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(define (+? x) (>= x 0)) ;;; Is x a positive number? | |
(define (-? x) (< x 0)) ;;; Is x a negative number? | |
(define (make-interval a b) (cons a b)) | |
(define (lower-bound i) (car i)) | |
(define (upper-bound i) (cdr i)) | |
(define (mul-interval x y) | |
(let ((a (lower-bound x)) | |
(b (upper-bound x)) | |
(c (lower-bound y)) | |
(d (upper-bound y))) | |
(cond ((and (+? a) (+? b) (+? c) (+? d)) (make-interval (* a c) (* b d))) | |
((and (+? a) (+? b) (-? c) (+? d)) (make-interval (* b c) (* b d))) | |
((and (+? a) (+? b) (-? c) (-? d)) (make-interval (* b c) (* a d))) | |
((and (-? a) (+? b) (+? c) (+? d)) (make-interval (* a d) (* b d))) | |
((and (-? a) (+? b) (-? c) (+? d)) | |
(let ((p1 (min (* a d) (* b c))) | |
(p2 (max (* a c) (* b d)))) | |
(make-interval p1 p2))) | |
((and (-? a) (+? b) (-? c) (-? d)) (make-interval (* b c) (* a c))) | |
((and (-? a) (-? b) (+? c) (+? d)) (make-interval (* a d) (* b c))) | |
((and (-? a) (-? b) (-? c) (+? d)) (make-interval (* a d) (* a c))) | |
((and (-? a) (-? b) (-? c) (-? d)) (make-interval (* b d) (* a c)))))) |
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