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Ingy döt Net 2023-07-01 11:58:00 -04:00
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46
Task/Primorial-numbers/Clojure/primorial-numbers-1.clj Normal file
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(ns example
(:gen-class))
; Generate Prime Numbers (Implementation from RosettaCode--link above)
(defn primes-hashmap
"Infinite sequence of primes using an incremental Sieve or Eratosthenes with a Hashmap"
[]
(letfn [(nxtoddprm [c q bsprms cmpsts]
(if (>= c q) ;; only ever equal
; Update cmpsts with primes up to sqrt c
(let [p2 (* (first bsprms) 2),
nbps (next bsprms),
nbp (first nbps)]
(recur (+ c 2) (* nbp nbp) nbps (assoc cmpsts (+ q p2) p2)))
(if (contains? cmpsts c)
; Not prime
(recur (+ c 2) q bsprms
(let [adv (cmpsts c), ncmps (dissoc cmpsts c)]
(assoc ncmps
(loop [try (+ c adv)] ;; ensure map entry is unique
(if (contains? ncmps try)
(recur (+ try adv))
try))
adv)))
; prime
(cons c (lazy-seq (nxtoddprm (+ c 2) q bsprms cmpsts))))))]
(do (def baseoddprms (cons 3 (lazy-seq (nxtoddprm 5 9 baseoddprms {}))))
(cons 2 (lazy-seq (nxtoddprm 3 9 baseoddprms {}))))))
;; Generate Primorial Numbers
(defn primorial [n]
" Function produces the nth primorial number"
(if (= n 0)
1 ; by definition
(reduce *' (take n (primes-hashmap))))) ; multiply first n primes (retrieving primes from lazy-seq which generates primes as needed)
;; Show Results
(let [start (System/nanoTime)
elapsed-secs (fn [] (/ (- (System/nanoTime) start) 1e9))] ; System start time
(doseq [i (concat (range 10) [1e2 1e3 1e4 1e5 1e6])
:let [p (primorial i)]] ; Generate ith primorial number
(if (< i 10)
(println (format "primorial ( %7d ) = %10d" i (biginteger p))) ; Output for first 10
(println (format "primorial ( %7d ) has %8d digits\tafter %.3f secs" ; Output with time since starting for remainder
(long i) (count (str p)) (elapsed-secs))))))

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Task/Primorial-numbers/Clojure/primorial-numbers-2.clj Normal file
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(ns example
(:gen-class))
(defn primes-hashmap
"Infinite sequence of primes using an incremental Sieve or Eratosthenes with a Hashmap"
[]
(letfn [(nxtoddprm [c q bsprms cmpsts]
(if (>= c q) ;; only ever equal
; Update cmpsts with primes up to sqrt c
(let [p2 (* (first bsprms) 2),
nbps (next bsprms),
nbp (first nbps)]
(recur (+ c 2) (* nbp nbp) nbps (assoc cmpsts (+ q p2) p2)))
(if (contains? cmpsts c)
; Not prime
(recur (+ c 2) q bsprms
(let [adv (cmpsts c), ncmps (dissoc cmpsts c)]
(assoc ncmps
(loop [try (+ c adv)] ;; ensure map entry is unique
(if (contains? ncmps try)
(recur (+ try adv))
try))
adv)))
; prime
(cons c (lazy-seq (nxtoddprm (+ c 2) q bsprms cmpsts))))))]
(do (def baseoddprms (cons 3 (lazy-seq (nxtoddprm 5 9 baseoddprms {}))))
(cons 2 (lazy-seq (nxtoddprm 3 9 baseoddprms {}))))))
;; Number of workers (threads) based upon number of available processors
(def workers
(+ 2 (.. Runtime getRuntime availableProcessors)))
;; Generate of primorial numbers (using multiple processors)
(defn primorial [n]
(if (= n 0)
1
;(reduce mul+ (pmap #(reduce *' %) (partition-all (max workers (long (/ n workers))) (take n (primes-hashmap)))))));(*' allows for big integer arithmetic as needed)
(->> ; Threads (i.e. pipes) sequence of expressions
(take n (primes-hashmap) ) ; generate primes
(partition-all (max workers (long (/ n workers)))) ; partition primes amongst workers
(pmap #(reduce *' %)) ; Multiply primes in each worker in parallel
(reduce *')))) ; multiply results of all workers together
;; Generate and Time Output
(let [start (System/nanoTime)
elapsed-secs (fn [] (/ (- (System/nanoTime) start) 1e9))] ; System start time
(doseq [i (concat (range 10) [1e2 1e3 1e4 1e5 1e6])
:let [p (primorial i)]] ; Generate ith primorial number
(if (< i 10)
(println (format "primorial ( %7d ) = %10d" i (biginteger p))) ; Output for first 10
(println (format "primorial ( %7d ) has %8d digits\tafter %.3f secs" ; Output with time since starting for remainder
(long i) (count (str p)) (elapsed-secs))))))