Generating pseudorandom numbers on a two's complement machine such as the IBM 360

Abstract

The familiar multiplicative congruential generator is examined in the context of the type of two's complement arithmetic used in the IBM 360 series. Different sequences of residues are considered and relationships established among them. It is shown that a sequence of positive and negative residues may be produced more simply and econimically than with the conventional approach and yet have twice the period of the latter without loss of desirable statistical properties. Another easily generated sequence involving absolute values is also shown to have twice the period but with the less attractive statistical properties. The statistical properties of these sequences are given and related to previously established criteria.