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
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
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 }