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