A fast random number generator with good statistical properties

Recently, P. A. Lewis, A. S. Goodman, and J. M. Miller carried out extensive statistical tests on a random number generator of congruential type [3]. They showed that this generator has good statistical properties. Based on a careful analysis of the number theoretical properties of a class of generators, of which the above is a member, we have significantly increased its speed. For example, on the IBM 360/67 the time per calculation of one random number has been reduced from 14.25 μs to 9.25 μs and on the IBM 360/91 from 3.25 μs to 1.3 μs. The modified generator owes its increased speed to a replacement of a division operation by an addition and two shift instructions and the removal of a subsequent overflow test. © 1970 Springer-Verlag.