sicp-124-125

#lang planet neil/sicp

 (define (square x) (* x x))

(define (fast-expt b n)
  (define (iter a b n)
    (cond ((= n 0) a)
          ((even? n) (iter a (square b) (/ n 2)))
          (else (iter (* a b) b (- n 1)))))
  (iter 1 b n))

(define (multi a b)
  (define (fast-multi-iter x y n)
    (cond ((= n 0) x)
          ((even? n) (fast-multi-iter x (double y) (/ n 2)))
          (else (fast-multi-iter (+ x y) y (- n 1)))))
  (fast-multi-iter 0 a b))

gcd(206, 40)
gcd(40, remainder(206, 40)) ;1
gcd(6, remainder(40, 6))   ;2
gcd(4, remainder(6, 4))  ;3
gcd(2, remainder(4, 2))  ;4

(gcd 206 40)
(gcd 40 (remainder 206 40))
->
(if (= (remainder 206 40) 0)
  40
  (gcd (remainder 206 40)
    (remainder 40 (remainder 206 40))))
->
(if (= (remainder 40 (remainder 206 40)) 0)
  (remainder 206 40)
  (gcd
    (remainder
      40
      (remainder 206 40))
    (remainder
      (remainder 206 40)
      (remainder
        40
        (remainder 206 40)))))
...