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 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25
26 /*
27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak clog = __clog
32
33
34 /*
35 * dcomplex clog(dcomplex z);
36 *
37 * _________
38 * / 2 2 -1 y
39 * log(x+iy) = log(\/ x + y ) + i tan (---)
40 * x
41 *
42 * 1 2 2 -1 y
43 * = --- log(x + y ) + i tan (---)
44 * 2 x
45 *
46 * Note that the arctangent ranges from -PI to +PI, thus the imaginary
47 * part of clog is atan2(y,x).
48 *
49 * EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)):
50 * clog(-0 + i 0 ) = -inf + i pi
51 * clog( 0 + i 0 ) = -inf + i 0
52 * clog( x + i inf ) = -inf + i pi/2, for finite x
53 * clog( x + i NaN ) = NaN + i NaN with invalid for finite x
54 * clog(-inf + iy )= +inf + i pi, for finite positive-signed y
55 * clog(+inf + iy )= +inf + i 0 , for finite positive-signed y
56 * clog(-inf + i inf)= inf + i 3pi/4
57 * clog(+inf + i inf)= inf + i pi/4
58 * clog(+-inf+ i NaN)= inf + i NaN
59 * clog(NaN + i y )= NaN + i NaN for finite y
60 * clog(NaN + i inf)= inf + i NaN
61 * clog(NaN + i NaN)= NaN + i NaN
62 */
63
64 #include <math.h> /* atan2/fabs/log/log1p */
65 #include "complex_wrapper.h"
66 #include "libm_protos.h" /* __k_clog_r */
67
68 static const double half = 0.5, one = 1.0;
69
70 dcomplex
71 __clog(dcomplex z)
72 {
73 dcomplex ans;
74 double x, y, t, ax, ay, w;
75 int n, ix, iy, hx, hy;
76 unsigned lx, ly;
77
78 x = D_RE(z);
79 y = D_IM(z);
80 hx = HI_WORD(x);
81 lx = LO_WORD(x);
82 hy = HI_WORD(y);
83 ly = LO_WORD(y);
84 ix = hx & 0x7fffffff;
85 iy = hy & 0x7fffffff;
86 ay = fabs(y);
87 ax = fabs(x);
88 D_IM(ans) = carg(z);
89
90 if (ix < iy || (ix == iy && lx < ly)) {
91 /* swap x and y to force ax >= ay */
92 t = ax;
93 ax = ay;
94 ay = t;
95 n = ix, ix = iy;
96 iy = n;
97 n = lx, lx = ly;
98 ly = n;
99 }
100
101 n = (ix - iy) >> 20;
102
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 - one) *
121 (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
137 return (ans);
138 }