1.19.scm

(define (fib n)
  (fib-iter 1 0 0 1 n))

(define (fib-iter a b p q count)
  (define (square n) (* n n))
  (cond ((= count 0) b)
        ((even? count) 
         (fib-iter
          a
          b 
          (+ (square p) (square q))
          (+ (* 2 p q) (square q))
          (/ count 2)))
        (else 
         (fib-iter 
          (+ (* b q) (* a q) (* a p))
          (+ (* b p) (* a q))
          p
          q
          (- count 1)))))