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 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #pragma weak sincospil = __sincospil
31
32 /*
33 * void sincospil(long double x, long double *s, long double *c)
34 * *s = sinl(pi*x); *c = cosl(pi*x);
35 *
36 * Algorithm, 10/17/2002, K.C. Ng
37 * ------------------------------
38 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
39 * 1. If y == z, then x is a multiple of pi/4. Return the following values:
40 * ---------------------------------------------------
41 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi)
42 * ---------------------------------------------------
43 * 000 0.00 +0 ___ +1 ___ +0
44 * 001 0.25 +\/0.5 +\/0.5 +1
45 * 010 0.50 +1 ___ +0 ___ +inf
46 * 011 0.75 +\/0.5 -\/0.5 -1
47 * 100 1.00 -0 ___ -1 ___ +0
48 * 101 1.25 -\/0.5 -\/0.5 +1
49 * 110 1.50 -1 ___ -0 ___ +inf
50 * 111 1.75 -\/0.5 +\/0.5 -1
51 * ---------------------------------------------------
54 * n t sin(x*pi) cos(x*pi) tan(x*pi)
55 * ---------------------------------------------------
56 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t)
57 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t)
58 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t)
59 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t)
60 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t)
61 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t)
62 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t)
63 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t)
64 * ---------------------------------------------------
65 *
66 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
67 * This will return a result with error slightly more than one ulp (but less
68 * than 2 ulp). If one wants accurate result, one may break up pi*t in
69 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
70 * instead.
71 */
72
73 #include "libm.h"
74 #include "libm_synonyms.h"
75 #include "longdouble.h"
76
77 #include <sys/isa_defs.h>
78
79 #define I(q, m) ((int *) &(q))[m]
80 #define U(q, m) ((unsigned *) &(q))[m]
81 #if defined(__i386) || defined(__amd64)
82 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
83 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
84 #define PREC 64
85 #define PRECM1 63
86 #define PRECM2 62
87 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
88 #else
89 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
90 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
91 #define PREC 113
92 #define PRECM1 112
93 #define PRECM2 111
94 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
|
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 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 /*
31 * void sincospil(long double x, long double *s, long double *c)
32 * *s = sinl(pi*x); *c = cosl(pi*x);
33 *
34 * Algorithm, 10/17/2002, K.C. Ng
35 * ------------------------------
36 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
37 * 1. If y == z, then x is a multiple of pi/4. Return the following values:
38 * ---------------------------------------------------
39 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi)
40 * ---------------------------------------------------
41 * 000 0.00 +0 ___ +1 ___ +0
42 * 001 0.25 +\/0.5 +\/0.5 +1
43 * 010 0.50 +1 ___ +0 ___ +inf
44 * 011 0.75 +\/0.5 -\/0.5 -1
45 * 100 1.00 -0 ___ -1 ___ +0
46 * 101 1.25 -\/0.5 -\/0.5 +1
47 * 110 1.50 -1 ___ -0 ___ +inf
48 * 111 1.75 -\/0.5 +\/0.5 -1
49 * ---------------------------------------------------
52 * n t sin(x*pi) cos(x*pi) tan(x*pi)
53 * ---------------------------------------------------
54 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t)
55 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t)
56 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t)
57 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t)
58 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t)
59 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t)
60 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t)
61 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t)
62 * ---------------------------------------------------
63 *
64 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
65 * This will return a result with error slightly more than one ulp (but less
66 * than 2 ulp). If one wants accurate result, one may break up pi*t in
67 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
68 * instead.
69 */
70
71 #include "libm.h"
72 #include "longdouble.h"
73
74 #include <sys/isa_defs.h>
75
76 #define I(q, m) ((int *) &(q))[m]
77 #define U(q, m) ((unsigned *) &(q))[m]
78 #if defined(__i386) || defined(__amd64)
79 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
80 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
81 #define PREC 64
82 #define PRECM1 63
83 #define PRECM2 62
84 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
85 #else
86 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
87 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
88 #define PREC 113
89 #define PRECM1 112
90 #define PRECM2 111
91 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
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