WA linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation.
WIn mathematics, the middle-square method is a method of generating pseudorandom numbers. In practice it is not a good method, since its period is usually very short and it has some severe weaknesses; repeated enough times, the middle-square method will either begin repeatedly generating the same number or cycle to a previous number in the sequence and loop indefinitely.
WThe MIXMAX generator is a family of pseudorandom number generators (PRNG) and is based on Anosov C-systems and Kolmogorov K-systems. It was introduced in a 1986 preprint by G. Savvidy and N. Ter-Arutyunyan-Savvidy and published in 1991.
WRANDU is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which has been used since the 1960s. It is defined by the recurrence:
WThe spectral test is a statistical test for the quality of a class of pseudorandom number generators (PRNGs), the linear congruential generators (LCGs). LCGs have a property that when plotted in 2 or more dimensions, lines or hyperplanes will form, on which all possible outputs can be found. The spectral test compares the distance between these planes; the further apart they are, the worse the generator is. As this test is devised to study the lattice structures of LCGs, it can not be applied to other families of PRNGs.
WXorshift random number generators, also called shift-register generators are a class of pseudorandom number generators that were discovered by George Marsaglia. They are a subset of linear-feedback shift registers (LFSRs) which allow a particularly efficient implementation in software without using excessively sparse polynomials. They generate the next number in their sequence by repeatedly taking the exclusive or of a number with a bit-shifted version of itself. This makes them execute extremely efficiently on modern computer architectures, but does not benefit efficiency in a hardware implementation. Like all LFSRs, the parameters have to be chosen very carefully in order to achieve a long period.
WThe ziggurat algorithm is an algorithm for pseudo-random number sampling. Belonging to the class of rejection sampling algorithms, it relies on an underlying source of uniformly-distributed random numbers, typically from a pseudo-random number generator, as well as precomputed tables. The algorithm is used to generate values from a monotonically decreasing probability distribution. It can also be applied to symmetric unimodal distributions, such as the normal distribution, by choosing a value from one half of the distribution and then randomly choosing which half the value is considered to have been drawn from. It was developed by George Marsaglia and others in the 1960s.