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This book provides algorithms and ideas for computationalists, 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.
Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.
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 fgures 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.
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