Beware of linear congruential generators with multipliers of the form a = +/- 2(q) +/- 2(r)
Linear congruential random-number generators with Mersenne prime modulus and multipliers of the form a = +/-2(q) +/-2(r) have been proposed recently. Their main advantage is the availability of a simple and fast implementation algorithm for such multipliers. This note generalizes this algorithm, points out statistical weaknesses of these multipliers when used in a straightforward manner, and suggests in what context they could be used safely.
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