40 lines
1.2 KiB
Haskell
40 lines
1.2 KiB
Haskell
module Prime
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( primes
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, is_prime
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, primeFactors
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, relativePrime
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)
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where
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import Data.List
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data Wheel = Wheel Int [Int]
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roll (Wheel n rs) = [n*k+r| k<-[0..], r<-rs]
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nextSize (Wheel n rs) p =
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Wheel (p*n) [r' | k <- [0..(p-1)], r <- rs,
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let r' = n*k+r, r' `mod` p /= 0]
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w0 = Wheel 1 [1]
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mkWheel ds = foldl nextSize w0 ds
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primes :: [Int]
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primes = small ++ large
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where
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1:p:candidates = roll $ mkWheel small
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small = [2,3,5,7]
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large = p : filter isPrime candidates
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isPrime n = all (not . divides n)
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$ takeWhile (\p -> p*p <= n) large
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divides n p = n `mod` p == 0
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is_prime n = n > 1 && n == head (primeFactors n)
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primeFactors 1 = []
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primeFactors n = go n primes
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where
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go n ps@(p:pt)
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| p*p > n = [n]
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| n `rem` p == 0 = p : go (n `quot` p) ps
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| otherwise = go n pt
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relativePrime :: Int -> Int -> Bool
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relativePrime p q = [] == intersect (primeFactors p) (primeFactors q)
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