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PurelyFunctional.tv Newsletter - Issue 314 - Puzzle - Sieve of Eratosthenes
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 {:deps {criterium {:mvn/version "0.4.4"}}}

The Sieve of Eratosthenes is a neat way to find all of the prime numbers below some number. If you do it on paper (and I suggest you do), you can easily find all primes below 100 within a few minutes. The challenge this week is to write a version in Clojure that lets you calculate all the primes below a given number `n`.

The biggest challenge with this is that you might run into problems with stack overflows or speed. Make sure the algorithm can still run with `n=100,000`.

I'd love to see your answers. Bonus points for creative and innovative solutions. I'll share the best next week. Fire up a REPL, try it out, and send me your answers. (Please note that, unless you tell me otherwise, I will share your name in the newsletter if you send me an answer.)

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 ;; Eric Normand's submission (defn sieve [n] (loop [primes [] unused (range 2 (inc n)) numbers (set (range 2 (inc n)))] (if (empty? numbers) primes (let [unused (drop-while (complement numbers) unused) f (first unused)] (recur (conj primes f) (next unused) (reduce disj numbers (range f (inc n) f))))))) ;; Running basic tests. ;; Passed tests. Running benchmark. ;; Evaluation count : 12 in 6 samples of 2 calls. ;; Execution time mean : 127.898632 ms ;; Execution time std-deviation : 9.454232 ms ;; Execution time lower quantile : 119.522809 ms ( 2.5%) ;; Execution time upper quantile : 138.652816 ms (97.5%) ;; Overhead used : 8.463208 ns
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 ;; James Elliott didn't submit an answer, but he did send me a ;; post he had written up about the sieve in Clojure. ;; https://github.com/Deep-Symmetry/afterglow/blob/master/doc/primes.md
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 ;; Josh Reighley's submission (defn filter-factors [primes unfiltered] (let [new-prime (first unfiltered) new-primes (conj primes new-prime) new-unfiltered (filter #(< 0 (mod % new-prime)) unfiltered)] (if (zero? (count new-unfiltered)) new-primes (recur new-primes new-unfiltered)))) (defn soe [n] (filter-factors [] (range 2 (inc n)))) ;; Running basic tests. ;; Passed tests. Running benchmark. ;; Evaluation count : 6 in 6 samples of 1 calls. ;; Execution time mean : 6.547815 sec ;; Execution time std-deviation : 169.437033 ms ;; Execution time lower quantile : 6.400218 sec ( 2.5%) ;; Execution time upper quantile : 6.814392 sec (97.5%) ;; Overhead used : 8.508955 ns ;; Found 1 outliers in 6 samples (16.6667 %) ;; low-severe 1 (16.6667 %) ;; Variance from outliers : 13.8889 % Variance is moderately inflated by outliers
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 ;; Mathieu Viel's submission (defn primes [n] (loop [remaining (range 2 n) prime []] (if (not (empty? remaining)) (let [i (first remaining) i2 (* i i) multiples (take-while (partial > n) (map (fn [n] (+ i2 (* n i))) (range)))] (recur (doall (remove (set multiples) (rest remaining))) (conj prime i))) prime))) (run-test primes) ;; Running basic tests. ;; Passed tests. Running benchmark. ;; 1 minute ;; Evaluation count : 6 in 6 samples of 1 calls. ;; Execution time mean : 6.874185 sec ;; Execution time std-deviation : 35.094687 ms ;; Execution time lower quantile : 6.828431 sec ( 2.5%) ;; Execution time upper quantile : 6.913848 sec (97.5%) ;; Overhead used : 8.469196 ns
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 ;; Peter Stromberg, creator of Calva, the Clojure plugin for ;; VS Code (defn sieve [n] (cond (< n 2) () (< n 3) (range 2 3) :else (let [sqrt-n (Math/sqrt n)] (loop [known (range 2 4) candidates (range 5 (inc n) 2) p 3] (if-not (< p sqrt-n) (concat known candidates) (let [remaining (remove #(= 0 (rem % p)) candidates) next-p (take 1 remaining)] (recur (concat known next-p) (drop 1 remaining) (first next-p)))))))) ;; Running basic tests. ;; Passed tests. Running benchmark. ;; Evaluation count : 18 in 6 samples of 3 calls. ;; Execution time mean : 48.673246 ms ;; Execution time std-deviation : 2.706933 ms ;; Execution time lower quantile : 46.948268 ms ( 2.5%) ;; Execution time upper quantile : 53.205339 ms (97.5%) ;; Overhead used : 8.463208 ns
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 ;; Steve Miner's submission (defn classic-sieve "Returns sequence of primes less than N" [n] (loop [nums (transient (vec (range n))) i 2] (cond (> (* i i) n) (remove nil? (nnext (persistent! nums))) (nums i) (recur (loop [nums nums j (* i i)] (if (< j n) (recur (assoc! nums j nil) (+ j i)) nums)) (inc i)) :else (recur nums (inc i))))) ;; Running basic tests. ;; Passed tests. Running benchmark. ;; Evaluation count : 54 in 6 samples of 9 calls. ;; Execution time mean : 12.837927 ms ;; Execution time std-deviation : 911.422860 µs ;; Execution time lower quantile : 11.738619 ms ( 2.5%) ;; Execution time upper quantile : 13.724696 ms (97.5%) ;; Overhead used : 8.463208 ns
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 (require '[criterium.core :as criterium]) (def tests (clojure.edn/read-string (slurp "tests.edn"))) (comment (with-open [w (clojure.java.io/writer "tests.edn")] (binding [*print-length* nil] (.write w "[") (.write w (clojure.string/join "\n " (map pr-str tests))) (.write w "]")))) (defmacro time2 [expr] `(let [t0# (System/nanoTime) r# ~expr] [(- (System/nanoTime) t0#) r#])) (def allowed-time (* 30 1e9)) ;; 30 seconds in nanoseconds (defn run-test [f] (let [run? (atom true)] (doto (Thread. (fn [] (loop [minutes 1] (Thread/sleep 60000) (when @run? (println minutes "minute") (recur (inc minutes)))))) .start) (try (println "Running basic tests.") (doseq [[n ex] tests] (let [[t ac] (time2 (f n))] (assert (= ex ac) (format "Test failed for n=%d." n)) (assert (<= t allowed-time) (format "Went over allowed time for n=%d." n)))) (println "Passed tests. Running benchmark.") (criterium/quick-bench (count (f 100000))) ;; make sure it's realized if it's lazy (finally (reset! run? false)))) :done)
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 ;; Valentin Waeselynck (defn primes-below "Finds all prime numbers less than n, returns them sorted in a vector" [n] (if (< n 2) [] (let [sieve (boolean-array n false) s (-> n Math/sqrt Math/floor int)] (loop [p 2] (if (> p s) (into [] (remove #(aget sieve %)) (range 2 n)) (do (when-not (aget sieve p) (loop [i (* 2 p)] (when (< i n) (aset sieve i true) (recur (+ i p))))) (recur (inc p)))))))) ;; Running basic tests. ;; Passed tests. Running benchmark. ;; Evaluation count : 222 in 6 samples of 37 calls. ;; Execution time mean : 2.866847 ms ;; Execution time std-deviation : 205.437091 µs ;; Execution time lower quantile : 2.679959 ms ( 2.5%) ;; Execution time upper quantile : 3.106558 ms (97.5%) ;; Overhead used : 8.594518 ns ;; Modification by Eric Normand: ;; If you add a primitive long type hint to the arg, it gets faster. ;; (defn primes-below ;; [^long n] ;; Running basic tests. ;; Passed tests. Running benchmark. ;; Evaluation count : 342 in 6 samples of 57 calls. ;; Execution time mean : 1.800897 ms ;; Execution time std-deviation : 54.997865 µs ;; Execution time lower quantile : 1.702391 ms ( 2.5%) ;; Execution time upper quantile : 1.852974 ms (97.5%) ;; Overhead used : 8.463208 ns

### PEZ commented Mar 5, 2021

Btw, @ericnormand, your Concurrency Tutorial, which I had tremendous help from reading, lacks a bit on the challenge of collecting the results in order. I got some hints from elsewhere to figure the above way out.