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The authors present their earlier results (not included in Hars and Petruska due to space and time limitations), as well as some updated versions of those, and a few more recent pseudorandom number generator designs. These tell a systems designer which computer word lengths are suitable for certain high-quality pseudorandom number generators, and which constructions of a large family of designs provide long cycles, the most important property of such generators. The employed mathematical tools could help assessing the bit-mixing and mapping properties of a large class of iterated functions, performing only non-multiplicative computer operations: SHIFT, ROTATE, ADD, and XOR.
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