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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.

You can also buy a printed version.

- Bit wizardry p.2
- Permutations and their operations p.102
- Sorting and searching p.134
- Data structures p.153
- Conventions and considerations p.172
- Combinations p.176
- Compositions p.194
- Subsets p.202
- Mixed radix numbers p.217
- Permutations p.232
- Permutations with special properties p.277
- k-permutations p.291
- Multisets p.295
- Gray codes for strings with restrictions p.304
- Parentheses strings p.323
- Integer partitions p.339
- Set partitions p.354
- Necklaces and Lyndon words p.370
- Hadamard and conference matrices p.384
- Searching paths in directed graphs p.391
- The Fourier transform p.410
- Convolution, correlation, and more FFT algorithms p.440
- The Walsh transform and its relatives p.459
- The Haar transform p.497
- The Hartley transform p.515
- Number theoretic transforms (NTTs) p.535
- Fast wavelet transforms p.543
- Fast multiplication and exponentiation p.550
- Root extraction p.567
- Iterations for the inversion of a function p.587
- The AGM, elliptic integrals, and algorithms for computing Pi p.599
- Logarithm and exponential function p.622
- Computing the elementary functions with limited resources p.641
- Numerical evaluation of power series p.651
- Recurrences and Chebyshev polynomials p.666
- Hypergeometric series p.685
- Cyclotomic polynomials, product forms, and continued fractions p.704
- Synthetic Iterations p.726
- Modular arithmetic and some number theory p.764
- Binary polynomials p.822
- Shift registers p.864
- Binary finite fields p.886

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