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d5602ceb | 1 | /* Return arc tangent of complex float type. |
688903eb | 2 | Copyright (C) 1997-2018 Free Software Foundation, Inc. |
f6d3a72e PM |
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 | ||
d5602ceb PM |
25 | CFLOAT |
26 | M_DECL_FUNC (__catan) (CFLOAT x) | |
f6d3a72e | 27 | { |
d5602ceb | 28 | CFLOAT res; |
f6d3a72e PM |
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 | { | |
d5602ceb PM |
36 | __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
37 | __imag__ res = M_COPYSIGN (0, __imag__ x); | |
f6d3a72e PM |
38 | } |
39 | else if (icls == FP_INFINITE) | |
40 | { | |
41 | if (rcls >= FP_ZERO) | |
d5602ceb | 42 | __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
f6d3a72e | 43 | else |
d5602ceb PM |
44 | __real__ res = M_NAN; |
45 | __imag__ res = M_COPYSIGN (0, __imag__ x); | |
f6d3a72e PM |
46 | } |
47 | else if (icls == FP_ZERO || icls == FP_INFINITE) | |
48 | { | |
d5602ceb PM |
49 | __real__ res = M_NAN; |
50 | __imag__ res = M_COPYSIGN (0, __imag__ x); | |
f6d3a72e PM |
51 | } |
52 | else | |
53 | { | |
d5602ceb PM |
54 | __real__ res = M_NAN; |
55 | __imag__ res = M_NAN; | |
f6d3a72e PM |
56 | } |
57 | } | |
58 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) | |
59 | { | |
60 | res = x; | |
61 | } | |
62 | else | |
63 | { | |
d5602ceb PM |
64 | if (M_FABS (__real__ x) >= 16 / M_EPSILON |
65 | || M_FABS (__imag__ x) >= 16 / M_EPSILON) | |
f6d3a72e | 66 | { |
d5602ceb PM |
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) | |
f6d3a72e PM |
71 | __imag__ res = __imag__ x / __real__ x / __real__ x; |
72 | else | |
73 | { | |
d5602ceb PM |
74 | FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2); |
75 | __imag__ res = __imag__ x / h / h / 4; | |
f6d3a72e PM |
76 | } |
77 | } | |
78 | else | |
79 | { | |
d5602ceb | 80 | FLOAT den, absx, absy; |
f6d3a72e | 81 | |
d5602ceb PM |
82 | absx = M_FABS (__real__ x); |
83 | absy = M_FABS (__imag__ x); | |
f6d3a72e PM |
84 | if (absx < absy) |
85 | { | |
d5602ceb | 86 | FLOAT t = absx; |
f6d3a72e PM |
87 | absx = absy; |
88 | absy = t; | |
89 | } | |
90 | ||
d5602ceb | 91 | if (absy < M_EPSILON / 2) |
f6d3a72e | 92 | { |
d5602ceb PM |
93 | den = (1 - absx) * (1 + absx); |
94 | if (den == 0) | |
95 | den = 0; | |
f6d3a72e | 96 | } |
d5602ceb PM |
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); | |
f6d3a72e | 101 | else |
d5602ceb | 102 | den = (1 - absx) * (1 + absx) - absy * absy; |
f6d3a72e | 103 | |
d5602ceb | 104 | __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den); |
f6d3a72e | 105 | |
d5602ceb PM |
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 | * ((FLOAT) M_MLIT (M_LN2) | |
110 | - M_LOG (M_FABS (__real__ x)))); | |
f6d3a72e PM |
111 | else |
112 | { | |
d5602ceb | 113 | FLOAT r2 = 0, num, f; |
f6d3a72e | 114 | |
d5602ceb | 115 | if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON) |
f6d3a72e PM |
116 | r2 = __real__ x * __real__ x; |
117 | ||
d5602ceb | 118 | num = __imag__ x + 1; |
f6d3a72e PM |
119 | num = r2 + num * num; |
120 | ||
d5602ceb | 121 | den = __imag__ x - 1; |
f6d3a72e PM |
122 | den = r2 + den * den; |
123 | ||
124 | f = num / den; | |
d5602ceb PM |
125 | if (f < M_LIT (0.5)) |
126 | __imag__ res = M_LIT (0.25) * M_LOG (f); | |
f6d3a72e PM |
127 | else |
128 | { | |
d5602ceb PM |
129 | num = 4 * __imag__ x; |
130 | __imag__ res = M_LIT (0.25) * M_LOG1P (num / den); | |
f6d3a72e PM |
131 | } |
132 | } | |
133 | } | |
134 | ||
135 | math_check_force_underflow_complex (res); | |
136 | } | |
137 | ||
138 | return res; | |
139 | } | |
d5602ceb PM |
140 | |
141 | declare_mgen_alias (__catan, catan) |