(define (fib n)
  (define (fib n k)
    (if (< 0 n)
	(fib (quotient n 2)
	     (lambda (a b)
	       (let ((c (* a (- (* 2 b) a)))
		     (d (+ (* a a) (* b b))))
		 (if (= 0 (remainder n 2))
		     (k c d)
		     (k d (+ c d))))))
	(k 0 1)))
  (guarantee-exact-nonnegative-integer n 'FIB)
  (fib n cons))