Calculate π through Euler-van Wijngaarden transformation of Gregory-Leibniz series

pi.clj

(use '[clojure.contrib.seq :only (reductions)])

;;; Calculate π through Euler-van Wijngaarden transformation of Gregory-Leibniz series

(def *use-exact-numbers* true)

(defn gregory-leibniz-series []
  (map #(/ 4 %)
       (interleave (iterate #(+ % 4) (if *use-exact-numbers* 1 1.))
                   (iterate #(- % 4) (if *use-exact-numbers* -3 -3.)))))

(defn partial-sums [s]
  (reductions + s))

(defn average-damp [s]
  (map #(/ (+ %1 %2) 2) s (rest s)))

(defn euler-transform [s]
  (iterate average-damp (partial-sums s)))

(defn van-wijngaarden-pi [n]
  (let [j (Math/floor (* 2/3 n))
        i (- n j)]
    (nth (nth (euler-transform (gregory-leibniz-series)) j) i)))

; (double (van-wijngaarden-pi 100)) ; => 3.141592653589793
; (binding [*use-exact-numbers* false] (van-wijngaarden-pi 100)) ; => 3.141592653589793