Note on Marsaglia's Xorshift Random Number Generators

Richard P. Brent

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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.

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