xref: /titanic_51/usr/src/lib/libm/common/C/asin.c (revision c0dbe950192897247de6003f2dea1ca3c466fe01)
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 #pragma weak __asin = asin
31 
32 /* INDENT OFF */
33 /*
34  * asin(x)
35  * Method :
36  *	Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
37  *	we approximate asin(x) on [0,0.5] by
38  *		asin(x) = x + x*x^2*R(x^2)
39  *	where
40  *		R(x^2) is a rational approximation of (asin(x)-x)/x^3
41  *	and its remez error is bounded by
42  *		|(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
43  *
44  *	For x in [0.5,1]
45  *		asin(x) = pi/2-2*asin(sqrt((1-x)/2))
46  *	Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
47  *	then for x>0.98
48  *		asin(x) = pi/2 - 2*(s+s*z*R(z))
49  *			= pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
50  *	For x<=0.98, let pio4_hi = pio2_hi/2, then
51  *		f = hi part of s;
52  *		c = sqrt(z) - f = (z-f*f)/(s+f) 	...f+c=sqrt(z)
53  *	and
54  *		asin(x) = pi/2 - 2*(s+s*z*R(z))
55  *			= pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
56  *			= pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
57  *
58  * Special cases:
59  *	if x is NaN, return x itself;
60  *	if |x|>1, return NaN with invalid signal.
61  *
62  */
63 /* INDENT ON */
64 
65 #include "libm_protos.h"	/* _SVID_libm_error */
66 #include "libm_macros.h"
67 #include <math.h>
68 
69 /* INDENT OFF */
70 static const double xxx[] = {
71 /* one */	 1.00000000000000000000e+00,	/* 3FF00000, 00000000 */
72 /* huge */	 1.000e+300,
73 /* pio2_hi */	 1.57079632679489655800e+00,	/* 3FF921FB, 54442D18 */
74 /* pio2_lo */	 6.12323399573676603587e-17,	/* 3C91A626, 33145C07 */
75 /* pio4_hi */	 7.85398163397448278999e-01,	/* 3FE921FB, 54442D18 */
76 /* coefficient for R(x^2) */
77 /* pS0 */	 1.66666666666666657415e-01,	/* 3FC55555, 55555555 */
78 /* pS1 */	-3.25565818622400915405e-01,	/* BFD4D612, 03EB6F7D */
79 /* pS2 */	 2.01212532134862925881e-01,	/* 3FC9C155, 0E884455 */
80 /* pS3 */	-4.00555345006794114027e-02,	/* BFA48228, B5688F3B */
81 /* pS4 */	 7.91534994289814532176e-04,	/* 3F49EFE0, 7501B288 */
82 /* pS5 */	 3.47933107596021167570e-05,	/* 3F023DE1, 0DFDF709 */
83 /* qS1 */	-2.40339491173441421878e+00,	/* C0033A27, 1C8A2D4B */
84 /* qS2 */	 2.02094576023350569471e+00,	/* 40002AE5, 9C598AC8 */
85 /* qS3 */	-6.88283971605453293030e-01,	/* BFE6066C, 1B8D0159 */
86 /* qS4 */	 7.70381505559019352791e-02	/* 3FB3B8C5, B12E9282 */
87 };
88 #define	one	xxx[0]
89 #define	huge	xxx[1]
90 #define	pio2_hi	xxx[2]
91 #define	pio2_lo	xxx[3]
92 #define	pio4_hi	xxx[4]
93 #define	pS0	xxx[5]
94 #define	pS1	xxx[6]
95 #define	pS2	xxx[7]
96 #define	pS3	xxx[8]
97 #define	pS4	xxx[9]
98 #define	pS5	xxx[10]
99 #define	qS1	xxx[11]
100 #define	qS2	xxx[12]
101 #define	qS3	xxx[13]
102 #define	qS4	xxx[14]
103 /* INDENT ON */
104 
105 double
106 asin(double x) {
107 	double t, w, p, q, c, r, s;
108 	int hx, ix, i;
109 
110 	hx = ((int *) &x)[HIWORD];
111 	ix = hx & 0x7fffffff;
112 	if (ix >= 0x3ff00000) {	/* |x| >= 1 */
113 		if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0)
114 			/* asin(1)=+-pi/2 with inexact */
115 			return (x * pio2_hi + x * pio2_lo);
116 		else if (isnan(x))
117 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
118 			return (ix >= 0x7ff80000 ? x : (x - x) / (x - x));
119 			/* assumes sparc-like QNaN */
120 #else
121 			return (x - x) / (x - x);	/* asin(|x|>1) is NaN */
122 #endif
123 		else
124 			return (_SVID_libm_err(x, x, 2));
125 	} else if (ix < 0x3fe00000) {	/* |x| < 0.5 */
126 		if (ix < 0x3e400000) {	/* if |x| < 2**-27 */
127 			if ((i = (int) x) == 0)
128 				/* return x with inexact if x != 0 */
129 				return (x);
130 		}
131 		t = x * x;
132 		p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 +
133 			t * (pS4 + t * pS5)))));
134 		q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
135 		w = p / q;
136 		return (x + x * w);
137 	}
138 	/* 1 > |x| >= 0.5 */
139 	w = one - fabs(x);
140 	t = w * 0.5;
141 	p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
142 	q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
143 	s = sqrt(t);
144 	if (ix >= 0x3FEF3333) {	/* if |x| > 0.975 */
145 		w = p / q;
146 		t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
147 	} else {
148 		w = s;
149 		((int *) &w)[LOWORD] = 0;
150 		c = (t - w * w) / (s + w);
151 		r = p / q;
152 		p = 2.0 * s * r - (pio2_lo - 2.0 * c);
153 		q = pio4_hi - 2.0 * w;
154 		t = pio4_hi - (p - q);
155 	}
156 	return (hx > 0 ? t : -t);
157 }
158