This document makes no specific differentiation between random, pseudorandom, and quasi-random numbers, nor between random, pseudorandom, and quasi-random number generators unless the context requires otherwise. For details, refer to the ‘

Random Numbers

’ section in VS Notesdocument provided at the

Intel® oneAPI Math Kernel Library

web page.

All generators of nonuniform distributions, both discrete and continuous, are built on the basis of the uniform distribution generators, called Basic Random Number Generators (BRNGs). The pseudorandom numbers with nonuniform distribution are obtained through an appropriate transformation of the uniformly distributed pseudorandom numbers. Such transformations are referred to as generation methods. For a given distribution, several generation methods can be used. See VS Notes for the description of methods available for each generator.

An RNG task determines environment in which random number generation is performed, in particular parameters of the BRNG and its internal state. Output of VS generators is a stream of random numbers that are used in Monte Carlo simulations. A

random stream descriptor

and a

random stream

are used as synonyms of an

RNG task

in the document unless the context requires otherwise.

The random stream descriptor specifies which BRNG should be used in a given transformation method. See the

Random Streams and RNGs in Parallel Computation

section of VS Notes.

The term computational node means a logical or physical unit that can process data in parallel.