/
ex2.12.scm
218 lines (184 loc) · 7.42 KB
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ex2.12.scm
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(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (sub-interval x y)
(make-interval (- (lower-bound x) (upper-bound y))
(- (upper-bound x) (lower-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-internal x y)
(if (< (* (lower-bound y) (upper-bound y)) 0)
(error "Division erro (interval spans 0)" y)
(mul-interval x
(make-interval (/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y))))))
(define (make-interval a b) (cons a b))
(define (lower-bound x) (min (car x) (cdr x)))
(define (upper-bound x) (max (car x) (cdr x)))
(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 (old-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 (mul-interval x y)
(cond ((and (< (lower-bound x) 0)
(< (upper-bound x) 0)
(< (lower-bound y) 0)
(< (upper-bound y) 0))
(make-interval (* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y)))
)
((and (< (lower-bound x) 0)
(not (< (upper-bound x) 0))
(< (lower-bound y) 0)
(< (upper-bound y) 0))
(make-interval (* (upper-bound x) (lower-bound y))
(* (lower-bound x) (lower-bound y)))
)
((and (not (< (lower-bound x) 0))
(not (< (upper-bound x) 0))
(< (lower-bound y) 0)
(< (upper-bound y) 0))
(make-interval (* (upper-bound x) (lower-bound y))
(* (lower-bound x) (upper-bound y)))
)
((and (< (lower-bound x) 0)
(< (upper-bound x) 0)
(< (lower-bound y) 0)
(not (< (upper-bound y) 0)))
(make-interval (* (lower-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y)))
)
((and (< (lower-bound x) 0)
(not (< (upper-bound x) 0))
(< (lower-bound y) 0)
(not (< (upper-bound y) 0)))
(make-interval (min (* (upper-bound x) (lower-bound y))
(* (lower-bound x) (upper-bound y)))
(max (* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y))))
)
((and (not (< (lower-bound x) 0))
(not (< (upper-bound x) 0))
(< (lower-bound y) 0)
(not (< (upper-bound y) 0)))
(make-interval (* (upper-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y)))
)
((and (< (lower-bound x) 0)
(< (upper-bound x) 0)
(not (< (lower-bound y) 0))
(not (< (upper-bound y) 0)))
(make-interval (* (lower-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y)))
)
((and (< (lower-bound x) 0)
(not (< (upper-bound x) 0))
(not (< (lower-bound y) 0))
(not (< (upper-bound y) 0)))
(make-interval (* (lower-bound x) (upper-bound y))
(* (upper-bound x) (upper-bound y)))
)
((and (not (< (lower-bound x) 0))
(not (< (upper-bound x) 0))
(not (< (lower-bound y) 0))
(not (< (upper-bound y) 0)))
(make-interval (* (lower-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y)))
)))
(define (eql-interval? a b)
(and (= (upper-bound a) (upper-bound b))
(= (lower-bound a) (lower-bound b))))
;; Fails if the new mult doesn't return the same answer as the old
;; naive mult.
(define (ensure-mult-works aH aL bH bL)
(let ((a (make-interval aL aH))
(b (make-interval bL bH)))
(if (eql-interval? (old-mul-interval a b)
(mul-interval a b))
true
(error "new mult returns different value!"
a
b
(old-mul-interval a b)
(mul-interval a b)))))
(ensure-mult-works +10 +10 +10 -10)
(mul-interval (make-interval +10 +10) (make-interval +10 -10))
(old-mul-interval (make-interval +10 +10) (make-interval +10 -10))
(ensure-mult-works +10 +10 +10 +10)
(ensure-mult-works +10 +10 +00 +10)
(ensure-mult-works +10 +10 +00 +00)
(ensure-mult-works +10 +10 +10 -10)
(ensure-mult-works +10 +10 -10 +00)
(ensure-mult-works +10 +10 -10 -10)
(ensure-mult-works +00 +10 +10 +10)
(ensure-mult-works +00 +10 +00 +10)
(ensure-mult-works +00 +10 +00 +00)
(ensure-mult-works +00 +10 +10 -10)
(ensure-mult-works +00 +10 -10 +00)
(ensure-mult-works +00 +10 -10 -10)
(ensure-mult-works +00 +00 +10 +10)
(ensure-mult-works +00 +00 +00 +10)
(ensure-mult-works +00 +00 +00 +00)
(ensure-mult-works +00 +00 +10 -10)
(ensure-mult-works +00 +00 -10 +00)
(ensure-mult-works +00 +00 -10 -10)
(ensure-mult-works +10 -10 +10 +10)
(ensure-mult-works +10 -10 +00 +10)
(ensure-mult-works +10 -10 +00 +00)
(ensure-mult-works +10 -10 +10 -10)
(ensure-mult-works +10 -10 -10 +00)
(ensure-mult-works +10 -10 -10 -10)
(ensure-mult-works -10 +00 +10 +10)
(ensure-mult-works -10 +00 +00 +10)
(ensure-mult-works -10 +00 +00 +00)
(ensure-mult-works -10 +00 +10 -10)
(ensure-mult-works -10 +00 -10 +00)
(ensure-mult-works -10 +00 -10 -10)
(ensure-mult-works -10 -10 +10 +10)
(ensure-mult-works -10 -10 +00 +10)
(ensure-mult-works -10 -10 +00 +00)
(ensure-mult-works -10 -10 +10 -10)
(ensure-mult-works -10 -10 -10 +00)
(ensure-mult-works -10 -10 -10 -10)
(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 (make-interval-center-percent c rt)
(make-interval (- c (* c (/ rt 100))) (+ c (* c (/ rt 100)))))
(define (center i)
(/ (+ (lower-bound i) (upper-bound i)) 2.0))
(define (percent-tolerance i)
(let ((center (/ (+ (upper-bound i) (lower-bound i)) 2.0))
(width (/ (- (upper-bound i) (lower-bound i)) 2.0)))
(* (/ width center) 100)))
;; A quick check:
(define i (make-interval-center-percent 10 50))
(lower-bound i)
(upper-bound i)
(center i)
(percent-tolerance i)
; The above returns
;Value: i
;Value: 5.
;Value: 15.
;Value: 10.
;Value: 50.