;;; mejja plays with let-values and dijkstras fib:
;;; www.cs.utexas.edu/users/EWD/ewd06xx/EWD654.PDF

(define (fib n)				;fantastic?
  (if (< 0 n)
      (let-values (((a b) (fib (quotient n 2))))
	(let ((c (* (- (* 2 b) a) a))
	      (d (+ (* b b) (* a a))))
	  (if (= 0 (remainder n 2))
	      (values c d)
	      (values d (+ c d)))))
      (values 0 1)))

(define (fib n)				;using let*-values
  ;; assumption: (div n d) => (values q r)
  (if (< 0 n)
      (let*-values (((q r) (div n 2)) ((a b) (fib q)))
	(let ((c (* a (- (* 2 b) a)))
	      (d (+ (* a a) (* b b))))
	  (if (= r 0)
	      (values c d)
	      (values d (+ c d)))))
      (values 0 1)))

(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))

(define (fib n #!optional cont)
  (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)))
  (if (and (exact? n) (not (negative? n)) (integer? n))
      (fib n (if (default-object? cont) cons cont))
      (error ":not-exact-nonnegative-integer" n 'FIB)))