libcerf\ manual

# NAME

cerfcx, erfcx - underflow-compensated complementary error function

# SYNOPSIS

#include <cerf.h>

double _Complex cerfcx ( double _Complex z );

double erfcx ( double x );

# DESCRIPTION

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.

# REFERENCES

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

The implementation of erfcx 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.

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).

# 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

# AUTHORS

Steven G. Johnson, http://math.mit.edu/~stevenj, Massachusetts Institute of Technology, researched the numerics, and implemented the Faddeeva function.

Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich, reorganized the code into a library, and wrote this man page.

Please report bugs to the authors.

# COPYING

Copyright (c) 2012 Massachusetts Institute of Technology

Copyright (c) 2013 Forschungszentrum Juelich GmbH

Software: MIT License.

This documentation: Creative Commons Attribution Share Alike.