43 lines
887 B
Racket
43 lines
887 B
Racket
|
(define (multiply a b)
|
||
|
|
(define (iter a b product)
|
||
|
|
(if (= b 0)
|
||
|
|
product
|
||
|
|
(iter a (- b 1) (+ product a))))
|
||
|
|
|
||
|
|
(iter a b 0))
|
||
|
|
; multiply
|
||
|
|
|
||
|
|
(define (sqr n)
|
||
|
|
(multiply n n))
|
||
|
|
|
||
|
|
(define (divide a b)
|
||
|
|
(define (iter a b product)
|
||
|
|
(cond ((= a 0) product)
|
||
|
|
((< a 0) (- product 1))
|
||
|
|
(else (iter (- a b) b (+ product 1)))))
|
||
|
|
|
||
|
|
(iter a b 0))
|
||
|
|
; divide
|
||
|
|
|
||
|
|
(define (halve a)
|
||
|
|
(divide a 2))
|
||
|
|
|
||
|
|
(define (fast-ext number power)
|
||
|
|
(define (iter number power product)
|
||
|
|
(cond ((= power 0) product)
|
||
|
|
((even? power) (iter (sqr number)
|
||
|
|
(halve power)
|
||
|
|
product))
|
||
|
|
(else (iter number
|
||
|
|
(- power 1)
|
||
|
|
(multiply number product)))))
|
||
|
|
|
||
|
|
(iter number power 1))
|
||
|
|
; fast-ext
|
||
|
|
|
||
|
|
(fast-ext 5 3)
|
||
|
|
(fast-ext 2 2)
|
||
|
|
(fast-ext 1 2)
|
||
|
|
(fast-ext 9 4)
|
||
|
|
(fast-ext 2 0)
|
||
|
|
(fast-ext 7 1)
|