cerf.h   cerf.h 
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* Authors: * Authors:
* Steven G. Johnson, Massachusetts Institute of Technology, 2012, core a uthor * Steven G. Johnson, Massachusetts Institute of Technology, 2012, core a uthor
* Joachim Wuttke, Forschungszentrum Jülich, 2013, package maintainer * Joachim Wuttke, Forschungszentrum Jülich, 2013, package maintainer
* *
* Website: * Website:
* http://apps.jcns.fz-juelich.de/libcerf * http://apps.jcns.fz-juelich.de/libcerf
* *
* Revision history: * Revision history:
* ../CHANGELOG * ../CHANGELOG
* *
* References:
* See man 3 w_of_z
*
* Man pages: * Man pages:
* w_of_z(3), erfcx(3), cerf(3), dawson(3), voigt(3) * w_of_z(3), dawson(3), voigt(3), cerf(3), erfcx(3), erfi(3)
*/ */
#include <complex.h> // C99 complex-number support #include <complex.h> // C99 complex-number support
#ifndef __CERF_H #ifndef __CERF_H
# define __CERF_H # define __CERF_H
# undef __BEGIN_DECLS # undef __BEGIN_DECLS
# undef __END_DECLS # undef __END_DECLS
# ifdef __cplusplus # ifdef __cplusplus
# define __BEGIN_DECLS extern "C" { # define __BEGIN_DECLS extern "C" {
# define __END_DECLS } # define __END_DECLS }
# else # else
# define __BEGIN_DECLS # define __BEGIN_DECLS
# define __END_DECLS # define __END_DECLS
# endif # endif
__BEGIN_DECLS __BEGIN_DECLS
// compute w(z) = exp(-z^2) erfc(-iz), Faddeeva's scaled complex error func tion // compute w(z) = exp(-z^2) erfc(-iz), Faddeeva's scaled complex error func tion
double _Complex w_of_z (double _Complex z); double _Complex w_of_z (double _Complex z);
double im_w_of_x(double x); // special case Im[w(x)] of real x double im_w_of_x(double x); // special case Im[w(x)] of real x
double re_w_of_z( double x, double y );
double im_w_of_z( double x, double y );
// compute erf(z), the error function of complex arguments // compute erf(z), the error function of complex arguments
double _Complex cerf (double _Complex z); double _Complex cerf (double _Complex z);
// compute erfc(z) = 1 - erf(z), the complementary error function // compute erfc(z) = 1 - erf(z), the complementary error function
double _Complex cerfc(double _Complex z); double _Complex cerfc(double _Complex z);
// compute erfcx(z) = exp(z^2) erfc(z), an underflow-compensated version of erfc // compute erfcx(z) = exp(z^2) erfc(z), an underflow-compensated version of erfc
double _Complex cerfcx(double _Complex z); double _Complex cerfcx(double _Complex z);
double erfcx (double x); // special case for real x double erfcx (double x); // special case for real x
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double _Complex cerfi(double _Complex z); double _Complex cerfi(double _Complex z);
double erfi (double x); // special case for real x double erfi (double x); // special case for real x
// compute dawson(z) = sqrt(pi)/2 * exp(-z^2) * erfi(z), Dawson's integral // compute dawson(z) = sqrt(pi)/2 * exp(-z^2) * erfi(z), Dawson's integral
double _Complex cdawson(double _Complex z); double _Complex cdawson(double _Complex z);
double dawson (double x); // special case for real x double dawson (double x); // special case for real x
// compute voigt(x,??), the convolution of a Gaussian and a Lorentzian // compute voigt(x,??), the convolution of a Gaussian and a Lorentzian
double voigt( double x, double sigma, double gamma ); double voigt( double x, double sigma, double gamma );
// EXPERIMENTAL
double cerf_experimental_imw( double x, double y );
double cerf_experimental_rew( double x, double y );
__END_DECLS __END_DECLS
#endif /* __CERF_H__ */ #endif /* __CERF_H__ */
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