I Low level algorithms
1 Bit wizardry
2 Permutations and their operations
3 Sorting and searching
4 Data structures

II Combinatorial generation
5 Conventions and considerations
6 Combinations
7 Compositions
8 Subsets
9 Mixed radix numbers
10 Permutations
11 Permutations with special properties
12 k-permutations
13 Multisets
14 Gray codes for strings with restrictions
15 Parentheses strings
16 Integer partitions
17 Set partitions
18 Necklaces and Lyndon words
19 Hadamard and conference matrices
20 Searching paths in directed graphs ‡

III Fast transforms
21 The Fourier transform
22 Convolution, correlation, and more FFT algorithms
23 The Walsh transform and its relatives
24 The Haar transform
25 The Hartley transform
26 Number theoretic transforms
27 Fast wavelet transforms

IV Fast arithmetic
28 Fast multiplication and exponentiation
29 Root extraction
30 Iterations for the inversion of a function
31 The AGM, elliptic integrals, and algorithms for computing (pi)
32 Logarithm and exponential function
33 Computing the elementary functions with limited resources
34 Numerical evaluation of power series
35 Recurrences and Chebyshev polynomials
36 Hypergeometric series
37 Cyclotomic polynomials, product forms, and continued fractions
38 Synthetic Iterations ‡

V Algorithms for finite fields
39 Modular arithmetic and some number theory
40 Binary polynomials
41 Shift registers
42 Binary finite fields: GF(2n )