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d5602ceb | 1 | /* Return arc hyperbolic tangent for a complex float type. |
dff8da6b | 2 | Copyright (C) 1997-2024 Free Software Foundation, Inc. |
f6d3a72e | 3 | This file is part of the GNU C Library. |
f6d3a72e PM |
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 | |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
f6d3a72e PM |
18 | |
19 | #include <complex.h> | |
20 | #include <math.h> | |
21 | #include <math_private.h> | |
8f5b00d3 | 22 | #include <math-underflow.h> |
f6d3a72e PM |
23 | #include <float.h> |
24 | ||
d5602ceb PM |
25 | CFLOAT |
26 | M_DECL_FUNC (__catanh) (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 (icls == FP_INFINITE) | |
35 | { | |
d5602ceb PM |
36 | __real__ res = M_COPYSIGN (0, __real__ x); |
37 | __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x); | |
f6d3a72e PM |
38 | } |
39 | else if (rcls == FP_INFINITE || rcls == FP_ZERO) | |
40 | { | |
d5602ceb | 41 | __real__ res = M_COPYSIGN (0, __real__ x); |
f6d3a72e | 42 | if (icls >= FP_ZERO) |
d5602ceb | 43 | __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x); |
f6d3a72e | 44 | else |
d5602ceb | 45 | __imag__ res = M_NAN; |
f6d3a72e PM |
46 | } |
47 | else | |
48 | { | |
d5602ceb PM |
49 | __real__ res = M_NAN; |
50 | __imag__ res = M_NAN; | |
f6d3a72e PM |
51 | } |
52 | } | |
53 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) | |
54 | { | |
55 | res = x; | |
56 | } | |
57 | else | |
58 | { | |
d5602ceb PM |
59 | if (M_FABS (__real__ x) >= 16 / M_EPSILON |
60 | || M_FABS (__imag__ x) >= 16 / M_EPSILON) | |
f6d3a72e | 61 | { |
d5602ceb PM |
62 | __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x); |
63 | if (M_FABS (__imag__ x) <= 1) | |
64 | __real__ res = 1 / __real__ x; | |
65 | else if (M_FABS (__real__ x) <= 1) | |
f6d3a72e PM |
66 | __real__ res = __real__ x / __imag__ x / __imag__ x; |
67 | else | |
68 | { | |
d5602ceb PM |
69 | FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2); |
70 | __real__ res = __real__ x / h / h / 4; | |
f6d3a72e PM |
71 | } |
72 | } | |
73 | else | |
74 | { | |
d5602ceb PM |
75 | if (M_FABS (__real__ x) == 1 |
76 | && M_FABS (__imag__ x) < M_EPSILON * M_EPSILON) | |
77 | __real__ res = (M_COPYSIGN (M_LIT (0.5), __real__ x) | |
347a5b59 | 78 | * (M_MLIT (M_LN2) |
d5602ceb | 79 | - M_LOG (M_FABS (__imag__ x)))); |
f6d3a72e PM |
80 | else |
81 | { | |
d5602ceb PM |
82 | FLOAT i2 = 0; |
83 | if (M_FABS (__imag__ x) >= M_EPSILON * M_EPSILON) | |
f6d3a72e PM |
84 | i2 = __imag__ x * __imag__ x; |
85 | ||
d5602ceb | 86 | FLOAT num = 1 + __real__ x; |
f6d3a72e PM |
87 | num = i2 + num * num; |
88 | ||
d5602ceb | 89 | FLOAT den = 1 - __real__ x; |
f6d3a72e PM |
90 | den = i2 + den * den; |
91 | ||
d5602ceb PM |
92 | FLOAT f = num / den; |
93 | if (f < M_LIT (0.5)) | |
94 | __real__ res = M_LIT (0.25) * M_LOG (f); | |
f6d3a72e PM |
95 | else |
96 | { | |
d5602ceb PM |
97 | num = 4 * __real__ x; |
98 | __real__ res = M_LIT (0.25) * M_LOG1P (num / den); | |
f6d3a72e PM |
99 | } |
100 | } | |
101 | ||
d5602ceb | 102 | FLOAT absx, absy, den; |
f6d3a72e | 103 | |
d5602ceb PM |
104 | absx = M_FABS (__real__ x); |
105 | absy = M_FABS (__imag__ x); | |
f6d3a72e PM |
106 | if (absx < absy) |
107 | { | |
d5602ceb | 108 | FLOAT t = absx; |
f6d3a72e PM |
109 | absx = absy; |
110 | absy = t; | |
111 | } | |
112 | ||
d5602ceb | 113 | if (absy < M_EPSILON / 2) |
f6d3a72e | 114 | { |
d5602ceb PM |
115 | den = (1 - absx) * (1 + absx); |
116 | if (den == 0) | |
117 | den = 0; | |
f6d3a72e | 118 | } |
d5602ceb PM |
119 | else if (absx >= 1) |
120 | den = (1 - absx) * (1 + absx) - absy * absy; | |
121 | else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5)) | |
122 | den = -M_SUF (__x2y2m1) (absx, absy); | |
f6d3a72e | 123 | else |
d5602ceb | 124 | den = (1 - absx) * (1 + absx) - absy * absy; |
f6d3a72e | 125 | |
d5602ceb | 126 | __imag__ res = M_LIT (0.5) * M_ATAN2 (2 * __imag__ x, den); |
f6d3a72e PM |
127 | } |
128 | ||
129 | math_check_force_underflow_complex (res); | |
130 | } | |
131 | ||
132 | return res; | |
133 | } | |
d5602ceb PM |
134 | |
135 | declare_mgen_alias (__catanh, catanh) |