# NAME

catanh, catanhf, catanhl - complex arc tangents hyperbolic

# SYNOPSIS

#include <complex.h>

double complex catanh(double complex `z`);
float complex catanhf(float complex `z`);
long double complex catanhl(long double complex `z`);

Link with `-lm`.

# DESCRIPTION

These functions calculate the complex arc hyperbolic tangent of `z`. If `y = catanh(z)`, then `z = ctanh(y)`. The imaginary part of `y` is chosen in the interval [-pi/2,pi/2].

One has:

``    catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))``

# VERSIONS

These functions first appeared in glibc in version 2.1.

# ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

 Interface Attribute Value catanh(), catanhf(), catanhl() Thread safety MT-Safe

# CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

# EXAMPLES

``````/* 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);
exit(EXIT_FAILURE);
}

z = atof(argv) + atof(argv) * 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);
}``````

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