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--- old/usr/src/lib/libmvec/common/__vcosf.c
+++ new/usr/src/lib/libmvec/common/__vcosf.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 21 /*
22 22 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 23 */
24 24 /*
25 25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 26 * Use is subject to license terms.
27 27 */
28 28
29 29 /*
30 30 * __vcosf: single precision vector cos
31 31 *
32 32 * Algorithm:
33 33 *
34 34 * For |x| < pi/4, approximate sin(x) by a polynomial x+x*z*(S0+
35 35 * z*(S1+z*S2)) and cos(x) by a polynomial 1+z*(-1/2+z*(C0+z*(C1+
36 36 * z*C2))), where z = x*x, all evaluated in double precision.
37 37 *
38 38 * Accuracy:
39 39 *
40 40 * The largest error is less than 0.6 ulps.
41 41 */
42 42
43 43 #include <sys/isa_defs.h>
44 44
45 45 #ifdef _LITTLE_ENDIAN
46 46 #define HI(x) *(1+(int *)&x)
47 47 #define LO(x) *(unsigned *)&x
48 48 #else
49 49 #define HI(x) *(int *)&x
50 50 #define LO(x) *(1+(unsigned *)&x)
51 51 #endif
52 52
53 53 #ifdef __RESTRICT
54 54 #define restrict _Restrict
55 55 #else
56 56 #define restrict
57 57 #endif
58 58
59 59 extern int __vlibm_rem_pio2m(double *, double *, int, int, int);
60 60
61 61 static const double C[] = {
62 62 -1.66666552424430847168e-01, /* 2^ -3 * -1.5555460000000 */
63 63 8.33219196647405624390e-03, /* 2^ -7 * 1.11077E0000000 */
64 64 -1.95187909412197768688e-04, /* 2^-13 * -1.9956B60000000 */
65 65 1.0,
66 66 -0.5,
67 67 4.16666455566883087158e-02, /* 2^ -5 * 1.55554A0000000 */
68 68 -1.38873036485165357590e-03, /* 2^-10 * -1.6C0C1E0000000 */
69 69 2.44309903791872784495e-05, /* 2^-16 * 1.99E24E0000000 */
70 70 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
71 71 6755399441055744.0, /* 2^ 52 * 1.8000000000000 */
72 72 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
73 73 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
74 74 };
75 75
76 76 #define S0 C[0]
77 77 #define S1 C[1]
78 78 #define S2 C[2]
79 79 #define one C[3]
80 80 #define mhalf C[4]
81 81 #define C0 C[5]
82 82 #define C1 C[6]
83 83 #define C2 C[7]
84 84 #define invpio2 C[8]
85 85 #define c3two51 C[9]
86 86 #define pio2_1 C[10]
87 87 #define pio2_t C[11]
88 88
89 89 #define PREPROCESS(N, index, label) \
90 90 hx = *(int *)x; \
91 91 ix = hx & 0x7fffffff; \
92 92 t = *x; \
93 93 x += stridex; \
94 94 if (ix <= 0x3f490fdb) { /* |x| < pi/4 */ \
95 95 if (ix == 0) { \
96 96 y[index] = one; \
97 97 goto label; \
98 98 } \
99 99 y##N = (double)t; \
100 100 n##N = 1; \
101 101 } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */ \
102 102 y##N = (double)t; \
103 103 medium = 1; \
104 104 } else { \
105 105 if (ix >= 0x7f800000) { /* inf or nan */ \
106 106 y[index] = t / t; \
107 107 goto label; \
108 108 } \
109 109 z##N = y##N = (double)t; \
110 110 hx = HI(y##N); \
111 111 n##N = ((hx >> 20) & 0x7ff) - 1046; \
112 112 HI(z##N) = (hx & 0xfffff) | 0x41600000; \
113 113 n##N = __vlibm_rem_pio2m(&z##N, &y##N, n##N, 1, 0) + 1; \
114 114 z##N = y##N * y##N; \
115 115 if (n##N & 1) { /* compute cos y */ \
116 116 f##N = (float)(one + z##N * (mhalf + z##N * \
117 117 (C0 + z##N * (C1 + z##N * C2)))); \
118 118 } else { /* compute sin y */ \
119 119 f##N = (float)(y##N + y##N * z##N * (S0 + \
120 120 z##N * (S1 + z##N * S2))); \
121 121 } \
122 122 y[index] = (n##N & 2)? -f##N : f##N; \
123 123 goto label; \
124 124 }
125 125
126 126 #define PROCESS(N) \
127 127 if (medium) { \
128 128 z##N = y##N * invpio2 + c3two51; \
129 129 n##N = LO(z##N) + 1; \
130 130 z##N -= c3two51; \
131 131 y##N = (y##N - z##N * pio2_1) - z##N * pio2_t; \
132 132 } \
133 133 z##N = y##N * y##N; \
134 134 if (n##N & 1) { /* compute cos y */ \
135 135 f##N = (float)(one + z##N * (mhalf + z##N * (C0 + \
136 136 z##N * (C1 + z##N * C2)))); \
137 137 } else { /* compute sin y */ \
138 138 f##N = (float)(y##N + y##N * z##N * (S0 + z##N * (S1 + \
139 139 z##N * S2))); \
140 140 } \
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141 141 *y = (n##N & 2)? -f##N : f##N; \
142 142 y += stridey
143 143
144 144 void
145 145 __vcosf(int n, float *restrict x, int stridex, float *restrict y,
146 146 int stridey)
147 147 {
148 148 double y0, y1, y2, y3;
149 149 double z0, z1, z2, z3;
150 150 float f0, f1, f2, f3, t;
151 - int n0, n1, n2, n3, hx, ix, medium;
151 + int n0 = 0, n1 = 0, n2 = 0, n3, hx, ix, medium;
152 152
153 153 y -= stridey;
154 154
155 155 for (;;) {
156 156 begin:
157 157 y += stridey;
158 158
159 159 if (--n < 0)
160 160 break;
161 161
162 162 medium = 0;
163 163 PREPROCESS(0, 0, begin);
164 164
165 165 if (--n < 0)
166 166 goto process1;
167 167
168 168 PREPROCESS(1, stridey, process1);
169 169
170 170 if (--n < 0)
171 171 goto process2;
172 172
173 173 PREPROCESS(2, (stridey << 1), process2);
174 174
175 175 if (--n < 0)
176 176 goto process3;
177 177
178 178 PREPROCESS(3, (stridey << 1) + stridey, process3);
179 179
180 180 if (medium) {
181 181 z0 = y0 * invpio2 + c3two51;
182 182 z1 = y1 * invpio2 + c3two51;
183 183 z2 = y2 * invpio2 + c3two51;
184 184 z3 = y3 * invpio2 + c3two51;
185 185
186 186 n0 = LO(z0) + 1;
187 187 n1 = LO(z1) + 1;
188 188 n2 = LO(z2) + 1;
189 189 n3 = LO(z3) + 1;
190 190
191 191 z0 -= c3two51;
192 192 z1 -= c3two51;
193 193 z2 -= c3two51;
194 194 z3 -= c3two51;
195 195
196 196 y0 = (y0 - z0 * pio2_1) - z0 * pio2_t;
197 197 y1 = (y1 - z1 * pio2_1) - z1 * pio2_t;
198 198 y2 = (y2 - z2 * pio2_1) - z2 * pio2_t;
199 199 y3 = (y3 - z3 * pio2_1) - z3 * pio2_t;
200 200 }
201 201
202 202 z0 = y0 * y0;
203 203 z1 = y1 * y1;
204 204 z2 = y2 * y2;
205 205 z3 = y3 * y3;
206 206
207 207 hx = (n0 & 1) | ((n1 & 1) << 1) | ((n2 & 1) << 2) |
208 208 ((n3 & 1) << 3);
209 209 switch (hx) {
210 210 case 0:
211 211 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
212 212 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
213 213 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
214 214 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
215 215 break;
216 216
217 217 case 1:
218 218 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
219 219 z0 * (C1 + z0 * C2))));
220 220 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
221 221 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
222 222 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
223 223 break;
224 224
225 225 case 2:
226 226 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
227 227 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
228 228 z1 * (C1 + z1 * C2))));
229 229 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
230 230 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
231 231 break;
232 232
233 233 case 3:
234 234 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
235 235 z0 * (C1 + z0 * C2))));
236 236 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
237 237 z1 * (C1 + z1 * C2))));
238 238 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
239 239 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
240 240 break;
241 241
242 242 case 4:
243 243 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
244 244 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
245 245 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
246 246 z2 * (C1 + z2 * C2))));
247 247 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
248 248 break;
249 249
250 250 case 5:
251 251 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
252 252 z0 * (C1 + z0 * C2))));
253 253 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
254 254 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
255 255 z2 * (C1 + z2 * C2))));
256 256 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
257 257 break;
258 258
259 259 case 6:
260 260 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
261 261 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
262 262 z1 * (C1 + z1 * C2))));
263 263 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
264 264 z2 * (C1 + z2 * C2))));
265 265 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
266 266 break;
267 267
268 268 case 7:
269 269 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
270 270 z0 * (C1 + z0 * C2))));
271 271 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
272 272 z1 * (C1 + z1 * C2))));
273 273 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
274 274 z2 * (C1 + z2 * C2))));
275 275 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
276 276 break;
277 277
278 278 case 8:
279 279 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
280 280 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
281 281 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
282 282 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
283 283 z3 * (C1 + z3 * C2))));
284 284 break;
285 285
286 286 case 9:
287 287 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
288 288 z0 * (C1 + z0 * C2))));
289 289 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
290 290 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
291 291 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
292 292 z3 * (C1 + z3 * C2))));
293 293 break;
294 294
295 295 case 10:
296 296 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
297 297 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
298 298 z1 * (C1 + z1 * C2))));
299 299 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
300 300 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
301 301 z3 * (C1 + z3 * C2))));
302 302 break;
303 303
304 304 case 11:
305 305 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
306 306 z0 * (C1 + z0 * C2))));
307 307 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
308 308 z1 * (C1 + z1 * C2))));
309 309 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
310 310 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
311 311 z3 * (C1 + z3 * C2))));
312 312 break;
313 313
314 314 case 12:
315 315 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
316 316 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
317 317 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
318 318 z2 * (C1 + z2 * C2))));
319 319 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
320 320 z3 * (C1 + z3 * C2))));
321 321 break;
322 322
323 323 case 13:
324 324 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
325 325 z0 * (C1 + z0 * C2))));
326 326 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
327 327 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
328 328 z2 * (C1 + z2 * C2))));
329 329 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
330 330 z3 * (C1 + z3 * C2))));
331 331 break;
332 332
333 333 case 14:
334 334 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
335 335 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
336 336 z1 * (C1 + z1 * C2))));
337 337 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
338 338 z2 * (C1 + z2 * C2))));
339 339 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
340 340 z3 * (C1 + z3 * C2))));
341 341 break;
342 342
343 343 default:
344 344 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
345 345 z0 * (C1 + z0 * C2))));
346 346 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
347 347 z1 * (C1 + z1 * C2))));
348 348 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
349 349 z2 * (C1 + z2 * C2))));
350 350 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
351 351 z3 * (C1 + z3 * C2))));
352 352 }
353 353
354 354 *y = (n0 & 2)? -f0 : f0;
355 355 y += stridey;
356 356 *y = (n1 & 2)? -f1 : f1;
357 357 y += stridey;
358 358 *y = (n2 & 2)? -f2 : f2;
359 359 y += stridey;
360 360 *y = (n3 & 2)? -f3 : f3;
361 361 continue;
362 362
363 363 process1:
364 364 PROCESS(0);
365 365 continue;
366 366
367 367 process2:
368 368 PROCESS(0);
369 369 PROCESS(1);
370 370 continue;
371 371
372 372 process3:
373 373 PROCESS(0);
374 374 PROCESS(1);
375 375 PROCESS(2);
376 376 }
377 377 }
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