Note on Marsaglia's Xorshift Random Number Generators

Abstract

Marsaglia (2003) 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.