1 /* @(#)e_fmod.c 1.3 95/01/18 */
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 * ====================================================
14 #include "math_private.h"
16 static const double Zero[] = {0.0, -0.0,};
19 * Return the IEEE remainder and set *quo to the last n bits of the
20 * quotient, rounded to the nearest integer. We choose n=31 because
21 * we wind up computing all the integer bits of the quotient anyway as
22 * a side-effect of computing the remainder by the shift and subtract
23 * method. In practice, this is far more bits than are needed to use
24 * remquo in reduction algorithms.
27 remquo(double x, double y, int *quo)
29 int32_t n,hx,hy,hz,ix,iy,sx,i;
30 uint32_t lx,ly,lz,q,sxy;
32 EXTRACT_WORDS(hx,lx,x);
33 EXTRACT_WORDS(hy,ly,y);
34 sxy = (hx ^ hy) & 0x80000000;
35 sx = hx&0x80000000; /* sign of x */
37 hy &= 0x7fffffff; /* |y| */
39 /* purge off exception values */
40 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
41 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
44 if((hx<hy)||(lx<ly)) {
46 goto fixup; /* |x|<|y| return x or x-y */
50 return Zero[(uint32_t)sx>>31]; /* |x|=|y| return x*0*/
54 /* determine ix = ilogb(x) */
55 if(hx<0x00100000) { /* subnormal x */
57 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
59 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
61 } else ix = (hx>>20)-1023;
63 /* determine iy = ilogb(y) */
64 if(hy<0x00100000) { /* subnormal y */
66 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
68 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
70 } else iy = (hy>>20)-1023;
72 /* set up {hx,lx}, {hy,ly} and align y to x */
74 hx = 0x00100000|(0x000fffff&hx);
75 else { /* subnormal x, shift x to normal */
78 hx = (hx<<n)|(lx>>(32-n));
86 hy = 0x00100000|(0x000fffff&hy);
87 else { /* subnormal y, shift y to normal */
90 hy = (hy<<n)|(ly>>(32-n));
102 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
103 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
104 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
107 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
108 if(hz>=0) {hx=hz;lx=lz;q++;}
110 /* convert back to floating value and restore the sign */
111 if((hx|lx)==0) { /* return sign(x)*0 */
112 *quo = (sxy ? -q : q);
113 return Zero[(uint32_t)sx>>31];
115 while(hx<0x00100000) { /* normalize x */
116 hx = hx+hx+(lx>>31); lx = lx+lx;
119 if(iy>= -1022) { /* normalize output */
120 hx = ((hx-0x00100000)|((iy+1023)<<20));
121 } else { /* subnormal output */
124 lx = (lx>>n)|((uint32_t)hx<<(32-n));
127 lx = (hx<<(32-n))|(lx>>n); hx = sx;
129 lx = hx>>(n-32); hx = sx;
133 INSERT_WORDS(x,hx,lx);
136 if (x+x>y || (x+x==y && (q & 1))) {
140 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
145 SET_HIGH_WORD(x,hx^sx);
147 *quo = (sxy ? -q : q);