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