1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
|
/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/*
* __vsincosf: single precision vector sincos
*
* Algorithm:
*
* For |x| < pi/4, approximate sin(x) by a polynomial x+x*z*(S0+
* z*(S1+z*S2)) and cos(x) by a polynomial 1+z*(-1/2+z*(C0+z*(C1+
* z*C2))), where z = x*x, all evaluated in double precision.
*
* Accuracy:
*
* The largest error is less than 0.6 ulps.
*/
#include <sys/isa_defs.h>
#ifdef _LITTLE_ENDIAN
#define HI(x) *(1+(int *)&x)
#define LO(x) *(unsigned *)&x
#else
#define HI(x) *(int *)&x
#define LO(x) *(1+(unsigned *)&x)
#endif
#ifdef __RESTRICT
#define restrict _Restrict
#else
#define restrict
#endif
extern int __vlibm_rem_pio2m(double *, double *, int, int, int);
static const double C[] = {
-1.66666552424430847168e-01, /* 2^ -3 * -1.5555460000000 */
8.33219196647405624390e-03, /* 2^ -7 * 1.11077E0000000 */
-1.95187909412197768688e-04, /* 2^-13 * -1.9956B60000000 */
1.0,
-0.5,
4.16666455566883087158e-02, /* 2^ -5 * 1.55554A0000000 */
-1.38873036485165357590e-03, /* 2^-10 * -1.6C0C1E0000000 */
2.44309903791872784495e-05, /* 2^-16 * 1.99E24E0000000 */
0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
6755399441055744.0, /* 2^ 52 * 1.8000000000000 */
1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
};
#define S0 C[0]
#define S1 C[1]
#define S2 C[2]
#define one C[3]
#define mhalf C[4]
#define C0 C[5]
#define C1 C[6]
#define C2 C[7]
#define invpio2 C[8]
#define c3two51 C[9]
#define pio2_1 C[10]
#define pio2_t C[11]
#define PREPROCESS(N, sindex, cindex, label) \
hx = *(int *)x; \
ix = hx & 0x7fffffff; \
t = *x; \
x += stridex; \
if (ix <= 0x3f490fdb) { /* |x| < pi/4 */ \
if (ix == 0) { \
s[sindex] = t; \
c[cindex] = one; \
goto label; \
} \
y##N = (double)t; \
n##N = 0; \
} else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */ \
y##N = (double)t; \
medium = 1; \
} else { \
if (ix >= 0x7f800000) { /* inf or nan */ \
s[sindex] = c[cindex] = t / t; \
goto label; \
} \
z##N = y##N = (double)t; \
hx = HI(y##N); \
n##N = ((hx >> 20) & 0x7ff) - 1046; \
HI(z##N) = (hx & 0xfffff) | 0x41600000; \
n##N = __vlibm_rem_pio2m(&z##N, &y##N, n##N, 1, 0); \
if (hx < 0) { \
y##N = -y##N; \
n##N = -n##N; \
} \
z##N = y##N * y##N; \
f##N = (float)(y##N + y##N * z##N * (S0 + z##N * \
(S1 + z##N * S2))); \
g##N = (float)(one + z##N * (mhalf + z##N * (C0 + \
z##N * (C1 + z##N * C2)))); \
if (n##N & 2) { \
f##N = -f##N; \
g##N = -g##N; \
} \
if (n##N & 1) { \
s[sindex] = g##N; \
c[cindex] = -f##N; \
} else { \
s[sindex] = f##N; \
c[cindex] = g##N; \
} \
goto label; \
}
#define PROCESS(N) \
if (medium) { \
z##N = y##N * invpio2 + c3two51; \
n##N = LO(z##N); \
z##N -= c3two51; \
y##N = (y##N - z##N * pio2_1) - z##N * pio2_t; \
} \
z##N = y##N * y##N; \
f##N = (float)(y##N + y##N * z##N * (S0 + z##N * (S1 + z##N * S2)));\
g##N = (float)(one + z##N * (mhalf + z##N * (C0 + z##N * \
(C1 + z##N * C2)))); \
if (n##N & 2) { \
f##N = -f##N; \
g##N = -g##N; \
} \
if (n##N & 1) { \
*s = g##N; \
*c = -f##N; \
} else { \
*s = f##N; \
*c = g##N; \
} \
s += strides; \
c += stridec
void
__vsincosf(int n, float *restrict x, int stridex,
float *restrict s, int strides, float *restrict c, int stridec)
{
double y0, y1, y2, y3;
double z0, z1, z2, z3;
float f0, f1, f2, f3, t;
float g0, g1, g2, g3;
int n0 = 0, n1 = 0, n2 = 0, n3, hx, ix, medium;
s -= strides;
c -= stridec;
for (;;) {
begin:
s += strides;
c += stridec;
if (--n < 0)
break;
medium = 0;
PREPROCESS(0, 0, 0, begin);
if (--n < 0)
goto process1;
PREPROCESS(1, strides, stridec, process1);
if (--n < 0)
goto process2;
PREPROCESS(2, (strides << 1), (stridec << 1), process2);
if (--n < 0)
goto process3;
PREPROCESS(3, (strides << 1) + strides,
(stridec << 1) + stridec, process3);
if (medium) {
z0 = y0 * invpio2 + c3two51;
z1 = y1 * invpio2 + c3two51;
z2 = y2 * invpio2 + c3two51;
z3 = y3 * invpio2 + c3two51;
n0 = LO(z0);
n1 = LO(z1);
n2 = LO(z2);
n3 = LO(z3);
z0 -= c3two51;
z1 -= c3two51;
z2 -= c3two51;
z3 -= c3two51;
y0 = (y0 - z0 * pio2_1) - z0 * pio2_t;
y1 = (y1 - z1 * pio2_1) - z1 * pio2_t;
y2 = (y2 - z2 * pio2_1) - z2 * pio2_t;
y3 = (y3 - z3 * pio2_1) - z3 * pio2_t;
}
z0 = y0 * y0;
z1 = y1 * y1;
z2 = y2 * y2;
z3 = y3 * y3;
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
g0 = (float)(one + z0 * (mhalf + z0 * (C0 + z0 *
(C1 + z0 * C2))));
g1 = (float)(one + z1 * (mhalf + z1 * (C0 + z1 *
(C1 + z1 * C2))));
g2 = (float)(one + z2 * (mhalf + z2 * (C0 + z2 *
(C1 + z2 * C2))));
g3 = (float)(one + z3 * (mhalf + z3 * (C0 + z3 *
(C1 + z3 * C2))));
if (n0 & 2) {
f0 = -f0;
g0 = -g0;
}
if (n1 & 2) {
f1 = -f1;
g1 = -g1;
}
if (n2 & 2) {
f2 = -f2;
g2 = -g2;
}
if (n3 & 2) {
f3 = -f3;
g3 = -g3;
}
if (n0 & 1) {
*s = g0;
*c = -f0;
} else {
*s = f0;
*c = g0;
}
s += strides;
c += stridec;
if (n1 & 1) {
*s = g1;
*c = -f1;
} else {
*s = f1;
*c = g1;
}
s += strides;
c += stridec;
if (n2 & 1) {
*s = g2;
*c = -f2;
} else {
*s = f2;
*c = g2;
}
s += strides;
c += stridec;
if (n3 & 1) {
*s = g3;
*c = -f3;
} else {
*s = f3;
*c = g3;
}
continue;
process1:
PROCESS(0);
continue;
process2:
PROCESS(0);
PROCESS(1);
continue;
process3:
PROCESS(0);
PROCESS(1);
PROCESS(2);
}
}
|
