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192.168.1.100 / T106_DC / 936fd5427a62002666663634b68e00331e05f88a / . / ap / libc / glibc / glibc-2.23 / math / s_catanh.c
blob: 11ea06246eb0c04b0b66aeb18f97ab342f454acf [file] [log] [blame]
xf.libdd93d52023-05-12 07:10:14 -0700[diff] [blame]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}
133weak_alias (__catanh, catanh)
134#ifdef NO_LONG_DOUBLE
135strong_alias (__catanh, __catanhl)
136weak_alias (__catanh, catanhl)
137#endif