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 /*
15  * __ieee754_fmod(x,y)
16  * Return x mod y in exact arithmetic
17  * Method: shift and subtract
18  */
19 
20 #include "fdlibm.h"
21 
22 #ifdef __STDC__
23 static const double one = 1.0, Zero[] = {0.0, -0.0,};
24 #else
25 static double one = 1.0, Zero[] = {0.0, -0.0,};
26 #endif
27 
28 #ifdef __STDC__
__ieee754_fmod(double x,double y)29 	double __ieee754_fmod(double x, double y)
30 #else
31 	double __ieee754_fmod(x,y)
32 	double x,y ;
33 #endif
34 {
35 	int n,hx,hy,hz,ix,iy,sx,i;
36 	unsigned lx,ly,lz;
37 
38 	hx = __HI(x);		/* high word of x */
39 	lx = __LO(x);		/* low  word of x */
40 	hy = __HI(y);		/* high word of y */
41 	ly = __LO(y);		/* low  word of y */
42 	sx = hx&0x80000000;		/* sign of x */
43 	hx ^=sx;		/* |x| */
44 	hy &= 0x7fffffff;	/* |y| */
45 
46     /* purge off exception values */
47 	if((hy|ly)==0||(hx>=0x7ff00000)||	/* y=0,or x not finite */
48 	  ((hy|((ly|-ly)>>31))>0x7ff00000))	/* or y is NaN */
49 	    return (x*y)/(x*y);
50 	if(hx<=hy) {
51 	    if((hx<hy)||(lx<ly)) return x;	/* |x|<|y| return x */
52 	    if(lx==ly)
53 		return Zero[(unsigned)sx>>31];	/* |x|=|y| return x*0*/
54 	}
55 
56     /* determine ix = ieee_ilogb(x) */
57 	if(hx<0x00100000) {	/* subnormal x */
58 	    if(hx==0) {
59 		for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
60 	    } else {
61 		for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
62 	    }
63 	} else ix = (hx>>20)-1023;
64 
65     /* determine iy = ieee_ilogb(y) */
66 	if(hy<0x00100000) {	/* subnormal y */
67 	    if(hy==0) {
68 		for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
69 	    } else {
70 		for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
71 	    }
72 	} else iy = (hy>>20)-1023;
73 
74     /* set up {hx,lx}, {hy,ly} and align y to x */
75 	if(ix >= -1022)
76 	    hx = 0x00100000|(0x000fffff&hx);
77 	else {		/* subnormal x, shift x to normal */
78 	    n = -1022-ix;
79 	    if(n<=31) {
80 	        hx = (hx<<n)|(lx>>(32-n));
81 	        lx <<= n;
82 	    } else {
83 		hx = lx<<(n-32);
84 		lx = 0;
85 	    }
86 	}
87 	if(iy >= -1022)
88 	    hy = 0x00100000|(0x000fffff&hy);
89 	else {		/* subnormal y, shift y to normal */
90 	    n = -1022-iy;
91 	    if(n<=31) {
92 	        hy = (hy<<n)|(ly>>(32-n));
93 	        ly <<= n;
94 	    } else {
95 		hy = ly<<(n-32);
96 		ly = 0;
97 	    }
98 	}
99 
100     /* fix point fmod */
101 	n = ix - iy;
102 	while(n--) {
103 	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
104 	    if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
105 	    else {
106 	    	if((hz|lz)==0) 		/* return sign(x)*0 */
107 		    return Zero[(unsigned)sx>>31];
108 	    	hx = hz+hz+(lz>>31); lx = lz+lz;
109 	    }
110 	}
111 	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
112 	if(hz>=0) {hx=hz;lx=lz;}
113 
114     /* convert back to floating value and restore the sign */
115 	if((hx|lx)==0) 			/* return sign(x)*0 */
116 	    return Zero[(unsigned)sx>>31];
117 	while(hx<0x00100000) {		/* normalize x */
118 	    hx = hx+hx+(lx>>31); lx = lx+lx;
119 	    iy -= 1;
120 	}
121 	if(iy>= -1022) {	/* normalize output */
122 	    hx = ((hx-0x00100000)|((iy+1023)<<20));
123 	    __HI(x) = hx|sx;
124 	    __LO(x) = lx;
125 	} else {		/* subnormal output */
126 	    n = -1022 - iy;
127 	    if(n<=20) {
128 		lx = (lx>>n)|((unsigned)hx<<(32-n));
129 		hx >>= n;
130 	    } else if (n<=31) {
131 		lx = (hx<<(32-n))|(lx>>n); hx = sx;
132 	    } else {
133 		lx = hx>>(n-32); hx = sx;
134 	    }
135 	    __HI(x) = hx|sx;
136 	    __LO(x) = lx;
137 	    x *= one;		/* create necessary signal */
138 	}
139 	return x;		/* exact output */
140 }
141