1 /* $NetBSD: catan.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */
2
3 /*-
4 * Copyright (c) 2007 The NetBSD Foundation, Inc.
5 * All rights reserved.
6 *
7 * This code is derived from software written by Stephen L. Moshier.
8 * It is redistributed by the NetBSD Foundation by permission of the author.
9 *
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
12 * are met:
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in the
17 * documentation and/or other materials provided with the distribution.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29 * POSSIBILITY OF SUCH DAMAGE.
30 *
31 * imported and modified include for newlib 2010/10/03
32 * Marco Atzeri <marco_atzeri@yahoo.it>
33 */
34
35 /*
36 FUNCTION
37 <<catan>>, <<catanf>>---complex arc tangent
38
39 INDEX
40 catan
41 INDEX
42 catanf
43
44 SYNOPSIS
45 #include <complex.h>
46 double complex catan(double complex <[z]>);
47 float complex catanf(float complex <[z]>);
48
49
50 DESCRIPTION
51 @ifnottex
52 These functions compute the complex arc tangent of <[z]>,
53 with branch cuts outside the interval [-i, +i] along the
54 imaginary axis.
55 @end ifnottex
56 @tex
57 These functions compute the complex arc tangent of <[z]>,
58 with branch cuts outside the interval [$-i$, $+i$] along the
59 imaginary axis.
60 @end tex
61
62 <<catanf>> is identical to <<catan>>, except that it performs
63 its calculations on <<floats complex>>.
64
65 RETURNS
66 @ifnottex
67 These functions return the complex arc tangent value, in the range
68 of a strip mathematically unbounded along the imaginary axis
69 and in the interval [-pi/2, +pi/2] along the real axis.
70 @end ifnottex
71 @tex
72 These functions return the complex arc tangent, in the range
73 of a strip mathematically unbounded along the imaginary axis
74 and in the interval [$-\pi/2$, $+\pi/2$] along the real axis.
75 @end tex
76
77 PORTABILITY
78 <<catan>> and <<catanf>> are ISO C99
79
80 QUICKREF
81 <<catan>> and <<catanf>> are ISO C99
82
83 */
84
85
86 #include <complex.h>
87 #include <math.h>
88 #include "cephes_subr.h"
89
90 #ifdef __weak_alias
__weak_alias(catan,_catan)91 __weak_alias(catan, _catan)
92 #endif
93
94 double complex
95 catan(double complex z)
96 {
97 double complex w;
98 double a, t, x, x2, y;
99
100 x = creal(z);
101 y = cimag(z);
102
103 if ((x == 0.0) && (y > 1.0))
104 goto ovrf;
105
106 x2 = x * x;
107 a = 1.0 - x2 - (y * y);
108
109 t = 0.5 * atan2(2.0 * x, a);
110 w = _redupi(t);
111
112 t = y - 1.0;
113 a = x2 + (t * t);
114 if (a == 0.0)
115 goto ovrf;
116
117 t = y + 1.0;
118 a = (x2 + (t * t))/a;
119 w = w + (0.25 * log(a)) * (double complex) I;
120 return w;
121
122 ovrf:
123 #if 0
124 mtherr ("catan", OVERFLOW);
125 #endif
126 w = HUGE_VAL + HUGE_VAL * (double complex) I;
127 return w;
128 }
129
