AliasMethodDiscreteSampler

Distribution sampler that uses the Alias method. It can be used to sample from n values each with an associated probability. This implementation is based on the detailed explanation of the alias method by Keith Schartz and implements Vose's algorithm.

Vose, M.D., A linear algorithm for generating random numbers with a given distribution, IEEE Transactions on Software Engineering, 17, 972-975, 1991. The algorithm will sample values in O(1) time after a pre-processing step of O(n) time.

The alias tables are constructed using fraction probabilities with an assumed denominator of 253. In the generic case sampling uses UniformRandomProvider.nextInt(int) and the upper 53-bits from UniformRandomProvider.nextLong().

Zero padding the input probabilities can be used to make more sampling more efficient. Any zero entry will always be aliased removing the requirement to compute a long. Increased sampling speed comes at the cost of increased storage space. The algorithm requires approximately 12 bytes of storage per input probability, that is n * 12 for size n. Zero-padding only requires 4 bytes of storage per padded value as the probability is known to be zero.

An optimisation is performed for small table sizes that are a power of 2. In this case the sampling uses 1 or 2 calls from UniformRandomProvider.nextInt() to generate up to 64-bits for creation of an 11-bit index and 53-bits for the long. This optimisation requires a generator with a high cycle length for the lower order bits.

Larger table sizes that are a power of 2 will benefit from fast algorithms for UniformRandomProvider.nextInt(int) that exploit the power of 2.

Based on Commons RNG implementation. See https://commons.apache.org/proper/commons-rng/commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/AliasMethodDiscreteSampler.html.