i'm implementing a benchmark which includes a detailed specification for a random number generator. for any of the kernels outlined in the benchmark, i might have to generate a set of random numbers R, which has a length n, using the following formulas:

R[k] = ((2^-46)(X[k])) mod 2^46, where

X[k] = (a^k)s

where the values of a and s are constant and defined below.
many of the kernels in the benchmark require a large number of randoms to be generated (in the tens of millions). when i invoke the following getRandAt function that many times to build up a list, evaluation of the list takes forever (somewhere between 5 and 10 minutes). i've tried optimizing this several different ways, with no luck. i though i might post my code here and see if anyone notices anything i'm doing wrong that might be causing such a large bottleneck:

--constants
a :: Int64
a = 5^13

divisor :: Int64
divisor = 2^46

multiplier :: Float
multiplier = 2**(-46)

--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

thanks all in advance for your help!
-james