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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 /*
30 * avoids: <built-in>: error: function 'clog' part of alias cycle
31 * Unclear if this is bug in compiler or not
32 * #pragma weak clog = __clog
33 */
34
35 /* INDENT OFF */
36 /*
37 * dcomplex clog(dcomplex z);
38 *
39 * _________
40 * / 2 2 -1 y
41 * log(x+iy) = log(\/ x + y ) + i tan (---)
42 * x
43 *
44 * 1 2 2 -1 y
45 * = --- log(x + y ) + i tan (---)
46 * 2 x
47 *
48 * Note that the arctangent ranges from -PI to +PI, thus the imaginary
49 * part of clog is atan2(y,x).
50 *
51 * EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)):
52 * clog(-0 + i 0 ) = -inf + i pi
53 * clog( 0 + i 0 ) = -inf + i 0
54 * clog( x + i inf ) = -inf + i pi/2, for finite x
55 * clog( x + i NaN ) = NaN + i NaN with invalid for finite x
56 * clog(-inf + iy )= +inf + i pi, for finite positive-signed y
57 * clog(+inf + iy )= +inf + i 0 , for finite positive-signed y
58 * clog(-inf + i inf)= inf + i 3pi/4
59 * clog(+inf + i inf)= inf + i pi/4
60 * clog(+-inf+ i NaN)= inf + i NaN
61 * clog(NaN + i y )= NaN + i NaN for finite y
62 * clog(NaN + i inf)= inf + i NaN
63 * clog(NaN + i NaN)= NaN + i NaN
64 */
65 /* INDENT ON */
66
67 #include <math.h> /* atan2/fabs/log/log1p */
68 #include "complex_wrapper.h"
69 #include "libm_protos.h" /* __k_clog_r */
70
71
72 static const double half = 0.5, one = 1.0;
73
74 dcomplex
__clog(dcomplex z)75 __clog(dcomplex z) {
76 dcomplex ans;
77 double x, y, t, ax, ay, w;
78 int n, ix, iy, hx, hy;
79 unsigned lx, ly;
80
81 x = D_RE(z);
82 y = D_IM(z);
83 hx = HI_WORD(x);
84 lx = LO_WORD(x);
85 hy = HI_WORD(y);
86 ly = LO_WORD(y);
87 ix = hx & 0x7fffffff;
88 iy = hy & 0x7fffffff;
89 ay = fabs(y);
90 ax = fabs(x);
91 D_IM(ans) = carg(z);
92 if (ix < iy || (ix == iy && lx < ly)) {
93 /* swap x and y to force ax >= ay */
94 t = ax;
95 ax = ay;
96 ay = t;
97 n = ix, ix = iy;
98 iy = n;
99 n = lx, lx = ly;
100 ly = n;
101 }
102 n = (ix - iy) >> 20;
103 if (ix >= 0x7ff00000) { /* x or y is Inf or NaN */
104 if (ISINF(ix, lx))
105 D_RE(ans) = ax;
106 else if (ISINF(iy, ly))
107 D_RE(ans) = ay;
108 else
109 D_RE(ans) = ax * ay;
110 } else if ((iy | ly) == 0) {
111 D_RE(ans) = ((ix | lx) == 0)? -one / ax : log(ax);
112 } else if (((0x3fffffff - ix) ^ (ix - 0x3fe00000)) >= 0) {
113 /* 0.5 <= x < 2 */
114 if (ix >= 0x3ff00000) {
115 if (((ix - 0x3ff00000) | lx) == 0)
116 D_RE(ans) = half * log1p(ay * ay);
117 else if (n >= 60)
118 D_RE(ans) = log(ax);
119 else
120 D_RE(ans) = half * (log1p(ay * ay + (ax -
121 one) * (ax + one)));
122 } else if (n >= 60) {
123 D_RE(ans) = log(ax);
124 } else {
125 D_RE(ans) = __k_clog_r(ax, ay, &w);
126 }
127 } else if (n >= 30) {
128 D_RE(ans) = log(ax);
129 } else if (ix < 0x5f300000 && iy >= 0x20b00000) {
130 /* 2**-500< y < x < 2**500 */
131 D_RE(ans) = half * log(ax * ax + ay * ay);
132 } else {
133 t = ay / ax;
134 D_RE(ans) = log(ax) + half * log1p(t * t);
135 }
136 return (ans);
137 }
138