pi.clj

(defn a&b [n]
  (loop [n n, a (/ 1.0 (* 2 (Math/pow 3 0.5))), b (/ 1.0 3)]
    (if (= n 0)
      [a b]
      (let [a' (/ (+ a b) 2)]
        (recur (dec n) a' (Math/pow (* a' b) 0.5))))))
        
;; => (time (/ 1 (first (a&b 100))))
;; "Elapsed time: 0.04547 msecs"
;; 3.141592653589795
;; => 

(declare b)

(defn ^:dynamic a [n]
  (if (= n 0)
    (/ 1 (* 2 (Math/pow 3 0.5)))
    (/ (+ (a (- n 1)) (b (- n 1))) 2)))

(defn ^:dynamic b [n]
  (if (= n 0)
    (/ 1.0 3)
    (Math/pow (* (a n) (b (- n 1))) 0.5)))

;; => (time
;;      (binding [a (memoize a)
;;                b (memoize b)]
;;        (/ 1 (a 100))))
;; "Elapsed time: 1.764405 msecs"
;; 3.141592653589795
;; =>