Abstract
Marsaglia (2003) has described a class of Xorshift random number generators (RNGs) with periods 2<sup>n</sup> - 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
Highlights
Marsaglia (2003) suggests “xorshift RNGs” using the “exclusive or” operation on 32-bit or 64-bit words with left- or right-shifted versions of the same word
Note that the same is true for a linear feedback shift register (LFSR) generator (Menezes, van Oorschot, and Vanstone 1997) using a recurrence defined by a primitive polynomial P (z) of degree 64 and operating in parallel on 64-bit words
First we introduce some notation and describe LFSR and xorshift random number generators, we show how the LFSR and xorshift generators are related
Summary
Marsaglia (2003) suggests “xorshift RNGs” using the “exclusive or” operation on 32-bit or 64-bit words with left- or right-shifted versions of the same word. Note that the same is true for a linear feedback shift register (LFSR) generator (Menezes, van Oorschot, and Vanstone 1997) using a recurrence defined by a primitive polynomial P (z) of degree 64 and operating in parallel on 64-bit words. This suggests that the two RNGs might be related. From the point of view of a software developer, Marsaglia’s idea is useful, because his implementation requires less space than a standard implementation of the corresponding LFSR generator This is possible because the initial conditions are special. First we introduce some notation and describe LFSR and xorshift random number generators, we show how the LFSR and xorshift generators are related
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