1 /* @(#)e_fmod.c 1.3 95/01/18 */
2 /*-
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  *
6  * Developed at SunSoft, 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 __FBSDID("$FreeBSD$");
15 
16 #include <float.h>
17 
18 #include "math.h"
19 #include "math_private.h"
20 
21 static const double Zero[] = {0.0, -0.0,};
22 
23 /*
24  * Return the IEEE remainder and set *quo to the last n bits of the
25  * quotient, rounded to the nearest integer.  We choose n=31 because
26  * we wind up computing all the integer bits of the quotient anyway as
27  * a side-effect of computing the remainder by the shift and subtract
28  * method.  In practice, this is far more bits than are needed to use
29  * remquo in reduction algorithms.
30  */
31 double
remquo(double x,double y,int * quo)32 remquo(double x, double y, int *quo)
33 {
34 	int32_t n,hx,hy,hz,ix,iy,sx,i;
35 	u_int32_t lx,ly,lz,q,sxy;
36 
37 	EXTRACT_WORDS(hx,lx,x);
38 	EXTRACT_WORDS(hy,ly,y);
39 	sxy = (hx ^ hy) & 0x80000000;
40 	sx = hx&0x80000000;		/* sign of x */
41 	hx ^=sx;		/* |x| */
42 	hy &= 0x7fffffff;	/* |y| */
43 
44     /* purge off exception values */
45 	if((hy|ly)==0||(hx>=0x7ff00000)||	/* y=0,or x not finite */
46 	  ((hy|((ly|-ly)>>31))>0x7ff00000))	/* or y is NaN */
47 	    return (x*y)/(x*y);
48 	if(hx<=hy) {
49 	    if((hx<hy)||(lx<ly)) {
50 		q = 0;
51 		goto fixup;	/* |x|<|y| return x or x-y */
52 	    }
53 	    if(lx==ly) {
54 		*quo = (sxy ? -1 : 1);
55 		return Zero[(u_int32_t)sx>>31];	/* |x|=|y| return x*0*/
56 	    }
57 	}
58 
59     /* determine ix = ilogb(x) */
60 	if(hx<0x00100000) {	/* subnormal x */
61 	    if(hx==0) {
62 		for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
63 	    } else {
64 		for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
65 	    }
66 	} else ix = (hx>>20)-1023;
67 
68     /* determine iy = ilogb(y) */
69 	if(hy<0x00100000) {	/* subnormal y */
70 	    if(hy==0) {
71 		for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
72 	    } else {
73 		for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
74 	    }
75 	} else iy = (hy>>20)-1023;
76 
77     /* set up {hx,lx}, {hy,ly} and align y to x */
78 	if(ix >= -1022)
79 	    hx = 0x00100000|(0x000fffff&hx);
80 	else {		/* subnormal x, shift x to normal */
81 	    n = -1022-ix;
82 	    if(n<=31) {
83 	        hx = (hx<<n)|(lx>>(32-n));
84 	        lx <<= n;
85 	    } else {
86 		hx = lx<<(n-32);
87 		lx = 0;
88 	    }
89 	}
90 	if(iy >= -1022)
91 	    hy = 0x00100000|(0x000fffff&hy);
92 	else {		/* subnormal y, shift y to normal */
93 	    n = -1022-iy;
94 	    if(n<=31) {
95 	        hy = (hy<<n)|(ly>>(32-n));
96 	        ly <<= n;
97 	    } else {
98 		hy = ly<<(n-32);
99 		ly = 0;
100 	    }
101 	}
102 
103     /* fix point fmod */
104 	n = ix - iy;
105 	q = 0;
106 	while(n--) {
107 	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
108 	    if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
109 	    else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
110 	    q <<= 1;
111 	}
112 	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
113 	if(hz>=0) {hx=hz;lx=lz;q++;}
114 
115     /* convert back to floating value and restore the sign */
116 	if((hx|lx)==0) {			/* return sign(x)*0 */
117 	    q &= 0x7fffffff;
118 	    *quo = (sxy ? -q : q);
119 	    return Zero[(u_int32_t)sx>>31];
120 	}
121 	while(hx<0x00100000) {		/* normalize x */
122 	    hx = hx+hx+(lx>>31); lx = lx+lx;
123 	    iy -= 1;
124 	}
125 	if(iy>= -1022) {	/* normalize output */
126 	    hx = ((hx-0x00100000)|((iy+1023)<<20));
127 	} else {		/* subnormal output */
128 	    n = -1022 - iy;
129 	    if(n<=20) {
130 		lx = (lx>>n)|((u_int32_t)hx<<(32-n));
131 		hx >>= n;
132 	    } else if (n<=31) {
133 		lx = (hx<<(32-n))|(lx>>n); hx = 0;
134 	    } else {
135 		lx = hx>>(n-32); hx = 0;
136 	    }
137 	}
138 fixup:
139 	INSERT_WORDS(x,hx,lx);
140 	y = fabs(y);
141 	if (y < 0x1p-1021) {
142 	    if (x+x>y || (x+x==y && (q & 1))) {
143 		q++;
144 		x-=y;
145 	    }
146 	} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
147 	    q++;
148 	    x-=y;
149 	}
150 	GET_HIGH_WORD(hx,x);
151 	SET_HIGH_WORD(x,hx^sx);
152 	q &= 0x7fffffff;
153 	*quo = (sxy ? -q : q);
154 	return x;
155 }
156 
157 #if LDBL_MANT_DIG == 53
158 __weak_reference(remquo, remquol);
159 #endif
160