Scheme code for Pollard's Rho algorithm -


i trying learn scheme implementing few algorithms.

pollards-rho(n)  g(x) = x2 + 1 mod n     x ← 2; y ← 2; d ← 1;     while d = 1:         x ← g(x)         y ← g(g(y))         d ← gcd(|x - y|, n)     if d = n, return failure.     else, return d

i trying implement above algorithm in scheme. appreciated. thanks

an implementation in racket:

;;; algorithm 19.8  pollard's rho method ; input   n>=3 neither prime nor perfect power ; output  either proper divisor of n or #f (: pollard : natural -> (u natural false)) (define (pollard n)   (let ([x0 (random-natural n)])     (do ([xi x0 (remainder (+ (* xi xi) 1) n)]          [yi x0 (remainder (+ (sqr (+ (* yi yi) 1)) 1) n)]          [i  0  (add1 i)]          [g  1  (gcd (- xi yi) n)])       [(or (< 1 g n) (> (sqrt n)))        (if (< 1 g n)            (cast g natural?)            #f)])))

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