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1 | /* Return arc hyperbole tangent for 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 | __catanh (__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 (icls == FP_INFINITE) | |
35 | { | |
36 | __real__ res = __copysign (0.0, __real__ x); | |
37 | __imag__ res = __copysign (M_PI_2, __imag__ x); | |
38 | } | |
39 | else if (rcls == FP_INFINITE || rcls == FP_ZERO) | |
40 | { | |
41 | __real__ res = __copysign (0.0, __real__ x); | |
42 | if (icls >= FP_ZERO) | |
43 | __imag__ res = __copysign (M_PI_2, __imag__ x); | |
44 | else | |
45 | __imag__ res = __nan (""); | |
46 | } | |
47 | else | |
48 | { | |
49 | __real__ res = __nan (""); | |
50 | __imag__ res = __nan (""); | |
51 | } | |
52 | } | |
53 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) | |
54 | { | |
55 | res = x; | |
56 | } | |
57 | else | |
58 | { | |
59 | if (fabs (__real__ x) >= 16.0 / DBL_EPSILON | |
60 | || fabs (__imag__ x) >= 16.0 / DBL_EPSILON) | |
61 | { | |
62 | __imag__ res = __copysign (M_PI_2, __imag__ x); | |
63 | if (fabs (__imag__ x) <= 1.0) | |
64 | __real__ res = 1.0 / __real__ x; | |
65 | else if (fabs (__real__ x) <= 1.0) | |
66 | __real__ res = __real__ x / __imag__ x / __imag__ x; | |
67 | else | |
68 | { | |
69 | double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0); | |
70 | __real__ res = __real__ x / h / h / 4.0; | |
71 | } | |
72 | } | |
73 | else | |
74 | { | |
75 | if (fabs (__real__ x) == 1.0 | |
76 | && fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON) | |
77 | __real__ res = (__copysign (0.5, __real__ x) | |
78 | * (M_LN2 - __ieee754_log (fabs (__imag__ x)))); | |
79 | else | |
80 | { | |
81 | double i2 = 0.0; | |
82 | if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON) | |
83 | i2 = __imag__ x * __imag__ x; | |
84 | ||
85 | double num = 1.0 + __real__ x; | |
86 | num = i2 + num * num; | |
87 | ||
88 | double den = 1.0 - __real__ x; | |
89 | den = i2 + den * den; | |
90 | ||
91 | double f = num / den; | |
92 | if (f < 0.5) | |
93 | __real__ res = 0.25 * __ieee754_log (f); | |
94 | else | |
95 | { | |
96 | num = 4.0 * __real__ x; | |
97 | __real__ res = 0.25 * __log1p (num / den); | |
98 | } | |
99 | } | |
100 | ||
101 | double absx, absy, den; | |
102 | ||
103 | absx = fabs (__real__ x); | |
104 | absy = fabs (__imag__ x); | |
105 | if (absx < absy) | |
106 | { | |
107 | double t = absx; | |
108 | absx = absy; | |
109 | absy = t; | |
110 | } | |
111 | ||
112 | if (absy < DBL_EPSILON / 2.0) | |
113 | { | |
114 | den = (1.0 - absx) * (1.0 + absx); | |
115 | if (den == -0.0) | |
116 | den = 0.0; | |
117 | } | |
118 | else if (absx >= 1.0) | |
119 | den = (1.0 - absx) * (1.0 + absx) - absy * absy; | |
120 | else if (absx >= 0.75 || absy >= 0.5) | |
121 | den = -__x2y2m1 (absx, absy); | |
122 | else | |
123 | den = (1.0 - absx) * (1.0 + absx) - absy * absy; | |
124 | ||
125 | __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den); | |
126 | } | |
127 | ||
128 | math_check_force_underflow_complex (res); | |
129 | } | |
130 | ||
131 | return res; | |
132 | } | |
133 | weak_alias (__catanh, catanh) | |
134 | #ifdef NO_LONG_DOUBLE | |
135 | strong_alias (__catanh, __catanhl) | |
136 | weak_alias (__catanh, catanhl) | |
137 | #endif |