[racket] Math - factorial.rkt, binomial.rkt and memoization

From: Laurent (laurent.orseau at gmail.com)
Date: Mon Apr 8 12:33:11 EDT 2013

Would it make sense to use memoization more broadly for the definition of
the factorial in the math lib, maybe with a `provide'd parameter to control
how many values can be memoized?

While building big numbers (around 800!) I had to redefine my own factorial
and binomial functions with memoization, otherwise it would take too long.

Also, probably `binomial' could take advantage of this memoization, just
like `permutations' does.

Currently (in DrRacket, so not entirely accurate, but should be close
> (time
   (for ([n 100])
     (binomial 10000 4000)))
cpu time: 4072 real time: 4075 gc time: 440
> (time
   (for ([n 10000])
     (binomial 800 400)))
cpu time: 9424 real time: 9430 gc time: 836
> (time (for ([i 1000])
          (factorial 10000)))
cpu time: 11441 real time: 11630 gc time: 276

which makes it impractical in some cases.

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