## Note on Marsaglia's xorshift RNGs

218. R. P. Brent,
Note on Marsaglia's xorshift random number generators,
* Journal of Statistical Software* 11, 5 (2004), 1-4.
Paper:
dvi (9K),
pdf (180K),
ps (56K).

## Abstract

Marsaglia [*Journal
Statistical Software* 8, 14 (2003), 1-9] has
described a class of "xorshift" random number generators (RNGs) with
periods 2^{n}-1
for *n* = 32, 64, etc. We show that the sequences generated by
these RNGs are identical to the sequences generated by certain linear
feedback shift register (LFSR) generators using "exclusive or" (xor)
operations on *n*-bit words, with a recurrence defined by a primitive
polynomial of degree *n*.

## Erratum

In the Introduction, after the comment that "the same is true for a linear
feedback shift register (LFSR) generator ... operating in parallel on 64-bit
words", we should add:
"provided that the 64 by 64 matrix of initial conditions is nonsingular".
## Software

A C implementation *xorgens* of some RNGs related to Marsaglia's
"xorshift" RNGs but with periods greater than 10^{1200} is available
here.
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