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 <float.h>
24
25#include "math.h"
26#include "math_private.h"
27
28static const double one = 1.0, Zero[] = {0.0, -0.0,};
29
30double
31__ieee754_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 (x*y)/(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