Some Long-Period Random Number Generators using Shifts and Xors

224. R. P. Brent, Some long-period random number generators using shifts and xors, ANZIAM Journal 48 (CTAC2006), C188-C202, 2007.
Presented at the 13th Biennial Computational Techniques and Applications Conference (CTAC06), Townsville, 2-5 July 2006. arXiv:1004.3115v1

Preprint: dvi (17K), pdf (168K), ps (136K).

Paper: anziamj.austms.org.au

Abstract

Marsaglia recently introduced a class of xorshift random number generators (RNGs) with periods 2n-1 for n = 32, 64, etc. Here we give a generalisation of Marsaglia's xorshift generators in order to obtain fast and high-quality RNGs with extremely long periods.

RNGs based on primitive trinomials may be unsatisfactory because a trinomial has very small weight. In contrast, our generators can be chosen so that their minimal polynomials have large weight (number of nonzero terms). A computer search using Magma has found good generators for n a power of two up to 4096. These have been implemented in a free software package xorgens.

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