4caa17b2a1
Underflow exception is only raised when the result is invalid, but fmod is always exact. x87 has a denormalization exception, but that's nonstandard. And the superflous *1.0 will be optimized away by any compiler that does not honor signaling nans.
145 lines
3.2 KiB
C
145 lines
3.2 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/e_fmod.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* fmod(x,y)
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* Return x mod y in exact arithmetic
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* Method: shift and subtract
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*/
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#include "libm.h"
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static const double Zero[] = {0.0, -0.0,};
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double fmod(double x, double y)
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{
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int32_t n,hx,hy,hz,ix,iy,sx,i;
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uint32_t lx,ly,lz;
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EXTRACT_WORDS(hx, lx, x);
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EXTRACT_WORDS(hy, ly, y);
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sx = hx & 0x80000000; /* sign of x */
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hx ^= sx; /* |x| */
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hy &= 0x7fffffff; /* |y| */
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/* purge off exception values */
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if ((hy|ly) == 0 || hx >= 0x7ff00000 || /* y=0,or x not finite */
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(hy|((ly|-ly)>>31)) > 0x7ff00000) /* or y is NaN */
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return (x*y)/(x*y);
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if (hx <= hy) {
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if (hx < hy || lx < ly) /* |x| < |y| */
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return x;
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if (lx == ly) /* |x| = |y|, return x*0 */
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return Zero[(uint32_t)sx>>31];
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}
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/* determine ix = ilogb(x) */
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if (hx < 0x00100000) { /* subnormal x */
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if (hx == 0) {
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for (ix = -1043, i = lx; i > 0; i <<= 1)
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ix -= 1;
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} else {
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for (ix = -1022, i = hx<<11; i > 0; i <<= 1)
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ix -= 1;
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}
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} else
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ix = (hx>>20) - 1023;
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/* determine iy = ilogb(y) */
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if (hy < 0x00100000) { /* subnormal y */
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if (hy == 0) {
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for (iy = -1043, i = ly; i > 0; i <<= 1)
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iy -= 1;
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} else {
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for (iy = -1022, i = hy<<11; i > 0; i <<= 1)
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iy -= 1;
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}
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} else
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iy = (hy>>20) - 1023;
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/* set up {hx,lx}, {hy,ly} and align y to x */
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if (ix >= -1022)
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hx = 0x00100000|(0x000fffff&hx);
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else { /* subnormal x, shift x to normal */
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n = -1022-ix;
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if (n <= 31) {
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hx = (hx<<n)|(lx>>(32-n));
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lx <<= n;
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} else {
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hx = lx<<(n-32);
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lx = 0;
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}
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}
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if(iy >= -1022)
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hy = 0x00100000|(0x000fffff&hy);
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else { /* subnormal y, shift y to normal */
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n = -1022-iy;
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if (n <= 31) {
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hy = (hy<<n)|(ly>>(32-n));
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ly <<= n;
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} else {
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hy = ly<<(n-32);
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ly = 0;
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}
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}
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/* fix point fmod */
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n = ix - iy;
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while (n--) {
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hz = hx-hy;
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lz = lx-ly;
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if (lx < ly)
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hz -= 1;
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if (hz < 0) {
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hx = hx+hx+(lx>>31);
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lx = lx+lx;
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} else {
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if ((hz|lz) == 0) /* return sign(x)*0 */
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return Zero[(uint32_t)sx>>31];
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hx = hz+hz+(lz>>31);
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lx = lz+lz;
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}
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}
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hz = hx-hy;
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lz = lx-ly;
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if (lx < ly)
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hz -= 1;
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if (hz >= 0) {
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hx = hz;
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lx = lz;
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}
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/* convert back to floating value and restore the sign */
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if ((hx|lx) == 0) /* return sign(x)*0 */
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return Zero[(uint32_t)sx>>31];
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while (hx < 0x00100000) { /* normalize x */
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hx = hx+hx+(lx>>31);
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lx = lx+lx;
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iy -= 1;
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}
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if (iy >= -1022) { /* normalize output */
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hx = ((hx-0x00100000)|((iy+1023)<<20));
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INSERT_WORDS(x, hx|sx, lx);
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} else { /* subnormal output */
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n = -1022 - iy;
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if (n <= 20) {
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lx = (lx>>n)|((uint32_t)hx<<(32-n));
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hx >>= n;
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} else if (n <= 31) {
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lx = (hx<<(32-n))|(lx>>n);
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hx = sx;
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} else {
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lx = hx>>(n-32); hx = sx;
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}
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INSERT_WORDS(x, hx|sx, lx);
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}
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return x; /* exact output */
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}
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