A study of 64-bit multipliers for Lehmer pseudorandom number generators

A study was conducted of multipliers for 64-bit congruential pseudorandom number generators. Extensive analysis and testing resulted in the identification of over 200 good multipliers of the form A = 5(k) where k is a prime number. The integer lattice structure from any single multiplier is so fine that it is not visible when REAL*4 values are returned in up to four dimensions. Known number-theoretic characteristics of m = 2(l) generators were exploited to provide a remarkably sensitive new lattice test, one that is based on analysis of spacings in several dimensions. That examination led to new methods that can provide lattice-free pseudorandom streams in up to 200 dimensions, and with extended period length. (C) 1997 Elsevier Science B.V.