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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak sincosf = __sincosf
30
31 /* INDENT OFF */
32 /*
33 * For |x| < pi/4, let z = x * x, and approximate sin(x) by
34 *
35 * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z)
36 * where
37 * S0 = 1.85735322054308378716204874632872525989806770558e-0003,
38 * S1 = -1.95035094218403635082921458859320791358115801259e-0004,
39 * S2 = 5.38400550766074785970952495168558701485841707252e+0002,
40 * S3 = -3.31975110777873728964197739157371509422022905947e+0001,
41 *
42 * with error bounded by |(sin(x) - S(x))/x| < 2**(-28.2), and
43 * cos(x) by
44 *
45 * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z)
46 * where
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 * with error bounded by |cos(x) - C(x)| < 2**(-34.2).
54 */
55 /* INDENT ON */
56
57 #include "libm.h"
58
59 extern const int _TBL_ipio2_inf[];
60 extern int __rem_pio2m(double *, double *, int, int, int, const int *);
61 #if defined(__i386) && !defined(__amd64)
62 extern int __swapRP(int);
63 #endif
64
65 static const double C[] = {
66 1.85735322054308378716204874632872525989806770558e-0003,
67 -1.95035094218403635082921458859320791358115801259e-0004,
68 5.38400550766074785970952495168558701485841707252e+0002,
69 -3.31975110777873728964197739157371509422022905947e+0001,
70 1.09349482127188401868272000389539985058873853699e-0003,
71 -5.03324285989964979398034700054920226866107675091e-0004,
72 2.43792880266971107750418061559602239831538067410e-0005,
73 9.14499072605666582228127405245558035523741471271e+0002,
74 -3.63151270591815439197122504991683846785293207730e+0001,
75 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
76 0.5,
77 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
78 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
79 };
80
81 #define S0 C[0]
82 #define S1 C[1]
83 #define S2 C[2]
84 #define S3 C[3]
85 #define C0 C[4]
86 #define C1 C[5]
87 #define C2 C[6]
88 #define C3 C[7]
89 #define C4 C[8]
90 #define invpio2 C[9]
91 #define half C[10]
92 #define pio2_1 C[11]
93 #define pio2_t C[12]
94
95 void
96 sincosf(float x, float *s, float *c)
97 {
98 double y, z, w;
99 float f, g;
100 int n, ix, hx, hy;
101 volatile int i;
102
103 hx = *((int *)&x);
104 ix = hx & 0x7fffffff;
105
106 y = (double)x;
107
108 if (ix <= 0x4016cbe4) { /* |x| < 3*pi/4 */
109 if (ix <= 0x3f490fdb) { /* |x| < pi/4 */
110 if (ix <= 0x39800000) { /* |x| <= 2**-12 */
111 i = (int)y;
112 #ifdef lint
113 i = i;
114 #endif
115 *s = x;
116 *c = 1.0f;
117 return;
118 }
119 z = y * y;
120 *s = (float)((y * (S0 + z * S1)) *
121 (S2 + z * (S3 + z)));
122 *c = (float)(((C0 + z * C1) + (z * z) * C2) *
123 (C3 + z * (C4 + z)));
124 } else if (hx > 0) {
125 y = (y - pio2_1) - pio2_t;
126 z = y * y;
127 *s = (float)(((C0 + z * C1) + (z * z) * C2) *
128 (C3 + z * (C4 + z)));
129 *c = (float)-((y * (S0 + z * S1)) *
130 (S2 + z * (S3 + z)));
131 } else {
132 y = (y + pio2_1) + pio2_t;
133 z = y * y;
134 *s = (float)-(((C0 + z * C1) + (z * z) * C2) *
135 (C3 + z * (C4 + z)));
136 *c = (float)((y * (S0 + z * S1)) *
137 (S2 + z * (S3 + z)));
138 }
139 return;
140 } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */
141 #if defined(__i386) && !defined(__amd64)
142 int rp;
143
144 rp = __swapRP(fp_extended);
145 #endif
146 w = y * invpio2;
147 if (hx < 0)
148 n = (int)(w - half);
149 else
150 n = (int)(w + half);
151 y = (y - n * pio2_1) - n * pio2_t;
152 #if defined(__i386) && !defined(__amd64)
153 if (rp != fp_extended)
154 (void) __swapRP(rp);
155 #endif
156 } else {
157 if (ix >= 0x7f800000) {
158 *s = *c = x / x;
159 return;
160 }
161 hy = ((int *)&y)[HIWORD];
162 n = ((hy >> 20) & 0x7ff) - 1046;
163 ((int *)&w)[HIWORD] = (hy & 0xfffff) | 0x41600000;
164 ((int *)&w)[LOWORD] = ((int *)&y)[LOWORD];
165 n = __rem_pio2m(&w, &y, n, 1, 0, _TBL_ipio2_inf);
166 if (hy < 0) {
167 y = -y;
168 n = -n;
169 }
170 }
171
172 z = y * y;
173 f = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z)));
174 g = (float)(((C0 + z * C1) + (z * z) * C2) *
175 (C3 + z * (C4 + z)));
176 if (n & 2) {
177 f = -f;
178 g = -g;
179 }
180 if (n & 1) {
181 *s = g;
182 *c = -f;
183 } else {
184 *s = f;
185 *c = g;
186 }
187 }