Matters Computational: Ideas, Algorithms, Source Code

This is a book for the computationalist, whether a working programmer or anyone interested in methods of computation. The focus is on material that does not usually appear in textbooks on algorithms.

Where necessary the underlying ideas are explained and the algorithms are given formally. It is assumed that the reader is able to understand the given source code, it is considered part of the text. We use the C++ programming language for low-level algorithms. However, only a minimal set of features beyond plain C is used, most importantly classes and templates. For material where technicalities in the C++ code would obscure the underlying ideas we use either pseudocode or, with arithmetical algorithms, the GP language. Appendix C gives an introduction to GP.

Example computations are often given with an algorithm, these are usually made with the demo programs referred to. Most of the listings and figures in this book were created with these programs. A recurring topic is practical efficiency of the implementations. Various optimization techniques are described and the actual performance of many given implementations is indicated.

The accompanying software, the FXT and the hfloat libraries, are written for POSIX compliant platforms such as the Linux and BSD operating systems. The license is the GNU General Public License (GPL), version 3 or later, see http://www.gnu.org/licenses/gpl.html.

Individual chapters are self-contained where possible and references to related material are given where needed. The symbol ‘ ‡ ’ marks sections that can be skipped at first reading. These typically contain excursions or more advanced material.

Each item in the bibliography is followed by a list of page numbers where citations occur. With papers that are available for free download the respective URL is given. Note that the URL may point to a preprint which can differ from the final version of the paper.