(defn fib [n]
  (defn fib-iter [n a b]
    (cond
      (= n 0) b
      (fib-iter (- n 1) (+ a b) a)))
  (fib-iter n 1 0))

(defn fib-fast [n]
  (defn even? [n]
    (= (mod n 2) 0))
  (defn square [n]
    (* n n))
  (defn fib-iter [a b p q n]
    (cond
      (= n 0) b
      (even? n)
        (fib-iter
          a b
          (+ (square p) (square q))
          (+ (* 2 p q) (square q))
          (/ n 2))
      (fib-iter
        (+ (* b q) (* a q) (* a p))
        (+ (* b p) (* a q))
        p q (- n 1))))
  (fib-iter 1 0 0 1 n))

(defn count-fib [n]
  (var c 0)
  (defn fib-iter [n a b]
    (set c (+ c 1))
    (cond
      (= n 0) b
      (fib-iter (- n 1) (+ a b) a)))
  (fib-iter n 1 0)
  c)

(defn count-fib-fast [n]
  (defn even? [n]
    (= (mod n 2) 0))
  (defn square [n]
    (* n n))
  (var c 0)
  (defn fib-iter [a b p q n]
    (set c (+ 1 c))
    (cond
      (= n 0) b
      (even? n)
        (fib-iter
          a b
          (+ (square p) (square q))
          (+ (* 2 p q) (square q))
          (/ n 2))
      (fib-iter
        (+ (* b q) (* a q) (* a p))
        (+ (* b p) (* a q))
        p q (- n 1))))
  (fib-iter 1 0 0 1 n)
  c)

(var k 0)
(while (< k 100000)
  (printf "%d,%d,%d" (+ k 1) (count-fib k) (count-fib-fast k))
  (set k (+ k 1)))