245 lines
7.3 KiB
C
245 lines
7.3 KiB
C
|
/* 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"
|
||
|
|
|
||
|
|
#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,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;
|
||
|
|
}
|