1 /* origin: FreeBSD /usr/src/lib/msun/src/s_remquo.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
13 * Return the IEEE remainder and set *quo to the last n bits of the
14 * quotient, rounded to the nearest integer. We choose n=31 because
15 * we wind up computing all the integer bits of the quotient anyway as
16 * a side-effect of computing the remainder by the shift and subtract
17 * method. In practice, this is far more bits than are needed to use
18 * remquo in reduction algorithms.
23 static const double Zero[] = {0.0, -0.0,};
25 double remquo(double x, double y, int *quo)
27 int32_t n,hx,hy,hz,ix,iy,sx,i;
28 uint32_t lx,ly,lz,q,sxy;
30 EXTRACT_WORDS(hx, lx, x);
31 EXTRACT_WORDS(hy, ly, y);
32 sxy = (hx ^ hy) & 0x80000000;
33 sx = hx & 0x80000000; /* sign of x */
35 hy &= 0x7fffffff; /* |y| */
37 /* purge off exception values */
38 if ((hy|ly) == 0 || hx >= 0x7ff00000 || /* y = 0, or x not finite */
39 (hy|((ly|-ly)>>31)) > 0x7ff00000) /* or y is NaN */
42 if (hx < hy || lx < ly) { /* |x| < |y| return x or x-y */
46 if (lx == ly) { /* |x| = |y| return x*0 */
48 return Zero[(uint32_t)sx>>31];
54 /* determine ix = ilogb(x) */
55 if (hx < 0x00100000) { /* subnormal x */
57 for (ix = -1043, i=lx; i>0; i<<=1) ix--;
59 for (ix = -1022, i=hx<<11; i>0; i<<=1) ix--;
64 /* determine iy = ilogb(y) */
65 if (hy < 0x00100000) { /* subnormal y */
67 for (iy = -1043, i=ly; i>0; i<<=1) iy--;
69 for (iy = -1022, i=hy<<11; i>0; i<<=1) iy--;
74 /* set up {hx,lx}, {hy,ly} and align y to x */
76 hx = 0x00100000|(0x000fffff&hx);
77 else { /* subnormal x, shift x to normal */
80 hx = (hx<<n)|(lx>>(32-n));
88 hy = 0x00100000|(0x000fffff&hy);
89 else { /* subnormal y, shift y to normal */
92 hy = (hy<<n)|(ly>>(32-n));
109 hx = hx + hx + (lx>>31);
112 hx = hz + hz + (lz>>31);
128 /* convert back to floating value and restore the sign */
129 if ((hx|lx) == 0) { /* return sign(x)*0 */
132 return Zero[(uint32_t)sx>>31];
134 while (hx < 0x00100000) { /* normalize x */
135 hx = hx + hx + (lx>>31);
139 if (iy >= -1022) { /* normalize output */
140 hx = (hx-0x00100000)|((iy+1023)<<20);
141 } else { /* subnormal output */
144 lx = (lx>>n)|((uint32_t)hx<<(32-n));
146 } else if (n <= 31) {
147 lx = (hx<<(32-n))|(lx>>n);
155 INSERT_WORDS(x, hx, lx);
158 if (x + x > y || (x + x == y && (q & 1))) {
162 } else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
166 GET_HIGH_WORD(hx, x);
167 SET_HIGH_WORD(x, hx ^ sx);