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diff --git a/source/luametatex/source/libraries/libcerf/README.md b/source/luametatex/source/libraries/libcerf/README.md new file mode 100644 index 000000000..e825f8f99 --- /dev/null +++ b/source/luametatex/source/libraries/libcerf/README.md @@ -0,0 +1,109 @@ +# libcerf + +This 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. + +# User Documentation + +## Synopsis + +In the following, "complex" stands for the C99 data type "double _Complex": + + * complex [cerf](http://apps.jcns.fz-juelich.de/man/cerf.html) (complex): The complex error function erf(z). + * complex [cerfc](http://apps.jcns.fz-juelich.de/man/cerf.html) (complex): The complex complementary error function erfc(z) = 1 - erf(z). + * complex [cerfcx](http://apps.jcns.fz-juelich.de/man/erfcx.html) (complex z): The underflow-compensating function erfcx(z) = exp(z^2) erfc(z). + * double [erfcx](http://apps.jcns.fz-juelich.de/man/erfcx.html) (double x): The same for real x. + * complex [cerfi](http://apps.jcns.fz-juelich.de/man/erfi.html) (complex z): The imaginary error function erfi(z) = -i erf(iz). + * double [erfi](http://apps.jcns.fz-juelich.de/man/erfi.html) (double x): The same for real x. + * 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). + * 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. + * 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). + * double [dawson](http://apps.jcns.fz-juelich.de/man/dawson.html) (double x): The same for real x. + * 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. + * 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. + +## Accuracy + +By 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. + +## Copyright and Citation + +Copyright (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. + +License: [MIT License](http://opensource.org/licenses/MIT) + +When using libcerf in scientific work, please cite as follows: + * S. G. Johnson, A. Cervellino, J. Wuttke: libcerf, numeric library for complex error functions, version [...], http://apps.jcns.fz-juelich.de/libcerf + +Please send bug reports to the authors, or submit them through the Gitlab issue tracker. + +## Further references + +Most function evaluations in this library rely on Faddeeva's function w(z). + +This function has been reimplemented from scratch by [Steven G. Johnson](http://math.mit.edu/~stevenj); +project web site http://ab-initio.mit.edu/Faddeeva. The implementation partly relies on algorithms from the following publications: + * Walter Gautschi, *Efficient computation of the complex error function,* SIAM J. Numer. Anal. 7, 187 (1970). + * G. P. M. Poppe and C. M. J. Wijers, *More efficient computation of the complex error function,* ACM Trans. Math. Soft. 16, 38 (1990). + * Mofreh R. Zaghloul and Ahmed N. Ali, *Algorithm 916: Computing the Faddeyeva and Voigt Functions,* ACM Trans. Math. Soft. 38, 15 (2011). + +# Installation + +## From source + +Download location: http://apps.jcns.fz-juelich.de/src/libcerf/ + +Build&install are based on CMake. Out-of-source build is enforced. +After unpacking the source, go to the source directory and do: + + mkdir build + cd build + cmake .. + make + make install + +To test, run the programs in directory test/. + +The 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*. + +## Binary packages + + * Linux: + * [rpm package](https://build.opensuse.org/package/show/science/libcerf) by Christoph Junghans + * [Gentoo package](http://packages.gentoo.org/package/sci-libs/libcerf) by Christoph Junghans + * [Debian package](https://packages.debian.org/jessie/libs/libcerf1) by Eugen Wintersberger + * OS X: + * [MacPorts::libcerf](http://www.macports.org/ports.php?by=name&substr=libcerf), by Mojca Miklavec + * [Homebrew/homebrew-science/libcerf.rb](https://formulae.brew.sh/formula/libcerf), by Roman Garnett + +# Code structure + +The code consists of +- the library's C source (directory lib/), +- test code (directory test/), +- manual pages (directory man/), +- build utilities (aclocal.m4, build-aux/, config*, m4/, Makefile*). + +## Compilation + +The 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. + +Otherwise, the library is self-contained, and installation should be +straightforward, using the usual command sequence + + ./configure + make + sudo make install + +The command ./configure takes various options that are explained in the +file INSTALL. + +## Language bindings + +For 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. + +The following bindings are available: + * **fortran**, by Antonio Cervellino (Paul Scherrer Institut) + +Further contributions will be highly welcome. + +Please report bugs to the package maintainer. |