catan, catanf, catanl — complex arc tangents

## Synopsis

`#include <complex.h>`

`double complex catan(double complex z);float complex catanf(float complex z);long double complex catanl(long double complex z);`

`Link with -lm.`

## Description

These functions calculate the complex arc tangent of z. If y = catan(z), then z = ctan(y). The real part of y is chosen in the interval [-pi/2,pi/2].

One has:

`    catan(z) = (clog(1 + i * z) - clog(1 - i * z)) / (2 * i)`

## 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
catan(), catanf(), catanl() Thread safety MT-Safe

## Conforming to

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

## 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;
double complex i = I;

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

z = atof(argv) + atof(argv) * I;

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

f = (clog(1 + i * z) - clog(1 - i * z)) / (2 * i);
printf("formula = %6.3f %6.3f*i\n", creal(f2), cimag(f2));

exit(EXIT_SUCCESS);
}```