#lang racket

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

(define half   (lambda (n) (/ n 2)))
(define double (lambda (n) (* n 2)))

;; ------------------------------------------------------------------------
;; Russian peasant multiplication, with display of intermediate state.
;; Assumes m is a power of 2.
;; ------------------------------------------------------------------------

(define multiply
  (lambda (m n)
    (display-mn m n)
    (if (= m 1)
        n
        (multiply (half m) (double n)))))

;; ------------------------------------------------------------------------
;; ... using a custom display procedure just for this exercise.
;; The function displayln, from your reading, would do, too.
;;    (require "utilities.rkt")
;;    (displayln m " " n)

(define display-mn
  (lambda (m n)
    (display m)
    (display " ")
    (display n)
    (newline)))

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