xref: /illumos-gate/usr/src/lib/libm/common/m9x/remquo.c (revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af)
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_protos.h"
44 #include <math.h>		/* fabs() */
45 #include <sys/isa_defs.h>
46 
47 #if defined(_BIG_ENDIAN)
48 #define	HIWORD	0
49 #define	LOWORD	1
50 #else
51 #define	HIWORD	1
52 #define	LOWORD	0
53 #endif
54 #define	__HI(x)	((int *) &x)[HIWORD]
55 #define	__LO(x)	((int *) &x)[LOWORD]
56 
57 static const double one = 1.0, Zero[] = {0.0, -0.0};
58 
59 static double
fmodquo(double x,double y,int * quo)60 fmodquo(double x, double y, int *quo) {
61 	int n, hx, hy, hz, ix, iy, sx, sq, i, m;
62 	unsigned lx, ly, lz;
63 
64 	hx = __HI(x);		/* high word of x */
65 	lx = __LO(x);		/* low  word of x */
66 	hy = __HI(y);		/* high word of y */
67 	ly = __LO(y);		/* low  word of y */
68 	sx = hx & 0x80000000;	/* sign of x */
69 	sq = (hx ^ hy) & 0x80000000;	/* sign of x/y */
70 	hx ^= sx;		/* |x| */
71 	hy &= 0x7fffffff;	/* |y| */
72 
73 	/* purge off exception values */
74 	*quo = 0;
75 	if ((hy | ly) == 0 || hx >= 0x7ff00000 ||	/* y=0, or x !finite */
76 	    (hy | ((ly | -ly) >> 31)) > 0x7ff00000)	/* or y is NaN */
77 		return ((x * y) / (x * y));
78 	if (hx <= hy) {
79 		if (hx < hy || lx < ly)
80 			return (x);	/* |x|<|y| return x */
81 		if (lx == ly) {
82 			*quo = 1 + (sq >> 30);
83 			/* |x|=|y| return x*0 */
84 			return (Zero[(unsigned) sx >> 31]);
85 		}
86 	}
87 
88 	/* determine ix = ilogb(x) */
89 	if (hx < 0x00100000) {	/* subnormal x */
90 		if (hx == 0) {
91 			for (ix = -1043, i = lx; i > 0; i <<= 1)
92 				ix -= 1;
93 		} else {
94 			for (ix = -1022, i = (hx << 11); i > 0; i <<= 1)
95 				ix -= 1;
96 		}
97 	} else
98 		ix = (hx >> 20) - 1023;
99 
100 	/* determine iy = ilogb(y) */
101 	if (hy < 0x00100000) {	/* subnormal y */
102 		if (hy == 0) {
103 			for (iy = -1043, i = ly; i > 0; i <<= 1)
104 				iy -= 1;
105 		} else {
106 			for (iy = -1022, i = (hy << 11); i > 0; i <<= 1)
107 				iy -= 1;
108 		}
109 	} else
110 		iy = (hy >> 20) - 1023;
111 
112 	/* set up {hx,lx}, {hy,ly} and align y to x */
113 	if (ix >= -1022)
114 		hx = 0x00100000 | (0x000fffff & hx);
115 	else {			/* subnormal x, shift x to normal */
116 		n = -1022 - ix;
117 		if (n <= 31) {
118 			hx = (hx << n) | (lx >> (32 - n));
119 			lx <<= n;
120 		} else {
121 			hx = lx << (n - 32);
122 			lx = 0;
123 		}
124 	}
125 	if (iy >= -1022)
126 		hy = 0x00100000 | (0x000fffff & hy);
127 	else {			/* subnormal y, shift y to normal */
128 		n = -1022 - iy;
129 		if (n <= 31) {
130 			hy = (hy << n) | (ly >> (32 - n));
131 			ly <<= n;
132 		} else {
133 			hy = ly << (n - 32);
134 			ly = 0;
135 		}
136 	}
137 
138 	/* fix point fmod */
139 	n = ix - iy;
140 	m = 0;
141 	while (n--) {
142 		hz = hx - hy;
143 		lz = lx - ly;
144 		if (lx < ly)
145 			hz -= 1;
146 		if (hz < 0) {
147 			hx = hx + hx + (lx >> 31);
148 			lx = lx + lx;
149 		} else {
150 			m += 1;
151 			if ((hz | lz) == 0) {	/* return sign(x)*0 */
152 				if (n < 31)
153 					m <<= 1 + n;
154 				else
155 					m = 0;
156 				m &= 0x7fffffff;
157 				*quo = sq >= 0 ? m : -m;
158 				return (Zero[(unsigned) sx >> 31]);
159 			}
160 			hx = hz + hz + (lz >> 31);
161 			lx = lz + lz;
162 		}
163 		m += m;
164 	}
165 	hz = hx - hy;
166 	lz = lx - ly;
167 	if (lx < ly)
168 		hz -= 1;
169 	if (hz >= 0) {
170 		hx = hz;
171 		lx = lz;
172 		m += 1;
173 	}
174 	m &= 0x7fffffff;
175 	*quo = sq >= 0 ? m : -m;
176 
177 	/* convert back to floating value and restore the sign */
178 	if ((hx | lx) == 0) {	/* return sign(x)*0 */
179 		return (Zero[(unsigned) sx >> 31]);
180 	}
181 	while (hx < 0x00100000) {	/* normalize x */
182 		hx = hx + hx + (lx >> 31);
183 		lx = lx + lx;
184 		iy -= 1;
185 	}
186 	if (iy >= -1022) {	/* normalize output */
187 		hx = (hx - 0x00100000) | ((iy + 1023) << 20);
188 		__HI(x) = hx | sx;
189 		__LO(x) = lx;
190 	} else {			/* subnormal output */
191 		n = -1022 - iy;
192 		if (n <= 20) {
193 			lx = (lx >> n) | ((unsigned) hx << (32 - n));
194 			hx >>= n;
195 		} else if (n <= 31) {
196 			lx = (hx << (32 - n)) | (lx >> n);
197 			hx = sx;
198 		} else {
199 			lx = hx >> (n - 32);
200 			hx = sx;
201 		}
202 		__HI(x) = hx | sx;
203 		__LO(x) = lx;
204 		x *= one;	/* create necessary signal */
205 	}
206 	return (x);		/* exact output */
207 }
208 
209 #define	zero	Zero[0]
210 
211 double
remquo(double x,double y,int * quo)212 remquo(double x, double y, int *quo) {
213 	int hx, hy, sx, sq;
214 	double v;
215 	unsigned ly;
216 
217 	hx = __HI(x);		/* high word of x */
218 	hy = __HI(y);		/* high word of y */
219 	ly = __LO(y);		/* low  word of y */
220 	sx = hx & 0x80000000;	/* sign of x */
221 	sq = (hx ^ hy) & 0x80000000;	/* sign of x/y */
222 	hx ^= sx;		/* |x| */
223 	hy &= 0x7fffffff;	/* |y| */
224 
225 	/* purge off exception values */
226 	*quo = 0;
227 	if ((hy | ly) == 0 || hx >= 0x7ff00000 ||	/* y=0, or x !finite */
228 	    (hy | ((ly | -ly) >> 31)) > 0x7ff00000)	/* or y is NaN */
229 		return ((x * y) / (x * y));
230 
231 	y = fabs(y);
232 	x = fabs(x);
233 	if (hy <= 0x7fdfffff) {
234 		x = fmodquo(x, y + y, quo);
235 		*quo = ((*quo) & 0x3fffffff) << 1;
236 	}
237 	if (hy < 0x00200000) {
238 		if (x + x > y) {
239 			*quo += 1;
240 			if (x == y)
241 				x = zero;
242 			else
243 				x -= y;
244 			if (x + x >= y) {
245 				x -= y;
246 				*quo += 1;
247 			}
248 		}
249 	} else {
250 		v = 0.5 * y;
251 		if (x > v) {
252 			*quo += 1;
253 			if (x == y)
254 				x = zero;
255 			else
256 				x -= y;
257 			if (x >= v) {
258 				x -= y;
259 				*quo += 1;
260 			}
261 		}
262 	}
263 	if (sq != 0)
264 		*quo = -(*quo);
265 	return (sx == 0 ? x : -x);
266 }
267