catan, catanf, catanl - complex arc tangents

#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.

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)

/* 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[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);
}

ccos(3), clog(3), ctan(3), complex(7)