Pseudorandom Number Generators Revisited

摘要

The paper concentrates on one class of generators, namely linear congruential generators. It splits up the full cycle of the multiplicative generator into equal parts, first into two parts, then into 2 sup (k) parts, showing that the pseudorandom numbers lie on two and on no more than 2 sup (k-1) parallel lines if k = 3 respectively. It briefly considers antithetic pseudorandom numbers studies the conditional variances and the correlation coefficient of the pseudorandom numbers paired across two parts. It summarizes the disadvantages of splitting a pseudorandom number stream into parts. Finally, it gives alternative generators for supercomputers.