kopia lustrzana https://github.com/micropython/micropython
lib/libm: Add implementations of erf, erfc, lgamma, tgamma.
Damien George
rodzic
3527085587
commit
9ab94c468c
|
|
@ -0,0 +1,255 @@
|
|||
/*
|
||||
* This file is part of the Micro Python project, http://micropython.org/
|
||||
*
|
||||
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||
*
|
||||
* Appropriate copyright headers are reproduced below.
|
||||
*/
|
||||
|
||||
/* erf_lgamma.c -- float version of er_lgamma.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#define __ieee754_logf logf
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
two23= 8.3886080000e+06, /* 0x4b000000 */
|
||||
half= 5.0000000000e-01, /* 0x3f000000 */
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
pi = 3.1415927410e+00, /* 0x40490fdb */
|
||||
a0 = 7.7215664089e-02, /* 0x3d9e233f */
|
||||
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
|
||||
a2 = 6.7352302372e-02, /* 0x3d89f001 */
|
||||
a3 = 2.0580807701e-02, /* 0x3ca89915 */
|
||||
a4 = 7.3855509982e-03, /* 0x3bf2027e */
|
||||
a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
|
||||
a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
|
||||
a7 = 5.1006977446e-04, /* 0x3a05b634 */
|
||||
a8 = 2.2086278477e-04, /* 0x39679767 */
|
||||
a9 = 1.0801156895e-04, /* 0x38e28445 */
|
||||
a10 = 2.5214456400e-05, /* 0x37d383a2 */
|
||||
a11 = 4.4864096708e-05, /* 0x383c2c75 */
|
||||
tc = 1.4616321325e+00, /* 0x3fbb16c3 */
|
||||
tf = -1.2148628384e-01, /* 0xbdf8cdcd */
|
||||
/* tt = -(tail of tf) */
|
||||
tt = 6.6971006518e-09, /* 0x31e61c52 */
|
||||
t0 = 4.8383611441e-01, /* 0x3ef7b95e */
|
||||
t1 = -1.4758771658e-01, /* 0xbe17213c */
|
||||
t2 = 6.4624942839e-02, /* 0x3d845a15 */
|
||||
t3 = -3.2788541168e-02, /* 0xbd064d47 */
|
||||
t4 = 1.7970675603e-02, /* 0x3c93373d */
|
||||
t5 = -1.0314224288e-02, /* 0xbc28fcfe */
|
||||
t6 = 6.1005386524e-03, /* 0x3bc7e707 */
|
||||
t7 = -3.6845202558e-03, /* 0xbb7177fe */
|
||||
t8 = 2.2596477065e-03, /* 0x3b141699 */
|
||||
t9 = -1.4034647029e-03, /* 0xbab7f476 */
|
||||
t10 = 8.8108185446e-04, /* 0x3a66f867 */
|
||||
t11 = -5.3859531181e-04, /* 0xba0d3085 */
|
||||
t12 = 3.1563205994e-04, /* 0x39a57b6b */
|
||||
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
|
||||
t14 = 3.3552918467e-04, /* 0x39afe9f7 */
|
||||
u0 = -7.7215664089e-02, /* 0xbd9e233f */
|
||||
u1 = 6.3282704353e-01, /* 0x3f2200f4 */
|
||||
u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
|
||||
u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
|
||||
u4 = 2.2896373272e-01, /* 0x3e6a7578 */
|
||||
u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
|
||||
v1 = 2.4559779167e+00, /* 0x401d2ebe */
|
||||
v2 = 2.1284897327e+00, /* 0x4008392d */
|
||||
v3 = 7.6928514242e-01, /* 0x3f44efdf */
|
||||
v4 = 1.0422264785e-01, /* 0x3dd572af */
|
||||
v5 = 3.2170924824e-03, /* 0x3b52d5db */
|
||||
s0 = -7.7215664089e-02, /* 0xbd9e233f */
|
||||
s1 = 2.1498242021e-01, /* 0x3e5c245a */
|
||||
s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
|
||||
s3 = 1.4635047317e-01, /* 0x3e15dce6 */
|
||||
s4 = 2.6642270386e-02, /* 0x3cda40e4 */
|
||||
s5 = 1.8402845599e-03, /* 0x3af135b4 */
|
||||
s6 = 3.1947532989e-05, /* 0x3805ff67 */
|
||||
r1 = 1.3920053244e+00, /* 0x3fb22d3b */
|
||||
r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
|
||||
r3 = 1.7193385959e-01, /* 0x3e300f6e */
|
||||
r4 = 1.8645919859e-02, /* 0x3c98bf54 */
|
||||
r5 = 7.7794247773e-04, /* 0x3a4beed6 */
|
||||
r6 = 7.3266842264e-06, /* 0x36f5d7bd */
|
||||
w0 = 4.1893854737e-01, /* 0x3ed67f1d */
|
||||
w1 = 8.3333335817e-02, /* 0x3daaaaab */
|
||||
w2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
w3 = 7.9365057172e-04, /* 0x3a500cfd */
|
||||
w4 = -5.9518753551e-04, /* 0xba1c065c */
|
||||
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
|
||||
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero= 0.0000000000e+00;
|
||||
#else
|
||||
static float zero= 0.0000000000e+00;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static float sin_pif(float x)
|
||||
#else
|
||||
static float sin_pif(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float y,z;
|
||||
__int32_t n,ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
|
||||
y = -x; /* x is assume negative */
|
||||
|
||||
/*
|
||||
* argument reduction, make sure inexact flag not raised if input
|
||||
* is an integer
|
||||
*/
|
||||
z = floorf(y);
|
||||
if(z!=y) { /* inexact anyway */
|
||||
y *= (float)0.5;
|
||||
y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
|
||||
n = (__int32_t) (y*(float)4.0);
|
||||
} else {
|
||||
if(ix>=0x4b800000) {
|
||||
y = zero; n = 0; /* y must be even */
|
||||
} else {
|
||||
if(ix<0x4b000000) z = y+two23; /* exact */
|
||||
GET_FLOAT_WORD(n,z);
|
||||
n &= 1;
|
||||
y = n;
|
||||
n<<= 2;
|
||||
}
|
||||
}
|
||||
switch (n) {
|
||||
case 0: y = __kernel_sinf(pi*y,zero,0); break;
|
||||
case 1:
|
||||
case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
|
||||
case 3:
|
||||
case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
|
||||
case 5:
|
||||
case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
|
||||
default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
|
||||
}
|
||||
return -y;
|
||||
}
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_lgammaf_r(float x, int *signgamp)
|
||||
#else
|
||||
float __ieee754_lgammaf_r(x,signgamp)
|
||||
float x; int *signgamp;
|
||||
#endif
|
||||
{
|
||||
float t,y,z,nadj = 0.0,p,p1,p2,p3,q,r,w;
|
||||
__int32_t i,hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return x*x;
|
||||
if(ix==0) return one/zero;
|
||||
if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_logf(-x);
|
||||
} else return -__ieee754_logf(x);
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
|
||||
return one/zero;
|
||||
t = sin_pif(x);
|
||||
if(t==zero) return one/zero; /* -integer */
|
||||
nadj = __ieee754_logf(pi/fabsf(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if (ix==0x3f800000||ix==0x40000000) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_logf(x);
|
||||
if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-(float)0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-(float)0.5*y + p1/p2);
|
||||
}
|
||||
}
|
||||
else if(ix<0x41000000) { /* x < 8.0 */
|
||||
i = (__int32_t)x;
|
||||
t = zero;
|
||||
y = x-(float)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+(float)6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+(float)5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+(float)4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+(float)3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+(float)2.0); /* FALLTHRU */
|
||||
r += __ieee754_logf(z); break;
|
||||
}
|
||||
/* 8.0 <= x < 2**58 */
|
||||
} else if (ix < 0x5c800000) {
|
||||
t = __ieee754_logf(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x*(__ieee754_logf(x)-one);
|
||||
if(hx<0) r = nadj - r;
|
||||
return r;
|
||||
}
|
||||
|
|
@ -117,13 +117,6 @@ float log10f(float x) { return logf(x) / (float)_M_LN10; }
|
|||
|
||||
float tanhf(float x) { return sinhf(x) / coshf(x); }
|
||||
|
||||
// TODO we need import these functions from some library (eg musl or newlib)
|
||||
float tgammaf(float x) { return 0.0; }
|
||||
float lgammaf(float x) { return 0.0; }
|
||||
float erff(float x) { return 0.0; }
|
||||
float erfcf(float x) { return 0.0; }
|
||||
float ldexpf(float x, int exp) { return 0.0; }
|
||||
|
||||
/*****************************************************************************/
|
||||
/*****************************************************************************/
|
||||
// __fpclassifyf from musl-0.9.15
|
||||
|
|
|
|||
|
|
@ -0,0 +1,257 @@
|
|||
/*
|
||||
* This file is part of the Micro Python project, http://micropython.org/
|
||||
*
|
||||
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||
*
|
||||
* Appropriate copyright headers are reproduced below.
|
||||
*/
|
||||
|
||||
/* sf_erf.c -- float version of s_erf.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#define __ieee754_expf expf
|
||||
|
||||
#ifdef __v810__
|
||||
#define const
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
tiny = 1e-30,
|
||||
half= 5.0000000000e-01, /* 0x3F000000 */
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
two = 2.0000000000e+00, /* 0x40000000 */
|
||||
/* c = (subfloat)0.84506291151 */
|
||||
erx = 8.4506291151e-01, /* 0x3f58560b */
|
||||
/*
|
||||
* Coefficients for approximation to erf on [0,0.84375]
|
||||
*/
|
||||
efx = 1.2837916613e-01, /* 0x3e0375d4 */
|
||||
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
|
||||
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
|
||||
pp1 = -3.2504209876e-01, /* 0xbea66beb */
|
||||
pp2 = -2.8481749818e-02, /* 0xbce9528f */
|
||||
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
|
||||
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
|
||||
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
|
||||
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
|
||||
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
|
||||
qq4 = 1.3249473704e-04, /* 0x390aee49 */
|
||||
qq5 = -3.9602282413e-06, /* 0xb684e21a */
|
||||
/*
|
||||
* Coefficients for approximation to erf in [0.84375,1.25]
|
||||
*/
|
||||
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
|
||||
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
|
||||
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
|
||||
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
|
||||
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
|
||||
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
|
||||
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
|
||||
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
|
||||
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
|
||||
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
|
||||
qa4 = 1.2617121637e-01, /* 0x3e013307 */
|
||||
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
|
||||
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1.25,1/0.35]
|
||||
*/
|
||||
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
|
||||
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
|
||||
ra2 = -1.0558626175e+01, /* 0xc128f022 */
|
||||
ra3 = -6.2375331879e+01, /* 0xc2798057 */
|
||||
ra4 = -1.6239666748e+02, /* 0xc322658c */
|
||||
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
|
||||
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
|
||||
ra7 = -9.8143291473e+00, /* 0xc11d077e */
|
||||
sa1 = 1.9651271820e+01, /* 0x419d35ce */
|
||||
sa2 = 1.3765776062e+02, /* 0x4309a863 */
|
||||
sa3 = 4.3456588745e+02, /* 0x43d9486f */
|
||||
sa4 = 6.4538726807e+02, /* 0x442158c9 */
|
||||
sa5 = 4.2900814819e+02, /* 0x43d6810b */
|
||||
sa6 = 1.0863500214e+02, /* 0x42d9451f */
|
||||
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
|
||||
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
|
||||
/*
|
||||
* Coefficients for approximation to erfc in [1/.35,28]
|
||||
*/
|
||||
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
|
||||
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
|
||||
rb2 = -1.7757955551e+01, /* 0xc18e104b */
|
||||
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
|
||||
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
|
||||
rb5 = -1.0250950928e+03, /* 0xc480230b */
|
||||
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
|
||||
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
|
||||
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
|
||||
sb3 = 1.5367296143e+03, /* 0x44c01759 */
|
||||
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
|
||||
sb5 = 2.5530502930e+03, /* 0x451f90ce */
|
||||
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
|
||||
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
|
||||
|
||||
#ifdef __STDC__
|
||||
float erff(float x)
|
||||
#else
|
||||
float erff(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
__int32_t hx,ix,i;
|
||||
float R,S,P,Q,s,y,z,r;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(!FLT_UWORD_IS_FINITE(ix)) { /* erf(nan)=nan */
|
||||
i = ((__uint32_t)hx>>31)<<1;
|
||||
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
|
||||
}
|
||||
|
||||
if(ix < 0x3f580000) { /* |x|<0.84375 */
|
||||
if(ix < 0x31800000) { /* |x|<2**-28 */
|
||||
if (ix < 0x04000000)
|
||||
/*avoid underflow */
|
||||
return (float)0.125*((float)8.0*x+efx8*x);
|
||||
return x + efx*x;
|
||||
}
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
return x + x*y;
|
||||
}
|
||||
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabsf(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
|
||||
}
|
||||
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
|
||||
if(hx>=0) return one-tiny; else return tiny-one;
|
||||
}
|
||||
x = fabsf(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/0.35 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
SET_FLOAT_WORD(z,ix&0xfffff000);
|
||||
r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
|
||||
if(hx>=0) return one-r/x; else return r/x-one;
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
float erfcf(float x)
|
||||
#else
|
||||
float erfcf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
__int32_t hx,ix;
|
||||
float R,S,P,Q,s,y,z,r;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(!FLT_UWORD_IS_FINITE(ix)) { /* erfc(nan)=nan */
|
||||
/* erfc(+-inf)=0,2 */
|
||||
return (float)(((__uint32_t)hx>>31)<<1)+one/x;
|
||||
}
|
||||
|
||||
if(ix < 0x3f580000) { /* |x|<0.84375 */
|
||||
if(ix < 0x23800000) /* |x|<2**-56 */
|
||||
return one-x;
|
||||
z = x*x;
|
||||
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
|
||||
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
|
||||
y = r/s;
|
||||
if(hx < 0x3e800000) { /* x<1/4 */
|
||||
return one-(x+x*y);
|
||||
} else {
|
||||
r = x*y;
|
||||
r += (x-half);
|
||||
return half - r ;
|
||||
}
|
||||
}
|
||||
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
|
||||
s = fabsf(x)-one;
|
||||
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
|
||||
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
|
||||
if(hx>=0) {
|
||||
z = one-erx; return z - P/Q;
|
||||
} else {
|
||||
z = erx+P/Q; return one+z;
|
||||
}
|
||||
}
|
||||
if (ix < 0x41e00000) { /* |x|<28 */
|
||||
x = fabsf(x);
|
||||
s = one/(x*x);
|
||||
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
|
||||
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
|
||||
ra5+s*(ra6+s*ra7))))));
|
||||
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
|
||||
sa5+s*(sa6+s*(sa7+s*sa8)))))));
|
||||
} else { /* |x| >= 1/.35 ~ 2.857143 */
|
||||
if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
|
||||
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
|
||||
rb5+s*rb6)))));
|
||||
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
|
||||
sb5+s*(sb6+s*sb7))))));
|
||||
}
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
SET_FLOAT_WORD(z,ix&0xfffff000);
|
||||
r = __ieee754_expf(-z*z-(float)0.5625)*
|
||||
__ieee754_expf((z-x)*(z+x)+R/S);
|
||||
if(hx>0) return r/x; else return two-r/x;
|
||||
} else {
|
||||
if(hx>0) return tiny*tiny; else return two-tiny;
|
||||
}
|
||||
}
|
||||
|
||||
#ifdef _DOUBLE_IS_32BITS
|
||||
|
||||
#ifdef __STDC__
|
||||
double erf(double x)
|
||||
#else
|
||||
double erf(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return (double) erff((float) x);
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double erfc(double x)
|
||||
#else
|
||||
double erfc(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return (double) erfcf((float) x);
|
||||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
|
|
@ -0,0 +1,53 @@
|
|||
/*
|
||||
* This file is part of the Micro Python project, http://micropython.org/
|
||||
*
|
||||
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||
*
|
||||
* Appropriate copyright headers are reproduced below.
|
||||
*/
|
||||
|
||||
/* sf_ldexp.c -- float version of s_ldexp.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
//#include <errno.h>
|
||||
|
||||
#ifdef __STDC__
|
||||
float ldexpf(float value, int exp)
|
||||
#else
|
||||
float ldexpf(value, exp)
|
||||
float value; int exp;
|
||||
#endif
|
||||
{
|
||||
if(!finitef(value)||value==(float)0.0) return value;
|
||||
value = scalbnf(value,exp);
|
||||
//if(!finitef(value)||value==(float)0.0) errno = ERANGE;
|
||||
return value;
|
||||
}
|
||||
|
||||
#ifdef _DOUBLE_IS_32BITS
|
||||
|
||||
#ifdef __STDC__
|
||||
double ldexp(double value, int exp)
|
||||
#else
|
||||
double ldexp(value, exp)
|
||||
double value; int exp;
|
||||
#endif
|
||||
{
|
||||
return (double) ldexpf((float) value, exp);
|
||||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
|
|
@ -0,0 +1,98 @@
|
|||
/*
|
||||
* This file is part of the Micro Python project, http://micropython.org/
|
||||
*
|
||||
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||
*
|
||||
* Appropriate copyright headers are reproduced below.
|
||||
*/
|
||||
|
||||
/* wf_lgamma.c -- float version of w_lgamma.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#define _IEEE_LIBM 1
|
||||
//#include <reent.h>
|
||||
//#include <errno.h>
|
||||
|
||||
#ifdef __STDC__
|
||||
float lgammaf(float x)
|
||||
#else
|
||||
float lgammaf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
int sign;
|
||||
return __ieee754_lgammaf_r(x,&sign);
|
||||
#else
|
||||
float y;
|
||||
struct exception exc;
|
||||
y = __ieee754_lgammaf_r(x,&(_REENT_SIGNGAM(_REENT)));
|
||||
if(_LIB_VERSION == _IEEE_) return y;
|
||||
if(!finitef(y)&&finitef(x)) {
|
||||
#ifndef HUGE_VAL
|
||||
#define HUGE_VAL inf
|
||||
double inf = 0.0;
|
||||
|
||||
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
|
||||
#endif
|
||||
exc.name = "lgammaf";
|
||||
exc.err = 0;
|
||||
exc.arg1 = exc.arg2 = (double)x;
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
if(floorf(x)==x&&x<=(float)0.0) {
|
||||
/* lgammaf(-integer) */
|
||||
exc.type = SING;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = EDOM;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = EDOM;
|
||||
}
|
||||
|
||||
} else {
|
||||
/* lgammaf(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
if (_LIB_VERSION == _POSIX_)
|
||||
errno = ERANGE;
|
||||
else if (!matherr(&exc)) {
|
||||
errno = ERANGE;
|
||||
}
|
||||
}
|
||||
if (exc.err != 0)
|
||||
errno = exc.err;
|
||||
return (float)exc.retval;
|
||||
} else
|
||||
return y;
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef _DOUBLE_IS_32BITS
|
||||
|
||||
#ifdef __STDC__
|
||||
double lgamma(double x)
|
||||
#else
|
||||
double lgamma(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return (double) lgammaf((float) x);
|
||||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
|
|
@ -0,0 +1,69 @@
|
|||
/*
|
||||
* This file is part of the Micro Python project, http://micropython.org/
|
||||
*
|
||||
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||
*
|
||||
* Appropriate copyright headers are reproduced below.
|
||||
*/
|
||||
|
||||
/* w_gammaf.c -- float version of w_gamma.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "fdlibm.h"
|
||||
#define _IEEE_LIBM 1
|
||||
|
||||
#ifdef __STDC__
|
||||
float tgammaf(float x)
|
||||
#else
|
||||
float tgammaf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float y;
|
||||
int local_signgam;
|
||||
y = expf(__ieee754_lgammaf_r(x,&local_signgam));
|
||||
if (local_signgam < 0) y = -y;
|
||||
#ifdef _IEEE_LIBM
|
||||
return y;
|
||||
#else
|
||||
if(_LIB_VERSION == _IEEE_) return y;
|
||||
|
||||
if(!finitef(y)&&finitef(x)) {
|
||||
if(floorf(x)==x&&x<=(float)0.0)
|
||||
/* tgammaf pole */
|
||||
return (float)__kernel_standard((double)x,(double)x,141);
|
||||
else
|
||||
/* tgammaf overflow */
|
||||
return (float)__kernel_standard((double)x,(double)x,140);
|
||||
}
|
||||
return y;
|
||||
#endif
|
||||
}
|
||||
|
||||
#ifdef _DOUBLE_IS_32BITS
|
||||
|
||||
#ifdef __STDC__
|
||||
double tgamma(double x)
|
||||
#else
|
||||
double tgamma(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return (double) tgammaf((float) x);
|
||||
}
|
||||
|
||||
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||
|
|
@ -78,11 +78,16 @@ SRC_LIB = $(addprefix lib/,\
|
|||
libm/kf_cos.c \
|
||||
libm/kf_tan.c \
|
||||
libm/ef_rem_pio2.c \
|
||||
libm/erf_lgamma.c \
|
||||
libm/sf_sin.c \
|
||||
libm/sf_cos.c \
|
||||
libm/sf_tan.c \
|
||||
libm/sf_frexp.c \
|
||||
libm/sf_modf.c \
|
||||
libm/sf_ldexp.c \
|
||||
libm/sf_erf.c \
|
||||
libm/wf_lgamma.c \
|
||||
libm/wf_tgamma.c \
|
||||
fatfs/ff.c \
|
||||
fatfs/option/ccsbcs.c \
|
||||
mp-readline/readline.c \
|
||||
|
|
|
|||
Ładowanie…
Reference in New Issue