ON THE PERIODS OF THE ${\tt ranshi}$ RANDOM NUMBER GENERATOR

The stochastic properties of the pseudo-random number generator ${\tt ranshi}$ are discussed, with emphasis on the average period. Within a factor 2 this turns out to be the root of the maximally possible period. The actual set of periods depends on minor details of the algorithm, and the system settles down in one of only a few different cycles. These features are in perfect agreement with absolute random motion in phase space, to the extent allowed by deterministic dynamics.