1
2 /* @(#)e_fmod.c 1.3 95/01/18 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16
17 /*
18 * fmod(x,y)
19 * Return x mod y in exact arithmetic
20 * Method: shift and subtract
21 */
22
23 #include <float.h>
24
25 #include "math.h"
26 #include "math_private.h"
27
28 static const double one = 1.0, Zero[] = {0.0, -0.0,};
29
30 double
fmod(double x,double y)31 fmod(double x, double y)
32 {
33 int32_t n,hx,hy,hz,ix,iy,sx,i;
34 u_int32_t lx,ly,lz;
35
36 EXTRACT_WORDS(hx,lx,x);
37 EXTRACT_WORDS(hy,ly,y);
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 nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
46 if(hx<=hy) {
47 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
48 if(lx==ly)
49 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
50 }
51
52 /* determine ix = ilogb(x) */
53 if(hx<0x00100000) { /* subnormal x */
54 if(hx==0) {
55 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
56 } else {
57 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
58 }
59 } else ix = (hx>>20)-1023;
60
61 /* determine iy = ilogb(y) */
62 if(hy<0x00100000) { /* subnormal y */
63 if(hy==0) {
64 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
65 } else {
66 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
67 }
68 } else iy = (hy>>20)-1023;
69
70 /* set up {hx,lx}, {hy,ly} and align y to x */
71 if(ix >= -1022)
72 hx = 0x00100000|(0x000fffff&hx);
73 else { /* subnormal x, shift x to normal */
74 n = -1022-ix;
75 if(n<=31) {
76 hx = (hx<<n)|(lx>>(32-n));
77 lx <<= n;
78 } else {
79 hx = lx<<(n-32);
80 lx = 0;
81 }
82 }
83 if(iy >= -1022)
84 hy = 0x00100000|(0x000fffff&hy);
85 else { /* subnormal y, shift y to normal */
86 n = -1022-iy;
87 if(n<=31) {
88 hy = (hy<<n)|(ly>>(32-n));
89 ly <<= n;
90 } else {
91 hy = ly<<(n-32);
92 ly = 0;
93 }
94 }
95
96 /* fix point fmod */
97 n = ix - iy;
98 while(n--) {
99 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
100 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
101 else {
102 if((hz|lz)==0) /* return sign(x)*0 */
103 return Zero[(u_int32_t)sx>>31];
104 hx = hz+hz+(lz>>31); lx = lz+lz;
105 }
106 }
107 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
108 if(hz>=0) {hx=hz;lx=lz;}
109
110 /* convert back to floating value and restore the sign */
111 if((hx|lx)==0) /* return sign(x)*0 */
112 return Zero[(u_int32_t)sx>>31];
113 while(hx<0x00100000) { /* normalize x */
114 hx = hx+hx+(lx>>31); lx = lx+lx;
115 iy -= 1;
116 }
117 if(iy>= -1022) { /* normalize output */
118 hx = ((hx-0x00100000)|((iy+1023)<<20));
119 INSERT_WORDS(x,hx|sx,lx);
120 } else { /* subnormal output */
121 n = -1022 - iy;
122 if(n<=20) {
123 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
124 hx >>= n;
125 } else if (n<=31) {
126 lx = (hx<<(32-n))|(lx>>n); hx = sx;
127 } else {
128 lx = hx>>(n-32); hx = sx;
129 }
130 INSERT_WORDS(x,hx|sx,lx);
131 x *= one; /* create necessary signal */
132 }
133 return x; /* exact output */
134 }
135
136 #if (LDBL_MANT_DIG == 53)
137 __weak_reference(fmod, fmodl);
138 #endif
139