# catanh - Man Page

complex arc tangents hyperbolic

## Library

Math library (libm, -lm)

## Synopsis

```#include <complex.h>

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

## 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))`

## Attributes

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

InterfaceAttributeValue

## Standards

C11, POSIX.1-2008.

## History

glibc 2.1. C99, POSIX.1-2001.

## Examples

```/* 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>\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(f), cimag(f));

exit(EXIT_SUCCESS);
}```