2009/2/26 James Swaine <james.swaine@gmail.com>

--gets r[k], which is the value at the kth
--position in the overall sequence of
--pseudorandom numbers
getRandAt :: Int64 -> Int64 -> Float
getRandAt 0 seed = multiplier * (fromIntegral seed)
getRandAt k seed = multiplier * (fromIntegral x_next)
    where
        x_prev = (a^k * seed) `mod` divisor
        x_next = (a * x_prev) `mod` divisor

One thing that comes to mind is that this exponentiation, with a very big exponent, could potentially take a very long time. I believe that GHC implements (^) using a repeated squaring technique, so it runs in log(k) time, which ought to be no problem. I'm not sure about other compilers though.

Also note:

(a^k * seed) `mod` divisor = ((a^k `mod` divisor) * seed) `mod` divisor = (a^(k `mod` phi(divisor)) * seed) `mod` divisor.

Where phi is the Euler totient function: phi(2^46) = 2^23.

Modulo errors... it's been a while since I've done this stuff.

Luke