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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 /*
30 * __vsinf: single precision vector sin
31 *
32 * Algorithm:
33 *
34 * For |x| < pi/4, approximate sin(x) by a polynomial x+x*z*(S0+
35 * z*(S1+z*S2)) and cos(x) by a polynomial 1+z*(-1/2+z*(C0+z*(C1+
36 * z*C2))), where z = x*x, all evaluated in double precision.
37 *
38 * Accuracy:
39 *
40 * The largest error is less than 0.6 ulps.
41 */
42
43 #include <sys/isa_defs.h>
44
45 #ifdef _LITTLE_ENDIAN
46 #define HI(x) *(1+(int *)&x)
47 #define LO(x) *(unsigned *)&x
48 #else
49 #define HI(x) *(int *)&x
50 #define LO(x) *(1+(unsigned *)&x)
51 #endif
52
53 #ifdef __RESTRICT
54 #define restrict _Restrict
55 #else
56 #define restrict
57 #endif
58
59 extern int __vlibm_rem_pio2m(double *, double *, int, int, int);
60
61 static const double C[] = {
62 -1.66666552424430847168e-01, /* 2^ -3 * -1.5555460000000 */
63 8.33219196647405624390e-03, /* 2^ -7 * 1.11077E0000000 */
64 -1.95187909412197768688e-04, /* 2^-13 * -1.9956B60000000 */
65 1.0,
66 -0.5,
67 4.16666455566883087158e-02, /* 2^ -5 * 1.55554A0000000 */
68 -1.38873036485165357590e-03, /* 2^-10 * -1.6C0C1E0000000 */
69 2.44309903791872784495e-05, /* 2^-16 * 1.99E24E0000000 */
70 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
71 6755399441055744.0, /* 2^ 52 * 1.8000000000000 */
72 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
73 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
74 };
75
76 #define S0 C[0]
77 #define S1 C[1]
78 #define S2 C[2]
79 #define one C[3]
80 #define mhalf C[4]
81 #define C0 C[5]
82 #define C1 C[6]
83 #define C2 C[7]
84 #define invpio2 C[8]
85 #define c3two51 C[9]
86 #define pio2_1 C[10]
87 #define pio2_t C[11]
88
89 #define PREPROCESS(N, index, label) \
90 hx = *(int *)x; \
91 ix = hx & 0x7fffffff; \
92 t = *x; \
93 x += stridex; \
94 if (ix <= 0x3f490fdb) { /* |x| < pi/4 */ \
95 if (ix == 0) { \
96 y[index] = t; \
97 goto label; \
98 } \
99 y##N = (double)t; \
100 n##N = 0; \
101 } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */ \
102 y##N = (double)t; \
103 medium = 1; \
104 } else { \
105 if (ix >= 0x7f800000) { /* inf or nan */ \
106 y[index] = t / t; \
107 goto label; \
108 } \
109 z##N = y##N = (double)t; \
110 hx = HI(y##N); \
111 n##N = ((hx >> 20) & 0x7ff) - 1046; \
112 HI(z##N) = (hx & 0xfffff) | 0x41600000; \
113 n##N = __vlibm_rem_pio2m(&z##N, &y##N, n##N, 1, 0); \
114 if (hx < 0) { \
115 y##N = -y##N; \
116 n##N = -n##N; \
117 } \
118 z##N = y##N * y##N; \
119 if (n##N & 1) { /* compute cos y */ \
120 f##N = (float)(one + z##N * (mhalf + z##N * \
121 (C0 + z##N * (C1 + z##N * C2)))); \
122 } else { /* compute sin y */ \
123 f##N = (float)(y##N + y##N * z##N * (S0 + \
124 z##N * (S1 + z##N * S2))); \
125 } \
126 y[index] = (n##N & 2)? -f##N : f##N; \
127 goto label; \
128 }
129
130 #define PROCESS(N) \
131 if (medium) { \
132 z##N = y##N * invpio2 + c3two51; \
133 n##N = LO(z##N); \
134 z##N -= c3two51; \
135 y##N = (y##N - z##N * pio2_1) - z##N * pio2_t; \
136 } \
137 z##N = y##N * y##N; \
138 if (n##N & 1) { /* compute cos y */ \
139 f##N = (float)(one + z##N * (mhalf + z##N * (C0 + \
140 z##N * (C1 + z##N * C2)))); \
141 } else { /* compute sin y */ \
142 f##N = (float)(y##N + y##N * z##N * (S0 + z##N * (S1 + \
143 z##N * S2))); \
144 } \
145 *y = (n##N & 2)? -f##N : f##N; \
146 y += stridey
147
148 void
149 __vsinf(int n, float *restrict x, int stridex, float *restrict y,
150 int stridey)
151 {
152 double y0, y1, y2, y3;
153 double z0, z1, z2, z3;
154 float f0, f1, f2, f3, t;
155 int n0, n1, n2, n3, hx, ix, medium;
156
157 y -= stridey;
158
159 for (;;) {
160 begin:
161 y += stridey;
162
163 if (--n < 0)
164 break;
165
166 medium = 0;
167 PREPROCESS(0, 0, begin);
168
169 if (--n < 0)
170 goto process1;
171
172 PREPROCESS(1, stridey, process1);
173
174 if (--n < 0)
175 goto process2;
176
177 PREPROCESS(2, (stridey << 1), process2);
178
179 if (--n < 0)
180 goto process3;
181
182 PREPROCESS(3, (stridey << 1) + stridey, process3);
183
184 if (medium) {
185 z0 = y0 * invpio2 + c3two51;
186 z1 = y1 * invpio2 + c3two51;
187 z2 = y2 * invpio2 + c3two51;
188 z3 = y3 * invpio2 + c3two51;
189
190 n0 = LO(z0);
191 n1 = LO(z1);
192 n2 = LO(z2);
193 n3 = LO(z3);
194
195 z0 -= c3two51;
196 z1 -= c3two51;
197 z2 -= c3two51;
198 z3 -= c3two51;
199
200 y0 = (y0 - z0 * pio2_1) - z0 * pio2_t;
201 y1 = (y1 - z1 * pio2_1) - z1 * pio2_t;
202 y2 = (y2 - z2 * pio2_1) - z2 * pio2_t;
203 y3 = (y3 - z3 * pio2_1) - z3 * pio2_t;
204 }
205
206 z0 = y0 * y0;
207 z1 = y1 * y1;
208 z2 = y2 * y2;
209 z3 = y3 * y3;
210
211 hx = (n0 & 1) | ((n1 & 1) << 1) | ((n2 & 1) << 2) |
212 ((n3 & 1) << 3);
213 switch (hx) {
214 case 0:
215 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
216 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
217 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
218 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
219 break;
220
221 case 1:
222 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
223 z0 * (C1 + z0 * C2))));
224 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
225 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
226 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
227 break;
228
229 case 2:
230 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
231 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
232 z1 * (C1 + z1 * C2))));
233 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
234 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
235 break;
236
237 case 3:
238 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
239 z0 * (C1 + z0 * C2))));
240 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
241 z1 * (C1 + z1 * C2))));
242 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
243 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
244 break;
245
246 case 4:
247 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
248 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
249 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
250 z2 * (C1 + z2 * C2))));
251 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
252 break;
253
254 case 5:
255 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
256 z0 * (C1 + z0 * C2))));
257 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
258 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
259 z2 * (C1 + z2 * C2))));
260 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
261 break;
262
263 case 6:
264 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
265 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
266 z1 * (C1 + z1 * C2))));
267 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
268 z2 * (C1 + z2 * C2))));
269 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
270 break;
271
272 case 7:
273 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
274 z0 * (C1 + z0 * C2))));
275 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
276 z1 * (C1 + z1 * C2))));
277 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
278 z2 * (C1 + z2 * C2))));
279 f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
280 break;
281
282 case 8:
283 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
284 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
285 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
286 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
287 z3 * (C1 + z3 * C2))));
288 break;
289
290 case 9:
291 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
292 z0 * (C1 + z0 * C2))));
293 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
294 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
295 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
296 z3 * (C1 + z3 * C2))));
297 break;
298
299 case 10:
300 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
301 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
302 z1 * (C1 + z1 * C2))));
303 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
304 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
305 z3 * (C1 + z3 * C2))));
306 break;
307
308 case 11:
309 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
310 z0 * (C1 + z0 * C2))));
311 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
312 z1 * (C1 + z1 * C2))));
313 f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
314 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
315 z3 * (C1 + z3 * C2))));
316 break;
317
318 case 12:
319 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
320 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
321 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
322 z2 * (C1 + z2 * C2))));
323 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
324 z3 * (C1 + z3 * C2))));
325 break;
326
327 case 13:
328 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
329 z0 * (C1 + z0 * C2))));
330 f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
331 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
332 z2 * (C1 + z2 * C2))));
333 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
334 z3 * (C1 + z3 * C2))));
335 break;
336
337 case 14:
338 f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
339 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
340 z1 * (C1 + z1 * C2))));
341 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
342 z2 * (C1 + z2 * C2))));
343 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
344 z3 * (C1 + z3 * C2))));
345 break;
346
347 default:
348 f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
349 z0 * (C1 + z0 * C2))));
350 f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
351 z1 * (C1 + z1 * C2))));
352 f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
353 z2 * (C1 + z2 * C2))));
354 f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
355 z3 * (C1 + z3 * C2))));
356 }
357
358 *y = (n0 & 2)? -f0 : f0;
359 y += stridey;
360 *y = (n1 & 2)? -f1 : f1;
361 y += stridey;
362 *y = (n2 & 2)? -f2 : f2;
363 y += stridey;
364 *y = (n3 & 2)? -f3 : f3;
365 continue;
366
367 process1:
368 PROCESS(0);
369 continue;
370
371 process2:
372 PROCESS(0);
373 PROCESS(1);
374 continue;
375
376 process3:
377 PROCESS(0);
378 PROCESS(1);
379 PROCESS(2);
380 }
381 }