;;;==================================================================
;;; Computing PI.
;;;==================================================================

;;;------------------------------------------------------------------
;;; Serial version.

(defn pi [num-rects]
  (let [width (/ 1.0 num-rects)]
    (loop [i    0
           sum  0]
      (if (= i num-rects)
          (* width sum)
          (let [mid     (* (+ i 0.5) width)
                height  (/ 4.0 (+ 1 (* mid mid)))]
            (recur (inc i) (+ sum height)))))))

;;;------------------------------------------------------------------
;;; Serial version using sequences.

(defn pi2 [num-rects]
  (let [width (/ 1.0 num-rects)]
    (->>
      (for [i (range num-rects)
            :let [mid     (* (+ i 0.5) width)
                  height  (/ 4.0 (+ 1 (* mid mid)))]] height)
      (reduce +)
      (* width))))


(def num-procs (.availableProcessors (Runtime/getRuntime)))

;;;------------------------------------------------------------------
;;; Parallel version.

(defn ppi [num-rects]
  (->>
    (generate-ranges num-rects num-procs)
    (pmap (fn [[start finish]] (pi-split start finish num-rects)))
    (reduce +)))

(defn generate-ranges [n t]
  (let [size (/ n t)]
    (->>
      (range 0 n size)
      (map #(vector % (+ % size))))))
      
(defn pi-split [start finish num-rects]
  (let [width (/ 1.0 num-rects)]
    (loop [i    start
           sum  0]
      (if (= i finish)
          (* width sum)
          (let [mid     (* (+ i 0.5) width)
                height  (/ 4.0 (+ 1 (* mid mid)))]
            (recur (inc i) (+ sum height)))))))