Implementation of a tail recursive algorithm for multiplication by means of repeated addition (doubling).
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| (define (double x) (+ x x)) | |
| (define (halve x) (/ x 2)) | |
| (define (odd? n) | |
| (= | |
| (remainder n 2) | |
| 1)) | |
| (define (even? n) | |
| (= | |
| (remainder n 2) | |
| 0)) | |
| (define (fast-mult-it b n) | |
| (fast-mult-iter 0 b n)) | |
| (define (fast-mult-iter a b n) | |
| (cond | |
| ((= n 0) a) | |
| ((even? n) | |
| (fast-mult-iter | |
| a | |
| (double b) | |
| (halve n))) | |
| ((odd? n) | |
| (fast-mult-iter | |
| (+ a b) | |
| b | |
| (- n 1))))) | |