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
21static 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 */
31double
32remquo(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	}
138fixup:
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