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5261 libm should stop using synonyms.h
5298 fabs is 0-sized, confuses dis(1) and others
Reviewed by: Josef 'Jeff' Sipek <jeffpc@josefsipek.net>
Approved by: Gordon Ross <gwr@nexenta.com>
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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
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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 -#pragma weak asin = __asin
30 +#pragma weak __asin = asin
31 31
32 32 /* INDENT OFF */
33 33 /*
34 34 * asin(x)
35 35 * Method :
36 36 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
37 37 * we approximate asin(x) on [0,0.5] by
38 38 * asin(x) = x + x*x^2*R(x^2)
39 39 * where
40 40 * R(x^2) is a rational approximation of (asin(x)-x)/x^3
41 41 * and its remez error is bounded by
42 42 * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
43 43 *
44 44 * For x in [0.5,1]
45 45 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
46 46 * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
47 47 * then for x>0.98
48 48 * asin(x) = pi/2 - 2*(s+s*z*R(z))
49 49 * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
50 50 * For x<=0.98, let pio4_hi = pio2_hi/2, then
51 51 * f = hi part of s;
52 52 * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
53 53 * and
54 54 * asin(x) = pi/2 - 2*(s+s*z*R(z))
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55 55 * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
56 56 * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
57 57 *
58 58 * Special cases:
59 59 * if x is NaN, return x itself;
60 60 * if |x|>1, return NaN with invalid signal.
61 61 *
62 62 */
63 63 /* INDENT ON */
64 64
65 -#include "libm_synonyms.h" /* __asin, __sqrt, __isnan */
66 65 #include "libm_protos.h" /* _SVID_libm_error */
67 66 #include "libm_macros.h"
68 67 #include <math.h>
69 68
70 69 /* INDENT OFF */
71 70 static const double xxx[] = {
72 71 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
73 72 /* huge */ 1.000e+300,
74 73 /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */
75 74 /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */
76 75 /* pio4_hi */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
77 76 /* coefficient for R(x^2) */
78 77 /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */
79 78 /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */
80 79 /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */
81 80 /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */
82 81 /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */
83 82 /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */
84 83 /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */
85 84 /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */
86 85 /* qS3 */ -6.88283971605453293030e-01, /* BFE6066C, 1B8D0159 */
87 86 /* qS4 */ 7.70381505559019352791e-02 /* 3FB3B8C5, B12E9282 */
88 87 };
89 88 #define one xxx[0]
90 89 #define huge xxx[1]
91 90 #define pio2_hi xxx[2]
92 91 #define pio2_lo xxx[3]
93 92 #define pio4_hi xxx[4]
94 93 #define pS0 xxx[5]
95 94 #define pS1 xxx[6]
96 95 #define pS2 xxx[7]
97 96 #define pS3 xxx[8]
98 97 #define pS4 xxx[9]
99 98 #define pS5 xxx[10]
100 99 #define qS1 xxx[11]
101 100 #define qS2 xxx[12]
102 101 #define qS3 xxx[13]
103 102 #define qS4 xxx[14]
104 103 /* INDENT ON */
105 104
106 105 double
107 106 asin(double x) {
108 107 double t, w, p, q, c, r, s;
109 108 int hx, ix, i;
110 109
111 110 hx = ((int *) &x)[HIWORD];
112 111 ix = hx & 0x7fffffff;
113 112 if (ix >= 0x3ff00000) { /* |x| >= 1 */
114 113 if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0)
115 114 /* asin(1)=+-pi/2 with inexact */
116 115 return (x * pio2_hi + x * pio2_lo);
117 116 else if (isnan(x))
118 117 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
119 118 return (ix >= 0x7ff80000 ? x : (x - x) / (x - x));
120 119 /* assumes sparc-like QNaN */
121 120 #else
122 121 return (x - x) / (x - x); /* asin(|x|>1) is NaN */
123 122 #endif
124 123 else
125 124 return (_SVID_libm_err(x, x, 2));
126 125 } else if (ix < 0x3fe00000) { /* |x| < 0.5 */
127 126 if (ix < 0x3e400000) { /* if |x| < 2**-27 */
128 127 if ((i = (int) x) == 0)
129 128 /* return x with inexact if x != 0 */
130 129 return (x);
131 130 }
132 131 t = x * x;
133 132 p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 +
134 133 t * (pS4 + t * pS5)))));
135 134 q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
136 135 w = p / q;
137 136 return (x + x * w);
138 137 }
139 138 /* 1 > |x| >= 0.5 */
140 139 w = one - fabs(x);
141 140 t = w * 0.5;
142 141 p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
143 142 q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
144 143 s = sqrt(t);
145 144 if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
146 145 w = p / q;
147 146 t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
148 147 } else {
149 148 w = s;
150 149 ((int *) &w)[LOWORD] = 0;
151 150 c = (t - w * w) / (s + w);
152 151 r = p / q;
153 152 p = 2.0 * s * r - (pio2_lo - 2.0 * c);
154 153 q = pio4_hi - 2.0 * w;
155 154 t = pio4_hi - (p - q);
156 155 }
157 156 return (hx > 0 ? t : -t);
158 157 }
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