#lang racket

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

(define (half   n) (quotient n 2))   ; or (arithmetic-shift n -1))
(define (double 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 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 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 item)
  (~a item #:min-width 6 #:align 'right #:left-pad-string " "))

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