1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
|
/* Return arc tangent of complex double value.
Copyright (C) 1997-2013 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <complex.h>
#include <math.h>
#include <math_private.h>
#include <float.h>
__complex__ double
__catan (__complex__ double x)
{
__complex__ double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (rcls == FP_INFINITE)
{
__real__ res = __copysign (M_PI_2, __real__ x);
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (icls == FP_INFINITE)
{
if (rcls >= FP_ZERO)
__real__ res = __copysign (M_PI_2, __real__ x);
else
__real__ res = __nan ("");
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (icls == FP_ZERO || icls == FP_INFINITE)
{
__real__ res = __nan ("");
__imag__ res = __copysign (0.0, __imag__ x);
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
res = x;
}
else
{
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
{
__real__ res = __copysign (M_PI_2, __real__ x);
if (fabs (__real__ x) <= 1.0)
__imag__ res = 1.0 / __imag__ x;
else if (fabs (__imag__ x) <= 1.0)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
__imag__ res = __imag__ x / h / h / 4.0;
}
}
else
{
double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
num = __imag__ x + 1.0;
num = r2 + num * num;
den = __imag__ x - 1.0;
den = r2 + den * den;
f = num / den;
if (f < 0.5)
__imag__ res = 0.25 * __ieee754_log (f);
else
{
num = 4.0 * __imag__ x;
__imag__ res = 0.25 * __log1p (num / den);
}
}
if (fabs (__real__ res) < DBL_MIN)
{
volatile double force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
if (fabs (__imag__ res) < DBL_MIN)
{
volatile double force_underflow = __imag__ res * __imag__ res;
(void) force_underflow;
}
}
return res;
}
weak_alias (__catan, catan)
#ifdef NO_LONG_DOUBLE
strong_alias (__catan, __catanl)
weak_alias (__catan, catanl)
#endif
|
