1/* Return arc tangent of complex double value.
2 Copyright (C) 1997-2016 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
19
20#include <complex.h>
21#include <math.h>
22#include <math_private.h>
23#include <float.h>
24
25__complex__ double
26__catan (__complex__ double x)
27{
28 __complex__ double res;
29 int rcls = fpclassify (__real__ x);
30 int icls = fpclassify (__imag__ x);
31
32 if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
33 {
34 if (rcls == FP_INFINITE)
35 {
36 __real__ res = __copysign (M_PI_2, __real__ x);
37 __imag__ res = __copysign (0.0, __imag__ x);
38 }
39 else if (icls == FP_INFINITE)
40 {
41 if (rcls >= FP_ZERO)
42 __real__ res = __copysign (M_PI_2, __real__ x);
43 else
44 __real__ res = __nan ("");
45 __imag__ res = __copysign (0.0, __imag__ x);
46 }
47 else if (icls == FP_ZERO || icls == FP_INFINITE)
48 {
49 __real__ res = __nan ("");
50 __imag__ res = __copysign (0.0, __imag__ x);
51 }
52 else
53 {
54 __real__ res = __nan ("");
55 __imag__ res = __nan ("");
56 }
57 }
58 else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
59 {
60 res = x;
61 }
62 else
63 {
64 if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
65 || fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
66 {
67 __real__ res = __copysign (M_PI_2, __real__ x);
68 if (fabs (__real__ x) <= 1.0)
69 __imag__ res = 1.0 / __imag__ x;
70 else if (fabs (__imag__ x) <= 1.0)
71 __imag__ res = __imag__ x / __real__ x / __real__ x;
72 else
73 {
74 double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
75 __imag__ res = __imag__ x / h / h / 4.0;
76 }
77 }
78 else
79 {
80 double den, absx, absy;
81
82 absx = fabs (__real__ x);
83 absy = fabs (__imag__ x);
84 if (absx < absy)
85 {
86 double t = absx;
87 absx = absy;
88 absy = t;
89 }
90
91 if (absy < DBL_EPSILON / 2.0)
92 {
93 den = (1.0 - absx) * (1.0 + absx);
94 if (den == -0.0)
95 den = 0.0;
96 }
97 else if (absx >= 1.0)
98 den = (1.0 - absx) * (1.0 + absx) - absy * absy;
99 else if (absx >= 0.75 || absy >= 0.5)
100 den = -__x2y2m1 (absx, absy);
101 else
102 den = (1.0 - absx) * (1.0 + absx) - absy * absy;
103
104 __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
105
106 if (fabs (__imag__ x) == 1.0
107 && fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON)
108 __imag__ res = (__copysign (0.5, __imag__ x)
109 * (M_LN2 - __ieee754_log (fabs (__real__ x))));
110 else
111 {
112 double r2 = 0.0, num, f;
113
114 if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON)
115 r2 = __real__ x * __real__ x;
116
117 num = __imag__ x + 1.0;
118 num = r2 + num * num;
119
120 den = __imag__ x - 1.0;
121 den = r2 + den * den;
122
123 f = num / den;
124 if (f < 0.5)
125 __imag__ res = 0.25 * __ieee754_log (f);
126 else
127 {
128 num = 4.0 * __imag__ x;
129 __imag__ res = 0.25 * __log1p (num / den);
130 }
131 }
132 }
133
134 math_check_force_underflow_complex (res);
135 }
136
137 return res;
138}
139weak_alias (__catan, catan)
140#ifdef NO_LONG_DOUBLE
141strong_alias (__catan, __catanl)
142weak_alias (__catan, catanl)
143#endif
144