exact.clj

; http://aphyr.com/posts/305-clojure-from-the-ground-up-macros
; Problem 5
; Using the rationalize function, write a macro exact
; which rewrites any use of +, -, *, or / to force the
; use of ratios instead of floating-point numbers.
; (* 2452.45 100) returns 245244.99999999997, but
; (exact (* 2452.45 100)) should return 245245N .
(defmacro exact
  [[f x y & more]]
  (cond
    (not x) `(~f)
    (not y) `(~f (rationalize ~x))
    :else   `(let [result# (~f (rationalize ~x) (rationalize ~y))]
               (if-let [next# (first [~@more])]
                 (~f result# (rationalize next#))
                 result#))))

(= (exact (*)) 1)
(= (exact (* 1.5)) 3/2)
(= (exact (* 2452.45 100)) 245245N)
(= (exact (/ 2452.45 100)) 49049/2000)
(= (exact (* 2452.45 100 2)) 490490N)

(macroexpand-1 '(exact (* 1.5)))