A fast and portable uniform quasi-random generator of very large period based ona generalized multi-moduli congruential method

Abstract

The present method generates machine-Independent uniform random sequences of real numbers in the interval (0.,1.) excluding 1. It uses a generalization of mulltiplicative linear gongruential generators working with prime numbers as moduli whose values have been fixed according to the positive integer arithmetic storage available from the system, and one or their corresponding primitive elements as multipliers to complete independently each full cycle.The periodicity can be considered as infinite: O (1092) for a 16-bit machine and O (10174) for a 32-bit machine and their respective integer arithmetic; the periodicity can be adjusted if it is required by the user in the normal version or statistically reaching the maximum in the enhanced 'stagger' version.An implementation of the method is available in the form of structured Fortran 77 functions and gives bettr results in term of velocity and periodicity than the other transportable functions compared with good quality of randomness.