1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
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 #include "libm.h"
32
33
34 /*
35 * void __k_sincosf(double x, float *s, float *c);
36 * kernel (float) sincos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
37 * Input x is in double and assumed to be bounded by ~pi/4 in magnitude.
38 *
39 * Method: Let z = x * x, then
40 * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z)
41 * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z)
42 * where
43 * S0 = 1.85735322054308378716204874632872525989806770558e-0003
44 * S1 = -1.95035094218403635082921458859320791358115801259e-0004
45 * S2 = 5.38400550766074785970952495168558701485841707252e+0002
46 * S3 = -3.31975110777873728964197739157371509422022905947e+0001
47 * C0 = 1.09349482127188401868272000389539985058873853699e-0003
48 * C1 = -5.03324285989964979398034700054920226866107675091e-0004
49 * C2 = 2.43792880266971107750418061559602239831538067410e-0005
50 * C3 = 9.14499072605666582228127405245558035523741471271e+0002
51 * C4 = -3.63151270591815439197122504991683846785293207730e+0001
52 *
53 * The remez error in S is bound by |(sin(x) - S(x))/x| < 2**(-28.2)
54 * The remez error in C is bound by |cos(x) - C(x)| < 2**(-34.2)
55 *
56 * Constants:
57 * The hexadecimal values are the intended ones for the following constants.
58 * The decimal values may be used, provided that the compiler will convert
59 * from decimal to binary accurately enough to produce the hexadecimal values
60 * shown.
61 */
62
63 static const double q[] = {
64 /* S0 = */
65 1.85735322054308378716204874632872525989806770558e-0003,
66 /* S1 = */ -1.95035094218403635082921458859320791358115801259e-0004,
67 /* S2 = */ 5.38400550766074785970952495168558701485841707252e+0002,
68 /* S3 = */ -3.31975110777873728964197739157371509422022905947e+0001,
69 /* C0 = */ 1.09349482127188401868272000389539985058873853699e-0003,
70 /* C1 = */ -5.03324285989964979398034700054920226866107675091e-0004,
71 /* C2 = */ 2.43792880266971107750418061559602239831538067410e-0005,
72 /* C3 = */ 9.14499072605666582228127405245558035523741471271e+0002,
73 /* C4 = */ -3.63151270591815439197122504991683846785293207730e+0001, };
74
75 #define S0 q[0]
76 #define S1 q[1]
77 #define S2 q[2]
78 #define S3 q[3]
79 #define C0 q[4]
80 #define C1 q[5]
81 #define C2 q[6]
82 #define C3 q[7]
83 #define C4 q[8]
84
85 void
86 __k_sincosf(double x, float *s, float *c)
87 {
88 double z;
89 int hx;
90
91 hx = ((int *)&x)[HIWORD]; /* hx = leading x */
92
93 /* small argument */
94 if ((hx & ~0x80000000) < 0x3f100000) { /* if |x| < 2**-14 */
95 *s = (float)x;
96 *c = (float)1;
97
98 if ((int)x == 0) /* raise inexact if x != 0 */
99 return;
100 }
101
102 z = x * x;
103 *s = (float)((x * (S0 + z * S1)) * (S2 + z * (S3 + z)));
104 *c = (float)(((C0 + z * C1) + (z * z) * C2) * (C3 + z * (C4 + z)));
105 }