erf(3)

💖 erf(3) — the error function, bestie edition 💖

okay so this is a page from the Library Functions Manual, and it's about erf, erff, and erfl. yes it's math. no you don't have to be scared. sit down, hydrate, let's go 🫶

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✨ NAME ✨

erf, erff, erfl — the error function. that's it, that's the whole vibe. not an error, not your error, THE error function. very demure, very mathematical 💅

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📚 LIBRARY 📚

Math library, aka libm, which you link with -lm. don't forget the -lm or you'll be sad and confused, and not in a cute way 😭

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🌸 SYNOPSIS 🌸

#include <math.h>

double erf(double x);
float erff(float x);
long double erfl(long double x);

three little functions, three different levels of precision, all iconic in their own way ✨

🎀 Feature Test Macro Requirements for glibc (see feature_test_macros(7)) 🎀

so like, glibc is particular about how you ask for these. you gotta declare your intentions, no cap.

erf():

_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
    || /* Since glibc 2.19: */ _DEFAULT_SOURCE
    || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

erff(), erfl():

_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
    || /* Since glibc 2.19: */ _DEFAULT_SOURCE
    || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

see how erff() and erfl() don't need _XOPEN_SOURCE? yeah. they're built different. noted. 📝

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🦋 DESCRIPTION 🦋

these functions return the error function of x, defined as:

erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(-t*t) dt

it's giving calculus. it's giving integral from 0 to x. it's giving exp(-t*t) dt. slay 💅

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👑 RETURN VALUE 👑

on success, these functions return the value of the error function of x, and that value lives in the range [-1, 1]. cozy little range, we love that for it 🌈

• if x is a NaN, a NaN is returned. (NaN in, NaN out, the circle of life 🦋)
• if x is +0 (-0), +0 (-0) is returned.
• if x is positive infinity (negative infinity), +1 (-1) is returned.
• if x is subnormal, a range error occurs, and the return value is 2*x/sqrt(pi).

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💀 ERRORS 💀

see math_error(7) for the whole lore on figuring out whether an error even happened when you called these functions. the tea is in there ☕

these are the errors that can occur:

Range error: result underflow (x is subnormal) : an underflow floating-point exception (FE_UNDERFLOW) is raised. not me getting an exception 😭

⚠️ important: these functions do not set errno. zero. zilch. nada. do not go checking errno and expecting an answer, bestie, it's not coming 🙈

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🧚 ATTRIBUTES 🧚

for an explanation of the terms used in this section, see attributes(7). the table in the original is very official, so here it is in bullet form, still 100% factual:

• Interface: erf(), erff(), erfl() — Attribute: Thread safety — Value: MT-Safe

MT-Safe. she's safe to call from multiple threads. main character energy AND team player energy 🔥

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⭐ STANDARDS ⭐

C11, POSIX.1-2008. certified, standardized, official. periodt.

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🌸 HISTORY 🌸

C99, POSIX.1-2001.

also: the variant returning double — that's erf() — also conforms to SVr4, 4.3BSD. ancient lineage, honestly kind of iconic 👑

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💜 SEE ALSO 💜

• cerf(3)
• erfc(3)
• exp(3)

go read those next, bestie, they're the extended universe 🫶

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and that's the page!! this was Linux man-pages 6.20, dated 2026-02-08, brought to you by the letter erf(3) 💖 no cap, you understood all of it. go forth and compute your error functions responsibly ✨🎀