Matters Computational - Ideas, Algorithms, Source Code

This is a book for computationalists, whether working programmers or anyone interested in methods of computation and algorithms. Where necessary, the underlying ideas are explained and the algorithms are formally presented. The C++ programming language is used for low-level algorithms, and there is only a minimal set of features beyond plain C. For material, where technicalities in the C++ code would obscure the underlying ideas, the author presents either pseudo-code or, with arithmetical algorithms, the GP language. Appendix C includes an introduction to GP. Example computations are mostly given with algorithms, some of them made with programs the author refers to.
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.

Inhaltsverzeichnis:

Low level algorithms.- Bit wizardry.- Permutations and their operations.- Sorting and searching.- Data structures.- Combinatorial generation.- Conventions and considerations.- Combinations.- Compositions.- Subsets.- Mixed radix numbers.- Permutations.- Multisets.- Gray codes for string with restrictions.- Parenthesis strings.- Integer partitions.- Set partitions.- Necklaces and Lyndon words.- Hadamard and conference matrices.- Searching paths in directed graphs.- Fast transforms.- The Fourier transform.- Convolution, correlation, and more FFT algorithms.- The Walsh transform and its relatives.- The Haar transform.- The Hartley transform.- Number theoretic transforms (NTTs).- Fast wavelet transforms.- Fast arithmetic.- Fast multiplication and exponentiation.- Root extraction.- Iterations for the inversion of a function.- The AGM, elliptic integrals, and algorithms for computing.- Logarithm and exponential function.- Computing the elementary functions with limited resources.- Numeri cal evaluation of power series.- Cyclotomic polynomials, product forms, and continued fractions.- Synthetic Iterations.-. Algorithms for finite fields.- Modular arithmetic and some number theory.- Binary polynomials.- Shift registers.- Binary finite fields.- The electronic version of the book.- Machine used for benchmarking.- The GP language.- Bibliography.- Index.

Rezension:

From the reviews:

"The book is a comprehensive compilation of well written software codes as well as short explanation texts for basic methods of computation. It fills a gap in the literature since most books in this area describe either the methods or the codes provided in specialized libraries." (Dana Petcu, Zentralblatt MATH, Vol. 1210, 2011)

"It is thorough, and covers many algorithms that one does not often see in algorithmic texts. ... This may be an invaluable reference to some people, since it does provide excellent coverage of algorithms that are not frequently compiled into a single volume. ... In short, this is a wonderful compilation of many algorithms that don't show up in other places, with reasonable ... commentary and an abundance of code. ... this is the kind of book libraries will put on their shelves ... ." (Jeffrey Putnam, ACM Computing Reviews, July, 2011)