;;;; Under Creative Commons Attribution-ShareAlike 4.0
;;;; International. See
;;;; <https://creativecommons.org/licenses/by-sa/4.0/>.

;;;
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;;; < +, - everything. >
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(define-module (net ricketyspace sicp one seventeen)
  #:export (double
            halve
            fast-*)
  #:replace (even?))

(define (double a)
  "Return A + A."
  (+ a a))

(define (halve b)
  "Return B/2.

B must be an even number."
  (cond ((= b 0) 0)
        (else (+ 1 (halve (- b 2))))))

(define (even? b)
  "Return #t if B is divisible by 2; #f otherwise."
  (cond ((= b 1) #f)
        ((= b 0) #t)
        (else (even? (- b 2)))))

(define (fast-* a b)
  "Return A * B."
  (cond ((= b 0) 0)
        ((even? b) (double (fast-* a (halve b))))
        (else (+ a (fast-* a (- b 1))))))