1 /* @(#)e_fmod.c 1.3 95/01/18 */
2 /*-
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
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
9 * is preserved.
10 * ====================================================
11 */
12
13 #include <sys/cdefs.h>
14 /* __FBSDID("$FreeBSD: src/lib/msun/src/s_remquo.c,v 1.1 2005/03/25 04:40:44 das Exp $"); */
15
16 #include "math.h"
17 #include "math_private.h"
18
19 static const double Zero[] = {0.0, -0.0,};
20
21 /*
22 * Return the IEEE remainder and set *quo to the last n bits of the
23 * quotient, rounded to the nearest integer. We choose n=31 because
24 * we wind up computing all the integer bits of the quotient anyway as
25 * a side-effect of computing the remainder by the shift and subtract
26 * method. In practice, this is far more bits than are needed to use
27 * remquo in reduction algorithms.
28 */
29 double
remquo(double x,double y,int * quo)30 remquo(double x, double y, int *quo)
31 {
32 int32_t n,hx,hy,hz,ix,iy,sx,i;
33 u_int32_t lx,ly,lz,q,sxy;
34
35 EXTRACT_WORDS(hx,lx,x);
36 EXTRACT_WORDS(hy,ly,y);
37 sxy = (hx ^ hy) & 0x80000000;
38 sx = hx&0x80000000; /* sign of x */
39 hx ^=sx; /* |x| */
40 hy &= 0x7fffffff; /* |y| */
41
42 /* purge off exception values */
43 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
44 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
45 return (x*y)/(x*y);
46 if(hx<=hy) {
47 if((hx<hy)||(lx<ly)) {
48 q = 0;
49 goto fixup; /* |x|<|y| return x or x-y */
50 }
51 if(lx==ly) {
52 *quo = 1;
53 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
54 }
55 }
56
57 /* determine ix = ilogb(x) */
58 if(hx<0x00100000) { /* subnormal x */
59 if(hx==0) {
60 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
61 } else {
62 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
63 }
64 } else ix = (hx>>20)-1023;
65
66 /* determine iy = ilogb(y) */
67 if(hy<0x00100000) { /* subnormal y */
68 if(hy==0) {
69 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
70 } else {
71 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
72 }
73 } else iy = (hy>>20)-1023;
74
75 /* set up {hx,lx}, {hy,ly} and align y to x */
76 if(ix >= -1022)
77 hx = 0x00100000|(0x000fffff&hx);
78 else { /* subnormal x, shift x to normal */
79 n = -1022-ix;
80 if(n<=31) {
81 hx = (hx<<n)|(lx>>(32-n));
82 lx <<= n;
83 } else {
84 hx = lx<<(n-32);
85 lx = 0;
86 }
87 }
88 if(iy >= -1022)
89 hy = 0x00100000|(0x000fffff&hy);
90 else { /* subnormal y, shift y to normal */
91 n = -1022-iy;
92 if(n<=31) {
93 hy = (hy<<n)|(ly>>(32-n));
94 ly <<= n;
95 } else {
96 hy = ly<<(n-32);
97 ly = 0;
98 }
99 }
100
101 /* fix point fmod */
102 n = ix - iy;
103 q = 0;
104 while(n--) {
105 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
106 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
107 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
108 q <<= 1;
109 }
110 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
111 if(hz>=0) {hx=hz;lx=lz;q++;}
112
113 /* convert back to floating value and restore the sign */
114 if((hx|lx)==0) { /* return sign(x)*0 */
115 *quo = (sxy ? -q : q);
116 return Zero[(u_int32_t)sx>>31];
117 }
118 while(hx<0x00100000) { /* normalize x */
119 hx = hx+hx+(lx>>31); lx = lx+lx;
120 iy -= 1;
121 }
122 if(iy>= -1022) { /* normalize output */
123 hx = ((hx-0x00100000)|((iy+1023)<<20));
124 } else { /* subnormal output */
125 n = -1022 - iy;
126 if(n<=20) {
127 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
128 hx >>= n;
129 } else if (n<=31) {
130 lx = (hx<<(32-n))|(lx>>n); hx = sx;
131 } else {
132 lx = hx>>(n-32); hx = sx;
133 }
134 }
135 fixup:
136 INSERT_WORDS(x,hx,lx);
137 y = fabs(y);
138 if (y < 0x1p-1021) {
139 if (x+x>y || (x+x==y && (q & 1))) {
140 q++;
141 x-=y;
142 }
143 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
144 q++;
145 x-=y;
146 }
147 GET_HIGH_WORD(hx,x);
148 SET_HIGH_WORD(x,hx^sx);
149 q &= 0x7fffffff;
150 *quo = (sxy ? -q : q);
151 return x;
152 }
153