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 acos = __acos
31
32 /* INDENT OFF */
33 /*
34 * acos(x)
35 * Method :
36 * acos(x) = pi/2 - asin(x)
37 * acos(-x) = pi/2 + asin(x)
38 * For |x|<=0.5
39 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
40 * For x>0.5
41 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
42 * = 2asin(sqrt((1-x)/2))
43 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
44 * = 2f + (2c + 2s*z*R(z))
45 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
46 * for f so that f+c ~ sqrt(z).
47 * For x<-0.5
48 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
49 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
50 *
51 * Special cases:
52 * if x is NaN, return x itself;
53 * if |x|>1, return NaN with invalid signal.
54 *
55 * Function needed: sqrt
56 */
57 /* INDENT ON */
58
59 #include "libm_synonyms.h" /* __acos, __sqrt, __isnan */
60 #include "libm_protos.h" /* _SVID_libm_error */
61 #include "libm_macros.h"
62 #include <math.h>
63
64 /* INDENT OFF */
65 static const double xxx[] = {
66 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
67 /* pi */ 3.14159265358979311600e+00, /* 400921FB, 54442D18 */
68 /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */
69 /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */
70 /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */
71 /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */
72 /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */
73 /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */
74 /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */
75 /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */
76 /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */
77 /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */
78 /* qS3 */ -6.88283971605453293030e-01, /* BFE6066C, 1B8D0159 */
79 /* qS4 */ 7.70381505559019352791e-02 /* 3FB3B8C5, B12E9282 */
80 };
81 #define one xxx[0]
82 #define pi xxx[1]
83 #define pio2_hi xxx[2]
84 #define pio2_lo xxx[3]
85 #define pS0 xxx[4]
86 #define pS1 xxx[5]
87 #define pS2 xxx[6]
88 #define pS3 xxx[7]
89 #define pS4 xxx[8]
90 #define pS5 xxx[9]
91 #define qS1 xxx[10]
92 #define qS2 xxx[11]
93 #define qS3 xxx[12]
94 #define qS4 xxx[13]
95 /* INDENT ON */
96
97 double
98 acos(double x) {
99 double z, p, q, r, w, s, c, df;
100 int hx, ix;
101
102 hx = ((int *) &x)[HIWORD];
103 ix = hx & 0x7fffffff;
104 if (ix >= 0x3ff00000) { /* |x| >= 1 */
105 if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) {
106 /* |x| == 1 */
107 if (hx > 0) /* acos(1) = 0 */
108 return (0.0);
109 else /* acos(-1) = pi */
110 return (pi + 2.0 * pio2_lo);
111 } else if (isnan(x))
112 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
113 return (ix >= 0x7ff80000 ? x : (x - x) / (x - x));
114 /* assumes sparc-like QNaN */
115 #else
116 return (x - x) / (x - x); /* acos(|x|>1) is NaN */
117 #endif
118 else
119 return (_SVID_libm_err(x, x, 1));
120 }
121 if (ix < 0x3fe00000) { /* |x| < 0.5 */
122 if (ix <= 0x3c600000)
123 return (pio2_hi + pio2_lo); /* if |x| < 2**-57 */
124 z = x * x;
125 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
126 z * (pS4 + z * pS5)))));
127 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
128 r = p / q;
129 return (pio2_hi - (x - (pio2_lo - x * r)));
130 } else if (hx < 0) {
131 /* x < -0.5 */
132 z = (one + x) * 0.5;
133 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
134 z * (pS4 + z * pS5)))));
135 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
136 s = sqrt(z);
137 r = p / q;
138 w = r * s - pio2_lo;
139 return (pi - 2.0 * (s + w));
140 } else {
141 /* x > 0.5 */
142 z = (one - x) * 0.5;
143 s = sqrt(z);
144 df = s;
145 ((int *) &df)[LOWORD] = 0;
146 c = (z - df * df) / (s + df);
147 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
148 z * (pS4 + z * pS5)))));
149 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
150 r = p / q;
151 w = r * s + c;
152 return (2.0 * (df + w));
153 }
154 }