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