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)
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 2) I have a couple of functions to donate if you want them: 2a) Probablistic primality test: ; function that performs a Miller-Rabin probabalistic primality test k times, returns #t if n is probably prime ; algorithm from http://rosettacode.org/wiki/Miller-Rabin_primality_test, code adapted from Lisp example ; (module+ test (check-equal? (is-mr-prime? 1000000000000037 8) #t)) (define (is-mr-prime? n k) ; function that returns two values r and e such that number = divisor^e * r, and r is not divisible by divisor (define (factor-out number divisor) (do ([e 0 (add1 e)] [r number (/ r divisor)]) ((not (zero? (remainder r divisor))) (values r e)))) ; function that performs fast modular exponentiation by repeated squaring (define (expt-mod base exponent modulus) (let expt-mod-iter ([b base] [e exponent] [p 1]) (cond [(zero? e) p] [(even? e) (expt-mod-iter (modulo (* b b) modulus) (/ e 2) p)] [else (expt-mod-iter b (sub1 e) (modulo (* b p) modulus))]))) ; function to return a random, exact number in the passed range (inclusive) (define (shifted-rand lower upper) (+ lower (random (add1 (- (modulo upper 4294967088) (modulo lower 4294967088)))))) (cond [(= n 1) #f] [(< n 4) #t] [(even? n) #f] [else (let-values ([(d s) (factor-out (- n 1) 2)]) ; represent n-1 as 2^s-d (let lp ([a (shifted-rand 2 (- n 2))] [cnt k]) (if (zero? cnt) #t (let ([x (expt-mod a d n)]) (if (or (= x 1) (= x (sub1 n))) (lp (shifted-rand 2 (- n 2)) (sub1 cnt)) (let ctestlp ([r 1] [ctest (modulo (* x x) n)]) (cond [(>= r s) #f] [(= ctest 1) #f] [(= ctest (sub1 n)) (lp (shifted-rand 2 (- n 2)) (sub1 cnt))] [else (ctestlp (add1 r) (modulo (* ctest ctest) n))])))))))])) 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)]))])) Thanks again! -Joe
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