catan(3) Library Functions Manual catan(3)

# NAME¶

catan, catanf, catanl - complex arc tangents

# LIBRARY¶

Math library (libm, -lm)

# SYNOPSIS¶

`#include <complex.h>`
```double complex catan(double complex z);
float complex catanf(float complex z);
long double complex catanl(long double complex z);```

# 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)
```

# ATTRIBUTES¶

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

 Interface Attribute Value catan (), catanf (), catanl () 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;

double complex i = I;

if (argc != 3) {

fprintf(stderr, "Usage: %s <real> <imag>\n", argv[0]);

exit(EXIT_FAILURE);

}

z = atof(argv[1]) + atof(argv[2]) * 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(f), cimag(f));

exit(EXIT_SUCCESS);
}
```