Re: Question about random number generators Message #16 Posted by Marcus von Cube, Germany on 5 July 2011, 10:42 a.m., in response to message #15 by Thomas Radtke
Thomas, I was not replying to you directly but to the complete thread. But I try to answer you questions anyway. ;)
Given you have a sequence S(n+1) := F(S(n)). The numeric precision of your device is limited. So you have only a limited set V of values, the set having N elements. Depending on F you split this set in subsets. The simplest function F is identity (not random at all). S(n+1) := S(n) for every S in V. You split V in N subsets.
If your function F cycles through just the half of the possible values and there are starting seeds S and S' which create distinct subsets, you split V in two subsets, one containing S and the other containing S'. This may still be a good random sequence but it limits the possible number of random numbers in a single sequence to a subset of the possible values. If the split is asymmetric (one set much larger than the other) you can either get a good sequence or a very bad one, depending on the seed.
F might have another unwanted behavior. Even if F can produce all numbers in V in a single run, there may be values in the sequence which lead to more or less short cycles. You can enter the cycle from anywhere in V but once in the loop, F never produces values outside the loop.
Edited: 5 July 2011, 10:44 a.m.
