Four-tap shift-register-sequence random-number generators

Abstract

Correlations in the generalized feedback shift-register random-number generator are shown to be greatly reduced when the number of feedback taps is increased from two to four (or more) and the tap offsets are made large. Simple formulas for producing maximal-cycle four-tap rules from available primitive trinomials are given, and explicit three- and four-point correlations are found for some of those rules. Several generators are also tested using a simple but sensitive random-walk simulation that relates to a problem in percolation theory. While virtually all two-tap generators fail this test, four-tap generators with offsets greater than about 500 pass it, have passed tests carried out by others, and appear to be good multipurpose high-quality random-number generators. © 1998 American Institute of Physics.