catan(3)

💖 catan — complex arc tangents 💖

okay bestie, sit DOWN, because today we're talking about catan, catanf and catanl from the math library, and honestly? iconic behavior from all three of them. this is a catan(3) situation, so it's the library-functions manual, and it's giving "trig but make it complex" 💅

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✨ LIBRARY ✨

Math library, and you gotta link it like -lm or she simply will not show up. rude? maybe. but that's the vibe. 🫶

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🌸 SYNOPSIS 🌸

#include <complex.h>

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

three flavors, one function, choose your precision like choosing your drink at starbucks: double, float, long double. periodt. ✨

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🦋 DESCRIPTION 🦋

so these functions calculate the complex arc tangent of z. that's it, that's the job, and they do it flawlessly.

here's the tea on how it works: if

y = catan(z)

then that literally means

z = ctan(y)

and the real part of y gets chosen in the interval [-pi/2, pi/2]. so it's the principal-branch girly, no chaotic branch-hopping happening here, she stays in her lane. 💅

also, one has:

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

like, that's the formula, and it's genuinely so elegant it makes me emotional 😭

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👑 ATTRIBUTES 👑

for an explanation of the terms used in this section, go check out attributes(7) — it's like the glossary bestie, very useful.

• Interface: catan(), catanf(), catanl()
• Attribute: Thread safety
• Value: MT-Safe

so yes, all three of them are <green>MT-Safe</green> 💚 which means you can call them from multiple threads without it turning into a whole situation. slay. 🔥

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⭐ STANDARDS ⭐

C11, POSIX.1-2008. certified, standardized, official. no cap. ✅

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🌈 HISTORY 🌈

• glibc 2.1.
• C99, POSIX.1-2001.

so she's been around since forever and she's still serving. longevity queen. 👑

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💜 EXAMPLES 💜

here's a whole little demo program, and remember: link with -lm or it's not gonna work, bestie, I'm warning you now 🙈

/* 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);
}

what's happening here, translated for the girlies: you pass in a <italic>real</italic> part and an <italic>imag</italic> part, it builds the complex number z, calls catan(z), prints the result, and then ALSO computes the same thing with the formula from up top and prints that too — so you can literally watch the function and the math agree with each other. matching outfits. bestie energy. 🎀 and yes, it exits with EXIT_SUCCESS because we're thriving.

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🧚 SEE ALSO 🧚

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

go read those next, they're all part of the same friend group. 🫶

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and that's the whole page, babe! this was pulled from Linux man-pages 6.20, dated 2026-02-08, for catan(3). mwah, love u, go compute some arc tangents 💖✨🌸