The generating and testing of random variables has provided some of the most widely used methods for Monte Carlo simulation. Several new methods have been developed for new kinds of computer architectures, notably the subtract-with-borrow method that is very fast, requires few memory locations, has extremely long periods and provable uniformity. Current efforts are directed toward methods that will take advantage of massively parallel systems, new mass storage devices and other supercomputer features so that software for statistical computing can keep up with and take advantage of the remarkable advances in hardware. Many computer simulation studies call for random input at various point because of uncertainties or complexities of the underlying models. The construction of "pseudo-random" numbers can be sufficiently sophisticated to give workable substitutes for true random observations from a natural process. At the same time these generated numbers are readily available and can, when needed be reproduced exactly for testing purposes or to compare two different computing approaches to the solution of extremely large and complicated mathematical problems.
