Calculate first N digits of PI using Clojure

core.clj

(require '[clojure.core.reducers :as r])

(defn pi
  "calculate accurately first k digits of PI"
  [k]
  (with-precision (+ 3 k)
    (let [f-exp (fn [k] (let [power (fn [x n] (reduce * (repeat n x)))
                              k8 (* 8M k)
                              a  (/ 1.0M (power 16M k))
                              b  (/ 4.0M (inc k8))
                              c  (/ 2.0M (+ 4M k8))
                              d  (/ 1.0M (+ 5M k8))
                              e  (/ 1.0M (+ 6M k8))
                              f  (- b c d e)]
                          (* a f)))]
      (bigdec (apply str (take (+ 2 k) (str (r/fold + (pmap f-exp (range (bigdec 0) k))))))))))


;; Etalon PI
;; 3,1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...

(pi 90)
;; 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825M