Matters Computational: Ideas, Algorithms, Source Code
This book provides algorithms and ideas for computationalists. 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.
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algorithm array base bits bool called coefficients combinations complex composite computation const ulong convolution corresponding created cycle cyclic define described digits double elements entry equals equivalent example factors field function given given in FXT gives Gray code identical implementation integer inverse irreducible iteration length lowest matrix method modulo move multiplication multiset normal Note obtained operations partitions permutation polynomial position prime primitive radix recursion relation representation result reversed root routine scheme sequence shift shown in figure snip sort square static inline ulong step strings subsets swap template typename Type2 transform Type ulong k=0 ulong n values vector void Walsh zero