Commit cc8c049f authored by Raymond Toy's avatar Raymond Toy
Browse files

Extract the log2 code out of e_pow.c to implement log2 function.

 * log2.c:
   * New file containing the parts of e_pow.c that implemented a log2
     function for use in pow().
 * GNUmakefile:
   * Compile log2.c as part of the build.
parent 9918ab2d
......@@ -13,7 +13,8 @@ FDLIBM = k_sin.c k_cos.c k_tan.c s_sin.c s_cos.c s_tan.c sincos.c \
e_atan2.c \
e_rem_pio2.c k_rem_pio2.c \
e_log10.c s_scalbn.c \
setexception.c
setexception.c \
log2.c
SRCS = lisp.c coreparse.c alloc.c monitor.c print.c interr.c \
vars.c parse.c interrupt.c search.c validate.c globals.c \
......
/*
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* This is the log2 algorithm pulled out of __ieee754_pow in e_pow.c
*/
/*
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
*/
#include "fdlibm.h"
static double
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero = 0.0,
one = 1.0,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09; /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
double cmucl_log2(double x)
{
double ax;
int k, hx, lx, ix;
union { int i[2]; double d; } ux;
ux.d = x;
hx = ux.i[HIWORD]; lx = ux.i[LOWORD];
ix = hx&0x7fffffff;
ax = fabs(x);
/* special value of x */
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0) {
/* log(+-0)=-inf */
return fdlibm_setexception(-1.0, FDLIBM_DIVIDE_BY_ZERO);
}
if (hx<0) {
/* log(-#) = NaN */
return fdlibm_setexception(x, FDLIBM_INVALID);
}
}
{
double ss,s2,s_h,s_l,t_h,t_l;
double z_h,z_l,p_h,p_l;
double r, u, v, t, t1, t2;
int n, j;
n = 0;
/* take care subnormal number */
if(ix<0x00100000) {
ax *= two53;
n -= 53;
ux.d = ax;
ix = ux.i[HIWORD];
}
n += ((ix)>>20)-0x3ff;
j = ix&0x000fffff;
/* determine interval */
ix = j|0x3ff00000; /* normalize ix */
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00100000;}
ux.d = ax;
ux.i[HIWORD] = ix;
ax = ux.d;
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one/(ax+bp[k]);
ss = u*v;
s_h = ss;
ux.d = s_h;
ux.i[LOWORD] = 0;
s_h = ux.d;
/* t_h=ax+bp[k] High */
t_h = zero;
ux.d = t_h;
ux.i[HIWORD]=((ix>>1)|0x20000000)+0x00080000+(k<<18);
t_h = ux.d;
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = ss*ss;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+ss);
s2 = s_h*s_h;
t_h = 3.0+s2+r;
ux.d = t_h;
ux.i[LOWORD] = 0;
t_h = ux.d;
t_l = r-((t_h-3.0)-s2);
/* u+v = ss*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*ss;
/* 2/(3log2)*(ss+...) */
p_h = u+v;
ux.d = p_h;
ux.i[LOWORD] = 0;
p_h = ux.d;
p_l = v-(p_h-u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
ux.d = t1;
ux.i[LOWORD] = 0;
t1 = ux.d;
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
return t1 + t2;
}
}
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