casinh(3)

💖 casinh(3) — bestie we're doing COMPLEX arc hyperbolic sine 💖

okay so this one lives in the Library Functions Manual, and honestly? she's lowkey iconic. it's giving math girlie. it's giving complex plane. let's get into it 🦋

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✨ NAME ✨

casinh, casinhf, casinhl — complex arc sine hyperbolic

(three girls, one job. the f and l ones are just the float and long double versions, no cap 💅)

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📚 LIBRARY 📚

Math library (libm, link it with -lm) — don't forget the flag bestie, or the linker will be SO dramatic about it 😭

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🌸 SYNOPSIS 🌸

#include <complex.h>

double complex casinh(double complex z);
float complex casinhf(float complex z);
long double complex casinhl(long double complex z);

look at her. gorgeous. three function signatures, all matching vibes 🎀

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💫 DESCRIPTION 💫

so like. these functions calculate the complex arc hyperbolic sine of z. that's the whole assignment, periodt.

if you got

y = casinh(z);

then that literally means

z = csinh(y);

they're inverse besties, it's reciprocal energy, it's giving yin and yang 🫶

the imaginary part of y? it gets picked inside the interval [-pi/2,pi/2]. that's the branch cut situation, she has rules, respect them ✨

and also, one has this lil identity which is genuinely so cute:

casinh(z) = clog(z + csqrt(z * z + 1))

look at that. clog and csqrt teaming up. main character energy fr fr 🌈

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🔥 ATTRIBUTES 🔥

(for an explanation of the terms used in this section, go peek at attributes(7) — she has the full glossary 🧚)

• casinh(), casinhf(), casinhl() — Thread safety: MT-Safe

that's right. all three of them, MT-Safe, thread-safe, no drama, safe to call from multiple threads at once. we love a stable queen 👑

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⭐ STANDARDS ⭐

C11, POSIX.1-2008.

certified. official. slay 💅

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🎀 HISTORY 🎀

glibc 2.1. also C99, POSIX.1-2001.

she's been around since forever, a real OG, ancestors ate 🍓

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🦋 SEE ALSO 🦋

• asinh(3)
• cabs(3)
• cimag(3)
• csinh(3)
• complex(7)

go read these too, they're all in the same friend group iykyk 💜

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bestie reminder: this is a math function, so link with -lm and include <complex.h>. no gatekeeping here, just facts 🤝

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mwah 💋 that's the whole page, and this lil sign-off is brought to you by Linux man-pages 6.20, dated 2026-02-08, for casinh(3). go forth and compute complex arc hyperbolic sines, you absolute legend 👑✨