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 2005 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __sincosf = sincosf
32
33
34 /*
35 * For |x| < pi/4, let z = x * x, and approximate sin(x) by
36 *
37 * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z)
38 * where
39 * S0 = 1.85735322054308378716204874632872525989806770558e-0003,
40 * S1 = -1.95035094218403635082921458859320791358115801259e-0004,
41 * S2 = 5.38400550766074785970952495168558701485841707252e+0002,
42 * S3 = -3.31975110777873728964197739157371509422022905947e+0001,
43 *
44 * with error bounded by |(sin(x) - S(x))/x| < 2**(-28.2), and
45 * cos(x) by
46 *
47 * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z)
48 * where
49 * C0 = 1.09349482127188401868272000389539985058873853699e-0003
50 * C1 = -5.03324285989964979398034700054920226866107675091e-0004
51 * C2 = 2.43792880266971107750418061559602239831538067410e-0005
52 * C3 = 9.14499072605666582228127405245558035523741471271e+0002
53 * C4 = -3.63151270591815439197122504991683846785293207730e+0001
54 *
55 * with error bounded by |cos(x) - C(x)| < 2**(-34.2).
56 */
57
58 #include "libm.h"
59
60 extern const int _TBL_ipio2_inf[];
61 extern int __rem_pio2m(double *, double *, int, int, int, const int *);
62
63 #if defined(__i386) && !defined(__amd64)
64 extern int __swapRP(int);
65 #endif
66
67 static const double C[] = {
68 1.85735322054308378716204874632872525989806770558e-0003,
69 -1.95035094218403635082921458859320791358115801259e-0004,
70 5.38400550766074785970952495168558701485841707252e+0002,
71 -3.31975110777873728964197739157371509422022905947e+0001,
72 1.09349482127188401868272000389539985058873853699e-0003,
73 -5.03324285989964979398034700054920226866107675091e-0004,
74 2.43792880266971107750418061559602239831538067410e-0005,
75 9.14499072605666582228127405245558035523741471271e+0002,
76 -3.63151270591815439197122504991683846785293207730e+0001,
77 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
78 0.5,
79 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
80 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
81 };
82
83 #define S0 C[0]
84 #define S1 C[1]
85 #define S2 C[2]
86 #define S3 C[3]
87 #define C0 C[4]
88 #define C1 C[5]
89 #define C2 C[6]
90 #define C3 C[7]
91 #define C4 C[8]
92 #define invpio2 C[9]
93 #define half C[10]
94 #define pio2_1 C[11]
95 #define pio2_t C[12]
96
97 void
98 sincosf(float x, float *s, float *c)
99 {
100 double y, z, w;
101 float f, g;
102 int n, ix, hx, hy;
103 volatile int i __unused;
104
105 hx = *((int *)&x);
106 ix = hx & 0x7fffffff;
107
108 y = (double)x;
109
110 if (ix <= 0x4016cbe4) { /* |x| < 3*pi/4 */
111 if (ix <= 0x3f490fdb) { /* |x| < pi/4 */
112 if (ix <= 0x39800000) { /* |x| <= 2**-12 */
113 i = (int)y;
114 #ifdef lint
115 i = i;
116 #endif
117 *s = x;
118 *c = 1.0f;
119 return;
120 }
121
122 z = y * y;
123 *s = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z)));
124 *c = (float)(((C0 + z * C1) + (z * z) * C2) * (C3 + z *
125 (C4 + z)));
126 } else if (hx > 0) {
127 y = (y - pio2_1) - pio2_t;
128 z = y * y;
129 *s = (float)(((C0 + z * C1) + (z * z) * C2) * (C3 + z *
130 (C4 + z)));
131 *c = (float)-((y * (S0 + z * S1)) * (S2 + z * (S3 +
132 z)));
133 } else {
134 y = (y + pio2_1) + pio2_t;
135 z = y * y;
136 *s = (float)-(((C0 + z * C1) + (z * z) * C2) * (C3 + z *
137 (C4 + z)));
138 *c = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z)));
139 }
140
141 return;
142 } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */
143 #if defined(__i386) && !defined(__amd64)
144 int rp;
145
146 rp = __swapRP(fp_extended);
147 #endif
148 w = y * invpio2;
149
150 if (hx < 0)
151 n = (int)(w - half);
152 else
153 n = (int)(w + half);
154
155 y = (y - n * pio2_1) - n * pio2_t;
156 #if defined(__i386) && !defined(__amd64)
157 if (rp != fp_extended)
158 (void) __swapRP(rp);
159 #endif
160 } else {
161 if (ix >= 0x7f800000) {
162 *s = *c = x / x;
163 return;
164 }
165
166 hy = ((int *)&y)[HIWORD];
167 n = ((hy >> 20) & 0x7ff) - 1046;
168 ((int *)&w)[HIWORD] = (hy & 0xfffff) | 0x41600000;
169 ((int *)&w)[LOWORD] = ((int *)&y)[LOWORD];
170 n = __rem_pio2m(&w, &y, n, 1, 0, _TBL_ipio2_inf);
171
172 if (hy < 0) {
173 y = -y;
174 n = -n;
175 }
176 }
177
178 z = y * y;
179 f = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z)));
180 g = (float)(((C0 + z * C1) + (z * z) * C2) * (C3 + z * (C4 + z)));
181
182 if (n & 2) {
183 f = -f;
184 g = -g;
185 }
186
187 if (n & 1) {
188 *s = g;
189 *c = -f;
190 } else {
191 *s = f;
192 *c = g;
193 }
194 }