-/* 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,};
+#include <math.h>
+#include <stdint.h>
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| */
+ union {double f; uint64_t i;} ux = {x}, uy = {y};
+ int ex = ux.i>>52 & 0x7ff;
+ int ey = uy.i>>52 & 0x7ff;
+ int sx = ux.i>>63;
+ int sy = uy.i>>63;
+ uint32_t q;
+ uint64_t i;
+ uint64_t uxi = ux.i;
- /* 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 */
+ *quo = 0;
+ if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
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 = sxy ? -1 : 1;
- return Zero[(uint32_t)sx>>31];
- }
- }
+ if (ux.i<<1 == 0)
+ return x;
- // 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;
- }
+ /* normalize x and y */
+ if (!ex) {
+ for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1);
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= -1ULL >> 12;
+ uxi |= 1ULL << 52;
}
- 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;
- }
+ if (!ey) {
+ for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1);
+ uy.i <<= -ey + 1;
+ } else {
+ uy.i &= -1ULL >> 12;
+ uy.i |= 1ULL << 52;
}
- /* 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;
+ if (ex < ey) {
+ if (ex+1 == ey)
+ goto end;
+ return x;
+ }
+
+ /* x mod y */
+ for (; ex > ey; ex--) {
+ i = uxi - uy.i;
+ if (i >> 63 == 0) {
+ uxi = i;
q++;
}
+ uxi <<= 1;
q <<= 1;
}
- hz = hx - hy;
- lz = lx - ly;
- if (lx < ly)
- hz--;
- if (hz >= 0) {
- hx = hz;
- lx = lz;
+ i = uxi - uy.i;
+ if (i >> 63 == 0) {
+ uxi = i;
q++;
}
-
- /* convert back to floating value and restore the sign */
- if ((hx|lx) == 0) { /* return sign(x)*0 */
- q &= 0x7fffffff;
- *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 (uxi == 0)
+ ex = -60;
+ else
+ for (; uxi>>52 == 0; uxi <<= 1, ex--);
+end:
+ /* scale result and decide between |x| and |x|-|y| */
+ if (ex > 0) {
+ uxi -= 1ULL << 52;
+ uxi |= (uint64_t)ex << 52;
+ } else {
+ uxi >>= -ex + 1;
}
- 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 = 0;
- } else {
- lx = hx>>(n-32);
- hx = 0;
- }
- }
-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++;
+ ux.i = uxi;
+ x = ux.f;
+ if (sy)
+ y = -y;
+ if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
x -= y;
+ q++;
}
- GET_HIGH_WORD(hx, x);
- SET_HIGH_WORD(x, hx ^ sx);
q &= 0x7fffffff;
- *quo = sxy ? -q : q;
- return x;
+ *quo = sx^sy ? -(int)q : (int)q;
+ return sx ? -x : x;
}
projects / musl / blobdiff