Four-tap shift-register-sequence random-number generators
- 1 July 1998
- journal article
- Published by AIP Publishing in Computers in Physics
- Vol. 12 (4), 385-392
- https://doi.org/10.1063/1.168692
Abstract
It is shown how correlations in the generalized feedback shift-register (GFSR) random-number generator are greatly diminished when the number of feedback taps is increased from two to four (or more) and the tap offsets are lengthened. 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. A number of 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 offset greater than about 500 pass it, have passed tests carried out by others, and appear to be good multi-purpose high-quality random-number generators.Keywords
This publication has 38 references indexed in Scilit:
- Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc latticesPhysical Review E, 1998
- Determination of the bond percolation threshold for the Kagomé latticeJournal of Physics A: General Physics, 1997
- Considerations on correlations in shift-register pseudorandom number generators and their removalComputer Physics Communications, 1997
- Physical Tests for Random Numbers in SimulationsPhysical Review Letters, 1994
- A Table of Primitive Binary PolynomialsMathematics of Computation, 1994
- Spanning probability in 2D percolationPhysical Review Letters, 1992
- The hierarchy of correlations in random binary sequencesJournal of Statistical Physics, 1991
- Figures of merit for digital multistep pseudorandom numbersMathematics of Computation, 1990
- Figures of Merit for Digital Multistep Pseudorandom NumbersMathematics of Computation, 1990
- Effects of the random number generator on computer simulationsPhysics Letters B, 1985