1/* Return arc tangent of complex float type.
2 Copyright (C) 1997-2020 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 <https://www.gnu.org/licenses/>. */
19
20#include <complex.h>
21#include <math.h>
22#include <math_private.h>
23#include <math-underflow.h>
24#include <float.h>
25
26CFLOAT
27M_DECL_FUNC (__catan) (CFLOAT x)
28{
29 CFLOAT res;
30 int rcls = fpclassify (__real__ x);
31 int icls = fpclassify (__imag__ x);
32
33 if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
34 {
35 if (rcls == FP_INFINITE)
36 {
37 __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
38 __imag__ res = M_COPYSIGN (0, __imag__ x);
39 }
40 else if (icls == FP_INFINITE)
41 {
42 if (rcls >= FP_ZERO)
43 __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
44 else
45 __real__ res = M_NAN;
46 __imag__ res = M_COPYSIGN (0, __imag__ x);
47 }
48 else if (icls == FP_ZERO || icls == FP_INFINITE)
49 {
50 __real__ res = M_NAN;
51 __imag__ res = M_COPYSIGN (0, __imag__ x);
52 }
53 else
54 {
55 __real__ res = M_NAN;
56 __imag__ res = M_NAN;
57 }
58 }
59 else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
60 {
61 res = x;
62 }
63 else
64 {
65 if (M_FABS (__real__ x) >= 16 / M_EPSILON
66 || M_FABS (__imag__ x) >= 16 / M_EPSILON)
67 {
68 __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
69 if (M_FABS (__real__ x) <= 1)
70 __imag__ res = 1 / __imag__ x;
71 else if (M_FABS (__imag__ x) <= 1)
72 __imag__ res = __imag__ x / __real__ x / __real__ x;
73 else
74 {
75 FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
76 __imag__ res = __imag__ x / h / h / 4;
77 }
78 }
79 else
80 {
81 FLOAT den, absx, absy;
82
83 absx = M_FABS (__real__ x);
84 absy = M_FABS (__imag__ x);
85 if (absx < absy)
86 {
87 FLOAT t = absx;
88 absx = absy;
89 absy = t;
90 }
91
92 if (absy < M_EPSILON / 2)
93 {
94 den = (1 - absx) * (1 + absx);
95 if (den == 0)
96 den = 0;
97 }
98 else if (absx >= 1)
99 den = (1 - absx) * (1 + absx) - absy * absy;
100 else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
101 den = -M_SUF (__x2y2m1) (absx, absy);
102 else
103 den = (1 - absx) * (1 + absx) - absy * absy;
104
105 __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den);
106
107 if (M_FABS (__imag__ x) == 1
108 && M_FABS (__real__ x) < M_EPSILON * M_EPSILON)
109 __imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x)
110 * ((FLOAT) M_MLIT (M_LN2)
111 - M_LOG (M_FABS (__real__ x))));
112 else
113 {
114 FLOAT r2 = 0, num, f;
115
116 if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON)
117 r2 = __real__ x * __real__ x;
118
119 num = __imag__ x + 1;
120 num = r2 + num * num;
121
122 den = __imag__ x - 1;
123 den = r2 + den * den;
124
125 f = num / den;
126 if (f < M_LIT (0.5))
127 __imag__ res = M_LIT (0.25) * M_LOG (f);
128 else
129 {
130 num = 4 * __imag__ x;
131 __imag__ res = M_LIT (0.25) * M_LOG1P (num / den);
132 }
133 }
134 }
135
136 math_check_force_underflow_complex (res);
137 }
138
139 return res;
140}
141
142declare_mgen_alias (__catan, catan)
143