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 catanf = __catanf
30
31 #include "libm.h"
32 #include "complex_wrapper.h"
33
34 #if defined(__i386) && !defined(__amd64)
35 extern int __swapRP(int);
36 #endif
37
38 static const float
39 pi_2 = 1.570796326794896558e+00F,
40 zero = 0.0F,
41 half = 0.5F,
42 two = 2.0F,
43 one = 1.0F;
44
45 fcomplex
46 catanf(fcomplex z) {
47 fcomplex ans;
48 float x, y, ax, ay, t;
49 double dx, dy, dt;
50 int hx, hy, ix, iy;
51
52 x = F_RE(z);
53 y = F_IM(z);
54 ax = fabsf(x);
55 ay = fabsf(y);
56 hx = THE_WORD(x);
57 hy = THE_WORD(y);
58 ix = hx & 0x7fffffff;
59 iy = hy & 0x7fffffff;
60
61 if (ix >= 0x7f800000) { /* x is inf or NaN */
62 if (ix == 0x7f800000) {
63 F_RE(ans) = pi_2;
64 F_IM(ans) = zero;
65 } else {
66 F_RE(ans) = x * x;
67 if (iy == 0 || iy == 0x7f800000)
68 F_IM(ans) = zero;
69 else
70 F_IM(ans) = (fabsf(y) - ay) / (fabsf(y) - ay);
71 }
72 } else if (iy >= 0x7f800000) { /* y is inf or NaN */
73 if (iy == 0x7f800000) {
74 F_RE(ans) = pi_2;
75 F_IM(ans) = zero;
76 } else {
77 F_RE(ans) = (fabsf(x) - ax) / (fabsf(x) - ax);
78 F_IM(ans) = y * y;
79 }
80 } else if (ix == 0) {
81 /* INDENT OFF */
82 /*
83 * x = 0
84 * 1 1
85 * A = --- * atan2(2x, 1-x*x-y*y) = --- atan2(0,1-|y|)
86 * 2 2
87 *
88 * 1 [ (y+1)*(y+1) ] 1 2 1 2y
89 * B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
90 * 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
91 */
92 /* INDENT ON */
93 t = one - ay;
94 if (iy == 0x3f800000) {
95 /* y=1: catan(0,1)=(0,+inf) with 1/0 signal */
96 F_IM(ans) = ay / ax;
97 F_RE(ans) = zero;
98 } else if (iy > 0x3f800000) { /* y>1 */
99 F_IM(ans) = half * log1pf(two / (-t));
100 F_RE(ans) = pi_2;
101 } else { /* y<1 */
102 F_IM(ans) = half * log1pf((ay + ay) / t);
103 F_RE(ans) = zero;
104 }
105 } else {
106 /* INDENT OFF */
107 /*
108 * use double precision x,y
109 * 1
110 * A = --- * atan2(2x, 1-x*x-y*y)
111 * 2
112 *
113 * 1 [ x*x+(y+1)*(y+1) ] 1 4y
114 * B = - log [ --------------- ] = - log (1+ -----------------)
115 * 4 [ x*x+(y-1)*(y-1) ] 4 x*x + (y-1)*(y-1)
116 */
117 /* INDENT ON */
118 #if defined(__i386) && !defined(__amd64)
119 int rp = __swapRP(fp_extended);
120 #endif
121 dx = (double)ax;
122 dy = (double)ay;
123 F_RE(ans) = (float)(0.5 * atan2(dx + dx,
124 1.0 - dx * dx - dy * dy));
125 dt = dy - 1.0;
126 F_IM(ans) = (float)(0.25 * log1p(4.0 * dy /
127 (dx * dx + dt * dt)));
128 #if defined(__i386) && !defined(__amd64)
129 if (rp != fp_extended)
130 (void) __swapRP(rp);
131 #endif
132 }
133 if (hx < 0)
134 F_RE(ans) = -F_RE(ans);
135 if (hy < 0)
136 F_IM(ans) = -F_IM(ans);
137 return (ans);
138 }