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35 lines
1.3 KiB
35 lines
1.3 KiB
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Exercise 2.11: In passing, Ben also cryptically
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comments: “By testing the signs of the endpoints of the intervals, it is
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possible to break mul-interval into nine cases, only one of which
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requires more than two multiplications.” Rewrite this procedure using Ben’s
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suggestion.
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After debugging her program, Alyssa shows it to a potential user, who complains
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that her program solves the wrong problem. He wants a program that can deal
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with numbers represented as a center value and an additive tolerance; for
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example, he wants to work with intervals such as 3.5
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±
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0.15 rather than
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[3.35, 3.65]. Alyssa returns to her desk and fixes this problem by supplying
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an alternate constructor and alternate selectors:
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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)
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(upper-bound i))
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2))
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(define (width i)
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(/ (- (upper-bound i)
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(lower-bound i))
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2))
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Unfortunately, most of Alyssa’s users are engineers. Real engineering
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situations usually involve measurements with only a small uncertainty, measured
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as the ratio of the width of the interval to the midpoint of the interval.
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Engineers usually specify percentage tolerances on the parameters of devices,
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as in the resistor specifications given earlier.
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