xref: /illumos-gate/usr/src/lib/libm/common/complex/clog.c (revision 856f710c9dc323b39da5935194d7928ffb99b67f)
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 #pragma weak clog = __clog
30 
31 /* INDENT OFF */
32 /*
33  * dcomplex clog(dcomplex z);
34  *
35  *                    _________
36  *                   / 2    2            -1   y
37  * log(x+iy) = log(\/ x  + y    ) + i tan   (---)
38  *                                            x
39  *
40  *              1       2    2         -1   y
41  *           = --- log(x  + y ) + i tan   (---)
42  *              2                           x
43  *
44  * Note that the arctangent ranges from -PI to +PI, thus the imaginary
45  * part of clog is atan2(y,x).
46  *
47  * EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)):
48  *    clog(-0 + i 0   ) =  -inf + i pi
49  *    clog( 0 + i 0   ) =  -inf + i 0
50  *    clog( x + i inf ) =  -inf + i pi/2, for finite x
51  *    clog( x + i NaN ) =  NaN  + i NaN with invalid for finite x
52  *    clog(-inf + iy   )=  +inf + i pi, for finite positive-signed y
53  *    clog(+inf + iy   )=  +inf + i 0 , for finite positive-signed y
54  *    clog(-inf + i inf)=  inf  + i 3pi/4
55  *    clog(+inf + i inf)=  inf  + i pi/4
56  *    clog(+-inf+ i NaN)=  inf  + i NaN
57  *    clog(NaN  + i y  )=  NaN  + i NaN for finite y
58  *    clog(NaN  + i inf)=  inf  + i NaN
59  *    clog(NaN  + i NaN)=  NaN  + i NaN
60  */
61 /* INDENT ON */
62 
63 #include <math.h>		/* atan2/fabs/log/log1p */
64 #include "complex_wrapper.h"
65 #include "libm_protos.h"	/* __k_clog_r */
66 
67 
68 static const double half = 0.5, one = 1.0;
69 
70 dcomplex
71 __clog(dcomplex z) {
72 	dcomplex	ans;
73 	double		x, y, t, ax, ay, w;
74 	int		n, ix, iy, hx, hy;
75 	unsigned	lx, ly;
76 
77 	x = D_RE(z);
78 	y = D_IM(z);
79 	hx = HI_WORD(x);
80 	lx = LO_WORD(x);
81 	hy = HI_WORD(y);
82 	ly = LO_WORD(y);
83 	ix = hx & 0x7fffffff;
84 	iy = hy & 0x7fffffff;
85 	ay = fabs(y);
86 	ax = fabs(x);
87 	D_IM(ans) = carg(z);
88 	if (ix < iy || (ix == iy && lx < ly)) {
89 		/* swap x and y to force ax >= ay */
90 		t = ax;
91 		ax = ay;
92 		ay = t;
93 		n = ix, ix = iy;
94 		iy = n;
95 		n = lx, lx = ly;
96 		ly = n;
97 	}
98 	n = (ix - iy) >> 20;
99 	if (ix >= 0x7ff00000) {	/* x or y is Inf or NaN */
100 		if (ISINF(ix, lx))
101 			D_RE(ans) = ax;
102 		else if (ISINF(iy, ly))
103 			D_RE(ans) = ay;
104 		else
105 			D_RE(ans) = ax * ay;
106 	} else if ((iy | ly) == 0) {
107 		D_RE(ans) = ((ix | lx) == 0)? -one / ax : log(ax);
108 	} else if (((0x3fffffff - ix) ^ (ix - 0x3fe00000)) >= 0) {
109 		/* 0.5 <= x < 2 */
110 		if (ix >= 0x3ff00000) {
111 			if (((ix - 0x3ff00000) | lx) == 0)
112 				D_RE(ans) = half * log1p(ay * ay);
113 			else if (n >= 60)
114 				D_RE(ans) = log(ax);
115 			else
116 				D_RE(ans) = half * (log1p(ay * ay + (ax -
117 				    one) * (ax + one)));
118 		} else if (n >= 60) {
119 			D_RE(ans) = log(ax);
120 		} else {
121 			D_RE(ans) = __k_clog_r(ax, ay, &w);
122 		}
123 	} else if (n >= 30) {
124 		D_RE(ans) = log(ax);
125 	} else if (ix < 0x5f300000 && iy >= 0x20b00000) {
126 		/* 2**-500< y < x < 2**500 */
127 		D_RE(ans) = half * log(ax * ax + ay * ay);
128 	} else {
129 		t = ay / ax;
130 		D_RE(ans) = log(ax) + half * log1p(t * t);
131 	}
132 	return (ans);
133 }
134