1# libcerf 2 3This is the home page of **libcerf**, a self-contained numeric library that provides an efficient and accurate implementation of complex error functions, along with Dawson, Faddeeva, and Voigt functions. 4 5# User Documentation 6 7## Synopsis 8 9In the following, "complex" stands for the C99 data type "double _Complex": 10 11 * complex [cerf](http://apps.jcns.fz-juelich.de/man/cerf.html) (complex): The complex error function erf(z). 12 * complex [cerfc](http://apps.jcns.fz-juelich.de/man/cerf.html) (complex): The complex complementary error function erfc(z) = 1 - erf(z). 13 * complex [cerfcx](http://apps.jcns.fz-juelich.de/man/erfcx.html) (complex z): The underflow-compensating function erfcx(z) = exp(z^2) erfc(z). 14 * double [erfcx](http://apps.jcns.fz-juelich.de/man/erfcx.html) (double x): The same for real x. 15 * complex [cerfi](http://apps.jcns.fz-juelich.de/man/erfi.html) (complex z): The imaginary error function erfi(z) = -i erf(iz). 16 * double [erfi](http://apps.jcns.fz-juelich.de/man/erfi.html) (double x): The same for real x. 17 * complex [w_of_z](http://apps.jcns.fz-juelich.de/man/w_of_z.html) (complex z): Faddeeva's scaled complex error function w(z) = exp(-z^2) erfc(-iz). 18 * double [im_w_of_x](http://apps.jcns.fz-juelich.de/man/w_of_z.html) (double x): The same for real x, returning the purely imaginary result as a real number. 19 * complex [cdawson](http://apps.jcns.fz-juelich.de/man/dawson.html) (complex z): Dawson's integral D(z) = sqrt(pi)/2 * exp(-z^2) * erfi(z). 20 * double [dawson](http://apps.jcns.fz-juelich.de/man/dawson.html) (double x): The same for real x. 21 * double [voigt](http://apps.jcns.fz-juelich.de/man/voigt.html) (double x, double sigma, double gamma): The convolution of a Gaussian and a Lorentzian. 22 * double [voigt_hwhm](http://apps.jcns.fz-juelich.de/man/voigt_hwhm.html) (double sigma, double gamma): The half width at half maximum of the Voigt profile. 23 24## Accuracy 25 26By construction, it is expected that the relative accuracy is generally better than 1E-13. This has been confirmed by comparison with high-precision Maple computations and with a *long double* computation using Fourier transform representation and double-exponential transform. 27 28## Copyright and Citation 29 30Copyright (C) [Steven G. Johnson](http:*math.mit.edu/~stevenj), Massachusetts Institute of Technology, 2012; [Joachim Wuttke](http:*www.fz-juelich.de/SharedDocs/Personen/JCNS/EN/Wuttke_J.html), Forschungszentrum Jülich, 2013. 31 32License: [MIT License](http://opensource.org/licenses/MIT) 33 34When using libcerf in scientific work, please cite as follows: 35 * S. G. Johnson, A. Cervellino, J. Wuttke: libcerf, numeric library for complex error functions, version [...], http://apps.jcns.fz-juelich.de/libcerf 36 37Please send bug reports to the authors, or submit them through the Gitlab issue tracker. 38 39## Further references 40 41Most function evaluations in this library rely on Faddeeva's function w(z). 42 43This function has been reimplemented from scratch by [Steven G. Johnson](http://math.mit.edu/~stevenj); 44project web site http://ab-initio.mit.edu/Faddeeva. The implementation partly relies on algorithms from the following publications: 45 * Walter Gautschi, *Efficient computation of the complex error function,* SIAM J. Numer. Anal. 7, 187 (1970). 46 * G. P. M. Poppe and C. M. J. Wijers, *More efficient computation of the complex error function,* ACM Trans. Math. Soft. 16, 38 (1990). 47 * Mofreh R. Zaghloul and Ahmed N. Ali, *Algorithm 916: Computing the Faddeyeva and Voigt Functions,* ACM Trans. Math. Soft. 38, 15 (2011). 48 49# Installation 50 51## From source 52 53Download location: http://apps.jcns.fz-juelich.de/src/libcerf/ 54 55Build&install are based on CMake. Out-of-source build is enforced. 56After unpacking the source, go to the source directory and do: 57 58 mkdir build 59 cd build 60 cmake .. 61 make 62 make install 63 64To test, run the programs in directory test/. 65 66The library has been developed using gcc-4.7. Reports about successful compilation with older versions of gcc would be welcome. For correct support of complex numbers it seems that at least gcc-4.3 is required. Compilation with gcc-4.2 works after removing of the "-Werror" flag from *configure*. 67 68## Binary packages 69 70 * Linux: 71 * [rpm package](https://build.opensuse.org/package/show/science/libcerf) by Christoph Junghans 72 * [Gentoo package](http://packages.gentoo.org/package/sci-libs/libcerf) by Christoph Junghans 73 * [Debian package](https://packages.debian.org/jessie/libs/libcerf1) by Eugen Wintersberger 74 * OS X: 75 * [MacPorts::libcerf](http://www.macports.org/ports.php?by=name&substr=libcerf), by Mojca Miklavec 76 * [Homebrew/homebrew-science/libcerf.rb](https://formulae.brew.sh/formula/libcerf), by Roman Garnett 77 78# Code structure 79 80The code consists of 81- the library's C source (directory lib/), 82- test code (directory test/), 83- manual pages (directory man/), 84- build utilities (aclocal.m4, build-aux/, config*, m4/, Makefile*). 85 86## Compilation 87 88The library libcerf is written in C. It can be compiled as C code (default) or as C++ code (with option -DCERF_CPP=ON). Compilation as C++ is useful especially under MS Windows because as per 2018 the C compiler of Visual Studio does not support C90, nor any newer language standard, and is unable to cope with complex numbers. 89 90Otherwise, the library is self-contained, and installation should be 91straightforward, using the usual command sequence 92 93 ./configure 94 make 95 sudo make install 96 97The command ./configure takes various options that are explained in the 98file INSTALL. 99 100## Language bindings 101 102For use with other programming languages, libcerf should be either linked directly, or provided with a trivial wrapper. Such language bindings are added to the libcerf package as contributed by their authors. 103 104The following bindings are available: 105 * **fortran**, by Antonio Cervellino (Paul Scherrer Institut) 106 107Further contributions will be highly welcome. 108 109Please report bugs to the package maintainer. 110