);
|
|
long double atan2l(long double y, long double x);
|
|
|
|
floating_point ceil (arithmetic x);
|
|
float ceilf(float x);
|
|
long double ceill(long double x);
|
|
|
|
floating_point cos (arithmetic x);
|
|
float cosf(float x);
|
|
long double cosl(long double x);
|
|
|
|
floating_point cosh (arithmetic x);
|
|
float coshf(float x);
|
|
long double coshl(long double x);
|
|
|
|
floating_point exp (arithmetic x);
|
|
float expf(float x);
|
|
long double expl(long double x);
|
|
|
|
floating_point fabs (arithmetic x);
|
|
float fabsf(float x);
|
|
long double fabsl(long double x);
|
|
|
|
floating_point floor (arithmetic x);
|
|
float floorf(float x);
|
|
long double floorl(long double x);
|
|
|
|
floating_point fmod (arithmetic x, arithmetic y);
|
|
float fmodf(float x, float y);
|
|
long double fmodl(long double x, long double y);
|
|
|
|
floating_point frexp (arithmetic value, int* exp);
|
|
float frexpf(float value, int* exp);
|
|
long double frexpl(long double value, int* exp);
|
|
|
|
floating_point ldexp (arithmetic value, int exp);
|
|
float ldexpf(float value, int exp);
|
|
long double ldexpl(long double value, int exp);
|
|
|
|
floating_point log (arithmetic x);
|
|
float logf(float x);
|
|
long double logl(long double x);
|
|
|
|
floating_point log10 (arithmetic x);
|
|
float log10f(float x);
|
|
long double log10l(long double x);
|
|
|
|
floating_point modf (floating_point value, floating_point* iptr);
|
|
float modff(float value, float* iptr);
|
|
long double modfl(long double value, long double* iptr);
|
|
|
|
floating_point pow (arithmetic x, arithmetic y);
|
|
float powf(float x, float y);
|
|
long double powl(long double x, long double y);
|
|
|
|
floating_point sin (arithmetic x);
|
|
float sinf(float x);
|
|
long double sinl(long double x);
|
|
|
|
floating_point sinh (arithmetic x);
|
|
float sinhf(float x);
|
|
long double sinhl(long double x);
|
|
|
|
floating_point sqrt (arithmetic x);
|
|
float sqrtf(float x);
|
|
long double sqrtl(long double x);
|
|
|
|
floating_point tan (arithmetic x);
|
|
float tanf(float x);
|
|
long double tanl(long double x);
|
|
|
|
floating_point tanh (arithmetic x);
|
|
float tanhf(float x);
|
|
long double tanhl(long double x);
|
|
|
|
// C99
|
|
|
|
bool signbit(arithmetic x);
|
|
|
|
int fpclassify(arithmetic x);
|
|
|
|
bool isfinite(arithmetic x);
|
|
bool isinf(arithmetic x);
|
|
bool isnan(arithmetic x);
|
|
bool isnormal(arithmetic x);
|
|
|
|
bool isgreater(arithmetic x, arithmetic y);
|
|
bool isgreaterequal(arithmetic x, arithmetic y);
|
|
bool isless(arithmetic x, arithmetic y);
|
|
bool islessequal(arithmetic x, arithmetic y);
|
|
bool islessgreater(arithmetic x, arithmetic y);
|
|
bool isunordered(arithmetic x, arithmetic y);
|
|
|
|
floating_point acosh (arithmetic x);
|
|
float acoshf(float x);
|
|
long double acoshl(long double x);
|
|
|
|
floating_point asinh (arithmetic x);
|
|
float asinhf(float x);
|
|
long double asinhl(long double x);
|
|
|
|
floating_point atanh (arithmetic x);
|
|
float atanhf(float x);
|
|
long double atanhl(long double x);
|
|
|
|
floating_point cbrt (arithmetic x);
|
|
float cbrtf(float x);
|
|
long double cbrtl(long double x);
|
|
|
|
floating_point copysign (arithmetic x, arithmetic y);
|
|
float copysignf(float x, float y);
|
|
long double copysignl(long double x, long double y);
|
|
|
|
floating_point erf (arithmetic x);
|
|
float erff(float x);
|
|
long double erfl(long double x);
|
|
|
|
floating_point erfc (arithmetic x);
|
|
float erfcf(float x);
|
|
long double erfcl(long double x);
|
|
|
|
floating_point exp2 (arithmetic x);
|
|
float exp2f(float x);
|
|
long double exp2l(long double x);
|
|
|
|
floating_point expm1 (arithmetic x);
|
|
float expm1f(float x);
|
|
long double expm1l(long double x);
|
|
|
|
floating_point fdim (arithmetic x, arithmetic y);
|
|
float fdimf(float x, float y);
|
|
long double fdiml(long double x, long double y);
|
|
|
|
floating_point fma (arithmetic x, arithmetic y, arithmetic z);
|
|
float fmaf(float x, float y, float z);
|
|
long double fmal(long double x, long double y, long double z);
|
|
|
|
floating_point fmax (arithmetic x, arithmetic y);
|
|
float fmaxf(float x, float y);
|
|
long double fmaxl(long double x, long double y);
|
|
|
|
floating_point fmin (arithmetic x, arithmetic y);
|
|
float fminf(float x, float y);
|
|
long double fminl(long double x, long double y);
|
|
|
|
floating_point hypot (arithmetic x, arithmetic y);
|
|
float hypotf(float x, float y);
|
|
long double hypotl(long double x, long double y);
|
|
|
|
double hypot(double x, double y, double z); // C++17
|
|
float hypot(float x, float y, float z); // C++17
|
|
long double hypot(long double x, long double y, long double z); // C++17
|
|
|
|
int ilogb (arithmetic x);
|
|
int ilogbf(float x);
|
|
int ilogbl(long double x);
|
|
|
|
floating_point lgamma (arithmetic x);
|
|
float lgammaf(float x);
|
|
long double lgammal(long double x);
|
|
|
|
long long llrint (arithmetic x);
|
|
long long llrintf(float x);
|
|
long long llrintl(long double x);
|
|
|
|
long long llround (arithmetic x);
|
|
long long llroundf(float x);
|
|
long long llroundl(long double x);
|
|
|
|
floating_point log1p (arithmetic x);
|
|
float log1pf(float x);
|
|
long double log1pl(long double x);
|
|
|
|
floating_point log2 (arithmetic x);
|
|
float log2f(float x);
|
|
long double log2l(long double x);
|
|
|
|
floating_point logb (arithmetic x);
|
|
float logbf(float x);
|
|
long double logbl(long double x);
|
|
|
|
long lrint (arithmetic x);
|
|
long lrintf(float x);
|
|
long lrintl(long double x);
|
|
|
|
long lround (arithmetic x);
|
|
long lroundf(float x);
|
|
long lroundl(long double x);
|
|
|
|
double nan (const char* str);
|
|
float nanf(const char* str);
|
|
long double nanl(const char* str);
|
|
|
|
floating_point nearbyint (arithmetic x);
|
|
float nearbyintf(float x);
|
|
long double nearbyintl(long double x);
|
|
|
|
floating_point nextafter (arithmetic x, arithmetic y);
|
|
float nextafterf(float x, float y);
|
|
long double nextafterl(long double x, long double y);
|
|
|
|
floating_point nexttoward (arithmetic x, long double y);
|
|
float nexttowardf(float x, long double y);
|
|
long double nexttowardl(long double x, long double y);
|
|
|
|
floating_point remainder (arithmetic x, arithmetic y);
|
|
float remainderf(float x, float y);
|
|
long double remainderl(long double x, long double y);
|
|
|
|
floating_point remquo (arithmetic x, arithmetic y, int* pquo);
|
|
float remquof(float x, float y, int* pquo);
|
|
long double remquol(long double x, long double y, int* pquo);
|
|
|
|
floating_point rint (arithmetic x);
|
|
float rintf(float x);
|
|
long double rintl(long double x);
|
|
|
|
floating_point round (arithmetic x);
|
|
float roundf(float x);
|
|
long double roundl(long double x);
|
|
|
|
floating_point scalbln (arithmetic x, long ex);
|
|
float scalblnf(float x, long ex);
|
|
long double scalblnl(long double x, long ex);
|
|
|
|
floating_point scalbn (arithmetic x, int ex);
|
|
float scalbnf(float x, int ex);
|
|
long double scalbnl(long double x, int ex);
|
|
|
|
floating_point tgamma (arithmetic x);
|
|
float tgammaf(float x);
|
|
long double tgammal(long double x);
|
|
|
|
floating_point trunc (arithmetic x);
|
|
float truncf(float x);
|
|
long double truncl(long double x);
|
|
|
|
} // std
|
|
|
|
*/
|
|
|
|
#include <__config>
|
|
#include <math.h>
|
|
#include <version>
|
|
#include <type_traits>
|
|
|
|
#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;
|
|
using ::fpclassify;
|
|
using ::isfinite;
|
|
using ::isinf;
|
|
using ::isnan;
|
|
using ::isnormal;
|
|
using ::isgreater;
|
|
using ::isgreaterequal;
|
|
using ::isless;
|
|
using ::islessequal;
|
|
using ::islessgreater;
|
|
using ::isunordered;
|
|
using ::isunordered;
|
|
|
|
using ::float_t;
|
|
using ::double_t;
|
|
|
|
#ifndef _AIX
|
|
using ::abs;
|
|
#endif
|
|
|
|
using ::acos;
|
|
using ::acosf;
|
|
using ::asin;
|
|
using ::asinf;
|
|
using ::atan;
|
|
using ::atanf;
|
|
using ::atan2;
|
|
using ::atan2f;
|
|
using ::ceil;
|
|
using ::ceilf;
|
|
using ::cos;
|
|
using ::cosf;
|
|
using ::cosh;
|
|
using ::coshf;
|
|
|
|
using ::exp;
|
|
using ::expf;
|
|
|
|
using ::fabs;
|
|
using ::fabsf;
|
|
using ::floor;
|
|
using ::floorf;
|
|
|
|
using ::fmod;
|
|
using ::fmodf;
|
|
|
|
using ::frexp;
|
|
using ::frexpf;
|
|
using ::ldexp;
|
|
using ::ldexpf;
|
|
|
|
using ::log;
|
|
using ::logf;
|
|
|
|
using ::log10;
|
|
using ::log10f;
|
|
using ::modf;
|
|
using ::modff;
|
|
|
|
using ::pow;
|
|
using ::powf;
|
|
|
|
using ::sin;
|
|
using ::sinf;
|
|
using ::sinh;
|
|
using ::sinhf;
|
|
|
|
using ::sqrt;
|
|
using ::sqrtf;
|
|
using ::tan;
|
|
using ::tanf;
|
|
|
|
using ::tanh;
|
|
using ::tanhf;
|
|
|
|
using ::acosh;
|
|
using ::acoshf;
|
|
using ::asinh;
|
|
using ::asinhf;
|
|
using ::atanh;
|
|
using ::atanhf;
|
|
using ::cbrt;
|
|
using ::cbrtf;
|
|
|
|
using ::copysign;
|
|
using ::copysignf;
|
|
|
|
using ::erf;
|
|
using ::erff;
|
|
using ::erfc;
|
|
using ::erfcf;
|
|
using ::exp2;
|
|
using ::exp2f;
|
|
using ::expm1;
|
|
using ::expm1f;
|
|
using ::fdim;
|
|
using ::fdimf;
|
|
using ::fmaf;
|
|
using ::fma;
|
|
using ::fmax;
|
|
using ::fmaxf;
|
|
using ::fmin;
|
|
using ::fminf;
|
|
using ::hypot;
|
|
using ::hypotf;
|
|
using ::ilogb;
|
|
using ::ilogbf;
|
|
using ::lgamma;
|
|
using ::lgammaf;
|
|
using ::llrint;
|
|
using ::llrintf;
|
|
using ::llround;
|
|
using ::llroundf;
|
|
using ::log1p;
|
|
using ::log1pf;
|
|
using ::log2;
|
|
using ::log2f;
|
|
using ::logb;
|
|
using ::logbf;
|
|
using ::lrint;
|
|
using ::lrintf;
|
|
using ::lround;
|
|
using ::lroundf;
|
|
|
|
using ::nan;
|
|
using ::nanf;
|
|
|
|
using ::nearbyint;
|
|
using ::nearbyintf;
|
|
using ::nextafter;
|
|
using ::nextafterf;
|
|
using ::nexttoward;
|
|
using ::nexttowardf;
|
|
using ::remainder;
|
|
using ::remainderf;
|
|
using ::remquo;
|
|
using ::remquof;
|
|
using ::rint;
|
|
using ::rintf;
|
|
using ::round;
|
|
using ::roundf;
|
|
using ::scalbln;
|
|
using ::scalblnf;
|
|
using ::scalbn;
|
|
using ::scalbnf;
|
|
using ::tgamma;
|
|
using ::tgammaf;
|
|
using ::trunc;
|
|
using ::truncf;
|
|
|
|
using ::acosl;
|
|
using ::asinl;
|
|
using ::atanl;
|
|
using ::atan2l;
|
|
using ::ceill;
|
|
using ::cosl;
|
|
using ::coshl;
|
|
using ::expl;
|
|
using ::fabsl;
|
|
using ::floorl;
|
|
using ::fmodl;
|
|
using ::frexpl;
|
|
using ::ldexpl;
|
|
using ::logl;
|
|
using ::log10l;
|
|
using ::modfl;
|
|
using ::powl;
|
|
using ::sinl;
|
|
using ::sinhl;
|
|
using ::sqrtl;
|
|
using ::tanl;
|
|
|
|
using ::tanhl;
|
|
using ::acoshl;
|
|
using ::asinhl;
|
|
using ::atanhl;
|
|
using ::cbrtl;
|
|
|
|
using ::copysignl;
|
|
|
|
using ::erfl;
|
|
using ::erfcl;
|
|
using ::exp2l;
|
|
using ::expm1l;
|
|
using ::fdiml;
|
|
using ::fmal;
|
|
using ::fmaxl;
|
|
using ::fminl;
|
|
using ::hypotl;
|
|
using ::ilogbl;
|
|
using ::lgammal;
|
|
using ::llrintl;
|
|
using ::llroundl;
|
|
using ::log1pl;
|
|
using ::log2l;
|
|
using ::logbl;
|
|
using ::lrintl;
|
|
using ::lroundl;
|
|
using ::nanl;
|
|
using ::nearbyintl;
|
|
using ::nextafterl;
|
|
using ::nexttowardl;
|
|
using ::remainderl;
|
|
using ::remquol;
|
|
using ::rintl;
|
|
using ::roundl;
|
|
using ::scalblnl;
|
|
using ::scalbnl;
|
|
using ::tgammal;
|
|
using ::truncl;
|
|
|
|
#if _LIBCPP_STD_VER > 14
|
|
inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); }
|
|
inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); }
|
|
inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); }
|
|
|
|
template <class _A1, class _A2, class _A3>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename __lazy_enable_if
|
|
<
|
|
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 hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
|
|
}
|
|
#endif
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
#if __has_builtin(__builtin_isnan)
|
|
return __builtin_isnan(__lcpp_x);
|
|
#else
|
|
return isnan(__lcpp_x);
|
|
#endif
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
return isnan(__lcpp_x);
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
#if __has_builtin(__builtin_isinf)
|
|
return __builtin_isinf(__lcpp_x);
|
|
#else
|
|
return isinf(__lcpp_x);
|
|
#endif
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
return isinf(__lcpp_x);
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
#if __has_builtin(__builtin_isfinite)
|
|
return __builtin_isfinite(__lcpp_x);
|
|
#else
|
|
return isfinite(__lcpp_x);
|
|
#endif
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
return isfinite(__lcpp_x);
|
|
}
|
|
|
|
template <class _IntT, class _FloatT,
|
|
bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits),
|
|
int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT {
|
|
static_assert(is_floating_point<_FloatT>::value, "must be a floating point type");
|
|
static_assert(is_integral<_IntT>::value, "must be an integral type");
|
|
static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix");
|
|
static_assert(is_same<_FloatT, float>::value || is_same<_FloatT, double>::value
|
|
|| is_same<_FloatT,long double>::value, "unsupported floating point type");
|
|
return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits);
|
|
}
|
|
|
|
// Convert a floating point number to the specified integral type after
|
|
// clamping to the integral types representable range.
|
|
//
|
|
// The behavior is undefined if `__r` is NaN.
|
|
template <class _IntT, class _RealT>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT {
|
|
using _Lim = std::numeric_limits<_IntT>;
|
|
const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>();
|
|
if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) {
|
|
return _Lim::max();
|
|
} else if (__r <= _Lim::lowest()) {
|
|
return _Lim::min();
|
|
}
|
|
return static_cast<_IntT>(__r);
|
|
}
|
|
|
|
_LIBCPP_END_NAMESPACE_STD
|
|
|
|
_LIBCPP_POP_MACROS
|
|
|
|
#endif // _LIBCPP_CMATH
|