xref: /illumos-gate/usr/src/lib/libm/common/R/sincosf.c (revision a6bde1a23b60f140c7ed78df979c2e22b1ed9b2c)
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 }
188