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
|
'\" t
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" and Copyright (C) 2011 Michael Kerrisk <mtk.manpages@gmail.com>
.\"
.\" SPDX-License-Identifier: GPL-1.0-or-later
.\"
.TH catanh 3 2024-06-15 "Linux man-pages (unreleased)"
.SH NAME
catanh, catanhf, catanhl \- complex arc tangents hyperbolic
.SH LIBRARY
Math library
.RI ( libm ", " \-lm )
.SH SYNOPSIS
.nf
.B #include <complex.h>
.P
.BI "double complex catanh(double complex " z );
.BI "float complex catanhf(float complex " z );
.BI "long double complex catanhl(long double complex " z );
.fi
.SH DESCRIPTION
These functions calculate the complex arc hyperbolic tangent of
.IR z .
If \fIy\~=\~catanh(z)\fP, then \fIz\~=\~ctanh(y)\fP.
The imaginary part of
.I y
is chosen in the interval [\-pi/2,pi/2].
.P
One has:
.P
.in +4n
.EX
catanh(z) = 0.5 * (clog(1 + z) \- clog(1 \- z))
.EE
.in
.SH ATTRIBUTES
For an explanation of the terms used in this section, see
.BR attributes (7).
.TS
allbox;
lbx lb lb
l l l.
Interface Attribute Value
T{
.na
.nh
.BR catanh (),
.BR catanhf (),
.BR catanhl ()
T} Thread safety MT-Safe
.TE
.SH STANDARDS
C11, POSIX.1-2008.
.SH HISTORY
glibc 2.1.
C99, POSIX.1-2001.
.SH EXAMPLES
.\" SRC BEGIN (catanh.c)
.EX
/* Link with "\-lm" */
\&
#include <complex.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
\&
int
main(int argc, char *argv[])
{
double complex z, c, f;
\&
if (argc != 3) {
fprintf(stderr, "Usage: %s <real> <imag>\[rs]n", argv[0]);
exit(EXIT_FAILURE);
}
\&
z = atof(argv[1]) + atof(argv[2]) * I;
\&
c = catanh(z);
printf("catanh() = %6.3f %6.3f*i\[rs]n", creal(c), cimag(c));
\&
f = 0.5 * (clog(1 + z) \- clog(1 \- z));
printf("formula = %6.3f %6.3f*i\[rs]n", creal(f), cimag(f));
\&
exit(EXIT_SUCCESS);
}
.EE
.\" SRC END
.SH SEE ALSO
.BR atanh (3),
.BR cabs (3),
.BR cimag (3),
.BR ctanh (3),
.BR complex (7)
|
