Common defects in initialization of pseudorandom number generators

Reviewer: Soubhik Chakraborty

It is a well-known fact that numbers generated by an arbitrarily selected seed for a pseudorandom number generator (PRNG) may not be statistically random. This paper demonstrates that many modern random number generators have some noticeable patterns, when initial seeds are chosen through a linear recurrence. Matsumoto et al. painstakingly experiment with 58 generators and discover as many as 40 to be defective. Further investigation reveals that the unwanted patterns are caused by the wrong choice of initialization rather than recursion. Accordingly, they advise PRNG designers to use a nonsystematic choice of seeds, or supply a better initialization scheme [1,2], and to test the randomness of the n -th output x ( n , s ) corresponding to a given seed s by varying both n and s . An interesting aspect missed by Matsumoto et al. is that PRNGs generally have a cycle, which, after completion, generates the same sequence, whereas the sequence of decimals of irrational numbers, such as pi, is nonrepeating and nonterminating. Pi, in fact, has been already proposed as a random number generator and the allegation that it is “less random than we thought” has been recently refuted by Marsaglia [3]. Of course, one has to generate these decimals easily and quickly on the computer. Examining some function of pi, rather than pi itself, is a worthwhile proposition. Online Computing Reviews Service