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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