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excercise-1.18

admin 11月 13, 2020 0

Exercise 1.18

Using the results of Exercise 1.16 and Exercise 1.17, devise a procedure that generates an iterative process for multiplying two integers in terms of adding, doubling, and halving and uses a logarithmic number of steps.

Ans

(define (double n)
    (+ n n))

(define (half n)
    (/ n 2))

(define (multi a b)
    (define (multi-iter a b ans)
        (cond ((= b 0) ans)
            ((even? b) (multi-iter (double a) (half b) ans))
            (else (multi-iter a (- b 1) (+ a ans)))))
    (multi-iter a b 0))