xref: /illumos-gate/usr/src/lib/libm/common/m9x/remquo.c (revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8)
1 /*
2  * CDDL HEADER START
3  *
4  * The contents of this file are subject to the terms of the
5  * Common Development and Distribution License (the "License").
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
17  * information: Portions Copyright [yyyy] [name of copyright owner]
18  *
19  * CDDL HEADER END
20  */
21 
22 /*
23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24  */
25 /*
26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29 
30 #pragma weak remquo = __remquo
31 
32 /* INDENT OFF */
33 /*
34  * double remquo(double x, double y, int *quo) return remainder(x,y) and an
35  * integer pointer quo such that *quo = N mod {2**31}, where N is the
36  * exact integral part of x/y rounded to nearest even.
37  *
38  * remquo call internal fmodquo
39  */
40 /* INDENT ON */
41 
42 #include "libm.h"
43 #include "libm_synonyms.h"
44 #include "libm_protos.h"
45 #include <math.h>		/* fabs() */
46 #include <sys/isa_defs.h>
47 
48 #if defined(_BIG_ENDIAN)
49 #define	HIWORD	0
50 #define	LOWORD	1
51 #else
52 #define	HIWORD	1
53 #define	LOWORD	0
54 #endif
55 #define	__HI(x)	((int *) &x)[HIWORD]
56 #define	__LO(x)	((int *) &x)[LOWORD]
57 
58 static const double one = 1.0, Zero[] = {0.0, -0.0};
59 
60 static double
61 fmodquo(double x, double y, int *quo) {
62 	int n, hx, hy, hz, ix, iy, sx, sq, i, m;
63 	unsigned lx, ly, lz;
64 
65 	hx = __HI(x);		/* high word of x */
66 	lx = __LO(x);		/* low  word of x */
67 	hy = __HI(y);		/* high word of y */
68 	ly = __LO(y);		/* low  word of y */
69 	sx = hx & 0x80000000;	/* sign of x */
70 	sq = (hx ^ hy) & 0x80000000;	/* sign of x/y */
71 	hx ^= sx;		/* |x| */
72 	hy &= 0x7fffffff;	/* |y| */
73 
74 	/* purge off exception values */
75 	*quo = 0;
76 	if ((hy | ly) == 0 || hx >= 0x7ff00000 ||	/* y=0, or x !finite */
77 	    (hy | ((ly | -ly) >> 31)) > 0x7ff00000)	/* or y is NaN */
78 		return ((x * y) / (x * y));
79 	if (hx <= hy) {
80 		if (hx < hy || lx < ly)
81 			return (x);	/* |x|<|y| return x */
82 		if (lx == ly) {
83 			*quo = 1 + (sq >> 30);
84 			/* |x|=|y| return x*0 */
85 			return (Zero[(unsigned) sx >> 31]);
86 		}
87 	}
88 
89 	/* determine ix = ilogb(x) */
90 	if (hx < 0x00100000) {	/* subnormal x */
91 		if (hx == 0) {
92 			for (ix = -1043, i = lx; i > 0; i <<= 1)
93 				ix -= 1;
94 		} else {
95 			for (ix = -1022, i = (hx << 11); i > 0; i <<= 1)
96 				ix -= 1;
97 		}
98 	} else
99 		ix = (hx >> 20) - 1023;
100 
101 	/* determine iy = ilogb(y) */
102 	if (hy < 0x00100000) {	/* subnormal y */
103 		if (hy == 0) {
104 			for (iy = -1043, i = ly; i > 0; i <<= 1)
105 				iy -= 1;
106 		} else {
107 			for (iy = -1022, i = (hy << 11); i > 0; i <<= 1)
108 				iy -= 1;
109 		}
110 	} else
111 		iy = (hy >> 20) - 1023;
112 
113 	/* set up {hx,lx}, {hy,ly} and align y to x */
114 	if (ix >= -1022)
115 		hx = 0x00100000 | (0x000fffff & hx);
116 	else {			/* subnormal x, shift x to normal */
117 		n = -1022 - ix;
118 		if (n <= 31) {
119 			hx = (hx << n) | (lx >> (32 - n));
120 			lx <<= n;
121 		} else {
122 			hx = lx << (n - 32);
123 			lx = 0;
124 		}
125 	}
126 	if (iy >= -1022)
127 		hy = 0x00100000 | (0x000fffff & hy);
128 	else {			/* subnormal y, shift y to normal */
129 		n = -1022 - iy;
130 		if (n <= 31) {
131 			hy = (hy << n) | (ly >> (32 - n));
132 			ly <<= n;
133 		} else {
134 			hy = ly << (n - 32);
135 			ly = 0;
136 		}
137 	}
138 
139 	/* fix point fmod */
140 	n = ix - iy;
141 	m = 0;
142 	while (n--) {
143 		hz = hx - hy;
144 		lz = lx - ly;
145 		if (lx < ly)
146 			hz -= 1;
147 		if (hz < 0) {
148 			hx = hx + hx + (lx >> 31);
149 			lx = lx + lx;
150 		} else {
151 			m += 1;
152 			if ((hz | lz) == 0) {	/* return sign(x)*0 */
153 				if (n < 31)
154 					m <<= 1 + n;
155 				else
156 					m = 0;
157 				m &= 0x7fffffff;
158 				*quo = sq >= 0 ? m : -m;
159 				return (Zero[(unsigned) sx >> 31]);
160 			}
161 			hx = hz + hz + (lz >> 31);
162 			lx = lz + lz;
163 		}
164 		m += m;
165 	}
166 	hz = hx - hy;
167 	lz = lx - ly;
168 	if (lx < ly)
169 		hz -= 1;
170 	if (hz >= 0) {
171 		hx = hz;
172 		lx = lz;
173 		m += 1;
174 	}
175 	m &= 0x7fffffff;
176 	*quo = sq >= 0 ? m : -m;
177 
178 	/* convert back to floating value and restore the sign */
179 	if ((hx | lx) == 0) {	/* return sign(x)*0 */
180 		return (Zero[(unsigned) sx >> 31]);
181 	}
182 	while (hx < 0x00100000) {	/* normalize x */
183 		hx = hx + hx + (lx >> 31);
184 		lx = lx + lx;
185 		iy -= 1;
186 	}
187 	if (iy >= -1022) {	/* normalize output */
188 		hx = (hx - 0x00100000) | ((iy + 1023) << 20);
189 		__HI(x) = hx | sx;
190 		__LO(x) = lx;
191 	} else {			/* subnormal output */
192 		n = -1022 - iy;
193 		if (n <= 20) {
194 			lx = (lx >> n) | ((unsigned) hx << (32 - n));
195 			hx >>= n;
196 		} else if (n <= 31) {
197 			lx = (hx << (32 - n)) | (lx >> n);
198 			hx = sx;
199 		} else {
200 			lx = hx >> (n - 32);
201 			hx = sx;
202 		}
203 		__HI(x) = hx | sx;
204 		__LO(x) = lx;
205 		x *= one;	/* create necessary signal */
206 	}
207 	return (x);		/* exact output */
208 }
209 
210 #define	zero	Zero[0]
211 
212 double
213 remquo(double x, double y, int *quo) {
214 	int hx, hy, sx, sq;
215 	double v;
216 	unsigned ly;
217 
218 	hx = __HI(x);		/* high word of x */
219 	hy = __HI(y);		/* high word of y */
220 	ly = __LO(y);		/* low  word of y */
221 	sx = hx & 0x80000000;	/* sign of x */
222 	sq = (hx ^ hy) & 0x80000000;	/* sign of x/y */
223 	hx ^= sx;		/* |x| */
224 	hy &= 0x7fffffff;	/* |y| */
225 
226 	/* purge off exception values */
227 	*quo = 0;
228 	if ((hy | ly) == 0 || hx >= 0x7ff00000 ||	/* y=0, or x !finite */
229 	    (hy | ((ly | -ly) >> 31)) > 0x7ff00000)	/* or y is NaN */
230 		return ((x * y) / (x * y));
231 
232 	y = fabs(y);
233 	x = fabs(x);
234 	if (hy <= 0x7fdfffff) {
235 		x = fmodquo(x, y + y, quo);
236 		*quo = ((*quo) & 0x3fffffff) << 1;
237 	}
238 	if (hy < 0x00200000) {
239 		if (x + x > y) {
240 			*quo += 1;
241 			if (x == y)
242 				x = zero;
243 			else
244 				x -= y;
245 			if (x + x >= y) {
246 				x -= y;
247 				*quo += 1;
248 			}
249 		}
250 	} else {
251 		v = 0.5 * y;
252 		if (x > v) {
253 			*quo += 1;
254 			if (x == y)
255 				x = zero;
256 			else
257 				x -= y;
258 			if (x >= v) {
259 				x -= y;
260 				*quo += 1;
261 			}
262 		}
263 	}
264 	if (sq != 0)
265 		*quo = -(*quo);
266 	return (sx == 0 ? x : -x);
267 }
268