89 lines
2.6 KiB
Racket
89 lines
2.6 KiB
Racket
#lang racket
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(define (mul-interval x y)
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(let ((p1 (* (lower-bound x) (lower-bound y)))
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(p2 (* (lower-bound x) (upper-bound y)))
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(p3 (* (upper-bound x) (lower-bound y)))
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(p4 (* (upper-bound x) (upper-bound y))))
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(make-interval (min p1 p2 p3 p4)
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(max p1 p2 p3 p4))))
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(define (make-interval a b) (cons a b))
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(define (add-interval a b)
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(make-interval (+ (lower-bound a) (lower-bound b))
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(+ (upper-bound a) (upper-bound b))))
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;; 2.7
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;; simple definitions.
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(define upper-bound cdr)
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(define lower-bound car)
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;; 2.8
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(define (interval-diff f a b)
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(make-interval (- (lower-bound a) (upper-bound b))
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(- (upper-bound a) (lower-bound b))))
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;; 2.9 this one's just about reasoning, no programming, and I feel too lazy to explain
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;; sorry.
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;; 2.10 : simple 'nuff.
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(define (div-interval x y)
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(if (= (lower-bound y) (upper-bound y))
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(error "WHY? WHY MUST YOU TORTURE ME SO?")
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(mul-interval
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x
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(make-interval (/ 1.0 (upper-bound y))
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(/ 1.0 (lower-bound y))))))
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;; 2.11 : This one's also somewhat simple.
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;; we ONLY need more than two multiplications
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;; if BOTH intervals have different signs on their upper
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;; and lower bounds. otherwise, naive logic works fine.
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(define (mul-interval2 x y)
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(define (different? n)
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(and (< (lower-bound n) 0) (< (upper-bound n) 0)))
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(if (and (different? x) (different? y))
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(let ((p1 (* (lower-bound x) (lower-bound y)))
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(p2 (* (lower-bound x) (upper-bound y)))
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(p3 (* (upper-bound x) (lower-bound y)))
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(p4 (* (upper-bound x) (upper-bound y))))
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(make-interval (min p1 p2 p3 p4)
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(max p1 p2 p3 p4)))
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(make-interval (* (lower-bound x) (lower-bound y))
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(* (upper-bound x) (upper-bound y)))))
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;; 2.12 : simple nuff.
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(define (make-center-width c w)
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(make-interval (- c w) (+ c w)))
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(define (center i)
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(/ (+ (lower-bound i) (upper-bound i)) 2))
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(define (width i)
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(/ (- (upper-bound i) (lower-bound i)) 2))
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(define (make-center-percent c p)
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(make-center-width c (* c (/ p 100))))
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(define (percent i)
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(* (/ (width i) 2) 100))
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;; 2.13 & 2.14
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(define (par1 r1 r2)
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(div-interval (mul-interval r1 r2)
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(add-interval r1 r2)))
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(define (par2 r1 r2)
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(let ((one (make-interval 1 1)))
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(div-interval
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one (add-interval (div-interval one r1)
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(div-interval one r2)))))
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(define A (make-interval 100 101))
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(define B (make-interval 200 201))
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(div-interval A A)
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(div-interval (make-interval 1 1) A)
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(div-interval B A)
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