How to write a haskell function without IO in type sig by hiding 'state' changes

I wrote a function in haskell that takes a few parameters like Word32, String (ignore currying) and outputs IO Word32. Now, this is a function in the true sense: for the same inputs, the output will always be the same. There are no side-effects. The reason the function returns IO Word32 instead of Word32 is that the function updates many 32 bit Linear Feedback Shift registers (lfsr) and other registers several times in a loop in order to compute the final Word32 output.

My question is this: Given that this function effectively has no side-effects, is it possible to hide those register updates inside the function implementation so that the function returns Word32 and not IO Word32? If so, how?