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

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 formA = 5K, wherek 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 ofm = 2l 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.