1 /* @(#)e_fmod.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, 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 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: e_fmod.c,v 1.12 2013/11/19 14:02:59 joerg Exp $");
16 #endif
17
18 /*
19 * __ieee754_fmod(x,y)
20 * Return x mod y in exact arithmetic
21 * Method: shift and subtract
22 */
23
24 #include "math.h"
25 #include "math_private.h"
26
27 static const double one = 1.0, Zero[] = {0.0, -0.0,};
28
29 #ifndef __HAVE_LONG_DOUBLE
__strong_alias(__ieee754_fmodl,__ieee754_fmod)30 __strong_alias(__ieee754_fmodl, __ieee754_fmod)
31 #endif
32
33 double
34 __ieee754_fmod(double x, double y)
35 {
36 int32_t n,hx,hy,hz,ix,iy,sx,i;
37 u_int32_t lx,ly,lz;
38
39 EXTRACT_WORDS(hx,lx,x);
40 EXTRACT_WORDS(hy,ly,y);
41 sx = hx&0x80000000; /* sign of x */
42 hx ^=sx; /* |x| */
43 hy &= 0x7fffffff; /* |y| */
44
45 /* purge off exception values */
46 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
47 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
48 return (x*y)/(x*y);
49 if(hx<=hy) {
50 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
51 if(lx==ly)
52 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
53 }
54
55 /* determine ix = ilogb(x) */
56 if(hx<0x00100000) { /* subnormal x */
57 if(hx==0) {
58 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
59 } else {
60 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
61 }
62 } else ix = (hx>>20)-1023;
63
64 /* determine iy = ilogb(y) */
65 if(hy<0x00100000) { /* subnormal y */
66 if(hy==0) {
67 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
68 } else {
69 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
70 }
71 } else iy = (hy>>20)-1023;
72
73 /* set up {hx,lx}, {hy,ly} and align y to x */
74 if(ix >= -1022)
75 hx = 0x00100000|(0x000fffff&hx);
76 else { /* subnormal x, shift x to normal */
77 n = -1022-ix;
78 if(n<=31) {
79 hx = (hx<<n)|(lx>>(32-n));
80 lx <<= n;
81 } else {
82 hx = lx<<(n-32);
83 lx = 0;
84 }
85 }
86 if(iy >= -1022)
87 hy = 0x00100000|(0x000fffff&hy);
88 else { /* subnormal y, shift y to normal */
89 n = -1022-iy;
90 if(n<=31) {
91 hy = (hy<<n)|(ly>>(32-n));
92 ly <<= n;
93 } else {
94 hy = ly<<(n-32);
95 ly = 0;
96 }
97 }
98
99 /* fix point fmod */
100 n = ix - iy;
101 while(n--) {
102 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
103 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
104 else {
105 if((hz|lz)==0) /* return sign(x)*0 */
106 return Zero[(u_int32_t)sx>>31];
107 hx = hz+hz+(lz>>31); lx = lz+lz;
108 }
109 }
110 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
111 if(hz>=0) {hx=hz;lx=lz;}
112
113 /* convert back to floating value and restore the sign */
114 if((hx|lx)==0) /* return sign(x)*0 */
115 return Zero[(u_int32_t)sx>>31];
116 while(hx<0x00100000) { /* normalize x */
117 hx = hx+hx+(lx>>31); lx = lx+lx;
118 iy -= 1;
119 }
120 if(iy>= -1022) { /* normalize output */
121 hx = ((hx-0x00100000)|((iy+1023)<<20));
122 INSERT_WORDS(x,hx|sx,lx);
123 } else { /* subnormal output */
124 n = -1022 - iy;
125 if(n<=20) {
126 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
127 hx >>= n;
128 } else if (n<=31) {
129 lx = (hx<<(32-n))|(lx>>n); hx = sx;
130 } else {
131 lx = hx>>(n-32); hx = sx;
132 }
133 INSERT_WORDS(x,hx|sx,lx);
134 x *= one; /* create necessary signal */
135 }
136 return x; /* exact output */
137 }
138