Twisted GFSR generators

Matsumoto Makoto

ACM Transactions on Modeling and Computer Simulation

The generalized feedback shift register(GFSR) algorithm suggested by Lewis and Payne is a widely used pseudorandom number generator, but has the following serious drawbacks: 1. Aninitialization scheme to assure higher order equidistribution is involved and is time-consuming. 2. Each bit of the generated words constitutes an m-sequence based on a primitive trinomial, which shows poor randomness with respect to weight distribution. 3. Large working area is necessary. 4. The period of sequence is far shorter than the theoretical upper bound. This paper presents the twisted GFSR(TGFSR) algorithm, as lightly but essentially modified version of the GFSR, which solves all the above problems without loss of merit. Some practical TGFSR generators were implemented and they passed strict empirical tests. These new generators are most suitable for simulation of a large distributive system, which requires a number of mutually independent pseudorandom number generators with compact size.

generalized feedback shift registers

matrix linear congruential generators

m-sequences

TLP-sequences

GF(2m)

Mathematics [ 410 ]

eng

ACM

Copyright (c) 1998 ACM. This is the author version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Modeling and Computer Simulation,Vol.2 No.3 ; http://dx.doi.org/10.1145/146382.146383

[ISSN] 1049-3301

[DOI] 10.1145/146382.146383

[NCID] AA10779230

[DOI] http://dx.doi.org/10.1145/146382.146383 isVersionOf