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("$FreeBSD$");
15
16 #include <float.h>
17
18 #include "math.h"
19 #include "math_private.h"
20
21 static const double Zero[] = {0.0, -0.0,};
22
23 /*
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.
30 */
31 double
remquo(double x,double y,int * quo)32 remquo(double x, double y, int *quo)
33 {
34 int32_t n,hx,hy,hz,ix,iy,sx,i;
35 u_int32_t lx,ly,lz,q,sxy;
36
37 EXTRACT_WORDS(hx,lx,x);
38 EXTRACT_WORDS(hy,ly,y);
39 sxy = (hx ^ hy) & 0x80000000;
40 sx = hx&0x80000000; /* sign of x */
41 hx ^=sx; /* |x| */
42 hy &= 0x7fffffff; /* |y| */
43
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 */
47 return (x*y)/(x*y);
48 if(hx<=hy) {
49 if((hx<hy)||(lx<ly)) {
50 q = 0;
51 goto fixup; /* |x|<|y| return x or x-y */
52 }
53 if(lx==ly) {
54 *quo = (sxy ? -1 : 1);
55 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
56 }
57 }
58
59 /* determine ix = ilogb(x) */
60 if(hx<0x00100000) { /* subnormal x */
61 if(hx==0) {
62 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
63 } else {
64 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
65 }
66 } else ix = (hx>>20)-1023;
67
68 /* determine iy = ilogb(y) */
69 if(hy<0x00100000) { /* subnormal y */
70 if(hy==0) {
71 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
72 } else {
73 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
74 }
75 } else iy = (hy>>20)-1023;
76
77 /* set up {hx,lx}, {hy,ly} and align y to x */
78 if(ix >= -1022)
79 hx = 0x00100000|(0x000fffff&hx);
80 else { /* subnormal x, shift x to normal */
81 n = -1022-ix;
82 if(n<=31) {
83 hx = (hx<<n)|(lx>>(32-n));
84 lx <<= n;
85 } else {
86 hx = lx<<(n-32);
87 lx = 0;
88 }
89 }
90 if(iy >= -1022)
91 hy = 0x00100000|(0x000fffff&hy);
92 else { /* subnormal y, shift y to normal */
93 n = -1022-iy;
94 if(n<=31) {
95 hy = (hy<<n)|(ly>>(32-n));
96 ly <<= n;
97 } else {
98 hy = ly<<(n-32);
99 ly = 0;
100 }
101 }
102
103 /* fix point fmod */
104 n = ix - iy;
105 q = 0;
106 while(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++;}
110 q <<= 1;
111 }
112 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
113 if(hz>=0) {hx=hz;lx=lz;q++;}
114
115 /* convert back to floating value and restore the sign */
116 if((hx|lx)==0) { /* return sign(x)*0 */
117 q &= 0x7fffffff;
118 *quo = (sxy ? -q : q);
119 return Zero[(u_int32_t)sx>>31];
120 }
121 while(hx<0x00100000) { /* normalize x */
122 hx = hx+hx+(lx>>31); lx = lx+lx;
123 iy -= 1;
124 }
125 if(iy>= -1022) { /* normalize output */
126 hx = ((hx-0x00100000)|((iy+1023)<<20));
127 } else { /* subnormal output */
128 n = -1022 - iy;
129 if(n<=20) {
130 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
131 hx >>= n;
132 } else if (n<=31) {
133 lx = (hx<<(32-n))|(lx>>n); hx = 0;
134 } else {
135 lx = hx>>(n-32); hx = 0;
136 }
137 }
138 fixup:
139 INSERT_WORDS(x,hx,lx);
140 y = fabs(y);
141 if (y < 0x1p-1021) {
142 if (x+x>y || (x+x==y && (q & 1))) {
143 q++;
144 x-=y;
145 }
146 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
147 q++;
148 x-=y;
149 }
150 GET_HIGH_WORD(hx,x);
151 SET_HIGH_WORD(x,hx^sx);
152 q &= 0x7fffffff;
153 *quo = (sxy ? -q : q);
154 return x;
155 }
156
157 #if LDBL_MANT_DIG == 53
158 __weak_reference(remquo, remquol);
159 #endif
160