cacosh(3)

💖 cacosh(3) — complex arc hyperbolic cosine 💖

okay bestie, sit down, hydrate, because we're about to talk about cacosh, from section 3 of the manual (that's Library Functions Manual, iykyk). it's giving math. it's giving complex numbers. it's giving slay.

✨ NAME ✨

cacosh, cacoshf, cacoshl — complex arc hyperbolic cosine

🎀 LIBRARY 🎀

Math library (libm, -lm)

fr fr, if you forget the -lm your linker is gonna ghost you. do not let that happen to you.

🌸 SYNOPSIS 🌸

#include <complex.h>

double complex cacosh(double complex z);
float complex cacoshf(float complex z);
long double complex cacoshl(long double complex z);

three functions, three vibes, one job: you want double? she's cacosh. you want float? she's cacoshf. you want long double? she's cacoshl, the queen, the icon, the moment. 👑

🦋 DESCRIPTION 🦋

these functions calculate the complex arc hyperbolic cosine of z. and like, what does that even mean? okay so: if y = cacosh(z), then z = ccosh(y). it's the inverse. the un-doing. the "bestie I need to go back" of it all.

here's the part where the nerds got specific and honestly? we love that for them:

• the imaginary part of y is chosen in the interval [-pi,pi]
• the real part of y is chosen nonnegative

and the formula, periodt:

cacosh(z) = 2 * clog(csqrt((z + 1) / 2) + csqrt((z - 1) / 2))

literally just clog and csqrt doing a collab. a crossover episode. no cap. 💅

🔥 ATTRIBUTES 🔥

for the full explanation of the terms used in this section, go check out attributes(7). but here's the tea:

• Interface: cacosh(), cacoshf(), cacoshl()
• Attribute: Thread safety
• Value: MT-Safe

translation bestie: she's MT-Safe. all three of them. you can take her into threads, she will not embarrass you. 🫶

⭐ STANDARDS ⭐

C11, POSIX.1-2008.

👑 HISTORY 👑

C99, POSIX.1-2001. glibc 2.1.

she's been around. she's seasoned. she's an elder who still ate. 🌈

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💀 EXAMPLES 💀

here's the demo program, and yes, you do need to link with -lm:

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

    f = 2 * clog(csqrt((z + 1)/2) + csqrt((z - 1)/2));
    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 imaginary part, it builds z, runs the real cacosh(), then double-checks it against the formula from up top. if those two lines of output agree, the vibe check passed. if they don't? 😭

bestie note: the program expects exactly two arguments beyond the program name, or it prints Usage: %s <real> <imag> to stderr and bails with EXIT_FAILURE. it exits happy with EXIT_SUCCESS otherwise. don't argue with her, she's right.

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🧚 SEE ALSO 🧚

acosh(3), cabs(3), ccosh(3), cimag(3), complex(7)

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and that's the whole page, no notes, we ate and left no crumbs. this one came from Linux man-pages 6.20, dated 2026-02-08, and that's on cacosh(3) specifically. love her, respect her, include <complex.h>. bye bestie, go compile something 🍓💜