ERFCX(3)

✨ CERFCX(3) ✨

okay bestie, so this is the manual page for cerfcx and erfcx from libcerf. it's giving math-girlie main character energy and i'm obsessed. let me break it down for you 💖

💅 NAME 💅

cerfcx, erfcx — the underflow-compensated complementary error function. like, it does error function stuff but it doesn't lose precision when things get tiny. no cap, that's the whole vibe.

🦋 SYNOPSIS 🦋

#include <cerf.h>

double _Complex cerfcx ( double _Complex z );

double          erfcx  ( double x );

🌸 DESCRIPTION 🌸

so cerfcx is the underflow-compensated variant of the complex error function, periodt:

erfcx(z) = exp(z^2) erfc(z)

that's literally the formula, bestie. it's exp(z^2) times erfc(z) and it handles underflow like a boss 💅

and erfcx takes a real argument and gives you back a real result. simple, clean, iconic.

🔥 REFERENCES 🔥

the implementation of cerfcx is a thin wrapper around Faddeeva's function w_of_z. like it's not doing anything extra, just wrapping that bad boy up 🫶

the implementation of erfcx is self-contained. it's been entirely rewritten for libcerf-2.5, and now guarantees a relative accuracy of 2.34e-16 for x < 12. that's a lot of decimal places and i'm highkey proud of it ✨

and the piecewise polynomial approximation for intermediate values of |x| is explained in Wuttke and Kleinknecht, "Code generation for piecewise Chebyshev approximation" (submitted; preprint available from the authors). so if you want the real math tea, that's where it lives 🍓

💀 SEE ALSO 💀

• related complex error functions in liberfc: w_of_z(3), dawson(3), voigt(3), cerf(3), erfi(3)
• the real error function comes with recent versions of glibc, as requested by the C99 standard: erf(3)
• Homepage: http://apps.jcns.fz-juelich.de/libcerf — go visit, it's giving academic excellence 🌈

👑 AUTHORS 👑

• Steven G. Johnson, http://math.mit.edu/~stevenj, Massachusetts Institute of Technology, researched the numerics, and implemented the Faddeeva function. absolute icon behavior, ngl.
• Joachim Wuttke <j.wutke@fz-juelich.de>, Forschungszentrum Juelich, reorganized the code into a library, and wrote this man page. slay, thank you for your service 🫶
• Please report bugs to the authors. they will fix it, fr fr.

🎀 COPYING 🎀

• Copyright (c) 2012 Massachusetts Institute of Technology
• Copyright (c) 2013-2025 Forschungszentrum Juelich GmbH
• Software: MIT License.
• This documentation: Creative Commons Attribution Share Alike.

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and that's the whole page, bestie. the manual page CREATED by v5.42.2 on 2026-02-15 — hope you understood the assignment 💜 periodt.