Overhauled WIN32 math and added missing functions:
1) Cleanup: moved function implementations from win32/include/math.h to win32/include/tcc/tcc_libm.h 2) Added missing math functions: MUSL: asinh(), acosh(), atanh(), scalbn(). My impl: log1p(), expm1(), ilogb(), scalbln(), nexttoward() - now only a few are missing: remquo(), remainder(), fma(), nan(), erf(), erfc(), nearbyint(). 3) Added/defined all missing *f() and *l() math functions. 4) Added functions have short but accurate/fast implementations. 5) Added <tgmath.h> for all platforms. (not too useful, IMO, but is C99 standard).
This commit is contained in:
Tyge Løvset
parent
82611f5e6d
commit
b11144d69c
3 changed files with 484 additions and 321 deletions
89
include/tgmath.h
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89
include/tgmath.h
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/*
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* ISO C Standard: 7.22 Type-generic math <tgmath.h>
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*/
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#ifndef _TGMATH_H
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#define _TGMATH_H
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#include <math.h>
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#ifndef __cplusplus
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#define __tgmath_real(x, F) \
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_Generic ((x), float: F##f, long double: F##l, default: F)(x)
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#define __tgmath_real_2_1(x, y, F) \
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_Generic ((x), float: F##f, long double: F##l, default: F)(x, y)
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#define __tgmath_real_2(x, y, F) \
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_Generic ((x)+(y), float: F##f, long double: F##l, default: F)(x, y)
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#define __tgmath_real_3_2(x, y, z, F) \
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_Generic ((x)+(y), float: F##f, long double: F##l, default: F)(x, y, z)
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#define __tgmath_real_3(x, y, z, F) \
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_Generic ((x)+(y)+(z), float: F##f, long double: F##l, default: F)(x, y, z)
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/* Functions defined in both <math.h> and <complex.h> (7.22p4) */
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#define acos(z) __tgmath_real(z, acos)
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#define asin(z) __tgmath_real(z, asin)
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#define atan(z) __tgmath_real(z, atan)
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#define acosh(z) __tgmath_real(z, acosh)
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#define asinh(z) __tgmath_real(z, asinh)
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#define atanh(z) __tgmath_real(z, atanh)
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#define cos(z) __tgmath_real(z, cos)
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#define sin(z) __tgmath_real(z, sin)
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#define tan(z) __tgmath_real(z, tan)
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#define cosh(z) __tgmath_real(z, cosh)
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#define sinh(z) __tgmath_real(z, sinh)
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#define tanh(z) __tgmath_real(z, tanh)
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#define exp(z) __tgmath_real(z, exp)
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#define log(z) __tgmath_real(z, log)
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#define pow(z1,z2) __tgmath_real_2(z1, z2, pow)
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#define sqrt(z) __tgmath_real(z, sqrt)
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#define fabs(z) __tgmath_real(z, fabs)
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/* Functions defined in <math.h> only (7.22p5) */
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#define atan2(x,y) __tgmath_real_2(x, y, atan2)
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#define cbrt(x) __tgmath_real(x, cbrt)
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#define ceil(x) __tgmath_real(x, ceil)
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#define copysign(x,y) __tgmath_real_2(x, y, copysign)
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#define erf(x) __tgmath_real(x, erf)
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#define erfc(x) __tgmath_real(x, erfc)
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#define exp2(x) __tgmath_real(x, exp2)
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#define expm1(x) __tgmath_real(x, expm1)
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#define fdim(x,y) __tgmath_real_2(x, y, fdim)
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#define floor(x) __tgmath_real(x, floor)
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#define fma(x,y,z) __tgmath_real_3(x, y, z, fma)
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#define fmax(x,y) __tgmath_real_2(x, y, fmax)
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#define fmin(x,y) __tgmath_real_2(x, y, fmin)
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#define fmod(x,y) __tgmath_real_2(x, y, fmod)
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#define frexp(x,y) __tgmath_real_2_1(x, y, frexp)
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#define hypot(x,y) __tgmath_real_2(x, y, hypot)
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#define ilogb(x) __tgmath_real(x, ilogb)
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#define ldexp(x,y) __tgmath_real_2_1(x, y, ldexp)
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#define lgamma(x) __tgmath_real(x, lgamma)
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#define llrint(x) __tgmath_real(x, llrint)
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#define llround(x) __tgmath_real(x, llround)
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#define log10(x) __tgmath_real(x, log10)
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#define log1p(x) __tgmath_real(x, log1p)
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#define log2(x) __tgmath_real(x, log2)
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#define logb(x) __tgmath_real(x, logb)
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#define lrint(x) __tgmath_real(x, lrint)
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#define lround(x) __tgmath_real(x, lround)
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#define nearbyint(x) __tgmath_real(x, nearbyint)
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#define nextafter(x,y) __tgmath_real_2(x, y, nextafter)
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#define nexttoward(x,y) __tgmath_real_2(x, y, nexttoward)
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#define remainder(x,y) __tgmath_real_2(x, y, remainder)
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#define remquo(x,y,z) __tgmath_real_3_2(x, y, z, remquo)
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#define rint(x) __tgmath_real(x, rint)
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#define round(x) __tgmath_real(x, round)
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#define scalbln(x,y) __tgmath_real_2_1(x, y, scalbln)
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#define scalbn(x,y) __tgmath_real_2_1(x, y, scalbn)
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#define tgamma(x) __tgmath_real(x, tgamma)
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#define trunc(x) __tgmath_real(x, trunc)
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/* Functions defined in <complex.h> only (7.22p6)
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#define carg(z) __tgmath_cplx_only(z, carg)
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#define cimag(z) __tgmath_cplx_only(z, cimag)
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#define conj(z) __tgmath_cplx_only(z, conj)
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#define cproj(z) __tgmath_cplx_only(z, cproj)
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#define creal(z) __tgmath_cplx_only(z, creal)
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*/
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#endif /* __cplusplus */
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#endif /* _TGMATH_H */
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int __cdecl _fpclassf(float _X);
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int __cdecl _fpclassf(float _X);
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#endif
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#endif
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#ifndef __cplusplus
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#define _hypotl(x,y) ((long double)_hypot((double)(x),(double)(y)))
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#define _matherrl _matherr
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__CRT_INLINE long double _chgsignl(long double _Number) { return _chgsign((double)(_Number)); }
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__CRT_INLINE long double _copysignl(long double _Number,long double _Sign) { return _copysign((double)(_Number),(double)(_Sign)); }
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__CRT_INLINE float frexpf(float _X,int *_Y) { return ((float)frexp((double)_X,_Y)); }
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#if !defined (__ia64__)
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__CRT_INLINE float __cdecl fabsf (float x)
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{
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#ifdef _WIN64
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*((int *) &x) &= 0x7fffffff;
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return x;
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#else
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float res;
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__asm__ ("fabs;" : "=t" (res) : "0" (x));
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return res;
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#endif
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}
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__CRT_INLINE float __cdecl ldexpf (float x, int expn) { return (float) ldexp (x, expn); }
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#endif
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#if defined (_WIN32) && !defined(_WIN64)
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__CRT_INLINE float acosf(float x) { return (float) acos(x); }
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__CRT_INLINE float asinf(float x) { return (float) asin(x); }
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__CRT_INLINE float atanf(float x) { return (float) atan(x); }
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__CRT_INLINE float atan2f(float x, float y) { return (float) atan2(x, y); }
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__CRT_INLINE float ceilf(float x) { return (float) ceil(x); }
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__CRT_INLINE float cosf(float x) { return (float) cos(x); }
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__CRT_INLINE float coshf(float x) { return (float) cosh(x); }
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__CRT_INLINE float expf(float x) { return (float) exp(x); }
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__CRT_INLINE float floorf(float x) { return (float) floor(x); }
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__CRT_INLINE float fmodf(float x, float y) { return (float) fmod(x, y); }
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__CRT_INLINE float logf(float x) { return (float) log(x); }
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__CRT_INLINE float logbf(float x) { return (float) logb(x); }
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__CRT_INLINE float log10f(float x) { return (float) log10(x); }
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__CRT_INLINE float modff(float x, float *y) {
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double di, df = modf(x, &di);
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*y = (float) di; return (float) df;
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}
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__CRT_INLINE float powf(float x, float y) { return (float) pow(x, y); }
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__CRT_INLINE float sinf(float x) { return (float) sin(x); }
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__CRT_INLINE float sinhf(float x) { return (float) sinh(x); }
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__CRT_INLINE float sqrtf(float x) { return (float) sqrt(x); }
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__CRT_INLINE float tanf(float x) { return (float) tan(x); }
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__CRT_INLINE float tanhf(float x) { return (float) tanh(x); }
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#endif
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#else
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// cplusplus
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__CRT_INLINE long double __cdecl fabsl (long double x)
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{
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long double res;
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__asm__ ("fabs;" : "=t" (res) : "0" (x));
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return res;
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}
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__CRT_INLINE long double modfl(long double _X,long double *_Y) {
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double _Di,_Df = modf((double)_X,&_Di);
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*_Y = (long double)_Di;
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return (_Df);
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}
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__CRT_INLINE long double _chgsignl(long double _Number) { return _chgsign(static_cast<double>(_Number)); }
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__CRT_INLINE long double _copysignl(long double _Number,long double _Sign) { return _copysign(static_cast<double>(_Number),static_cast<double>(_Sign)); }
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__CRT_INLINE float frexpf(float _X,int *_Y) { return ((float)frexp((double)_X,_Y)); }
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#ifndef __ia64__
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__CRT_INLINE float __cdecl fabsf (float x)
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{
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float res;
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__asm__ ("fabs;" : "=t" (res) : "0" (x));
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return res;
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}
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__CRT_INLINE float __cdecl ldexpf (float x, int expn) { return (float) ldexp (x, expn); }
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#ifndef __x86_64
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__CRT_INLINE float acosf(float _X) { return ((float)acos((double)_X)); }
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__CRT_INLINE float asinf(float _X) { return ((float)asin((double)_X)); }
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__CRT_INLINE float atanf(float _X) { return ((float)atan((double)_X)); }
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__CRT_INLINE float atan2f(float _X,float _Y) { return ((float)atan2((double)_X,(double)_Y)); }
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__CRT_INLINE float ceilf(float _X) { return ((float)ceil((double)_X)); }
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__CRT_INLINE float cosf(float _X) { return ((float)cos((double)_X)); }
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__CRT_INLINE float coshf(float _X) { return ((float)cosh((double)_X)); }
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__CRT_INLINE float expf(float _X) { return ((float)exp((double)_X)); }
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__CRT_INLINE float floorf(float _X) { return ((float)floor((double)_X)); }
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__CRT_INLINE float fmodf(float _X,float _Y) { return ((float)fmod((double)_X,(double)_Y)); }
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__CRT_INLINE float logf(float _X) { return ((float)log((double)_X)); }
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__CRT_INLINE float log10f(float _X) { return ((float)log10((double)_X)); }
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__CRT_INLINE float modff(float _X,float *_Y) {
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double _Di,_Df = modf((double)_X,&_Di);
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*_Y = (float)_Di;
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return ((float)_Df);
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}
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__CRT_INLINE float powf(float _X,float _Y) { return ((float)pow((double)_X,(double)_Y)); }
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__CRT_INLINE float sinf(float _X) { return ((float)sin((double)_X)); }
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__CRT_INLINE float sinhf(float _X) { return ((float)sinh((double)_X)); }
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__CRT_INLINE float sqrtf(float _X) { return ((float)sqrt((double)_X)); }
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__CRT_INLINE float tanf(float _X) { return ((float)tan((double)_X)); }
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__CRT_INLINE float tanhf(float _X) { return ((float)tanh((double)_X)); }
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#endif
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#endif
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#endif
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#ifndef NO_OLDNAMES
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#ifndef NO_OLDNAMES
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#define matherr _matherr
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#define matherr _matherr
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extern int __cdecl __fpclassify (double);
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extern int __cdecl __fpclassify (double);
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extern int __cdecl __fpclassifyl (long double);
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extern int __cdecl __fpclassifyl (long double);
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/* Implemented at tcc/tcc_libm.h */
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/* Implemented at tcc/tcc_libm.h
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#define fpclassify(x) (sizeof (x) == sizeof (float) ? __fpclassifyf (x) \
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#define fpclassify(x) (sizeof (x) == sizeof (float) ? __fpclassifyf (x) \
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: sizeof (x) == sizeof (double) ? __fpclassify (x) \
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: sizeof (x) == sizeof (double) ? __fpclassify (x) \
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: __fpclassifyl (x))
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: __fpclassifyl (x))
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*/
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#define fpclassify(x) \
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_Generic(x, float: __fpclassifyf, double: __fpclassify, long double: __fpclassifyl)(x)
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/* 7.12.3.2 */
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/* 7.12.3.2 */
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#define isfinite(x) ((fpclassify(x) & FP_NAN) == 0)
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#define isfinite(x) ((fpclassify(x) & FP_NAN) == 0)
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extern int __cdecl __signbit (double);
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extern int __cdecl __signbit (double);
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extern int __cdecl __signbitl (long double);
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extern int __cdecl __signbitl (long double);
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/* Implemented at tcc/tcc_libm.h */
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/* Implemented at tcc/tcc_libm.h
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#define signbit(x) (sizeof (x) == sizeof (float) ? __signbitf (x) \
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#define signbit(x) (sizeof (x) == sizeof (float) ? __signbitf (x) \
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: sizeof (x) == sizeof (double) ? __signbit (x) \
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: sizeof (x) == sizeof (double) ? __signbit (x) \
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: __signbitl (x))
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: __signbitl (x))
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*/
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#define signbit(x) \
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_Generic(x, float: __signbitf, double: __signbit, long double: signbitl)(x)
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extern double __cdecl exp2(double);
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extern double __cdecl exp2(double);
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extern float __cdecl exp2f(float);
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extern float __cdecl exp2f(float);
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extern double __cdecl logb (double);
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extern double __cdecl logb (double);
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extern float __cdecl logbf (float);
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extern float __cdecl logbf (float);
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extern long double __cdecl logbl (long double);
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extern long double __cdecl logbl (long double);
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#ifndef _WIN32
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__CRT_INLINE double __cdecl logb (double x)
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{
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double res;
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__asm__ ("fxtract\n\t"
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"fstp %%st" : "=t" (res) : "0" (x));
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return res;
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}
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__CRT_INLINE float __cdecl logbf (float x)
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{
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float res;
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__asm__ ("fxtract\n\t"
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"fstp %%st" : "=t" (res) : "0" (x));
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return res;
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}
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__CRT_INLINE long double __cdecl logbl (long double x)
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{
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long double res;
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__asm__ ("fxtract\n\t"
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"fstp %%st" : "=t" (res) : "0" (x));
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return res;
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}
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#endif
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extern long double __cdecl modfl (long double, long double*);
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extern long double __cdecl modfl (long double, long double*);
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extern float __cdecl cbrtf (float);
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extern float __cdecl cbrtf (float);
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extern long double __cdecl cbrtl (long double);
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extern long double __cdecl cbrtl (long double);
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__CRT_INLINE float __cdecl hypotf (float x, float y)
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extern double __cdecl hypot (double, double);
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{ return (float) hypot (x, y);}
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extern float __cdecl hypotf (float, float);
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extern long double __cdecl hypotl (long double, long double);
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extern long double __cdecl hypotl (long double, long double);
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extern long double __cdecl powl (long double, long double);
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extern long double __cdecl powl (long double, long double);
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/* 7.12.9.4 */
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/* 7.12.9.4 */
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/* round, using fpu control word settings */
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/* round, using fpu control word settings */
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__CRT_INLINE double __cdecl rint (double x)
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extern double __cdecl rint (double);
|
||||||
{
|
extern float __cdecl rintf (float);
|
||||||
double retval;
|
extern long double __cdecl rintl (long double);
|
||||||
__asm__ (
|
|
||||||
"fldl %1\n"
|
|
||||||
"frndint \n"
|
|
||||||
"fstpl %0\n" : "=m" (retval) : "m" (x));
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE float __cdecl rintf (float x)
|
extern long __cdecl lrint (double);
|
||||||
{
|
extern long __cdecl lrintf (float);
|
||||||
float retval;
|
extern long __cdecl lrintl (long double);
|
||||||
__asm__ (
|
|
||||||
"flds %1\n"
|
|
||||||
"frndint \n"
|
|
||||||
"fstps %0\n" : "=m" (retval) : "m" (x));
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE long double __cdecl rintl (long double x)
|
extern long long __cdecl llrint (double);
|
||||||
{
|
extern long long __cdecl llrintf (float);
|
||||||
#ifdef _WIN32
|
extern long long __cdecl llrintl (long double);
|
||||||
// on win32 'long double' is double internally
|
|
||||||
return rint(x);
|
|
||||||
#else
|
|
||||||
long double retval;
|
|
||||||
__asm__ (
|
|
||||||
"fldt %1\n"
|
|
||||||
"frndint \n"
|
|
||||||
"fstpt %0\n" : "=m" (retval) : "m" (x));
|
|
||||||
return retval;
|
|
||||||
#endif
|
|
||||||
}
|
|
||||||
|
|
||||||
/* 7.12.9.5 */
|
|
||||||
__CRT_INLINE long __cdecl lrint (double x)
|
|
||||||
{
|
|
||||||
long retval;
|
|
||||||
__asm__ __volatile__ \
|
|
||||||
("fldl %1\n" \
|
|
||||||
"fistpl %0" : "=m" (retval) : "m" (x)); \
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE long __cdecl lrintf (float x)
|
|
||||||
{
|
|
||||||
long retval;
|
|
||||||
__asm__ __volatile__ \
|
|
||||||
("flds %1\n" \
|
|
||||||
"fistpl %0" : "=m" (retval) : "m" (x)); \
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE long __cdecl lrintl (long double x)
|
|
||||||
{
|
|
||||||
long retval;
|
|
||||||
__asm__ __volatile__ \
|
|
||||||
("fldt %1\n" \
|
|
||||||
"fistpl %0" : "=m" (retval) : "m" (x)); \
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE long long __cdecl llrint (double x)
|
|
||||||
{
|
|
||||||
long long retval;
|
|
||||||
__asm__ __volatile__ \
|
|
||||||
("fldl %1\n" \
|
|
||||||
"fistpll %0" : "=m" (retval) : "m" (x)); \
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE long long __cdecl llrintf (float x)
|
|
||||||
{
|
|
||||||
long long retval;
|
|
||||||
__asm__ __volatile__ \
|
|
||||||
("flds %1\n" \
|
|
||||||
"fistpll %0" : "=m" (retval) : "m" (x)); \
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
__CRT_INLINE long long __cdecl llrintl (long double x)
|
|
||||||
{
|
|
||||||
long long retval;
|
|
||||||
__asm__ __volatile__ \
|
|
||||||
("fldt %1\n" \
|
|
||||||
"fistpll %0" : "=m" (retval) : "m" (x)); \
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
#define FE_TONEAREST 0x0000
|
#define FE_TONEAREST 0x0000
|
||||||
#define FE_DOWNWARD 0x0400
|
#define FE_DOWNWARD 0x0400
|
||||||
#define FE_UPWARD 0x0800
|
#define FE_UPWARD 0x0800
|
||||||
#define FE_TOWARDZERO 0x0c00
|
#define FE_TOWARDZERO 0x0c00
|
||||||
|
|
||||||
__CRT_INLINE double trunc (double _x)
|
|
||||||
{
|
|
||||||
double retval;
|
|
||||||
unsigned short saved_cw;
|
|
||||||
unsigned short tmp_cw;
|
|
||||||
__asm__ ("fnstcw %0;" : "=m" (saved_cw)); /* save FPU control word */
|
|
||||||
tmp_cw = (saved_cw & ~(FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO))
|
|
||||||
| FE_TOWARDZERO;
|
|
||||||
__asm__ ("fldcw %0;" : : "m" (tmp_cw));
|
|
||||||
__asm__ ("fldl %1;"
|
|
||||||
"frndint;"
|
|
||||||
"fstpl %0;" : "=m" (retval) : "m" (_x)); /* round towards zero */
|
|
||||||
__asm__ ("fldcw %0;" : : "m" (saved_cw) ); /* restore saved control word */
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
/* 7.12.9.6 */
|
/* 7.12.9.6 */
|
||||||
/* round away from zero, regardless of fpu control word settings */
|
/* round away from zero, regardless of fpu control word settings */
|
||||||
extern double __cdecl round (double);
|
extern double __cdecl round (double);
|
||||||
|
|
@ -685,70 +473,12 @@ extern "C" {
|
||||||
extern long double __cdecl fmal (long double, long double, long double);
|
extern long double __cdecl fmal (long double, long double, long double);
|
||||||
|
|
||||||
|
|
||||||
#if 0 // gr: duplicate, see below
|
|
||||||
/* 7.12.14 */
|
|
||||||
/*
|
|
||||||
* With these functions, comparisons involving quiet NaNs set the FP
|
|
||||||
* condition code to "unordered". The IEEE floating-point spec
|
|
||||||
* dictates that the result of floating-point comparisons should be
|
|
||||||
* false whenever a NaN is involved, with the exception of the != op,
|
|
||||||
* which always returns true: yes, (NaN != NaN) is true).
|
|
||||||
*/
|
|
||||||
|
|
||||||
#if __GNUC__ >= 3
|
|
||||||
|
|
||||||
#define isgreater(x, y) __builtin_isgreater(x, y)
|
|
||||||
#define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
|
|
||||||
#define isless(x, y) __builtin_isless(x, y)
|
|
||||||
#define islessequal(x, y) __builtin_islessequal(x, y)
|
|
||||||
#define islessgreater(x, y) __builtin_islessgreater(x, y)
|
|
||||||
#define isunordered(x, y) __builtin_isunordered(x, y)
|
|
||||||
|
|
||||||
#else
|
|
||||||
/* helper */
|
|
||||||
__CRT_INLINE int __cdecl
|
|
||||||
__fp_unordered_compare (long double x, long double y){
|
|
||||||
unsigned short retval;
|
|
||||||
__asm__ ("fucom %%st(1);"
|
|
||||||
"fnstsw;": "=a" (retval) : "t" (x), "u" (y));
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
|
|
||||||
#define isgreater(x, y) ((__fp_unordered_compare(x, y) \
|
|
||||||
& 0x4500) == 0)
|
|
||||||
#define isless(x, y) ((__fp_unordered_compare (y, x) \
|
|
||||||
& 0x4500) == 0)
|
|
||||||
#define isgreaterequal(x, y) ((__fp_unordered_compare (x, y) \
|
|
||||||
& FP_INFINITE) == 0)
|
|
||||||
#define islessequal(x, y) ((__fp_unordered_compare(y, x) \
|
|
||||||
& FP_INFINITE) == 0)
|
|
||||||
#define islessgreater(x, y) ((__fp_unordered_compare(x, y) \
|
|
||||||
& FP_SUBNORMAL) == 0)
|
|
||||||
#define isunordered(x, y) ((__fp_unordered_compare(x, y) \
|
|
||||||
& 0x4500) == 0x4500)
|
|
||||||
|
|
||||||
#endif
|
|
||||||
#endif //0
|
|
||||||
|
|
||||||
|
|
||||||
#endif /* __STDC_VERSION__ >= 199901L */
|
#endif /* __STDC_VERSION__ >= 199901L */
|
||||||
#endif /* __NO_ISOCEXT */
|
#endif /* __NO_ISOCEXT */
|
||||||
|
|
||||||
#ifdef __cplusplus
|
#ifdef __cplusplus
|
||||||
}
|
}
|
||||||
extern "C++" {
|
|
||||||
template<class _Ty> inline _Ty _Pow_int(_Ty _X,int _Y) {
|
|
||||||
unsigned int _N;
|
|
||||||
if(_Y >= 0) _N = (unsigned int)_Y;
|
|
||||||
else _N = (unsigned int)(-_Y);
|
|
||||||
for(_Ty _Z = _Ty(1);;_X *= _X) {
|
|
||||||
if((_N & 1)!=0) _Z *= _X;
|
|
||||||
if((_N >>= 1)==0) return (_Y < 0 ? _Ty(1) / _Z : _Z);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
#endif
|
#endif
|
||||||
|
|
||||||
#pragma pack(pop)
|
#pragma pack(pop)
|
||||||
|
|
||||||
/* 7.12.14 */
|
/* 7.12.14 */
|
||||||
|
|
|
||||||
|
|
@ -122,17 +122,9 @@ __CRT_INLINE long double __cdecl fmaxl (long double x, long double y) {
|
||||||
|
|
||||||
/* *round* */
|
/* *round* */
|
||||||
|
|
||||||
#define TCCFP_FORCE_EVAL(x) do { \
|
#define TCCFP_FORCE_EVAL(x) do { \
|
||||||
if (sizeof(x) == sizeof(float)) { \
|
volatile typeof(x) __x; \
|
||||||
volatile float __x; \
|
__x = (x); \
|
||||||
__x = (x); \
|
|
||||||
} else if (sizeof(x) == sizeof(double)) { \
|
|
||||||
volatile double __x; \
|
|
||||||
__x = (x); \
|
|
||||||
} else { \
|
|
||||||
volatile long double __x; \
|
|
||||||
__x = (x); \
|
|
||||||
} \
|
|
||||||
} while(0)
|
} while(0)
|
||||||
|
|
||||||
__CRT_INLINE double __cdecl round (double x) {
|
__CRT_INLINE double __cdecl round (double x) {
|
||||||
|
|
@ -150,15 +142,8 @@ __CRT_INLINE double __cdecl round (double x) {
|
||||||
return 0*u.f;
|
return 0*u.f;
|
||||||
}
|
}
|
||||||
y = (double)(x + 0x1p52) - 0x1p52 - x;
|
y = (double)(x + 0x1p52) - 0x1p52 - x;
|
||||||
if (y > 0.5)
|
y = y + x - (y > 0.5) + (y <= -0.5); /* branchless */
|
||||||
y = y + x - 1;
|
return (u.i >> 63) ? -y : y;
|
||||||
else if (y <= -0.5)
|
|
||||||
y = y + x + 1;
|
|
||||||
else
|
|
||||||
y = y + x;
|
|
||||||
if (u.i >> 63)
|
|
||||||
y = -y;
|
|
||||||
return y;
|
|
||||||
}
|
}
|
||||||
|
|
||||||
__CRT_INLINE long __cdecl lround (double x) {
|
__CRT_INLINE long __cdecl lround (double x) {
|
||||||
|
|
@ -194,17 +179,334 @@ __CRT_INLINE long long __cdecl llroundl (long double x) {
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
/* MUSL asinh, acosh, atanh */
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl asinh(double x) {
|
||||||
|
union {double f; uint64_t i;} u = {x};
|
||||||
|
unsigned e = u.i >> 52 & 0x7ff, s = u.i >> 63;
|
||||||
|
u.i &= -1ull / 2, x = u.f;
|
||||||
|
if (e >= 0x3ff + 26) x = log(x) + 0.69314718055994530941723212145818;
|
||||||
|
else if (e >= 0x3ff + 1) x = log(2*x + 1 / (sqrt(x*x + 1) + x));
|
||||||
|
else if (e >= 0x3ff - 26) x = log1p(x + x*x / (sqrt(x*x + 1) + 1));
|
||||||
|
else TCCFP_FORCE_EVAL(x + 0x1p120f);
|
||||||
|
return s ? -x : x;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl acosh(double x) {
|
||||||
|
union {double f; uint64_t i;} u = {x};
|
||||||
|
unsigned e = u.i >> 52 & 0x7ff;
|
||||||
|
if (e < 0x3ff + 1) return log1p(x - 1 + sqrt((x - 1)*(x - 1) + 2*(x - 1)));
|
||||||
|
if (e < 0x3ff + 26) return log(2*x - 1 / (x + sqrt(x*x - 1)));
|
||||||
|
return log(x) + 0.69314718055994530941723212145818;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl atanh(double x) {
|
||||||
|
union {double f; uint64_t i;} u = {x};
|
||||||
|
unsigned e = u.i >> 52 & 0x7ff, s = u.i >> 63;
|
||||||
|
u.i &= -1ull / 2, x = u.f;
|
||||||
|
if (e < 0x3ff - 1) {
|
||||||
|
if (e < 0x3ff - 32) { if (e == 0) TCCFP_FORCE_EVAL((float)x); }
|
||||||
|
else x = 0.5 * log1p(2*x + 2*x*x / (1 - x)); /* |x| < 0.5 */
|
||||||
|
} else x = 0.5 * log1p(2*(x / (1 - x))); /* avoid overflow */
|
||||||
|
return s ? -x : x;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* MUSL scalbn */
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl scalbn(double x, int n) {
|
||||||
|
union {double f; uint64_t i;} u;
|
||||||
|
if (n > 1023) {
|
||||||
|
x *= 0x1p1023, n -= 1023;
|
||||||
|
if (n > 1023) {
|
||||||
|
x *= 0x1p1023, n -= 1023;
|
||||||
|
if (n > 1023) n = 1023;
|
||||||
|
}
|
||||||
|
} else if (n < -1022) {
|
||||||
|
x *= 0x1p-1022 * 0x1p53, n += 1022 - 53;
|
||||||
|
if (n < -1022) {
|
||||||
|
x *= 0x1p-1022 * 0x1p53, n += 1022 - 53;
|
||||||
|
if (n < -1022) n = -1022;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
u.i = (0x3ffull + n) << 52;
|
||||||
|
return x * u.f;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
/*******************************************************************************
|
/*******************************************************************************
|
||||||
End of code based on MUSL
|
End of code based on MUSL
|
||||||
*******************************************************************************/
|
*******************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
/* Following are math functions missing from msvcrt.dll, and not defined
|
||||||
|
* in math.h or above. Functions still remaining:
|
||||||
|
* remquo(), remainder(), fma(), nan(), erf(), erfc(), nearbyint().
|
||||||
|
* In <stdlib.h>: lldiv().
|
||||||
|
*/
|
||||||
|
|
||||||
|
__CRT_INLINE float __cdecl scalbnf(float x, int n) {
|
||||||
|
return scalbn(x, n);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl scalbnl(long double x, int n) {
|
||||||
|
return scalbn(x, n);
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl scalbln(double x, long n) {
|
||||||
|
int m = n > INT_MAX ? INT_MAX : (n < INT_MIN ? INT_MIN : n);
|
||||||
|
return scalbn(x, m);
|
||||||
|
}
|
||||||
|
__CRT_INLINE float __cdecl scalblnf(float x, long n) {
|
||||||
|
int m = n > INT_MAX ? INT_MAX : (n < INT_MIN ? INT_MIN : n);
|
||||||
|
return scalbn(x, m);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE float __cdecl ldexpf(float x, int expn) {
|
||||||
|
return scalbn(x, expn);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl ldexpl(long double x, int expn) {
|
||||||
|
return scalbn(x, expn);
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE float __cdecl frexpf(float x, int *y) {
|
||||||
|
return frexp(x, y);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl frexpl (long double x, int* y) {
|
||||||
|
return frexp(x, y);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl rint(double x) {
|
||||||
|
double retval;
|
||||||
|
__asm__ (
|
||||||
|
"fldl %1\n"
|
||||||
|
"frndint \n"
|
||||||
|
"fstpl %0\n" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE float __cdecl rintf(float x) {
|
||||||
|
float retval;
|
||||||
|
__asm__ (
|
||||||
|
"flds %1\n"
|
||||||
|
"frndint \n"
|
||||||
|
"fstps %0\n" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
/* 7.12.9.5 */
|
||||||
|
__CRT_INLINE long __cdecl lrint(double x) {
|
||||||
|
long retval;
|
||||||
|
__asm__ __volatile__
|
||||||
|
("fldl %1\n"
|
||||||
|
"fistpl %0" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE long __cdecl lrintf(float x) {
|
||||||
|
long retval;
|
||||||
|
__asm__ __volatile__
|
||||||
|
("flds %1\n"
|
||||||
|
"fistpl %0" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE long long __cdecl llrint(double x) {
|
||||||
|
long long retval;
|
||||||
|
__asm__ __volatile__
|
||||||
|
("fldl %1\n"
|
||||||
|
"fistpll %0" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE long long __cdecl llrintf(float x) {
|
||||||
|
long long retval;
|
||||||
|
__asm__ __volatile__
|
||||||
|
("flds %1\n"
|
||||||
|
"fistpll %0" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
__CRT_INLINE long double __cdecl rintl (long double x) {
|
||||||
|
long double retval;
|
||||||
|
__asm__ (
|
||||||
|
"fldt %1\n"
|
||||||
|
"frndint \n"
|
||||||
|
"fstpt %0\n" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
__CRT_INLINE long __cdecl lrintl (long double x) {
|
||||||
|
long retval;
|
||||||
|
__asm__ __volatile__
|
||||||
|
("fldt %1\n"
|
||||||
|
"fistpl %0" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
__CRT_INLINE long long __cdecl llrintl (long double x) {
|
||||||
|
long long retval;
|
||||||
|
__asm__ __volatile__
|
||||||
|
("fldt %1\n"
|
||||||
|
"fistpll %0" : "=m" (retval) : "m" (x));
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
__CRT_INLINE float __cdecl fabsf (float x) {
|
||||||
|
float res;
|
||||||
|
__asm__ ("fabs;" : "=t" (res) : "0" (x));
|
||||||
|
return res;
|
||||||
|
}
|
||||||
|
*/
|
||||||
|
|
||||||
|
__CRT_INLINE long double __cdecl rintl(long double x) {
|
||||||
|
return rint(x);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long __cdecl lrintl(long double x) {
|
||||||
|
return lrint(x);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long long __cdecl llrintl(long double x) {
|
||||||
|
return llrint(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE double trunc(double _x) {
|
||||||
|
double retval;
|
||||||
|
unsigned short saved_cw;
|
||||||
|
unsigned short tmp_cw;
|
||||||
|
__asm__ ("fnstcw %0;" : "=m" (saved_cw)); /* save FPU control word */
|
||||||
|
tmp_cw = (saved_cw & ~(FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO))
|
||||||
|
| FE_TOWARDZERO;
|
||||||
|
__asm__ ("fldcw %0;" : : "m" (tmp_cw));
|
||||||
|
__asm__ ("fldl %1;"
|
||||||
|
"frndint;"
|
||||||
|
"fstpl %0;" : "=m" (retval) : "m" (_x)); /* round towards zero */
|
||||||
|
__asm__ ("fldcw %0;" : : "m" (saved_cw) ); /* restore saved control word */
|
||||||
|
return retval;
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE float __cdecl truncf(float x) {
|
||||||
|
return (float) ((int) x);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl truncl(long double x) {
|
||||||
|
return trunc(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE long double __cdecl nextafterl(long double x, long double to) {
|
||||||
|
return nextafter(x, to);
|
||||||
|
}
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl nexttoward(double x, long double to) {
|
||||||
|
return nextafter(x, to);
|
||||||
|
}
|
||||||
|
__CRT_INLINE float __cdecl nexttowardf(float x, long double to) {
|
||||||
|
return nextafterf(x, to);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl nexttowardl(long double x, long double to) {
|
||||||
|
return nextafter(x, to);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE float __cdecl fabsf (float x) {
|
||||||
|
union {float f; uint32_t i;} u = {x};
|
||||||
|
u.i &= 0x7fffffff;
|
||||||
|
return u.f;
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl fabsl (long double x) {
|
||||||
|
return fabs(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
#if defined(_WIN32) && !defined(_WIN64) && !defined(__ia64__)
|
||||||
|
__CRT_INLINE float acosf(float x) { return acos(x); }
|
||||||
|
__CRT_INLINE float asinf(float x) { return asin(x); }
|
||||||
|
__CRT_INLINE float atanf(float x) { return atan(x); }
|
||||||
|
__CRT_INLINE float atan2f(float x, float y) { return atan2(x, y); }
|
||||||
|
__CRT_INLINE float ceilf(float x) { return ceil(x); }
|
||||||
|
__CRT_INLINE float cosf(float x) { return cos(x); }
|
||||||
|
__CRT_INLINE float coshf(float x) { return cosh(x); }
|
||||||
|
__CRT_INLINE float expf(float x) { return exp(x); }
|
||||||
|
__CRT_INLINE float floorf(float x) { return floor(x); }
|
||||||
|
__CRT_INLINE float fmodf(float x, float y) { return fmod(x, y); }
|
||||||
|
__CRT_INLINE float logf(float x) { return log(x); }
|
||||||
|
__CRT_INLINE float logbf(float x) { return logb(x); }
|
||||||
|
__CRT_INLINE float log10f(float x) { return log10(x); }
|
||||||
|
__CRT_INLINE float modff(float x, float *y) { double di, df = modf(x, &di); *y = di; return df; }
|
||||||
|
__CRT_INLINE float powf(float x, float y) { return pow(x, y); }
|
||||||
|
__CRT_INLINE float sinf(float x) { return sin(x); }
|
||||||
|
__CRT_INLINE float sinhf(float x) { return sinh(x); }
|
||||||
|
__CRT_INLINE float sqrtf(float x) { return sqrt(x); }
|
||||||
|
__CRT_INLINE float tanf(float x) { return tan(x); }
|
||||||
|
__CRT_INLINE float tanhf(float x) { return tanh(x); }
|
||||||
|
#endif
|
||||||
|
__CRT_INLINE float __cdecl asinhf(float x) { return asinh(x); }
|
||||||
|
__CRT_INLINE float __cdecl acoshf(float x) { return acosh(x); }
|
||||||
|
__CRT_INLINE float __cdecl atanhf(float x) { return atanh(x); }
|
||||||
|
|
||||||
|
__CRT_INLINE long double __cdecl asinhl(long double x) { return asinh(x); }
|
||||||
|
__CRT_INLINE long double __cdecl acoshl(long double x) { return acosh(x); }
|
||||||
|
__CRT_INLINE long double __cdecl atanhl(long double x) { return atanh(x); }
|
||||||
|
__CRT_INLINE long double __cdecl asinl(long double x) { return asin(x); }
|
||||||
|
__CRT_INLINE long double __cdecl acosl(long double x) { return acos(x); }
|
||||||
|
__CRT_INLINE long double __cdecl atanl(long double x) { return atan(x); }
|
||||||
|
__CRT_INLINE long double __cdecl ceill(long double x) { return ceil(x); }
|
||||||
|
__CRT_INLINE long double __cdecl coshl(long double x) { return cosh(x); }
|
||||||
|
__CRT_INLINE long double __cdecl cosl(long double x) { return cos(x); }
|
||||||
|
__CRT_INLINE long double __cdecl expl(long double x) { return exp(x); }
|
||||||
|
__CRT_INLINE long double __cdecl floorl(long double x) { return floor(x); }
|
||||||
|
__CRT_INLINE long double __cdecl fmodl(long double x, long double y) { return fmod(x, y); }
|
||||||
|
__CRT_INLINE long double __cdecl hypotl(long double x, long double y) { return hypot(x, y); }
|
||||||
|
__CRT_INLINE long double __cdecl logl(long double x) { return log(x); }
|
||||||
|
__CRT_INLINE long double __cdecl logbl(long double x) { return logb(x); }
|
||||||
|
__CRT_INLINE long double __cdecl log10l(long double x) { return log10(x); }
|
||||||
|
__CRT_INLINE long double __cdecl modfl(long double x, long double* y) { return modf(x, y); }
|
||||||
|
__CRT_INLINE long double __cdecl powl(long double x, long double y) { return pow(x, y); }
|
||||||
|
__CRT_INLINE long double __cdecl sinhl(long double x) { return sinh(x); }
|
||||||
|
__CRT_INLINE long double __cdecl sinl(long double x) { return sin(x); }
|
||||||
|
__CRT_INLINE long double __cdecl sqrtl(long double x) { return sqrt(x); }
|
||||||
|
__CRT_INLINE long double __cdecl tanhl(long double x) { return tanh(x); }
|
||||||
|
__CRT_INLINE long double __cdecl tanl(long double x) { return tan(x); }
|
||||||
|
|
||||||
|
/* Following are accurate, but much shorter implementations than MUSL lib. */
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl log1p(double x) {
|
||||||
|
double u = 1.0 + x;
|
||||||
|
return u == 1.0 ? x : log(u)*(x / (u - 1.0));
|
||||||
|
}
|
||||||
|
__CRT_INLINE float __cdecl log1pf(float x) {
|
||||||
|
float u = 1.0f + x;
|
||||||
|
return u == 1.0f ? x : logf(u)*(x / (u - 1.0f));
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl log1pl(long double x) {
|
||||||
|
return log1p(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl expm1(double x) {
|
||||||
|
if (fabs(x) > 0.0024) return exp(x) - 1.0;
|
||||||
|
double u, v = x*x, t = x + 0.5*v + 0.1666666666666666667*(u = v*x);
|
||||||
|
return t + 0.04166666666666666667*u*x;
|
||||||
|
}
|
||||||
|
__CRT_INLINE float __cdecl expm1f(float x) {
|
||||||
|
if (fabsf(x) > 0.085f) return expf(x) - 1.0f;
|
||||||
|
float u, v = x*x, t = x + 0.5f*v + 0.1666666666666666667f*(u = v*x);
|
||||||
|
return t + 0.04166666666666666667f*u*x;
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl expm1l(long double x) {
|
||||||
|
return expm1(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
__CRT_INLINE double __cdecl cbrt(double x) {
|
__CRT_INLINE double __cdecl cbrt(double x) {
|
||||||
return (1.0 - ((x < 0.0) << 1)) * pow(fabs(x), 1.0 / 3.0);
|
return (1 - ((x < 0.0) << 1)) * pow(fabs(x), 1/3.0);
|
||||||
}
|
}
|
||||||
__CRT_INLINE float __cdecl cbrtf(float x) {
|
__CRT_INLINE float __cdecl cbrtf(float x) {
|
||||||
return (1.0f - ((x < 0.0f) << 1)) * (float) pow(fabs(x), 1.0 / 3.0);
|
return (1 - ((x < 0.0f) << 1)) * powf(fabsf((float) x), 1/3.0f);
|
||||||
}
|
}
|
||||||
|
__CRT_INLINE long double __cdecl cbrtl(long double x) {
|
||||||
|
return (1 - ((x < 0.0) << 1)) * pow(fabs(x), 1/3.0);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
__CRT_INLINE double __cdecl log2(double x) {
|
__CRT_INLINE double __cdecl log2(double x) {
|
||||||
return log(x) * 1.4426950408889634073599246810019;
|
return log(x) * 1.4426950408889634073599246810019;
|
||||||
|
|
@ -212,6 +514,10 @@ __CRT_INLINE double __cdecl log2(double x) {
|
||||||
__CRT_INLINE float __cdecl log2f(float x) {
|
__CRT_INLINE float __cdecl log2f(float x) {
|
||||||
return logf(x) * 1.4426950408889634073599246810019f;
|
return logf(x) * 1.4426950408889634073599246810019f;
|
||||||
}
|
}
|
||||||
|
__CRT_INLINE long double __cdecl log2l(long double x) {
|
||||||
|
return log(x) * 1.4426950408889634073599246810019;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
__CRT_INLINE double __cdecl exp2(double x) {
|
__CRT_INLINE double __cdecl exp2(double x) {
|
||||||
return exp(x * 0.69314718055994530941723212145818);
|
return exp(x * 0.69314718055994530941723212145818);
|
||||||
|
|
@ -219,48 +525,86 @@ __CRT_INLINE double __cdecl exp2(double x) {
|
||||||
__CRT_INLINE float __cdecl exp2f(float x) {
|
__CRT_INLINE float __cdecl exp2f(float x) {
|
||||||
return expf(x * 0.69314718055994530941723212145818f);
|
return expf(x * 0.69314718055994530941723212145818f);
|
||||||
}
|
}
|
||||||
|
__CRT_INLINE long double __cdecl exp2l(long double x) {
|
||||||
|
return exp(x * 0.69314718055994530941723212145818);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE int __cdecl ilogb(double x) {
|
||||||
|
return (int) logb(x);
|
||||||
|
}
|
||||||
|
__CRT_INLINE int __cdecl ilogbf(float x) {
|
||||||
|
return (int) logbf(x);
|
||||||
|
}
|
||||||
|
__CRT_INLINE int __cdecl ilogbl(long double x) {
|
||||||
|
return (int) logb(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__CRT_INLINE double __cdecl fdim(double x, double y) {
|
||||||
|
if (isnan(x) || isnan(y)) return NAN;
|
||||||
|
return x > y ? x - y : 0;
|
||||||
|
}
|
||||||
|
__CRT_INLINE float __cdecl fdimf(float x, float y) {
|
||||||
|
if (isnan(x) || isnan(y)) return NAN;
|
||||||
|
return x > y ? x - y : 0;
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl fdiml(long double x, long double y) {
|
||||||
|
if (isnan(x) || isnan(y)) return NAN;
|
||||||
|
return x > y ? x - y : 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
/* tgamma and lgamma: Lanczos approximation
|
/* tgamma and lgamma: Lanczos approximation
|
||||||
* https://rosettacode.org/wiki/Gamma_function
|
* https://rosettacode.org/wiki/Gamma_function
|
||||||
* https://www.johndcook.com/blog/cpp_gamma
|
* https://www.johndcook.com/blog/cpp_gamma
|
||||||
*/
|
*/
|
||||||
__CRT_INLINE double __cdecl lgamma(double x);
|
|
||||||
|
|
||||||
__CRT_INLINE double __cdecl tgamma(double x) {
|
__CRT_INLINE double __cdecl tgamma(double x) {
|
||||||
double m = 1.0, t = 3.14159265358979323;
|
double m = 1.0, t = 3.14159265358979323;
|
||||||
if (x == (int)x) {
|
if (x > 172.0)
|
||||||
|
return INFINITY;
|
||||||
|
if (x == floor(x)) {
|
||||||
for (int k = 2; k < x; ++k) m *= k;
|
for (int k = 2; k < x; ++k) m *= k;
|
||||||
return x > 0.0 ? m : (x == 0.0 ? INFINITY : NAN);
|
return x > 0.0 ? m : (x == 0.0 ? INFINITY : NAN);
|
||||||
}
|
}
|
||||||
if (x < 0.5)
|
if (x < 0.5)
|
||||||
return t / (sin(t * x) * tgamma(1.0 - x));
|
return t / (sin(t*x)*tgamma(1.0 - x));
|
||||||
if (x > 12.0)
|
if (x > 12.0)
|
||||||
return exp(lgamma(x));
|
return exp(lgamma(x));
|
||||||
|
|
||||||
static const double c[8] = {676.5203681218851, -1259.1392167224028,
|
static const double c[8] = {676.5203681218851, -1259.1392167224028,
|
||||||
771.32342877765313, -176.61502916214059,
|
771.32342877765313, -176.61502916214059,
|
||||||
12.507343278686905, -0.13857109526572012,
|
12.507343278686905, -0.13857109526572012,
|
||||||
9.9843695780195716e-6, 1.5056327351493116e-7};
|
9.9843695780195716e-6, 1.5056327351493116e-7};
|
||||||
m = 0.99999999999980993, t = x + (8 - 1.5);
|
m = 0.99999999999980993, t = x + 6.5; /* x-1+8-.5 */
|
||||||
for (int k = 0; k < 8; ++k) m += c[k] / (x + k);
|
for (int k = 0; k < 8; ++k) m += c[k] / (x + k);
|
||||||
return 2.50662827463100050 * pow(t, x - 0.5) * exp(-t) * m; /* sqrt(2pi) */
|
return 2.50662827463100050 * pow(t, x - 0.5)*exp(-t)*m; /* C=sqrt(2pi) */
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
__CRT_INLINE double __cdecl lgamma(double x) {
|
__CRT_INLINE double __cdecl lgamma(double x) {
|
||||||
if (x < 12.0)
|
if (x < 12.0)
|
||||||
return x <= 0.0 && x == (int)x ? INFINITY : log(fabs(tgamma(x)));
|
return x > 0.0 || x != floor(x) ? log(fabs(tgamma(x))) : INFINITY;
|
||||||
|
|
||||||
static const double c[7] = {1.0/12.0, -1.0/360.0, 1.0/1260.0, -1.0/1680.0,
|
static const double c[7] = {1.0/12.0, -1.0/360.0, 1.0/1260.0, -1.0/1680.0,
|
||||||
1.0/1188.0, -691.0/360360.0, 1.0/156.0};
|
1.0/1188.0, -691.0/360360.0, 1.0/156.0};
|
||||||
double m = -3617.0/122400.0, z = 1.0 / (x * x);
|
double m = -3617.0/122400.0, t = 1.0 / (x*x);
|
||||||
for (int k = 6; k >= 0; --k) m = m * z + c[k];
|
for (int k = 6; k >= 0; --k) m = m*t + c[k];
|
||||||
return (x - 0.5) * log(x) - x + 0.918938533204672742 + m / x; /* log(2pi)/2 */
|
return (x - 0.5)*log(x) - x + 0.918938533204672742 + m / x; /* C=log(2pi)/2 */
|
||||||
}
|
}
|
||||||
|
|
||||||
__CRT_INLINE float __cdecl tgammaf(float x) {
|
__CRT_INLINE float __cdecl tgammaf(float x) {
|
||||||
return tgamma(x);
|
return tgamma(x);
|
||||||
}
|
}
|
||||||
|
|
||||||
__CRT_INLINE float __cdecl lgammaf(float x) {
|
__CRT_INLINE float __cdecl lgammaf(float x) {
|
||||||
return lgamma(x);
|
return lgamma(x);
|
||||||
}
|
}
|
||||||
|
__CRT_INLINE long double __cdecl tgammal(long double x) {
|
||||||
|
return tgamma(x);
|
||||||
|
}
|
||||||
|
__CRT_INLINE long double __cdecl lgammal(long double x) {
|
||||||
|
return lgamma(x);
|
||||||
|
}
|
||||||
|
|
||||||
#endif /* _TCC_LIBM_H_ */
|
#endif /* _TCC_LIBM_H_ */
|
||||||
|
|
|
||||||
Loading…
Add table
Reference in a new issue