COMPOUND CUBIC CONGRUENTIAL PSEUDORANDOM NUMBERS

Nonlinear congruential methods for generating uniform pseudorandom num bers show several attractive properties. The present paper deals with a particularly simple compound approach, which is based on cubic permu tation polynomials over finite fields. These pseudorandom number gener ators allow a fast (and parallelized) implementation in single precisi on. Statistical independence properties of the generated sequences are studied. An upper bound for the discrepancy of tuples of successive p seudorandom numbers is established, which rests on a classical result of A. Weil on exponential sums. Finally, a ready-to-program example of a compound cubic congruential generator is given.