© 1988 by Institute of Mathematics and its Applications
Analysis and synthesis of Ultra-uniform Pseudorandom Number Generators
School of Mathematics and Physics, University of East Anglia Norwich NR4 7TJ, UK
Department of Electrical Engineering and Electronics, Faculty of Technology Brunel The University of West London Uxbridge, Middlesex UB8 3PH, UK
The Wichmann–Hill algorithm is a high-performance generator of uniformly distributed pseudorandom numbers, designed for use on, and portability between, 8-bit of 16-bit machines. Two analyses (one number-theoretic, the other probability-theoretic) are presented in order to explain its superb performance. It is shown that the original Wichmann–Hill configuration can be regarded as a single linear congruential generator with unrealizably large multiplier and modulus decomposed into three realizable subgenerators. This provides an obvious insight into the source of the generator's high quality, but more importantly permits, for the first time, the application of the extremely stringent Coveyou-MacPherson spectral test—which is passed with flying colours.
The techniques used for analysis have also been applied to design and test a large family of three-component generalized Wichmann–Hill-type generators with substantially the same very high performance as the original. Over one hundred such generators have been found. There is no difficulty in extending the design to configurations suitable for 32-bit machines, with some improvement in the quality. Increasing the number of subgenerators produces a more dramatic enhancement: this is illustrated by means of an example employing four components.