[racket] Mutable state vs RAM on fire

From: Arthur Nunes-Harwitt (anh at cs.rit.edu)
Date: Thu May 3 11:07:05 EDT 2012

Dear Stephen,

   It turns out that the "fast" multiplication algorithm isn't so fast for 
polynomials.  See Norvig's Paradigms of AI Programming or Zippel's 
Effective Polynomial Computation.

-Arthur

==============================================================
Arthur Nunes-Harwitt
Computer Science Department, Rochester Institute of Technology
Room 70-3509
585-475-4916
==============================================================

"I don't know what the language of the future will be
called, but it will look like LISP."

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On Thu, 3 May 2012, Stephen Bloch wrote:

>
> 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
>
>
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