Multiplication using iterative addition

multiplication-using-addition.lisp

(defun double (n)
  (+ n n))

(defun halve (n)
  (/ n 2))
;;; Normal
(defun mul (a b)
  (if (= b 1)
      a
      (+ a (mul a (- b 1)))))
;;; log
;;  ex 1.17
(defun mul-log (a b)
 (if (= b 1)
     a
     (if (evenp b)
         (double (mul-log a (halve b)))
         (+ a (mul-log a (- b 1))))))

;;; iterative
;;  ex 1.18
(defun mul-log-iter (a b)
  (labels (
           (iter (acc a b)
            ;; (format t "~& ACC: ~A ~& A: ~A ~&B: ~A ~& ACC+(a * b) :~A" acc a b (+ acc (* a b)) )
             (cond ((= b 1) (+ acc a))
                   ((evenp b) (iter acc (double a) (halve b)))
                   (t (iter (+ acc a) a (- b 1))))))
    (iter 0 a b)))