;; /home/comp212/Labs/lab4/sum.ss
;; By Dan Grossman, 96.Sep.30
;;
;; Some examples showing innacuracies using floating-point numbers,
;; and how to try to get around them.
;;
(define make-list
     (lambda (n s)
       (if (zero? n)
	   null
	   (cons s (make-list (sub1 n) s)))))

(define a (make-list 101 5))

; b: 1.0e16 followed by 101 5's
; c: 101 5's followed by 1.0e16
; d: 50 5's followed by 1.0e16 followed by 51 5's
; e: 1.0e16 followed by 50 5's
(define b (cons 1.0e16 a))
(define c (append a (list 1.0e16)))
(define d (append (make-list 50 5) (cons 1.0e16 (make-list 51 5))))
(define e (cons 1.0e16 (make-list 50 5)))

(define sum
  (lambda (l)
    (cond ((null? l) 0)
	  (else (+ (car l) (sum (cdr l)))))))

;; better-Sum
;; take a list of numbers, and sum the elements
;; trying to avoid imprecision errors.
;;
;; (N.B. "sort" is a built-in dr.scheme function!)
;;
(define better-sum
  (lambda (alon)
    (sum (sort (lambda (x y) (> (abs x) (abs y)))
               alon))))


; Compare (sum b) with (better-sum b),
; and similarly for the lists c,d,e.
; Why is there a difference?


(define janus (list 99
                    3.2e+270
                    -99
                    -2.4e+270
                    1234
                    4
                    -8e+269
                    -4))
; (sum janus)           = ??
; (sum (reverse janus)) = ??
; (better-sum janus)    = ??
; The correct answer    = !!