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).


Marsaglia [Journal Statistical Software 8, 14 (2003), 1-9] has described a class of "xorshift" random number generators (RNGs) with periods 2n-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.


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".


A C implementation xorgens of some RNGs related to Marsaglia's "xorshift" RNGs but with periods greater than 101200 is available here.

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