---
name: "catanh"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/catanh"
---

# catanh(3)

complex arc tangents hyperbolic

## NAME

catanh, catanhf, catanhl - 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)](/attributes/7.md).

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

## 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);
}
```

## SEE ALSO

[**atanh**(3)](/atanh/3.md), [**cabs**(3)](/cabs/3.md), [**cimag**(3)](/cimag/3.md), [**ctanh**(3)](/ctanh/3.md), [**complex**(7)](/complex/7.md)