# [racket] Mutable state vs RAM on fire

On May 2, 2012, at 11:50 PM, Deren Dohoda wrote:
>* Well I am sure it will try to use all the memory it can. Anyway, my
*>* functional code can raise the polynomial you gave '(1 1 1 1 1 1 0) to
*>* the 300th power in about four seconds on my machine, with half a
*>* second of garbage collection....
*>* But you can factor '(1 1 1 1 1 1 0) into '((1 0) (1 1) (1 0 1 0 1))....
*
Are we trying to multiply a bunch of arbitrary polynomials, or raise a single one to a large power?
If the latter, you can probably get a much more dramatic speed improvement by using "fast exponentiation":
(define (fast-expt p n)
(cond [(= n 1) p]
[(even? n)
(let [(p2 (mult p p))]
(fast-expt p2 (quotient n 2)))]
[(odd? n)
(let [(p2 (mult p p))]
(mult p (fast-expt p2 (quotient n 2))))]))
This reduces O(n) many multiplications to O(log(n)) many multiplications, which will dwarf most of the other optimizations people have mentioned.
Stephen Bloch
sbloch at adelphi.edu