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 * ====================================================
13 #include <sys/cdefs.h>
14 __FBSDID("$FreeBSD$");
19 #include "math_private.h"
21 static const double Zero[] = {0.0, -0.0,};
24 * Return the IEEE remainder and set *quo to the last n bits of the
25 * quotient, rounded to the nearest integer. We choose n=31 because
26 * we wind up computing all the integer bits of the quotient anyway as
27 * a side-effect of computing the remainder by the shift and subtract
28 * method. In practice, this is far more bits than are needed to use
29 * remquo in reduction algorithms.
32 remquo(double x, double y, int *quo)
34 int32_t n,hx,hy,hz,ix,iy,sx,i;
35 u_int32_t lx,ly,lz,q,sxy;
37 EXTRACT_WORDS(hx,lx,x);
38 EXTRACT_WORDS(hy,ly,y);
39 sxy = (hx ^ hy) & 0x80000000;
40 sx = hx&0x80000000; /* sign of x */
42 hy &= 0x7fffffff; /* |y| */
44 /* purge off exception values */
45 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
46 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
49 if((hx<hy)||(lx<ly)) {
51 goto fixup; /* |x|<|y| return x or x-y */
54 *quo = (sxy ? -1 : 1);
55 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
59 /* determine ix = ilogb(x) */
60 if(hx<0x00100000) { /* subnormal x */
62 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
64 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
66 } else ix = (hx>>20)-1023;
68 /* determine iy = ilogb(y) */
69 if(hy<0x00100000) { /* subnormal y */
71 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
73 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
75 } else iy = (hy>>20)-1023;
77 /* set up {hx,lx}, {hy,ly} and align y to x */
79 hx = 0x00100000|(0x000fffff&hx);
80 else { /* subnormal x, shift x to normal */
83 hx = (hx<<n)|(lx>>(32-n));
91 hy = 0x00100000|(0x000fffff&hy);
92 else { /* subnormal y, shift y to normal */
95 hy = (hy<<n)|(ly>>(32-n));
107 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
108 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
109 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
112 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
113 if(hz>=0) {hx=hz;lx=lz;q++;}
115 /* convert back to floating value and restore the sign */
116 if((hx|lx)==0) { /* return sign(x)*0 */
118 *quo = (sxy ? -q : q);
119 return Zero[(u_int32_t)sx>>31];
121 while(hx<0x00100000) { /* normalize x */
122 hx = hx+hx+(lx>>31); lx = lx+lx;
125 if(iy>= -1022) { /* normalize output */
126 hx = ((hx-0x00100000)|((iy+1023)<<20));
127 } else { /* subnormal output */
130 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
133 lx = (hx<<(32-n))|(lx>>n); hx = 0;
135 lx = hx>>(n-32); hx = 0;
139 INSERT_WORDS(x,hx,lx);
142 if (x+x>y || (x+x==y && (q & 1))) {
146 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
151 SET_HIGH_WORD(x,hx^sx);
153 *quo = (sxy ? -q : q);
157 #if LDBL_MANT_DIG == 53
158 __weak_reference(remquo, remquol);