Am Donnerstag, 26. Februar 2009 18:48 schrieb Luke Palmer:
2009/2/26 James Swaine
--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.
Another thing: if you don't need to pick random indices, but use them in order, it may be faster to have a list of the random numbers : randInts = iterate ((`mod` divisor) . (*a)) seed or carry x[k] around as state.
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.
phi(2^n) = 2^(n-1). Apart from that, correct.
Modulo errors... it's been a while since I've done this stuff.
Luke