How can I best generate a static array of random number on demand?

Question

An application I\'m working on requires a matrix of random numbers. The matrix can grow in any direction at any time, and isn\'t always full. (I\'ll probably end up re-imple

Answer 1

You want a random number generator with random access to the elements, instead of sequential access. (Note that you can reduce your two coordinates into a single index i.e. by computing i = x + (y << 16).)

A cool example of such a generator is Blum Blum Shub, which is a cryptographically secure PRNG with easy random-access. Unfortunately, it is very slow.

A more practical example is the well-known linear congruential generator. You can easily modify one to allow random access. Consider the definition:

X(0) = S
X(n) = B + X(n-1)*A (mod M)

Evaluating this directly would take O(n) time (that's pseudo linear, not linear), but you can convert to a non-recursive form:

//Expand a few times to see the pattern:
X(n) = B + X(n-1)*A (mod M)
X(n) = B + (B + X(n-2)*A)*A (mod M)
X(n) = B + (B + (B + X(n-3)*A)*A)*A (mod M)
//Aha! I see it now, and I can reduce it to a closed form:
X(n) = B + B*A + B*A*A + ... + B*A^(N-1) + S*A^N (mod M)
X(n) = S*A^N + B*SUM[i:0..n-1](A^i) (mod M)
X(n) = S*A^N + B*(A^N-1)/(A-1) (mod M)

That last equation can be computed relatively quickly, although the second part of it is a bit tricky to get right (because division doesn't distribute over mod the same way addition and multiplication do).