about summary refs log tree commit diff
path: root/src/math/remquo.c
blob: 085466e6a2f84ba16bdabfe8eb6d94bfa7e8a7b1 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
/* origin: FreeBSD /usr/src/lib/msun/src/s_remquo.c */
/*-
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
/*
 * Return the IEEE remainder and set *quo to the last n bits of the
 * quotient, rounded to the nearest integer.  We choose n=31 because
 * we wind up computing all the integer bits of the quotient anyway as
 * a side-effect of computing the remainder by the shift and subtract
 * method.  In practice, this is far more bits than are needed to use
 * remquo in reduction algorithms.
 */

#include "libm.h"

static const double Zero[] = {0.0, -0.0,};

double remquo(double x, double y, int *quo)
{
	int32_t n,hx,hy,hz,ix,iy,sx,i;
	uint32_t lx,ly,lz,q,sxy;

	EXTRACT_WORDS(hx, lx, x);
	EXTRACT_WORDS(hy, ly, y);
	sxy = (hx ^ hy) & 0x80000000;
	sx = hx & 0x80000000;   /* sign of x */
	hx ^= sx;               /* |x| */
	hy &= 0x7fffffff;       /* |y| */

	/* purge off exception values */
	if ((hy|ly) == 0 || hx >= 0x7ff00000 ||  /* y = 0, or x not finite */
	    (hy|((ly|-ly)>>31)) > 0x7ff00000)    /* or y is NaN */
		return (x*y)/(x*y);
	if (hx <= hy) {
		if (hx < hy || lx < ly) {  /* |x| < |y| return x or x-y */
			q = 0;
			goto fixup;
		}
		if (lx == ly) {            /* |x| = |y| return x*0 */
			*quo = sxy ? -1 : 1;
			return Zero[(uint32_t)sx>>31];
		}
	}

	// FIXME: use ilogb?

	/* determine ix = ilogb(x) */
	if (hx < 0x00100000) {  /* subnormal x */
		if (hx == 0) {
			for (ix = -1043, i=lx; i>0; i<<=1) ix--;
		} else {
			for (ix = -1022, i=hx<<11; i>0; i<<=1) ix--;
		}
	} else
		ix = (hx>>20) - 1023;

	/* determine iy = ilogb(y) */
	if (hy < 0x00100000) {  /* subnormal y */
		if (hy == 0) {
			for (iy = -1043, i=ly; i>0; i<<=1) iy--;
		} else {
			for (iy = -1022, i=hy<<11; i>0; i<<=1) iy--;
		}
	} else
		iy = (hy>>20) - 1023;

	/* set up {hx,lx}, {hy,ly} and align y to x */
	if (ix >= -1022)
		hx = 0x00100000|(0x000fffff&hx);
	else {  /* subnormal x, shift x to normal */
		n = -1022 - ix;
		if (n <= 31) {
			hx = (hx<<n)|(lx>>(32-n));
			lx <<= n;
		} else {
			hx = lx<<(n-32);
			lx = 0;
		}
	}
	if (iy >= -1022)
		hy = 0x00100000|(0x000fffff&hy);
	else {  /* subnormal y, shift y to normal */
		n = -1022 - iy;
		if (n <= 31) {
			hy = (hy<<n)|(ly>>(32-n));
			ly <<= n;
		} else {
			hy = ly<<(n-32);
			ly = 0;
		}
	}

	/* fix point fmod */
	n = ix - iy;
	q = 0;
	while (n--) {
		hz = hx - hy;
		lz = lx - ly;
		if (lx < ly)
			hz--;
		if (hz < 0) {
			hx = hx + hx + (lx>>31);
			lx = lx + lx;
		} else {
			hx = hz + hz + (lz>>31);
			lx = lz + lz;
			q++;
		}
		q <<= 1;
	}
	hz = hx - hy;
	lz = lx - ly;
	if (lx < ly)
		hz--;
	if (hz >= 0) {
		hx = hz;
		lx = lz;
		q++;
	}

	/* convert back to floating value and restore the sign */
	if ((hx|lx) == 0) {  /* return sign(x)*0 */
		q &= 0x7fffffff;
		*quo = sxy ? -q : q;
		return Zero[(uint32_t)sx>>31];
	}
	while (hx < 0x00100000) {  /* normalize x */
		hx = hx + hx + (lx>>31);
		lx = lx + lx;
		iy--;
	}
	if (iy >= -1022) {         /* normalize output */
		hx = (hx-0x00100000)|((iy+1023)<<20);
	} else {                   /* subnormal output */
		n = -1022 - iy;
		if (n <= 20) {
			lx = (lx>>n)|((uint32_t)hx<<(32-n));
			hx >>= n;
		} else if (n <= 31) {
			lx = (hx<<(32-n))|(lx>>n);
			hx = 0;
		} else {
			lx = hx>>(n-32);
			hx = 0;
		}
	}
fixup:
	INSERT_WORDS(x, hx, lx);
	y = fabs(y);
	if (y < 0x1p-1021) {
		if (x + x > y || (x + x == y && (q & 1))) {
			q++;
			x -= y;
		}
	} else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
		q++;
		x -= y;
	}
	GET_HIGH_WORD(hx, x);
	SET_HIGH_WORD(x, hx ^ sx);
	q &= 0x7fffffff;
	*quo = sxy ? -q : q;
	return x;
}