On 02/19/2013 05:28 PM, Joe Gilray wrote:
Racketeers,
Thanks for putting together the fantastic math library. It will be a
wonderful resource. Here are some quick impressions (after playing
mostly with math/number-theory)
The thanks in this case goes to Jens Axel, who wrote almost all of the
number theory functions.
1) The functions passed all my tests and were very fast. If you need
even more speed you can keep a list of primes around and write functions
to use that, but that should be rarely necessary
I'm glad to hear they passed your tests as well. FWIW, when I reviewed
Jens Axel's code before its initial commit, I didn't find any errors,
either. (Which is amazing. Usually, adding another observer to a
software system collapses its state to a mess of bug-ridden filth.)
...
2b) combinations calculator
; function that returns the number of combinations, not the combinations
themselves
; faster than using n! / (r! (n-r)!)
(define (combinations n r)
(cond
[(or (< n 0) (< r 0)) (error "combinations: illegal arguments, n
and r must be >= 0")]
[(> r n) 0]
[else
(let lp ([mord n] [total 1] [mult #t])
(cond
[(or (= 0 mord) (= 1 mord)) total]
[(and mult (= mord (- n r))) (lp r total #f)]
[(and mult (= mord r)) (lp (- n r) total #f)]
[mult (lp (sub1 mord) (* total mord) #t)]
[else (lp (sub1 mord) (/ total mord) #f)]))]))
We have this one under the name `binomial'. But yours is about 8% faster
in my tests with random inputs in [0..1000], which has me curious.
Neil ⊥
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