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