s_remquo.c revision 1.3 
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/* LINTLIBRARY */
14
15#include <float.h>
16#include <math.h>
17
18#include "math_private.h"
19
20static const double Zero[] = {0.0, -0.0,};
21
22/*
23 * Return the IEEE remainder and set *quo to the last n bits of the
24 * quotient, rounded to the nearest integer.  We choose n=31 because
25 * we wind up computing all the integer bits of the quotient anyway as
26 * a side-effect of computing the remainder by the shift and subtract
27 * method.  In practice, this is far more bits than are needed to use
28 * remquo in reduction algorithms.
29 */
30double
31remquo(double x, double y, int *quo)
32{
33	int32_t n,hx,hy,hz,ix,iy,sx,i;
34	u_int32_t lx,ly,lz,q,sxy;
35
36	EXTRACT_WORDS(hx,lx,x);
37	EXTRACT_WORDS(hy,ly,y);
38	sxy = (hx ^ hy) & 0x80000000;
39	sx = hx&0x80000000;		/* sign of x */
40	hx ^=sx;		/* |x| */
41	hy &= 0x7fffffff;	/* |y| */
42
43    /* purge off exception values */
44	if((hy|ly)==0||(hx>=0x7ff00000)||	/* y=0,or x not finite */
45	  ((hy|((ly|-ly)>>31))>0x7ff00000))	/* or y is NaN */
46	    return (x*y)/(x*y);
47	if(hx<=hy) {
48	    if((hx<hy)||(lx<ly)) {
49		q = 0;
50		goto fixup;	/* |x|<|y| return x or x-y */
51	    }
52	    if(lx==ly) {
53		*quo = 1;
54		return Zero[(u_int32_t)sx>>31];	/* |x|=|y| return x*0*/
55	    }
56	}
57
58    /* determine ix = ilogb(x) */
59	if(hx<0x00100000) {	/* subnormal x */
60	    if(hx==0) {
61		for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
62	    } else {
63		for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
64	    }
65	} else ix = (hx>>20)-1023;
66
67    /* determine iy = ilogb(y) */
68	if(hy<0x00100000) {	/* subnormal y */
69	    if(hy==0) {
70		for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
71	    } else {
72		for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
73	    }
74	} else iy = (hy>>20)-1023;
75
76    /* set up {hx,lx}, {hy,ly} and align y to x */
77	if(ix >= -1022)
78	    hx = 0x00100000|(0x000fffff&hx);
79	else {		/* subnormal x, shift x to normal */
80	    n = -1022-ix;
81	    if(n<=31) {
82	        hx = (hx<<n)|(lx>>(32-n));
83	        lx <<= n;
84	    } else {
85		hx = lx<<(n-32);
86		lx = 0;
87	    }
88	}
89	if(iy >= -1022)
90	    hy = 0x00100000|(0x000fffff&hy);
91	else {		/* subnormal y, shift y to normal */
92	    n = -1022-iy;
93	    if(n<=31) {
94	        hy = (hy<<n)|(ly>>(32-n));
95	        ly <<= n;
96	    } else {
97		hy = ly<<(n-32);
98		ly = 0;
99	    }
100	}
101
102    /* fix point fmod */
103	n = ix - iy;
104	q = 0;
105	while(n--) {
106	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
107	    if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
108	    else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
109	    q <<= 1;
110	}
111	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
112	if(hz>=0) {hx=hz;lx=lz;q++;}
113
114    /* convert back to floating value and restore the sign */
115	if((hx|lx)==0) {			/* return sign(x)*0 */
116	    *quo = (sxy ? -q : q);
117	    return Zero[(u_int32_t)sx>>31];
118	}
119	while(hx<0x00100000) {		/* normalize x */
120	    hx = hx+hx+(lx>>31); lx = lx+lx;
121	    iy -= 1;
122	}
123	if(iy>= -1022) {	/* normalize output */
124	    hx = ((hx-0x00100000)|((iy+1023)<<20));
125	} else {		/* subnormal output */
126	    n = -1022 - iy;
127	    if(n<=20) {
128		lx = (lx>>n)|((u_int32_t)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	}
136fixup:
137	INSERT_WORDS(x,hx,lx);
138	y = fabs(y);
139	if (y < 0x1p-1021) {
140	    if (x+x>y || (x+x==y && (q & 1))) {
141		q++;
142		x-=y;
143	    }
144	} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
145	    q++;
146	    x-=y;
147	}
148	GET_HIGH_WORD(hx,x);
149	SET_HIGH_WORD(x,hx^sx);
150	q &= 0x7fffffff;
151	*quo = (sxy ? -q : q);
152	return x;
153}
154
155#if	LDBL_MANT_DIG == 53
156#ifdef	lint
157/* PROTOLIB1 */
158long double remquol(long double, long double, int *);
159#else	/* lint */
160__weak_alias(remquol, remquo);
161#endif	/* lint */
162#endif	/* LDBL_MANT_DIG == 53 */
163