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