2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunSoft, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
9 * ====================================================
12 #include <sys/cdefs.h>
16 #include "math_private.h"
18 static const double Zero[] = {0.0, -0.0,};
21 * Return the IEEE remainder and set *quo to the last n bits of the
22 * quotient, rounded to the nearest integer. We choose n=31 because
23 * we wind up computing all the integer bits of the quotient anyway as
24 * a side-effect of computing the remainder by the shift and subtract
25 * method. In practice, this is far more bits than are needed to use
26 * remquo in reduction algorithms.
29 remquo(double x, double y, int *quo)
31 int32_t n,hx,hy,hz,ix,iy,sx,i;
32 u_int32_t lx,ly,lz,q,sxy;
34 EXTRACT_WORDS(hx,lx,x);
35 EXTRACT_WORDS(hy,ly,y);
36 sxy = (hx ^ hy) & 0x80000000;
37 sx = hx&0x80000000; /* sign of x */
39 hy &= 0x7fffffff; /* |y| */
41 /* purge off exception values */
42 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
43 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
44 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
46 if((hx<hy)||(lx<ly)) {
48 goto fixup; /* |x|<|y| return x or x-y */
51 *quo = (sxy ? -1 : 1);
52 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
56 /* determine ix = ilogb(x) */
57 if(hx<0x00100000) { /* subnormal x */
59 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
61 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
63 } else ix = (hx>>20)-1023;
65 /* determine iy = ilogb(y) */
66 if(hy<0x00100000) { /* subnormal y */
68 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
70 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
72 } else iy = (hy>>20)-1023;
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));
104 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
105 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
106 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
109 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
110 if(hz>=0) {hx=hz;lx=lz;q++;}
112 /* convert back to floating value and restore the sign */
113 if((hx|lx)==0) { /* return sign(x)*0 */
115 *quo = (sxy ? -q : q);
116 return Zero[(u_int32_t)sx>>31];
118 while(hx<0x00100000) { /* normalize x */
119 hx = hx+hx+(lx>>31); lx = lx+lx;
122 if(iy>= -1022) { /* normalize output */
123 hx = ((hx-0x00100000)|((iy+1023)<<20));
124 } else { /* subnormal output */
127 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
130 lx = (hx<<(32-n))|(lx>>n); hx = 0;
132 lx = hx>>(n-32); hx = 0;
136 INSERT_WORDS(x,hx,lx);
139 if (x+x>y || (x+x==y && (q & 1))) {
143 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
148 SET_HIGH_WORD(x,hx^sx);
150 *quo = (sxy ? -q : q);
154 #if LDBL_MANT_DIG == 53
155 __weak_reference(remquo, remquol);