Sunday, December 12, 2010

How long is the period of random numbers created by java.util.Random?

The answer is, pretty darn long! 


I feel a bit cheated for not knowning, while I had several times seen the code the years before.


So it uses a good old linear congruential generator:


x = A * x + C


So, java.util.Random uses these two constants (A and C respectively):


    private final static long multiplier = 0x5DEECE66DL;
    private final static long addend = 0xBL;

Quite appropriate to place two "random" numbers in the Random class, right? Only these are not entirely random...

0x5DEECE66DL % 8 == 5
and 
0xBL is an odd.

So what? 


It turns out, when these exact conditions are satisfied, the defined period is maximal, so the generated period (x is long) is 2^64. This piece of magic is documented here, page 9. The "why" of it is beyond me. 

If any ninja mathematician comes across this post, please leave some explanation if you can.


EDIT: oops. I overlooked that java.util.Random uses a mask to only reduce itself to 48 bits, instead of 64, so correspondingly the period is 2^48 instead of 2^64; apparently in an attempt to increase the quality of the generated numbers. In any case, if you need longer period, the technique described here will do the trick.