COMPOUND NONLINEAR CONGRUENTIAL PSEUDORANDOM NUMBERS

The nonlinear congruential method for generating uniform pseudorandom numbers has several very promising properties. However, an implementation in multiprecision of these pseudorandom number generators is usually 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 statistical independence properties. The results that are established are essentially best possible and show that the generated pseudorandom numbers model true random numbers very closely. The method of proof relies heavily on a thorough analysis of exponential sums.