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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __remquo = remquo
32
33
34 /*
35 * double remquo(double x, double y, int *quo) return remainder(x,y) and an
36 * integer pointer quo such that *quo = N mod {2**31}, where N is the
37 * exact integral part of x/y rounded to nearest even.
38 *
39 * remquo call internal fmodquo
40 */
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 static double
59 fmodquo(double x, double y, int *quo)
60 {
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
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
80 if (hx <= hy) {
81 if (hx < hy || lx < ly)
82 return (x); /* |x|<|y| return x */
83
84 if (lx == ly) {
85 *quo = 1 + (sq >> 30);
86 /* |x|=|y| return x*0 */
87 return (Zero[(unsigned)sx >> 31]);
88 }
89 }
90
91 /* determine ix = ilogb(x) */
92 if (hx < 0x00100000) { /* subnormal x */
93 if (hx == 0) {
94 for (ix = -1043, i = lx; i > 0; i <<= 1)
95 ix -= 1;
96 } else {
97 for (ix = -1022, i = (hx << 11); i > 0; i <<= 1)
98 ix -= 1;
99 }
100 } else {
101 ix = (hx >> 20) - 1023;
102 }
103
104 /* determine iy = ilogb(y) */
105 if (hy < 0x00100000) { /* subnormal y */
106 if (hy == 0) {
107 for (iy = -1043, i = ly; i > 0; i <<= 1)
108 iy -= 1;
109 } else {
110 for (iy = -1022, i = (hy << 11); i > 0; i <<= 1)
111 iy -= 1;
112 }
113 } else {
114 iy = (hy >> 20) - 1023;
115 }
116
117 /* set up {hx,lx}, {hy,ly} and align y to x */
118 if (ix >= -1022) {
119 hx = 0x00100000 | (0x000fffff & hx);
120 } else { /* subnormal x, shift x to normal */
121 n = -1022 - ix;
122
123 if (n <= 31) {
124 hx = (hx << n) | (lx >> (32 - n));
125 lx <<= n;
126 } else {
127 hx = lx << (n - 32);
128 lx = 0;
129 }
130 }
131
132 if (iy >= -1022) {
133 hy = 0x00100000 | (0x000fffff & hy);
134 } else { /* subnormal y, shift y to normal */
135 n = -1022 - iy;
136
137 if (n <= 31) {
138 hy = (hy << n) | (ly >> (32 - n));
139 ly <<= n;
140 } else {
141 hy = ly << (n - 32);
142 ly = 0;
143 }
144 }
145
146 /* fix point fmod */
147 n = ix - iy;
148 m = 0;
149
150 while (n--) {
151 hz = hx - hy;
152 lz = lx - ly;
153
154 if (lx < ly)
155 hz -= 1;
156
157 if (hz < 0) {
158 hx = hx + hx + (lx >> 31);
159 lx = lx + lx;
160 } else {
161 m += 1;
162
163 if ((hz | lz) == 0) { /* return sign(x)*0 */
164 if (n < 31)
165 m <<= 1 + n;
166 else
167 m = 0;
168
169 m &= 0x7fffffff;
170 *quo = sq >= 0 ? m : -m;
171 return (Zero[(unsigned)sx >> 31]);
172 }
173
174 hx = hz + hz + (lz >> 31);
175 lx = lz + lz;
176 }
177
178 m += m;
179 }
180
181 hz = hx - hy;
182 lz = lx - ly;
183
184 if (lx < ly)
185 hz -= 1;
186
187 if (hz >= 0) {
188 hx = hz;
189 lx = lz;
190 m += 1;
191 }
192
193 m &= 0x7fffffff;
194 *quo = sq >= 0 ? m : -m;
195
196 /* convert back to floating value and restore the sign */
197 if ((hx | lx) == 0) /* return sign(x)*0 */
198 return (Zero[(unsigned)sx >> 31]);
199
200 while (hx < 0x00100000) { /* normalize x */
201 hx = hx + hx + (lx >> 31);
202 lx = lx + lx;
203 iy -= 1;
204 }
205
206 if (iy >= -1022) { /* normalize output */
207 hx = (hx - 0x00100000) | ((iy + 1023) << 20);
208 __HI(x) = hx | sx;
209 __LO(x) = lx;
210 } else { /* subnormal output */
211 n = -1022 - iy;
212
213 if (n <= 20) {
214 lx = (lx >> n) | ((unsigned)hx << (32 - n));
215 hx >>= n;
216 } else if (n <= 31) {
217 lx = (hx << (32 - n)) | (lx >> n);
218 hx = sx;
219 } else {
220 lx = hx >> (n - 32);
221 hx = sx;
222 }
223
224 __HI(x) = hx | sx;
225 __LO(x) = lx;
226 x *= one; /* create necessary signal */
227 }
228
229 return (x); /* exact output */
230 }
231
232 #define zero Zero[0]
233
234 double
235 remquo(double x, double y, int *quo)
236 {
237 int hx, hy, sx, sq;
238 double v;
239 unsigned ly;
240
241 hx = __HI(x); /* high word of x */
242 hy = __HI(y); /* high word of y */
243 ly = __LO(y); /* low word of y */
244 sx = hx & 0x80000000; /* sign of x */
245 sq = (hx ^ hy) & 0x80000000; /* sign of x/y */
246 hx ^= sx; /* |x| */
247 hy &= 0x7fffffff; /* |y| */
248
249 /* purge off exception values */
250 *quo = 0;
251
252 if ((hy | ly) == 0 || hx >= 0x7ff00000 || /* y=0, or x !finite */
253 (hy | ((ly | -ly) >> 31)) > 0x7ff00000) /* or y is NaN */
254 return ((x * y) / (x * y));
255
256 y = fabs(y);
257 x = fabs(x);
258
259 if (hy <= 0x7fdfffff) {
260 x = fmodquo(x, y + y, quo);
261 *quo = ((*quo) & 0x3fffffff) << 1;
262 }
263
264 if (hy < 0x00200000) {
265 if (x + x > y) {
266 *quo += 1;
267
268 if (x == y)
269 x = zero;
270 else
271 x -= y;
272
273 if (x + x >= y) {
274 x -= y;
275 *quo += 1;
276 }
277 }
278 } else {
279 v = 0.5 * y;
280
281 if (x > v) {
282 *quo += 1;
283
284 if (x == y)
285 x = zero;
286 else
287 x -= y;
288
289 if (x >= v) {
290 x -= y;
291 *quo += 1;
292 }
293 }
294 }
295
296 if (sq != 0)
297 *quo = -(*quo);
298
299 return (sx == 0 ? x : -x);
300 }