COMPOUND NONLINEAR CONGRUENTIAL PSEUDORANDOM NUMBERS

The nonlinear congruential method for generating uniform pseudorandom numbers has several very promising properties. However, an implementat ion in multiprecision of these pseudorandom number generators is usual ly necessary. In the present paper a compound version of the nonlinear congruential method is introduced, which overcomes this disadvantage. It is shown that the generated sequences have very attractive statist ical independence properties. The results that are established are ess entially best possible and show that the generated pseudorandom number s model true random numbers very closely. The method of proof relies h eavily on a thorough analysis of exponential sums.