Package org.apache.commons.rng.simple

Randomness providers

This package provides factory methods by which low-level classes implemented in module "commons-rng-core" are instantiated.
Classes in package org.apache.commons.rng.simple.internal should not be used directly.
The generators are not thread-safe: Parallel applications must use different generator instances in different threads.

In the case of pseudo-random generators, the source of randomness is usually a set of numbers whose bits representation are scrambled in such a way as to produce a random-looking sequence.
The main property of the sequence is that the numbers must be uniformly distributed within their allowed range.
Classes in this package do not provide any further processing of the number generation such as to match other types of distribution.

Which source of randomness to choose may depend on which properties are more important. Considerations can include speed of generation, memory usage, period size, equidistribution, correlation, etc.
For some of the generators, interesting properties (of the reference implementations) are proven in scientific papers. Some generators can also suffer from potential weaknesses.

For simple sampling, any of the generators implemented in this library may be sufficient.
For Monte-Carlo simulations that require generating high-dimensional vectors), equidistribution and non-correlation are crucial. The Mersenne Twister and Well generators have equidistribution properties proven according to their bits pool size which is directly related to their period (all of them have maximal period, i.e. a generator with size n pool has a period 2n-1). They also have equidistribution properties for 32 bits blocks up to s/32 dimension where s is their pool size.
For example, Well19937c is equidistributed up to dimension 623 (i.e. 19937 divided by 32). It means that a Monte-Carlo simulation generating vectors of n (32-bits integer) variables at each iteration has some guarantee on the properties of its components as long as n < 623. Note that if the variables are of type double, the limit is divided by two (since 64 bits are needed to create a double).
Reference to the relevant publications are listed in the specific documentation of each class.

Memory usage can vary a lot between providers. The state of MersenneTwister is composed of 624 integers, using about 2.5 kB. The Well generators use 6 integer arrays, the length of each being equal to the pool size; thus, for example, Well44497b uses about 33 kB.

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