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--- old/usr/src/lib/libm/common/C/asin.c
+++ new/usr/src/lib/libm/common/C/asin.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 21
22 22 /*
23 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 25 /*
26 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 27 * Use is subject to license terms.
28 28 */
29 29
30 30 #pragma weak asin = __asin
31 31
32 32 /* INDENT OFF */
33 33 /* asin(x)
34 34 * Method :
35 35 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
36 36 * we approximate asin(x) on [0,0.5] by
37 37 * asin(x) = x + x*x^2*R(x^2)
38 38 * where
39 39 * R(x^2) is a rational approximation of (asin(x)-x)/x^3
40 40 * and its remez error is bounded by
41 41 * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
42 42 *
43 43 * For x in [0.5,1]
44 44 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
45 45 * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
46 46 * then for x>0.98
47 47 * asin(x) = pi/2 - 2*(s+s*z*R(z))
48 48 * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
49 49 * For x<=0.98, let pio4_hi = pio2_hi/2, then
50 50 * f = hi part of s;
51 51 * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
52 52 * and
53 53 * asin(x) = pi/2 - 2*(s+s*z*R(z))
54 54 * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
55 55 * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
56 56 *
57 57 * Special cases:
58 58 * if x is NaN, return x itself;
59 59 * if |x|>1, return NaN with invalid signal.
60 60 *
61 61 */
62 62 /* INDENT ON */
63 63
64 64 #include "libm_synonyms.h" /* __asin, __sqrt, __isnan */
65 65 #include "libm_protos.h" /* _SVID_libm_error */
66 66 #include "libm_macros.h"
67 67 #include <math.h>
68 68
69 69 /* INDENT OFF */
70 70 static const double xxx[] = {
71 71 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
72 72 /* huge */ 1.000e+300,
73 73 /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */
74 74 /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */
75 75 /* pio4_hi */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
76 76 /* coefficient for R(x^2) */
77 77 /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */
78 78 /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */
79 79 /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */
80 80 /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */
81 81 /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */
82 82 /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */
83 83 /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */
84 84 /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */
85 85 /* qS3 */ -6.88283971605453293030e-01, /* BFE6066C, 1B8D0159 */
86 86 /* qS4 */ 7.70381505559019352791e-02 /* 3FB3B8C5, B12E9282 */
87 87 };
88 88 #define one xxx[0]
89 89 #define huge xxx[1]
90 90 #define pio2_hi xxx[2]
91 91 #define pio2_lo xxx[3]
92 92 #define pio4_hi xxx[4]
93 93 #define pS0 xxx[5]
94 94 #define pS1 xxx[6]
95 95 #define pS2 xxx[7]
96 96 #define pS3 xxx[8]
97 97 #define pS4 xxx[9]
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98 98 #define pS5 xxx[10]
99 99 #define qS1 xxx[11]
100 100 #define qS2 xxx[12]
101 101 #define qS3 xxx[13]
102 102 #define qS4 xxx[14]
103 103 /* INDENT ON */
104 104
105 105 double
106 106 asin(double x) {
107 107 double t, w, p, q, c, r, s;
108 - int hx, ix;
108 + int hx, ix, i;
109 109
110 110 hx = ((int *) &x)[HIWORD];
111 111 ix = hx & 0x7fffffff;
112 112 if (ix >= 0x3ff00000) { /* |x| >= 1 */
113 113 if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0)
114 114 /* asin(1)=+-pi/2 with inexact */
115 115 return x * pio2_hi + x * pio2_lo;
116 116 else if (isnan(x))
117 117 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
118 118 return ix >= 0x7ff80000 ? x : (x - x) / (x - x);
119 119 /* assumes sparc-like QNaN */
120 120 #else
121 121 return (x - x) / (x - x); /* asin(|x|>1) is NaN */
122 122 #endif
123 123 else
124 124 return _SVID_libm_err(x, x, 2);
125 125 }
126 126 else if (ix < 0x3fe00000) { /* |x| < 0.5 */
127 127 if (ix < 0x3e400000) { /* if |x| < 2**-27 */
128 - if (huge + x > one)
128 + if ((i = (int) x) == 0)
129 129 return x; /* return x with inexact if
130 130 * x != 0 */
131 131 }
132 - else
133 - t = x * x;
132 + t = x * x;
134 133 p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 +
135 134 t * (pS4 + t * pS5)))));
136 135 q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
137 136 w = p / q;
138 137 return x + x * w;
139 138 }
140 139 /* 1 > |x| >= 0.5 */
141 140 w = one - fabs(x);
142 141 t = w * 0.5;
143 142 p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
144 143 q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
145 144 s = sqrt(t);
146 145 if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
147 146 w = p / q;
148 147 t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
149 148 }
150 149 else {
151 150 w = s;
152 151 ((int *) &w)[LOWORD] = 0;
153 152 c = (t - w * w) / (s + w);
154 153 r = p / q;
155 154 p = 2.0 * s * r - (pio2_lo - 2.0 * c);
156 155 q = pio4_hi - 2.0 * w;
157 156 t = pio4_hi - (p - q);
158 157 }
159 158 return hx > 0 ? t : -t;
160 159 }
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