## 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 2^{n}-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.

## Erratum

In Section 3 of the paper the condition that the parameters (a, b, c, d)
should be distinct was inadvertently omitted
(it is stated in the associated file `xortable.txt`).

Thanks to George Spelvin for noticing this omission.
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