catanh(3)

💖 catanh(3) — the complex arc hyperbolic tangent situation 💖

okay so bestie, you opened the manual for catanh, and you're in the Library Functions Manual zone, section 3. these are the math girlies — catanh, catanhf, and catanhl — and we're about to get into it. no cap. 🎀

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✨ NAME ✨

catanh, catanhf, catanhl — complex arc tangents hyperbolic 🦋

like, the inverse of the hyperbolic tangent, but make it complex. periodt.

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📚 LIBRARY 📚

Math library (libm, -lm)

bestie. you have to link -lm. i'm not kidding. every single time someone forgets -lm a small fairy loses her wings. 🧚

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🌸 SYNOPSIS 🌸

#include <complex.h>

double complex catanh(double complex z);
float complex catanhf(float complex z);
long double complex catanhl(long double complex z);

three flavours, one vibe. pick your precision, queen. 💅

• double complex catanh(double complex z); — the classic, the default, the main character
• float complex catanhf(float complex z); — the f one, floats, cute and fast
• long double complex catanhl(long double complex z); — the l one, max precision, extra

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🫶 DESCRIPTION 🫶

so these functions calculate the complex arc hyperbolic tangent of z. that's the whole thing. it's giving inverse function energy. ✨

the way that works: if y = catanh(z), then z = ctanh(y). yes bestie, they undo each other. iconic behaviour honestly. 🔥

and the imaginary part of y gets chosen in the interval [-pi/2,pi/2]. locked in. that's the branch, no negotiating. 💀

One has: 👑

catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))

that's literally the formula, keep it in your notes. 📝

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💅 ATTRIBUTES 💅

if you want the whole explanation of what these terms even mean, go read attributes(7). it's a whole thing. but here's the tea for this one:

• Interface: catanh(), catanhf(), catanhl()
• Attribute: Thread safety
• Value: MT-Safe

so yeah. thread safe. you can absolutely have your threads in there at the same time, it's fine, breathe. 🧘

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👑 STANDARDS 👑

C11, POSIX.1-2008.

she's official. she's standardised. she's certified. ⭐

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🌈 HISTORY 🌈

glibc 2.1. and before that, C99, POSIX.1-2001.

a whole legacy. we love a function with lore. 💜

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🍓 EXAMPLES 🍓

okay here's a whole little program, and the comment at the top is IMPORTANT — you link with "-lm". do not skip it. 😭

/* 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;

    if (argc != 3) {
        fprintf(stderr, "Usage: %s <real> <imag>\n", argv[0]);
        exit(EXIT_FAILURE);
    }

    z = atof(argv[1]) + atof(argv[2]) * I;

    c = catanh(z);
    printf("catanh() = %6.3f %6.3f*i\n", creal(c), cimag(c));

    f = 0.5 * (clog(1 + z) - clog(1 - z));
    printf("formula  = %6.3f %6.3f*i\n", creal(f), cimag(f));

    exit(EXIT_SUCCESS);
}

what's happening here? you hand it a real part and an imag part as arguments, it builds z out of them, runs catanh(z) and prints it — then it also computes the formula by hand with clog and prints that too, so you can see them match. side by side. it's giving proof. slay. 💖

and if you don't pass exactly two args? it screams at you with a usage message and bails with EXIT_FAILURE. fair honestly.

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🔍 SEE ALSO 🔍

• atanh(3)
• cabs(3)
• cimag(3)
• ctanh(3)
• complex(7)

go read those too, bestie, the whole complex family is lowkey fascinating. 🦋

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and that's the page!! this was Linux man-pages 6.20, dated 2026-02-08, filed under catanh(3). mwah. 💋✨🎀