'\" 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 2023-03-30 "Linux man-pages 6.04"
.SH NAME
catanh, catanhf, catanhl \- complex arc tangents hyperbolic
.SH LIBRARY
Math library
.RI ( libm ", " \-lm )
.SH SYNOPSIS
.nf
.B #include <complex.h>
.PP
.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].
.PP
One has:
.PP
.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).
.ad l
.nh
.TS
allbox;
lbx lb lb
l l l.
Interface	Attribute	Value
T{
.BR catanh (),
.BR catanhf (),
.BR catanhl ()
T}	Thread safety	MT-Safe
.TE
.hy
.ad
.sp 1
.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>\en", argv[0]);
        exit(EXIT_FAILURE);
    }

    z = atof(argv[1]) + atof(argv[2]) * I;

    c = catanh(z);
    printf("catanh() = %6.3f %6.3f*i\en", creal(c), cimag(c));

    f = 0.5 * (clog(1 + z) \- clog(1 \- z));
    printf("formula  = %6.3f %6.3f*i\en", 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)
