Problems with Linear Congruential Generators

Linear congruential generators are very efficient, are theoretically quite well understood, and work well for many applications. However they have some drawbacks (which can be generally be improved by increasing M):

• The maximum period is M-1, which is much too small for 32-bit generators where , which can be exhausted in a few minutes on a workstation. Need to use integers with at least 48 and preferably closer to 64 bits. On most machines this requires multiple precision arithmetic which can be slow.

• d-tuples of such numbers show a regular lattice structure when plotted in d-dimensions. This is called the scatter plot test.

• These generators have been proven to have correlations between numbers that are apart in the sequence. This can be a major problem for applications using a regular grid or lattice.