(load "util.scm")
(load "misc/sicp-regsim.scm")

(display "\nex-5.1 draw-factorial\n")

; See misc directory for drawing.

(display "[answered]\n")

(display "\nex-5.2 design-factorial\n")

(define factorial-machine
  (make-machine
    '(counter product n)
    (list (list '> >) (list '* *) (list '+ +))
    '(controller
       (assign product (const 1))
       (assign counter (const 1))
       test-counter
         (test (op >) (reg counter) (reg n))
         (branch (label factorial-done))
         (assign product (op *) (reg product) (reg counter))
         (assign counter (op +) (reg counter) (const 1))
         (goto (label test-counter))
      factorial-done)))

(set-register-contents! factorial-machine 'n 6)
(start factorial-machine)
(assert (get-register-contents factorial-machine 'product) 720)

(display "\nex-5.3 - sqrt-newton\n")

(define (sqrt-newton n)
  (define (improve guess)
    (average guess (/ n guess)))
  (define (average a b)
    (/ (+ a b) 2))
  (define (good-enough? guess)
    (< (abs (- (* guess guess) n)) 0.01))
  (define (iter guess)
    (if (good-enough? guess)
      guess
      (iter (average guess (/ n guess)))))
  (iter 1.))


(display (sqrt-newton 2))


;(display "\nex-5.4\n")