in reply to Predict Random Numbers

Looks very interesting; I'll probably play with it a little when I get home.

OTOH, it looked a lot more intersting before I read the code. I was wondering, how do you determinte the a, b, n, and m? Is it possible to write an algo to determinte them for an unknown RNG? Given only M (which seems to be 1<<number of bits of output)? Given nothing? Using srand()? Without changing the seed?

We are using here a powerful strategy of synthesis: wishful thinking. -- The Wizard Book

Update:Changed "N" to "M" in "given only N".

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Re: Re: Predict Random Numbers
by no_slogan (Deacon) on Mar 14, 2002 at 18:06 UTC
    For drand48(), the manpage tells you the constants a, b, and m. To get n (the number of outputs from int(rand*256) that are used), I used trial and error. There's a mathematical derivation of what values of n are likely to work in another paper, but that doesn't seem to be available online.

    Determining a, b, and m using srand() can be automated in some cases, but it takes a bit of guesswork. If m is a power of 2 and b is small enough, you'll see an obvious pattern in the output of: 

    for (0..30) {
  srand(1<<$_);
  printf "%030b\n", rand()*(2**30);
}

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    You can work out a and take a guess at m and b from that -- a is the part that moves, b is the part that stays still, and m is whatever seems big enough to hold it all.

    There are several papers (including the one I mentioned before) on determining those constants using only the output from rand(). Some of them use the L3 algorithm as well.

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