/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
* Conversion to float fixed By Steven G. Kargl.
*/
/*
* ====================================================
* 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 <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
static const volatile float vzero = 0;
static const float
zero= 0,
half= 0.5,
one = 1,
pi = 3.1415927410e+00, /* 0x40490fdb */
/*
* Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]:
* |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4
*/
a0 = 7.72156641e-02, /* 0x3d9e233f */
a1 = 3.22467119e-01, /* 0x3ea51a69 */
a2 = 6.73484802e-02, /* 0x3d89ee00 */
a3 = 2.06395667e-02, /* 0x3ca9144f */
a4 = 6.98275631e-03, /* 0x3be4cf9b */
a5 = 4.11768444e-03, /* 0x3b86eda4 */
/*
* Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]:
* |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8.
*/
tc = 1.46163213e+00, /* 0x3fbb16c3 */
tf = -1.21486291e-01, /* 0xbdf8cdce */
t0 = -2.94064460e-11, /* 0xae0154b7 */
t1 = -2.35939837e-08, /* 0xb2caabb8 */
t2 = 4.83836412e-01, /* 0x3ef7b968 */
t3 = -1.47586212e-01, /* 0xbe1720d7 */
t4 = 6.46013096e-02, /* 0x3d844db1 */
t5 = -3.28450352e-02, /* 0xbd068884 */
t6 = 1.86483748e-02, /* 0x3c98c47a */
t7 = -9.89206228e-03, /* 0xbc221251 */
/*
* Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]:
* |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2
*/
u0 = -7.72156641e-02, /* 0xbd9e233f */
u1 = 7.36789703e-01, /* 0x3f3c9e40 */
u2 = 4.95649040e-01, /* 0x3efdc5b6 */
v1 = 1.10958421e+00, /* 0x3f8e06db */
v2 = 2.10598111e-01, /* 0x3e57a708 */
v3 = -1.02995494e-02, /* 0xbc28bf71 */
/*
* Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]:
* |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0
* with y = x - 2.
*/
s0 = -7.72156641e-02, /* 0xbd9e233f */
s1 = 2.69987404e-01, /* 0x3e8a3bca */
s2 = 1.42851010e-01, /* 0x3e124789 */
s3 = 1.19389519e-02, /* 0x3c439b98 */
r1 = 6.79650068e-01, /* 0x3f2dfd8c */
r2 = 1.16058730e-01, /* 0x3dedb033 */
r3 = 3.75673687e-03, /* 0x3b763396 */
/*
* Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]:
* |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6.
*/
w0 = 4.18938547e-01, /* 0x3ed67f1d */
w1 = 8.33332464e-02, /* 0x3daaaa9f */
w2 = -2.76129087e-03; /* 0xbb34f6c6 */
static float
sin_pif(float x)
{
volatile float vz;
float y,z;
int n;
y = -x;
vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */
z = vz-0x1p23F; /* rintf(y) for the above range */
if (z == y)
return zero;
vz = y+0x1p21F;
GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */
z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */
if (z > y) {
z -= 0.25F; /* adjust to round down */
n--;
}
n &= 7; /* octant of y mod 2 */
y = y - z + n * 0.25F; /* y mod 2 */
switch (n) {
case 0: y = __kernel_sindf(pi*y); break;
case 1:
case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break;
case 3:
case 4: y = __kernel_sindf(pi*(one-y)); break;
case 5:
case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break;
default: y = __kernel_sindf(pi*(y-(float)2.0)); break;
}
return -y;
}
float
__ieee754_lgammaf_r(float x, int *signgamp)
{
float nadj,p,p1,p2,p3,q,r,t,w,y,z;
int32_t hx;
int i,ix;
GET_FLOAT_WORD(hx,x);
/* purge +-Inf and NaNs */
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return x*x;
/* purge +-0 and tiny arguments */
*signgamp = 1-2*((uint32_t)hx>>31);
if(ix<0x32000000) { /* |x|<2**-27, return -log(|x|) */
if(ix==0)
return one/vzero;
return -__ieee754_logf(fabsf(x));
}
/* purge negative integers and start evaluation for other x < 0 */
if(hx<0) {
*signgamp = 1;
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
return one/vzero;
t = sin_pif(x);
if(t==zero) return one/vzero; /* -integer */
nadj = __ieee754_logf(pi/fabsf(t*x));
if(t<zero) *signgamp = -1;
x = -x;
}
/* purge 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=2-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);
p2 = z*(a1+z*(a3+z*a5));
p = y*p1+p2;
r += p-y/2; break;
case 1:
p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7)))));
r += tf + p; break;
case 2:
p1 = y*(u0+y*(u1+y*u2));
p2 = one+y*(v1+y*(v2+y*v3));
r += p1/p2-y/2;
}
}
/* x < 8.0 */
else if(ix<0x41000000) {
i = x;
y = x-i;
p = y*(s0+y*(s1+y*(s2+y*s3)));
q = one+y*(r1+y*(r2+y*r3));
r = y/2+p/q;
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
switch(i) {
case 7: z *= (y+6); /* FALLTHRU */
case 6: z *= (y+5); /* FALLTHRU */
case 5: z *= (y+4); /* FALLTHRU */
case 4: z *= (y+3); /* FALLTHRU */
case 3: z *= (y+2); /* FALLTHRU */
r += __ieee754_logf(z); break;
}
/* 8.0 <= x < 2**27 */
} else if (ix < 0x4d000000) {
t = __ieee754_logf(x);
z = one/x;
y = z*z;
w = w0+z*(w1+y*w2);
r = (x-half)*(t-one)+w;
} else
/* 2**27 <= x <= inf */
r = x*(__ieee754_logf(x)-one);
if(hx<0) r = nadj - r;
return r;
}