## 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`)`;

Note Link with `−lm`.

## DESCRIPTION

The `catanh`() function calculates 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.

C99.

## EXAMPLE

```/* 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);
}
```

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