;; Some examples showing innacuracies using floating-point numbers,
;; and how to try to get around them.
;;
; make-list : natnum any -> list-of-any
; returns a list of n copies of s
(define (make-list n s)
  (cond
    [(zero? n) empty]
    [else      (cons s (make-list (sub1 n) s))]))

; example lists for addition
; list1: 1.0e16 followed by 101 5's
; list2: 101 5's followed by 1.0e16
; list3: 50 5's followed by 1.0e16 followed by 51 5's
(define list1 (cons 1.0e16 (make-list 101 5)))
(define list2 (append (make-list 101 5) (list 1.0e16)))
(define list3 (append (make-list 50 5) (cons 1.0e16 (make-list 51 5))))
(define janus (list 99
		    3.2e+270
		    -99
		    -2.4e+270
		    1234
		    4
		    -8e+269
		    -4))



; sum : list-of-number -> number
; Returns the sum of the elements of the list
(define (sum l)
  (cond [(empty? l) 0]
	[else       (+ (first l) (sum (rest l)))]))


; better-sum : list-of-number -> number
; Returns the sum of the elements of the list, trying to avoid
; imprecision errors by adding small magnitude numbers first.
;
; (Note: "quicksort" is a built-in DrScheme function!)
;
(define (better-sum alon)
  (local [(define (compare x y) (> (abs x) (abs y)))]
    (sum (quicksort alon compare))))