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/* origin: FreeBSD /usr/src/lib/msun/src/s_remquo.c */
/*-
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* Return the IEEE remainder and set *quo to the last n bits of the
* quotient, rounded to the nearest integer. We choose n=31 because
* we wind up computing all the integer bits of the quotient anyway as
* a side-effect of computing the remainder by the shift and subtract
* method. In practice, this is far more bits than are needed to use
* remquo in reduction algorithms.
*/
#include "libm.h"
static const double Zero[] = {0.0, -0.0,};
double remquo(double x, double y, int *quo)
{
int32_t n,hx,hy,hz,ix,iy,sx,i;
uint32_t lx,ly,lz,q,sxy;
EXTRACT_WORDS(hx, lx, x);
EXTRACT_WORDS(hy, ly, y);
sxy = (hx ^ hy) & 0x80000000;
sx = hx & 0x80000000; /* sign of x */
hx ^= sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
/* purge off exception values */
if ((hy|ly) == 0 || hx >= 0x7ff00000 || /* y = 0, or x not finite */
(hy|((ly|-ly)>>31)) > 0x7ff00000) /* or y is NaN */
return (x*y)/(x*y);
if (hx <= hy) {
if (hx < hy || lx < ly) { /* |x| < |y| return x or x-y */
q = 0;
goto fixup;
}
if (lx == ly) { /* |x| = |y| return x*0 */
*quo = 1;
return Zero[(uint32_t)sx>>31];
}
}
// FIXME: use ilogb?
/* determine ix = ilogb(x) */
if (hx < 0x00100000) { /* subnormal x */
if (hx == 0) {
for (ix = -1043, i=lx; i>0; i<<=1) ix--;
} else {
for (ix = -1022, i=hx<<11; i>0; i<<=1) ix--;
}
} else
ix = (hx>>20) - 1023;
/* determine iy = ilogb(y) */
if (hy < 0x00100000) { /* subnormal y */
if (hy == 0) {
for (iy = -1043, i=ly; i>0; i<<=1) iy--;
} else {
for (iy = -1022, i=hy<<11; i>0; i<<=1) iy--;
}
} else
iy = (hy>>20) - 1023;
/* set up {hx,lx}, {hy,ly} and align y to x */
if (ix >= -1022)
hx = 0x00100000|(0x000fffff&hx);
else { /* subnormal x, shift x to normal */
n = -1022 - ix;
if (n <= 31) {
hx = (hx<<n)|(lx>>(32-n));
lx <<= n;
} else {
hx = lx<<(n-32);
lx = 0;
}
}
if (iy >= -1022)
hy = 0x00100000|(0x000fffff&hy);
else { /* subnormal y, shift y to normal */
n = -1022 - iy;
if (n <= 31) {
hy = (hy<<n)|(ly>>(32-n));
ly <<= n;
} else {
hy = ly<<(n-32);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
q = 0;
while (n--) {
hz = hx - hy;
lz = lx - ly;
if (lx < ly)
hz--;
if (hz < 0) {
hx = hx + hx + (lx>>31);
lx = lx + lx;
} else {
hx = hz + hz + (lz>>31);
lx = lz + lz;
q++;
}
q <<= 1;
}
hz = hx - hy;
lz = lx - ly;
if (lx < ly)
hz--;
if (hz >= 0) {
hx = hz;
lx = lz;
q++;
}
/* convert back to floating value and restore the sign */
if ((hx|lx) == 0) { /* return sign(x)*0 */
*quo = sxy ? -q : q;
return Zero[(uint32_t)sx>>31];
}
while (hx < 0x00100000) { /* normalize x */
hx = hx + hx + (lx>>31);
lx = lx + lx;
iy--;
}
if (iy >= -1022) { /* normalize output */
hx = (hx-0x00100000)|((iy+1023)<<20);
} else { /* subnormal output */
n = -1022 - iy;
if (n <= 20) {
lx = (lx>>n)|((uint32_t)hx<<(32-n));
hx >>= n;
} else if (n <= 31) {
lx = (hx<<(32-n))|(lx>>n);
hx = sx;
} else {
lx = hx>>(n-32);
hx = sx;
}
}
fixup:
INSERT_WORDS(x, hx, lx);
y = fabs(y);
if (y < 0x1p-1021) {
if (x + x > y || (x + x == y && (q & 1))) {
q++;
x -= y;
}
} else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
q++;
x -= y;
}
GET_HIGH_WORD(hx, x);
SET_HIGH_WORD(x, hx ^ sx);
q &= 0x7fffffff;
*quo = sxy ? -q : q;
return x;
}
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