Beware of linear congruential generators with multipliers of the form a = ±2 q ±2 r
Pierre L’Ecuyer, Richard Simard · ACM Transactions on Mathematical Software · 1999
Linear congruential random-number generators with Mersenne prime modulus and multipliers of the form a = ±2 q ± 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.