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erfcx(3) libcerf manual erfcx(3)


cerfcx, erfcx - underflow-compensated complementary error function


#include <cerf.h>

double _Complex cerfcx ( double _Complex z );

double erfcx ( double x );


The function cerfcx is an underflow-compensated variant of the complex error function: erfcx(z) = exp(z^2) erfc(z).

The function erfcx takes a real argument and returns a real result.


The implementation of cerfcx is a thin wrapper around Faddeeva's function w_of_z.

The implementation of erfcx is self-contained, and improves upon the SLATEC DERFC function (or an erfcx function derived therefrom) or Cody's CALERF function (from, while retaining near machine precision in accuracy.


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)



Steven G. Johnson,,
Massachusetts Institute of Technology,
researched the numerics, and implemented the Faddeeva function.

Joachim Wuttke <>, Forschungszentrum Juelich,
reorganized the code into a library, and wrote this man page.

Please report bugs to the authors.


Copyright (c) 2012 Massachusetts Institute of Technology

Copyright (c) 2013 Forschungszentrum Juelich GmbH

Software: MIT License.

This documentation: Creative Commons Attribution Share Alike.

2023-08-05 perl v5.36.0