Compound cubic congruential pseudorandom numbers

Nonlinear congruential methods for generating uniform pseudorandom numbers show several attractive properties. The present paper deals with a particularly simple compound approach, which is based on cubic permutation polynomials over finite fields. These pseudorandom number generators allow a fast (and parallelized) implementation in single precision. Statistical independence properties of the generated sequences are studied. An upper bound for the discrepancy of tuples of successive pseudorandom 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.