__vsinf.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* 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.
*/
/*
* __vsinf: single precision vector sin
*
* 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, index, label) \
hx = *(int *)x; \
ix = hx & 0x7fffffff; \
t = *x; \
x += stridex; \
if (ix <= 0x3f490fdb) { /* |x| < pi/4 */ \
if (ix == 0) { \
y[index] = t; \
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 */ \
y[index] = 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; \
if (n##N & 1) { /* compute cos y */ \
f##N = (float)(one + z##N * (mhalf + z##N * \
(C0 + z##N * (C1 + z##N * C2)))); \
} else { /* compute sin y */ \
f##N = (float)(y##N + y##N * z##N * (S0 + \
z##N * (S1 + z##N * S2))); \
} \
y[index] = (n##N & 2)? -f##N : f##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; \
if (n##N & 1) { /* compute cos y */ \
f##N = (float)(one + z##N * (mhalf + z##N * (C0 + \
z##N * (C1 + z##N * C2)))); \
} else { /* compute sin y */ \
f##N = (float)(y##N + y##N * z##N * (S0 + z##N * (S1 + \
z##N * S2))); \
} \
*y = (n##N & 2)? -f##N : f##N; \
y += stridey
void
__vsinf(int n, float *restrict x, int stridex, float *restrict y,
int stridey)
{
double y0, y1, y2, y3;
double z0, z1, z2, z3;
float f0, f1, f2, f3, t;
int n0 = 0, n1 = 0, n2 = 0, n3, hx, ix, medium;
y -= stridey;
for (;;) {
begin:
y += stridey;
if (--n < 0)
break;
medium = 0;
PREPROCESS(0, 0, begin);
if (--n < 0)
goto process1;
PREPROCESS(1, stridey, process1);
if (--n < 0)
goto process2;
PREPROCESS(2, (stridey << 1), process2);
if (--n < 0)
goto process3;
PREPROCESS(3, (stridey << 1) + stridey, 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;
hx = (n0 & 1) | ((n1 & 1) << 1) | ((n2 & 1) << 2) |
((n3 & 1) << 3);
switch (hx) {
case 0:
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)));
break;
case 1:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
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)));
break;
case 2:
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
break;
case 3:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
break;
case 4:
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
break;
case 5:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
break;
case 6:
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
break;
case 7:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(y3 + y3 * z3 * (S0 + z3 * (S1 + z3 * S2)));
break;
case 8:
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)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
case 9:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
case 10:
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
case 11:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(y2 + y2 * z2 * (S0 + z2 * (S1 + z2 * S2)));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
case 12:
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
case 13:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(y1 + y1 * z1 * (S0 + z1 * (S1 + z1 * S2)));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
case 14:
f0 = (float)(y0 + y0 * z0 * (S0 + z0 * (S1 + z0 * S2)));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
break;
default:
f0 = (float)(one + z0 * (mhalf + z0 * (C0 +
z0 * (C1 + z0 * C2))));
f1 = (float)(one + z1 * (mhalf + z1 * (C0 +
z1 * (C1 + z1 * C2))));
f2 = (float)(one + z2 * (mhalf + z2 * (C0 +
z2 * (C1 + z2 * C2))));
f3 = (float)(one + z3 * (mhalf + z3 * (C0 +
z3 * (C1 + z3 * C2))));
}
*y = (n0 & 2)? -f0 : f0;
y += stridey;
*y = (n1 & 2)? -f1 : f1;
y += stridey;
*y = (n2 & 2)? -f2 : f2;
y += stridey;
*y = (n3 & 2)? -f3 : f3;
continue;
process1:
PROCESS(0);
continue;
process2:
PROCESS(0);
PROCESS(1);
continue;
process3:
PROCESS(0);
PROCESS(1);
PROCESS(2);
}
}