xref: /illumos-gate/usr/src/lib/libm/common/Q/asinl.c (revision 177d5b5f)
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  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29 
30 #if defined(ELFOBJ)
31 #pragma weak asinl = __asinl
32 #endif
33 
34 /*
35  *	asinl(x) = atan2l(x,sqrt(1-x*x));
36  *
37  * For better accuracy, 1-x*x is computed as follows
38  *	1-x*x                     if x <  0.5,
39  *	2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
40  *
41  * Special cases:
42  *	if x is NaN, return x itself;
43  *	if |x|>1, return NaN with invalid signal.
44  */
45 
46 #include "libm.h"
47 
48 static const long double zero = 0.0L, small = 1.0e-20L, half = 0.5L, one = 1.0L;
49 #ifndef lint
50 static const long double big = 1.0e+20L;
51 #endif
52 
53 long double
54 asinl(long double x) {
55 	long double t, w;
56 	volatile long double dummy;
57 
58 	w = fabsl(x);
59 	if (isnanl(x))
60 		return (x + x);
61 	else if (w <= half) {
62 		if (w < small) {
63 #ifndef lint
64 			dummy = w + big;
65 							/* inexact if w != 0 */
66 #endif
67 			return (x);
68 		} else
69 			return (atanl(x / sqrtl(one - x * x)));
70 	} else if (w < one) {
71 		t = one - w;
72 		w = t + t;
73 		return (atanl(x / sqrtl(w - t * t)));
74 	} else if (w == one)
75 		return (atan2l(x, zero));	/* asin(+-1) =  +- PI/2 */
76 	else
77 		return (zero / zero);		/* |x| > 1: invalid */
78 }
79