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.
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
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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