SIMPLE SOLUTIONS

# CATAN, CATANF, CATANL - reference manual online

Complex arc tangents.

Chapter
2015-04-19
```CATAN(3)                            Linux Programmer's Manual                            CATAN(3)

NAME
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);

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

#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[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(f2), cimag(f2));

exit(EXIT_SUCCESS);
}