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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/R/atanf.c
+++ new/usr/src/lib/libm/common/R/atanf.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 atanf = __atanf
30 +#pragma weak __atanf = atanf
31 31
32 32 /* INDENT OFF */
33 33 /*
34 34 * float atanf(float x);
35 35 * Table look-up algorithm
36 36 * By K.C. Ng, March 9, 1989
37 37 *
38 38 * Algorithm.
39 39 *
40 40 * The algorithm is based on atan(x)=atan(y)+atan((x-y)/(1+x*y)).
41 41 * We use poly1(x) to approximate atan(x) for x in [0,1/8] with
42 42 * error (relative)
43 43 * |(atan(x)-poly1(x))/x|<= 2^-115.94 long double
44 44 * |(atan(x)-poly1(x))/x|<= 2^-58.85 double
45 45 * |(atan(x)-poly1(x))/x|<= 2^-25.53 float
46 46 * and use poly2(x) to approximate atan(x) for x in [0,1/65] with
47 47 * error (absolute)
48 48 * |atan(x)-poly2(x)|<= 2^-122.15 long double
49 49 * |atan(x)-poly2(x)|<= 2^-64.79 double
50 50 * |atan(x)-poly2(x)|<= 2^-35.36 float
51 51 * and use poly3(x) to approximate atan(x) for x in [1/8,7/16] with
52 52 * error (relative, on for single precision)
53 53 * |(atan(x)-poly1(x))/x|<= 2^-25.53 float
54 54 *
55 55 * Here poly1-3 are odd polynomial with the following form:
56 56 * x + x^3*(a1+x^2*(a2+...))
57 57 *
58 58 * (0). Purge off Inf and NaN and 0
59 59 * (1). Reduce x to positive by atan(x) = -atan(-x).
60 60 * (2). For x <= 1/8, use
61 61 * (2.1) if x < 2^(-prec/2-2), atan(x) = x with inexact
62 62 * (2.2) Otherwise
63 63 * atan(x) = poly1(x)
64 64 * (3). For x >= 8 then
65 65 * (3.1) if x >= 2^(prec+2), atan(x) = atan(inf) - pio2lo
66 66 * (3.2) if x >= 2^(prec/3+2), atan(x) = atan(inf) - 1/x
67 67 * (3.3) if x > 65, atan(x) = atan(inf) - poly2(1/x)
68 68 * (3.4) Otherwise, atan(x) = atan(inf) - poly1(1/x)
69 69 *
70 70 * (4). Now x is in (0.125, 8)
71 71 * Find y that match x to 4.5 bit after binary (easy).
72 72 * If iy is the high word of y, then
73 73 * single : j = (iy - 0x3e000000) >> 19
74 74 * (single is modified to (iy-0x3f000000)>>19)
75 75 * double : j = (iy - 0x3fc00000) >> 16
76 76 * quad : j = (iy - 0x3ffc0000) >> 12
77 77 *
78 78 * Let s = (x-y)/(1+x*y). Then
79 79 * atan(x) = atan(y) + poly1(s)
80 80 * = _TBL_r_atan_hi[j] + (_TBL_r_atan_lo[j] + poly2(s) )
81 81 *
82 82 * Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125
83 83 *
84 84 */
85 85
86 86 #include "libm.h"
87 87
88 88 extern const float _TBL_r_atan_hi[], _TBL_r_atan_lo[];
89 89 static const float
90 90 big = 1.0e37F,
91 91 one = 1.0F,
92 92 p1 = -3.333185951111688247225368498733544672172e-0001F,
93 93 p2 = 1.969352894213455405211341983203180636021e-0001F,
94 94 q1 = -3.332921964095646819563419704110132937456e-0001F,
95 95 a1 = -3.333323465223893614063523351509338934592e-0001F,
96 96 a2 = 1.999425625935277805494082274808174062403e-0001F,
97 97 a3 = -1.417547090509737780085769846290301788559e-0001F,
98 98 a4 = 1.016250813871991983097273733227432685084e-0001F,
99 99 a5 = -5.137023693688358515753093811791755221805e-0002F,
100 100 pio2hi = 1.570796371e+0000F,
101 101 pio2lo = -4.371139000e-0008F;
102 102 /* INDENT ON */
103 103
104 104 float
105 105 atanf(float xx) {
106 106 float x, y, z, r, p, s;
107 107 volatile double dummy;
108 108 int ix, iy, sign, j;
109 109
110 110 x = xx;
111 111 ix = *(int *) &x;
112 112 sign = ix & 0x80000000;
113 113 ix ^= sign;
114 114
115 115 /* for |x| < 1/8 */
116 116 if (ix < 0x3e000000) {
117 117 if (ix < 0x38800000) { /* if |x| < 2**(-prec/2-2) */
118 118 dummy = big + x; /* get inexact flag if x != 0 */
119 119 #ifdef lint
120 120 dummy = dummy;
121 121 #endif
122 122 return (x);
123 123 }
124 124 z = x * x;
125 125 if (ix < 0x3c000000) { /* if |x| < 2**(-prec/4-1) */
126 126 x = x + (x * z) * p1;
127 127 return (x);
128 128 } else {
129 129 x = x + (x * z) * (p1 + z * p2);
130 130 return (x);
131 131 }
132 132 }
133 133
134 134 /* for |x| >= 8.0 */
135 135 if (ix >= 0x41000000) {
136 136 *(int *) &x = ix;
137 137 if (ix < 0x42820000) { /* x < 65 */
138 138 r = one / x;
139 139 z = r * r;
140 140 y = r * (one + z * (p1 + z * p2)); /* poly1 */
141 141 y -= pio2lo;
142 142 } else if (ix < 0x44800000) { /* x < 2**(prec/3+2) */
143 143 r = one / x;
144 144 z = r * r;
145 145 y = r * (one + z * q1); /* poly2 */
146 146 y -= pio2lo;
147 147 } else if (ix < 0x4c800000) { /* x < 2**(prec+2) */
148 148 y = one / x - pio2lo;
149 149 } else if (ix < 0x7f800000) { /* x < inf */
150 150 y = -pio2lo;
151 151 } else { /* x is inf or NaN */
152 152 if (ix > 0x7f800000) {
153 153 return (x * x); /* - -> * for Cheetah */
154 154 }
155 155 y = -pio2lo;
156 156 }
157 157
158 158 if (sign == 0)
159 159 x = pio2hi - y;
160 160 else
161 161 x = y - pio2hi;
162 162 return (x);
163 163 }
164 164
165 165
166 166 /* now x is between 1/8 and 8 */
167 167 if (ix < 0x3f000000) { /* between 1/8 and 1/2 */
168 168 z = x * x;
169 169 x = x + (x * z) * (a1 + z * (a2 + z * (a3 + z * (a4 +
170 170 z * a5))));
171 171 return (x);
172 172 }
173 173 *(int *) &x = ix;
174 174 iy = (ix + 0x00040000) & 0x7ff80000;
175 175 *(int *) &y = iy;
176 176 j = (iy - 0x3f000000) >> 19;
177 177
178 178 if (ix == iy)
179 179 p = x - y; /* p=0.0 */
180 180 else {
181 181 if (sign == 0)
182 182 s = (x - y) / (one + x * y);
183 183 else
184 184 s = (y - x) / (one + x * y);
185 185 z = s * s;
186 186 p = s * (one + z * q1);
187 187 }
188 188 if (sign == 0) {
189 189 r = p + _TBL_r_atan_lo[j];
190 190 x = r + _TBL_r_atan_hi[j];
191 191 } else {
192 192 r = p - _TBL_r_atan_lo[j];
193 193 x = r - _TBL_r_atan_hi[j];
194 194 }
195 195 return (x);
196 196 }
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