.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" and Copyright (C) 2011 Michael Kerrisk <mtk.manpages@gamil.com>
.\" Distributed under GPL
.\"
.TH CATANH 3 2011-09-15 "" "Linux Programmer's Manual"
.SH NAME
catanh, catanhf, catanhl \- complex arc tangents hyperbolic
.SH SYNOPSIS
.B #include <complex.h>
.sp
.BI "double complex catanh(double complex " z );
.br
.BI "float complex catanhf(float complex " z );
.br
.BI "long double complex catanhl(long double complex " z );
.sp
Link with \fI\-lm\fP.
.SH DESCRIPTION
The
.BR catanh ()
function calculates 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].
.LP
One has:
.nf

    catanh(z) = 0.5 * (clog(1 + z) \- clog(1 \- z))
.fi
.SH VERSIONS
These functions first appeared in glibc in version 2.1.
.SH "CONFORMING TO"
C99.
.SH EXAMPLE
.nf
/* Link with "\-lm" */

#include <complex.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdio.h>

int
main(int argc, char *argv[])
{
    double complex z, c, f;

    if (argc != 3) {
        fprintf(stderr, "Usage: %s <real> <imag>\\n", argv[0]);
        exit(EXIT_FAILURE);
    }

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

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

    f = 0.5 * (clog(1 + z) \- clog(1 \- z));
    printf("formula  = %6.3f %6.3f*i\\n", creal(f2), cimag(f2));

    exit(EXIT_SUCCESS);
}
.fi
.SH "SEE ALSO"
.BR atanh (3),
.BR cabs (3),
.BR cimag (3),
.BR ctanh (3),
.BR complex (7)