1 | /* Return arc tangent of complex float type. |
2 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <complex.h> |
20 | #include <math.h> |
21 | #include <math_private.h> |
22 | #include <math-underflow.h> |
23 | #include <float.h> |
24 | |
25 | CFLOAT |
26 | M_DECL_FUNC (__catan) (CFLOAT x) |
27 | { |
28 | CFLOAT 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 = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
37 | __imag__ res = M_COPYSIGN (0, __imag__ x); |
38 | } |
39 | else if (icls == FP_INFINITE) |
40 | { |
41 | if (rcls >= FP_ZERO) |
42 | __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
43 | else |
44 | __real__ res = M_NAN; |
45 | __imag__ res = M_COPYSIGN (0, __imag__ x); |
46 | } |
47 | else if (icls == FP_ZERO || icls == FP_INFINITE) |
48 | { |
49 | __real__ res = M_NAN; |
50 | __imag__ res = M_COPYSIGN (0, __imag__ x); |
51 | } |
52 | else |
53 | { |
54 | __real__ res = M_NAN; |
55 | __imag__ res = M_NAN; |
56 | } |
57 | } |
58 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
59 | { |
60 | res = x; |
61 | } |
62 | else |
63 | { |
64 | if (M_FABS (__real__ x) >= 16 / M_EPSILON |
65 | || M_FABS (__imag__ x) >= 16 / M_EPSILON) |
66 | { |
67 | __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
68 | if (M_FABS (__real__ x) <= 1) |
69 | __imag__ res = 1 / __imag__ x; |
70 | else if (M_FABS (__imag__ x) <= 1) |
71 | __imag__ res = __imag__ x / __real__ x / __real__ x; |
72 | else |
73 | { |
74 | FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2); |
75 | __imag__ res = __imag__ x / h / h / 4; |
76 | } |
77 | } |
78 | else |
79 | { |
80 | FLOAT den, absx, absy; |
81 | |
82 | absx = M_FABS (__real__ x); |
83 | absy = M_FABS (__imag__ x); |
84 | if (absx < absy) |
85 | { |
86 | FLOAT t = absx; |
87 | absx = absy; |
88 | absy = t; |
89 | } |
90 | |
91 | if (absy < M_EPSILON / 2) |
92 | { |
93 | den = (1 - absx) * (1 + absx); |
94 | if (den == 0) |
95 | den = 0; |
96 | } |
97 | else if (absx >= 1) |
98 | den = (1 - absx) * (1 + absx) - absy * absy; |
99 | else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5)) |
100 | den = -M_SUF (__x2y2m1) (absx, absy); |
101 | else |
102 | den = (1 - absx) * (1 + absx) - absy * absy; |
103 | |
104 | __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den); |
105 | |
106 | if (M_FABS (__imag__ x) == 1 |
107 | && M_FABS (__real__ x) < M_EPSILON * M_EPSILON) |
108 | __imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x) |
109 | * (M_MLIT (M_LN2) |
110 | - M_LOG (M_FABS (__real__ x)))); |
111 | else |
112 | { |
113 | FLOAT r2 = 0, num, f; |
114 | |
115 | if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON) |
116 | r2 = __real__ x * __real__ x; |
117 | |
118 | num = __imag__ x + 1; |
119 | num = r2 + num * num; |
120 | |
121 | den = __imag__ x - 1; |
122 | den = r2 + den * den; |
123 | |
124 | f = num / den; |
125 | if (f < M_LIT (0.5)) |
126 | __imag__ res = M_LIT (0.25) * M_LOG (f); |
127 | else |
128 | { |
129 | num = 4 * __imag__ x; |
130 | __imag__ res = M_LIT (0.25) * M_LOG1P (num / den); |
131 | } |
132 | } |
133 | } |
134 | |
135 | math_check_force_underflow_complex (res); |
136 | } |
137 | |
138 | return res; |
139 | } |
140 | |
141 | declare_mgen_alias (__catan, catan) |
142 | |