Abstract
In this chapter, we review several of the approaches for generating pseudorandom numbers (PRNs) on the unit interval. These are numbers that exhibit many of the properties of actual random numbers but are generated using deterministic algorithms. Also discussed are many of the desired features of PRN generators, such as uniformity, portability, large periods, and efficiency. In particular, we consider linear and nonlinear congruential generators, linear feedback shift register generators, and generators based on cellular automata. Some specific PRN generators such as Park and Miller's “minimal standard congruential generator”, the Wichmann–Hill generator, the L'Ecuyer generator, the Tausworthe bit-level generator, and the Mersenne Twister generator are presented. In addition, some of the many tests that prove useful in evaluating PRN generators are considered. A brief summary of PRN generator development from 1991 to 2020 is presented in order to stress the intense interest in and diversity among PRN generators. This chapter is provided for completeness and in order to stress the necessity to use “good” generators but it is not essential for users to understand all of the contents in order to perform useful MC calculations.
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