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 /*
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 * tanl(x)
32 * Table look-up algorithm by K.C. Ng, November, 1989.
33 *
34 * kernel function:
35 * __k_tanl ... tangent function on [-pi/4,pi/4]
36 * __rem_pio2l ... argument reduction routine
37 *
38 * Method.
39 * Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
40 * 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
41 * [-pi/2 , +pi/2], and let n = k mod 4.
42 * 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
43 *
44 * n sin(x) cos(x) tan(x)
47 * 1 C -S -C/S
48 * 2 -S -C S/C
49 * 3 -C S -C/S
50 * ----------------------------------------------------------
51 *
52 * Special cases:
53 * Let trig be any of sin, cos, or tan.
54 * trig(+-INF) is NaN, with signals;
55 * trig(NaN) is that NaN;
56 *
57 * Accuracy:
58 * computer TRIG(x) returns trig(x) nearly rounded.
59 */
60
61 #pragma weak __tanl = tanl
62
63 #include "libm.h"
64 #include "longdouble.h"
65
66 long double
67 tanl(long double x) {
68 long double y[2], z = 0.0L;
69 int n, ix;
70
71 ix = *(int *) &x; /* High word of x */
72 ix &= 0x7fffffff;
73 if (ix <= 0x3ffe9220) /* |x| ~< pi/4 */
74 return (__k_tanl(x, z, 0));
75 else if (ix >= 0x7fff0000) /* trig(Inf or NaN) is NaN */
76 return (x - x);
77 else { /* argument reduction needed */
78 n = __rem_pio2l(x, y);
79 return (__k_tanl(y[0], y[1], (n & 1)));
80 }
81 }
|
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 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25
26 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 /*
32 * tanl(x)
33 * Table look-up algorithm by K.C. Ng, November, 1989.
34 *
35 * kernel function:
36 * __k_tanl ... tangent function on [-pi/4,pi/4]
37 * __rem_pio2l ... argument reduction routine
38 *
39 * Method.
40 * Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
41 * 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
42 * [-pi/2 , +pi/2], and let n = k mod 4.
43 * 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
44 *
45 * n sin(x) cos(x) tan(x)
48 * 1 C -S -C/S
49 * 2 -S -C S/C
50 * 3 -C S -C/S
51 * ----------------------------------------------------------
52 *
53 * Special cases:
54 * Let trig be any of sin, cos, or tan.
55 * trig(+-INF) is NaN, with signals;
56 * trig(NaN) is that NaN;
57 *
58 * Accuracy:
59 * computer TRIG(x) returns trig(x) nearly rounded.
60 */
61
62 #pragma weak __tanl = tanl
63
64 #include "libm.h"
65 #include "longdouble.h"
66
67 long double
68 tanl(long double x)
69 {
70 long double y[2], z = 0.0L;
71 int n, ix;
72
73 ix = *(int *)&x; /* High word of x */
74 ix &= 0x7fffffff;
75
76 if (ix <= 0x3ffe9220) { /* |x| ~< pi/4 */
77 return (__k_tanl(x, z, 0));
78 } else if (ix >= 0x7fff0000) { /* trig(Inf or NaN) is NaN */
79 return (x - x);
80 } else { /* argument reduction needed */
81 n = __rem_pio2l(x, y);
82 return (__k_tanl(y[0], y[1], (n & 1)));
83 }
84 }
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