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#lang racket
(require "../../shared/intervals.rkt")
;; Could be written to use less comparisons with nested cond, but this is more readable.
(define (pos? x)
(> x 0))
(define (neg? x)
(< x 0))
(define (mul-interval x y)
(cond
;; 1. all positive
((and
(pos? (lower-bound x))
(pos? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (lower-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y))))
;; 2. one lower-bound neg
((and
(neg? (lower-bound x))
(pos? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (lower-bound x) (upper-bound y))
(* (upper-bound x) (upper-bound y))))
;; 3. one lower-bound neg
((and
(pos? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (upper-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y))))
;; 4. one interval neg
((and
(neg? (lower-bound x))
(pos? (lower-bound y))
(neg? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y))))
;; 5. one interval neg
((and
(pos? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(neg? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y))))
;; 6. one interval neg, one interval crossing zero
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(neg? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y))))
;; 7. one interval neg, one interval crossing zero
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(neg? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y))))
;; 8. all neg
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(neg? (upper-bound x))
(neg? (upper-bound y)))
(make-interval (* (lower-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y))))
;; 9. both crossing zero
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval ((lambda (a b) (if (< a b) a b))
(* (lower-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y)))
((lambda (a b) (if (> a b) a b))
(* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y)))))))
(mul-interval
(make-interval -3 3)
(make-interval -4 4))
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