-/* origin: FreeBSD /usr/src/lib/msun/src/e_fmod.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.
- * ====================================================
- */
-/*
- * fmod(x,y)
- * Return x mod y in exact arithmetic
- * Method: shift and subtract
- */
-
-#include "libm.h"
-
-static const double one = 1.0, Zero[] = {0.0, -0.0,};
+#include <math.h>
+#include <stdint.h>
double fmod(double x, double y)
{
- int32_t n,hx,hy,hz,ix,iy,sx,i;
- uint32_t lx,ly,lz;
+ 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;
+ uint64_t i;
- EXTRACT_WORDS(hx, lx, x);
- EXTRACT_WORDS(hy, ly, y);
- sx = hx & 0x80000000; /* sign of x */
- hx ^= sx; /* |x| */
- hy &= 0x7fffffff; /* |y| */
+ /* in the followings uxi should be ux.i, but then gcc wrongly adds */
+ /* float load/store to inner loops ruining performance and code size */
+ 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 */
+ 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;
- if (lx == ly) /* |x| = |y|, return x*0 */
- return Zero[(uint32_t)sx>>31];
+ if (uxi<<1 <= uy.i<<1) {
+ if (uxi<<1 == uy.i<<1)
+ return 0*x;
+ return x;
}
- /* determine ix = ilogb(x) */
- if (hx < 0x00100000) { /* subnormal x */
- if (hx == 0) {
- for (ix = -1043, i = lx; i > 0; i <<= 1)
- ix -= 1;
- } else {
- for (ix = -1022, i = hx<<11; i > 0; i <<= 1)
- ix -= 1;
- }
- } 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 -= 1;
- } else {
- for (iy = -1022, i = hy<<11; i > 0; i <<= 1)
- iy -= 1;
- }
- } 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;
- while (n--) {
- hz = hx-hy;
- lz = lx-ly;
- if (lx < ly)
- hz -= 1;
- if (hz < 0) {
- hx = hx+hx+(lx>>31);
- lx = lx+lx;
- } else {
- if ((hz|lz) == 0) /* return sign(x)*0 */
- return Zero[(uint32_t)sx>>31];
- hx = hz+hz+(lz>>31);
- lx = lz+lz;
+ /* x mod y */
+ for (; ex > ey; ex--) {
+ i = uxi - uy.i;
+ if (i >> 63 == 0) {
+ if (i == 0)
+ return 0*x;
+ uxi = i;
}
+ uxi <<= 1;
}
- hz = hx-hy;
- lz = lx-ly;
- if (lx < ly)
- hz -= 1;
- if (hz >= 0) {
- hx = hz;
- lx = lz;
+ i = uxi - uy.i;
+ if (i >> 63 == 0) {
+ if (i == 0)
+ return 0*x;
+ uxi = i;
}
+ for (; uxi>>52 == 0; uxi <<= 1, ex--);
- /* convert back to floating value and restore the sign */
- if ((hx|lx) == 0) /* return sign(x)*0 */
- return Zero[(uint32_t)sx>>31];
- while (hx < 0x00100000) { /* normalize x */
- hx = hx+hx+(lx>>31);
- lx = lx+lx;
- iy -= 1;
- }
- if (iy >= -1022) { /* normalize output */
- hx = ((hx-0x00100000)|((iy+1023)<<20));
- INSERT_WORDS(x, hx|sx, lx);
- } 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;
- }
- INSERT_WORDS(x, hx|sx, lx);
- x *= one; /* create necessary signal */
+ /* scale result */
+ if (ex > 0) {
+ uxi -= 1ULL << 52;
+ uxi |= (uint64_t)ex << 52;
+ } else {
+ uxi >>= -ex + 1;
}
- return x; /* exact output */
+ uxi |= (uint64_t)sx << 63;
+ ux.i = uxi;
+ return ux.f;
}
projects / musl / blobdiff