#lang racket

;; ------------------------------------------------------------------------
;; The only multiplication operators we have for the this exercise:
;; ------------------------------------------------------------------------

(define half   (lambda (n) (quotient n 2)))  ; or (arithmetic-shift n -1)))
(define double (lambda (n) (* n 2)))         ; or (arithmetic-shift n  1)))

;; ------------------------------------------------------------------------
;; Full Russian peasant multiplication, which allows m to be odd.  This
;; function is an interface procedure to a local recursive helper that
;; uses an accumulator variable.
;; ------------------------------------------------------------------------

(define multiply
  (lambda (m n)
    (letrec ((loop (lambda (m n acc)
                     (display3 m n acc)
                     (if (zero? m)
                         acc
                         (loop (half m)
                               (double n)
                               (+ acc (if (odd? m) n 0)))))))
      (loop m n 0))))

;; --------------------------------------------------------------------------
;; This function uses a C-style format string to display its arguments.
;; Racket contains multitudes!

(define display3
  (lambda (m n acc)
    (printf "~a ~a ~a\n" (pad m) (pad n) (pad acc))))

;; --------------------------------------------------------------------------
;; This function creates a right-justified string of size 6 for its argument.

(define pad
  (lambda (i)
    (~a i #:min-width 6 #:align 'right #:left-pad-string " ")))

;; ------------------------------------------------------------------------
;; Performing multiplication and division with a bit-shift operation:
;; ------------------------------------------------------------------------

;(define half   (arithmetic-shift n -1))
;(define double (arithmetic-shift n  1))

;; --------------------------------------------------------------------------