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.IX Title "build::libcerf::src::libcerf::man::erfcx 3"
.TH build::libcerf::src::libcerf::man::erfcx 3 2025-10-25 "perl v5.42.0" "libcerf manual"
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.SH NAME
cerfcx, erfcx \- underflow\-compensated complementary error function
.SH SYNOPSIS
.IX Header "SYNOPSIS"
\&\fB#include <cerf.h\fR>
.PP
\&\fBdouble _Complex cerfcx ( double _Complex z );\fR
.PP
\&\fBdouble          erfcx  ( double x );\fR
.SH DESCRIPTION
.IX Header "DESCRIPTION"
The function \fBcerfcx\fR is an underflow\-compensated variant of the complex error function: erfcx(z) = exp(z^2) erfc(z).
.PP
The function \fBerfcx\fR takes a real argument and returns a real result.
.SH REFERENCES
.IX Header "REFERENCES"
The implementation of \fBcerfcx\fR is a thin wrapper around Faddeeva\*(Aqs
function \fBw_of_z\fR.
.PP
The implementation of \fBerfcx\fR is self\-contained. It has been entirely rewritten
for libcerf\-2.5, and now guarantees a relative accuracy of 2.34e\-16 for x < 12.
.PP
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).
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Related complex error functions in liberfc:
\&\fBw_of_z\fR(3), \fBdawson\fR(3), \fBvoigt\fR(3), \fBcerf\fR(3), \fBerfi\fR(3).
.PP
The real error function comes with recent versions of glibc, as requested by the C99 standard:
\&\fBerf\fR(3)
.PP
Homepage: http://apps.jcns.fz\-juelich.de/libcerf
.SH AUTHORS
.IX Header "AUTHORS"
Steven G. Johnson, http://math.mit.edu/~stevenj,
  Massachusetts Institute of Technology,
  researched the numerics, and implemented the Faddeeva function.
.PP
Joachim Wuttke <j.wuttke@fz\-juelich.de>, Forschungszentrum Juelich,
  reorganized the code into a library, and wrote this man page.
.PP
Please report bugs to the authors.
.SH COPYING
.IX Header "COPYING"
Copyright (c) 2012 Massachusetts Institute of Technology
.PP
Copyright (c) 2013\-2025 Forschungszentrum Juelich GmbH
.PP
Software: MIT License.
.PP
This documentation: Creative Commons Attribution Share Alike.