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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/atan.c
+++ new/usr/src/lib/libm/common/C/atan.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.
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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 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 28 * Use is subject to license terms.
28 29 */
29 30
30 31 #pragma weak __atan = atan
31 32
32 -/* INDENT OFF */
33 +
33 34 /*
34 35 * atan(x)
35 36 * Accurate Table look-up algorithm with polynomial approximation in
36 37 * partially product form.
37 38 *
38 39 * -- K.C. Ng, October 17, 2004
39 40 *
40 41 * Algorithm
41 42 *
42 43 * (1). Purge off Inf and NaN and 0
43 44 * (2). Reduce x to positive by atan(x) = -atan(-x).
44 45 * (3). For x <= 1/8 and let z = x*x, return
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45 46 * (2.1) if x < 2^(-prec/2), atan(x) = x with inexact flag raised
46 47 * (2.2) if x < 2^(-prec/4-1), atan(x) = x+(x/3)(x*x)
47 48 * (2.3) if x < 2^(-prec/6-2), atan(x) = x+(z-5/3)(z*x/5)
48 49 * (2.4) Otherwise
49 50 * atan(x) = poly1(x) = x + A * B,
50 51 * where
51 52 * A = (p1*x*z) * (p2+z(p3+z))
52 53 * B = (p4+z)+z*z) * (p5+z(p6+z))
53 54 * Note: (i) domain of poly1 is [0, 1/8], (ii) remez relative
54 55 * approximation error of poly1 is bounded by
55 - * |(atan(x)-poly1(x))/x| <= 2^-57.61
56 + * |(atan(x)-poly1(x))/x| <= 2^-57.61
56 57 * (4). For x >= 8 then
57 58 * (3.1) if x >= 2^prec, atan(x) = atan(inf) - pio2lo
58 59 * (3.2) if x >= 2^(prec/3), atan(x) = atan(inf) - 1/x
59 60 * (3.3) if x <= 65, atan(x) = atan(inf) - poly1(1/x)
60 61 * (3.4) otherwise atan(x) = atan(inf) - poly2(1/x)
61 62 * where
62 63 * poly2(r) = (q1*r) * (q2+z(q3+z)) * (q4+z),
63 64 * its domain is [0, 0.0154]; and its remez absolute
64 65 * approximation error is bounded by
65 66 * |atan(x)-poly2(x)|<= 2^-59.45
66 67 *
67 68 * (5). Now x is in (0.125, 8).
68 69 * Recall identity
69 70 * atan(x) = atan(y) + atan((x-y)/(1+x*y)).
70 71 * Let j = (ix - 0x3fc00000) >> 16, 0 <= j < 96, where ix is the high
71 72 * part of x in IEEE double format. Then
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72 73 * atan(x) = atan(y[j]) + poly2((x-y[j])/(1+x*y[j]))
73 74 * where y[j] are carefully chosen so that it matches x to around 4.5
74 75 * bits and at the same time atan(y[j]) is very close to an IEEE double
75 76 * floating point number. Calculation indicates that
76 77 * max|(x-y[j])/(1+x*y[j])| < 0.0154
77 78 * j,x
78 79 *
79 80 * Accuracy: Maximum error observed is bounded by 0.6 ulp after testing
80 81 * more than 10 million random arguments
81 82 */
82 -/* INDENT ON */
83 83
84 84 #include "libm.h"
85 85 #include "libm_protos.h"
86 86
87 87 extern const double _TBL_atan[];
88 +
88 89 static const double g[] = {
89 -/* one = */ 1.0,
90 -/* p1 = */ 8.02176624254765935351230154992663301527500152588e-0002,
91 -/* p2 = */ 1.27223421700559402580665846471674740314483642578e+0000,
92 -/* p3 = */ -1.20606901800503640842521235754247754812240600586e+0000,
93 -/* p4 = */ -2.36088967922325565496066701598465442657470703125e+0000,
94 -/* p5 = */ 1.38345799501389166152875986881554126739501953125e+0000,
95 -/* p6 = */ 1.06742368078953453469637224770849570631980895996e+0000,
90 +/* one = */
91 + 1.0,
92 +/* p1 = */8.02176624254765935351230154992663301527500152588e-0002,
93 +/* p2 = */1.27223421700559402580665846471674740314483642578e+0000,
94 +/* p3 = */-1.20606901800503640842521235754247754812240600586e+0000,
95 +/* p4 = */-2.36088967922325565496066701598465442657470703125e+0000,
96 +/* p5 = */1.38345799501389166152875986881554126739501953125e+0000,
97 +/* p6 = */1.06742368078953453469637224770849570631980895996e+0000,
96 98 /* q1 = */ -1.42796626333911796935538518482644576579332351685e-0001,
97 -/* q2 = */ 3.51427110447873227059810477159863497078605962912e+0000,
98 -/* q3 = */ 5.92129112708164262457444237952586263418197631836e-0001,
99 +/* q2 = */ 3.51427110447873227059810477159863497078605962912e+0000,
100 +/* q3 = */ 5.92129112708164262457444237952586263418197631836e-0001,
99 101 /* q4 = */ -1.99272234785683144409063061175402253866195678711e+0000,
100 -/* pio2hi */ 1.570796326794896558e+00,
101 -/* pio2lo */ 6.123233995736765886e-17,
102 +/* pio2hi */ 1.570796326794896558e+00,
103 +/* pio2lo */ 6.123233995736765886e-17,
102 104 /* t1 = */ -0.333333333333333333333333333333333,
103 -/* t2 = */ 0.2,
105 +/* t2 = */ 0.2,
104 106 /* t3 = */ -1.666666666666666666666666666666666,
105 107 };
106 108
107 -#define one g[0]
108 -#define p1 g[1]
109 -#define p2 g[2]
110 -#define p3 g[3]
111 -#define p4 g[4]
112 -#define p5 g[5]
113 -#define p6 g[6]
114 -#define q1 g[7]
115 -#define q2 g[8]
116 -#define q3 g[9]
117 -#define q4 g[10]
118 -#define pio2hi g[11]
119 -#define pio2lo g[12]
120 -#define t1 g[13]
121 -#define t2 g[14]
122 -#define t3 g[15]
123 -
109 +#define one g[0]
110 +#define p1 g[1]
111 +#define p2 g[2]
112 +#define p3 g[3]
113 +#define p4 g[4]
114 +#define p5 g[5]
115 +#define p6 g[6]
116 +#define q1 g[7]
117 +#define q2 g[8]
118 +#define q3 g[9]
119 +#define q4 g[10]
120 +#define pio2hi g[11]
121 +#define pio2lo g[12]
122 +#define t1 g[13]
123 +#define t2 g[14]
124 +#define t3 g[15]
124 125
125 126 double
126 -atan(double x) {
127 +atan(double x)
128 +{
127 129 double y, z, r, p, s;
128 130 int ix, lx, hx, j;
129 131
130 - hx = ((int *) &x)[HIWORD];
131 - lx = ((int *) &x)[LOWORD];
132 + hx = ((int *)&x)[HIWORD];
133 + lx = ((int *)&x)[LOWORD];
132 134 ix = hx & ~0x80000000;
133 135 j = ix >> 20;
134 136
135 137 /* for |x| < 1/8 */
136 138 if (j < 0x3fc) {
137 - if (j < 0x3f5) { /* when |x| < 2**(-prec/6-2) */
138 - if (j < 0x3e3) { /* if |x| < 2**(-prec/2-2) */
139 - return ((int) x == 0 ? x : one);
140 - }
139 + if (j < 0x3f5) { /* when |x| < 2**(-prec/6-2) */
140 + if (j < 0x3e3) /* if |x| < 2**(-prec/2-2) */
141 + return ((int)x == 0 ? x : one);
142 +
141 143 if (j < 0x3f1) { /* if |x| < 2**(-prec/4-1) */
142 144 return (x + (x * t1) * (x * x));
143 - } else { /* if |x| < 2**(-prec/6-2) */
145 + } else { /* if |x| < 2**(-prec/6-2) */
144 146 z = x * x;
145 147 s = t2 * x;
146 148 return (x + (t3 + z) * (s * z));
147 149 }
148 150 }
149 - z = x * x; s = p1 * x;
151 +
152 + z = x * x;
153 + s = p1 * x;
150 154 return (x + ((s * z) * (p2 + z * (p3 + z))) *
151 - (((p4 + z) + z * z) * (p5 + z * (p6 + z))));
155 + (((p4 + z) + z * z) * (p5 + z * (p6 + z))));
152 156 }
153 157
154 158 /* for |x| >= 8.0 */
155 159 if (j >= 0x402) {
156 160 if (j < 0x436) {
157 161 r = one / x;
162 +
158 163 if (hx >= 0) {
159 - y = pio2hi; p = pio2lo;
164 + y = pio2hi;
165 + p = pio2lo;
160 166 } else {
161 - y = -pio2hi; p = -pio2lo;
167 + y = -pio2hi;
168 + p = -pio2lo;
162 169 }
170 +
163 171 if (ix < 0x40504000) { /* x < 65 */
164 172 z = r * r;
165 173 s = p1 * r;
166 - return (y + ((p - r) - ((s * z) *
167 - (p2 + z * (p3 + z))) *
168 - (((p4 + z) + z * z) *
169 - (p5 + z * (p6 + z)))));
174 + return (y + ((p - r) - ((s * z) * (p2 + z *
175 + (p3 + z))) * (((p4 + z) + z * z) *
176 + (p5 + z * (p6 + z)))));
170 177 } else if (j < 0x412) {
171 178 z = r * r;
172 - return (y + (p - ((q1 * r) * (q4 + z)) *
173 - (q2 + z * (q3 + z))));
174 - } else
179 + return (y + (p - ((q1 * r) * (q4 + z)) * (q2 +
180 + z * (q3 + z))));
181 + } else {
175 182 return (y + (p - r));
183 + }
176 184 } else {
177 - if (j >= 0x7ff) /* x is inf or NaN */
185 + if (j >= 0x7ff) /* x is inf or NaN */
178 186 if (((ix - 0x7ff00000) | lx) != 0)
179 187 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
180 188 return (ix >= 0x7ff80000 ? x : x - x);
181 - /* assumes sparc-like QNaN */
189 +
190 + /* assumes sparc-like QNaN */
182 191 #else
183 192 return (x - x);
184 193 #endif
185 194 y = -pio2lo;
186 195 return (hx >= 0 ? pio2hi - y : y - pio2hi);
187 196 }
188 - } else { /* now x is between 1/8 and 8 */
197 + } else { /* now x is between 1/8 and 8 */
189 198 double *w, w0, w1, s, z;
190 - w = (double *) _TBL_atan + (((ix - 0x3fc00000) >> 16) << 1);
191 - w0 = (hx >= 0)? w[0] : -w[0];
199 +
200 + w = (double *)_TBL_atan + (((ix - 0x3fc00000) >> 16) << 1);
201 + w0 = (hx >= 0) ? w[0] : -w[0];
192 202 s = (x - w0) / (one + x * w0);
193 - w1 = (hx >= 0)? w[1] : -w[1];
203 + w1 = (hx >= 0) ? w[1] : -w[1];
194 204 z = s * s;
195 205 return (((q1 * s) * (q4 + z)) * (q2 + z * (q3 + z)) + w1);
196 206 }
197 207 }
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