;;; Copyright Igor Rivin 2004, 2005, all rights reserved.

(load "utils.ss")

;; prints out all positive integers....
(define inf-loop
  (lambda (n)
    (let ((nn n))
      (let ((x (call/cc (lambda (k) k))))
        (display nn)
        (newline)
        (set! nn (+ 1 nn))
        (x x)))))

(define inf-loop2
  (lambda (n m)
    (let ((nn n)
          (mm m))
      (let ((x (call/cc (lambda (k) k))))
        (display nn)
        (newline)
        (set! nn (+ 1 nn))
        (set! mm (- mm 1))
        (if (> mm 0)
            (x x))))))

(define dog (list->vector '(1 2 3)))


 ; computes the nth fibonacci number (non-recursively).

(define fib
  (lambda (n)
    (let fibaux ((a 0) (b 1) (m 0))
      (if (= m n) a (fibaux b (+ a b) (+ m 1))))))

;; Newton's method for computing square roots.
(define mysqrt
  (lambda (N start tol numiter)
    (if (< (abs (- (* start start) N)) tol)
        start
        (let ((iter (lambda (x)(* 0.5 (+ x (/ N x))))))
          (let sqrtit ((guess start)(iterleft numiter))
            (let ((newguess (iter guess))
                  (newiter (- iterleft 1)))
              (if (or (< (abs (- newguess guess)) (* tol guess)) (<= newiter 0))
                  guess
                  (sqrtit newguess newiter))))))))



(define fact
  (lambda (n)
    (let factaux ((prod 1) (n n))
      (if (= n 0)
          prod
          (factaux (* prod n) (- n 1))))))