Considerations on correlations in shift-register pseudorandom number generators and their removal Original Research Article

We present a simple calculation quantitatively explaining the triplet correlations in the popular shift-register random number generator “R250”, which were recently observed numerically by Schmid and Wilding, and are known from general analysis of this type of generator. Starting from these considerations, we discuss various methods to remove these correlations by combining different shift-register generators. We implement and test a particularly simple and fast version, based on an XOR combination of two independent shift-register generators with different time lags. The results indicate that this generator has much better statistical properties than R250, while being only a factor of two slower. This is consistent with previous analytical considerations and successful applications of this type of generator. The known nine-point correlations still present in the generator are quantitavely understood by our simple arguments.