Chowla numbers: Difference between revisions
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m (→{{header|Haskell}}: use STM TChan vs Chan. Significant performance improvement.) |
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Uses arithmoi Library: https://hackage.haskell.org/package/arithmoi-0.11.0.0 |
Uses arithmoi Library: https://hackage.haskell.org/package/arithmoi-0.11.0.0 |
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compiled with "-O2 -threaded -rtsopts"<br/> |
compiled with "-O2 -threaded -rtsopts"<br/> |
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<lang haskell>import Control.Concurrent (setNumCapabilities |
<lang haskell>import Control.Concurrent (setNumCapabilities) |
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import Control. |
import Control.Monad.Par (runPar, get, spawnP) |
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import Control.Monad (join, (>=>)) |
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import Control.Monad (forever, replicateM_, replicateM) |
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import Data.List.Split (chunksOf) |
import Data.List.Split (chunksOf) |
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import Data.List (intercalate, mapAccumL, genericTake, genericDrop) |
import Data.List (intercalate, mapAccumL, genericTake, genericDrop) |
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f = (-) =<< pred . product . fmap sumFactor . factorise |
f = (-) =<< pred . product . fmap sumFactor . factorise |
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sumFactor (n, e) = foldr (\p s -> s + unPrime n^p) 1 [1..e] |
sumFactor (n, e) = foldr (\p s -> s + unPrime n^p) 1 [1..e] |
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| ⚫ | |||
chowlas [] = [] |
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chowlas xs = runPar $ join <$> |
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(mapM (spawnP . fmap ((,) <*> chowla)) >=> mapM get) (chunksOf (10^6) xs) |
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chowlaPrimes :: [(Word, Word)] -> (Word, Word) -> (Word, Word) |
chowlaPrimes :: [(Word, Word)] -> (Word, Word) -> (Word, Word) |
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chowlaPerfects :: [(Word, Word)] -> [Word] |
chowlaPerfects :: [(Word, Word)] -> [Word] |
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chowlaPerfects = fmap fst . filter isPerfect |
chowlaPerfects = fmap fst . filter isPerfect |
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where |
where |
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isPerfect (1, _) = False |
isPerfect (1, _) = False |
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isPerfect (n, c) = c == pred n |
isPerfect (n, c) = c == pred n |
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commas :: (Show a, Integral a) => a -> String |
commas :: (Show a, Integral a) => a -> String |
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commas = reverse . intercalate "," . chunksOf 3 . reverse . show |
commas = reverse . intercalate "," . chunksOf 3 . reverse . show |
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| ⚫ | |||
chowlaWorker input output = forever (atomically (readTChan input) >>= |
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atomically . writeTChan output . ((,) <*> chowla)) |
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main :: IO () |
main :: IO () |
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setNumCapabilities cores |
setNumCapabilities cores |
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printf "Using %d cores\n" cores |
printf "Using %d cores\n" cores |
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allChowlas <- parallelChowlas cores |
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mapM_ (uncurry (printf "chowla(%2d) = %d\n")) $ take 37 allChowlas |
mapM_ (uncurry (printf "chowla(%2d) = %d\n")) $ take 37 allChowlas |
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mapM_ (uncurry (printf "There are %8s primes < %10s\n")) |
mapM_ (uncurry (printf "There are %8s primes < %10s\n")) |
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(chowlaP |
(chowlaP |
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[ (1, 10^2) |
[ (1, 10^2) |
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, (succ $ 10^2, 10^3) |
, (succ $ 10^2, 10^3) |
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, (succ $ 10^6, 10^7) ]) |
, (succ $ 10^6, 10^7) ]) |
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| ⚫ | |||
mapM_ (printf "%10s is a perfect number.\n" . commas) perfects |
mapM_ (printf "%10s is a perfect number.\n" . commas) perfects |
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printf "There are %2d perfect numbers < 35,000,000\n" $ length perfects |
printf "There are %2d perfect numbers < 35,000,000\n" $ length perfects |
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where |
where |
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chowlaP |
chowlaP = fmap (bimap commas commas) . snd |
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. mapAccumL (\total (count, max) -> (total + count, (total + count, max))) 0 |
. mapAccumL (\total (count, max) -> (total + count, (total + count, max))) 0 |
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. fmap (chowlaPrimes $ take (10^7) |
. fmap (chowlaPrimes $ take (10^7) allChowlas) |
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| ⚫ | |||
allChowlas = chowlas [1..35*10^6]</lang> |
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parallelChowlas cores = do |
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inputChan <- atomically newTChan |
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outputChan <- atomically newTChan |
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replicateM_ cores (forkIO $ chowlaWorker inputChan outputChan) |
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mapM_ (atomically . writeTChan inputChan) [1..35*10^6] |
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replicateM (35*10^5) (atomically (readTChan outputChan))</lang> |
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{{out}} |
{{out}} |
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<pre>Using 4 cores |
<pre>Using 4 cores |
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