SICP Exercise 1.17 -- fast-times

gistfile1.el

; Now suppose we include, together with addition,
; operations double, which doubles an integer,
; and halve, which divides an (even) integer by 2.
; Using these, design a multiplication procedure analogous to
; fast-expt that uses a logarithmic number of steps.
(defun fast_times (multiplicand multiplier)
  (cond ((= multiplier 0) 0)
        ((even? multiplier)
         (double (fast_times multiplicand (half multiplier))))
        (else
         (+ multiplicand (fast_times multiplicand (- multiplier 1))))))

My solution:

(define (fast-multi a b)
  (define (double x)
    (+ x x))
  (define (halve x)
    (/ x 2))
  (define (even? n)
    (= (remainder n 2) 0))
  (define (multi-iter a b r)
    (cond ((= b 0) r)
          ((even? b) (multi-iter (double a) (halve b) r))
          (else (multi-iter a (- b 1) (+ r a)))))
  (multi-iter a b 0))