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
26static const double one = 1.0, Zero[] = {0.0, -0.0,};
27
28double
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