Exercise 2.12: Define a constructor make-center-percent that takes a center and a
percentage tolerance and produces the desired interval. You must also define a selector percent
that produces the percentage tolerance for a given interval. The center selector is the same
as the one shown above.
(define (make-center-percent value p)
(make-center-width value (* value (/ p 100.0))))
(define (percent int)
(* 100 (/ (width int) (center int))))
(define (make-interval a b)
(cons a b))
(define (lower-bound int) (car int))
(define (upper-bound int) (cdr int))
(define (make-center-width c w)
(make-interval (- c w) (+ c w)))
(define (center i)
(/ (+ (lower-bound i) (upper-bound i)) 2))
(define (width i)
(/ (- (upper-bound i) (lower-bound i)) 2))
(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (mul-interval x y)
(let ((p1 (* (lower-bound x) (lower-bound y)))
(p2 (* (lower-bound x) (upper-bound y)))
(p3 (* (upper-bound x) (lower-bound y)))
(p4 (* (upper-bound x) (upper-bound y))))
(make-interval (min p1 p2 p3 p4)
(max p1 p2 p3 p4))))
(define (div-interval x y)
(define (spans-zero? i)
(and
(not (> (lower-bound i) 0))
(not (< (upper-bound i) 0))))
(if (spans-zero? y)
(error "The dividing interval cannot span 0.")
(mul-interval x
(make-interval (/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y))))))
(define (sub-interval2 x y)
(let ((p1 (- (lower-bound x) (lower-bound y)))
(p2 (- (lower-bound x) (upper-bound y)))
(p3 (- (upper-bound x) (lower-bound y)))
(p4 (- (upper-bound x) (upper-bound y))))
(make-interval (min p1 p2 p3 p4)
(max p1 p2 p3 p4))))
(define (sub-interval x y)
(make-interval (- (lower-bound x) (upper-bound y))
(- (upper-bound x) (lower-bound y))))
(define (print int)
(newline)
(display "[")
(display (lower-bound int))
(display ",")
(display (upper-bound int))
(display "]")
(newline))
> (print (make-center-percent 10 12))
[8.8,11.2]
> (percent (make-center-percent 10 12))
11.999999999999993