Exercise 2.10. Ben Bitdiddle, an expert systems programmer, looks over Alyssa’s shoulder and comments that it is not clear what it means to divide by an interval that spans zero. Modify Alyssa’s code to check for this condition and to signal an error if it occurs.
(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))))
;;; check the condition that an interval spans zero in div
(define (div-interval x y)
(cond ((and (< (lower-bound y) 0)
(> (upper-bound y) 0))
(error 'div-interval "divide by an interval that spans zero!"))
(else
(mul-interval x
(make-interval (/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y)))))))
;;; tests begin
(load "../testframe.scm")
(load "7-interval-selector.scm")
(let ((x (make-interval 19 20))
(y (make-interval -1 1))
(z (make-interval 4 5)))
(assert/exn (div-interval x y) "divide"))