Notes for Intel® oneAPI Math Kernel Library Vector Statistics

ID 772987
Date 12/04/2020
Document Table of Contents

Testing of Distribution Random Number Generators

Product and Performance Information

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VS generators are tested with a set of tests to control the quality of random number sequences of general discrete and continuous distributions.

Random numbers of discrete and continuous distributions are generated by transforming random numbers of uniform distribution. A source of uniformly distributed random numbers is a random stream produced by a basic generator. Quality of the random number sequences with non-uniform distribution greatly depends on the quality of the respective basic generator. Therefore, generators of discrete and continuous distributions are tested for each individual basic generator.

VS can provide several methods of random number generation for any probability distribution. For example, two methods are implemented for Poisson distribution: PTPE acceptance/rejection algorithm and PoisNorm inverse transformation algorithm, based on transformation of normal distribution. The generator is tested for each of the implemented methods.

VS offers two different implementations for each of continuous distributions:

  1. single-precision real arithmetic

  2. double-precision real arithmetic

As a rule, a single-precision version of the generator is faster than a double-precision one. Moreover, single-precision version is quite sufficient for most applications. VS offers only one version for discrete distributions.

Apart from the above-mentioned factors, RNGs are dependent for their quality on distribution parameters. For example, different transformation techniques may be used for different parameters. Therefore, generators are also tested for different parameter sets.