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
 | 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);
    }

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