diff --git a/Data/Numbers/Primes.hs b/Data/Numbers/Primes.hs --- a/Data/Numbers/Primes.hs +++ b/Data/Numbers/Primes.hs @@ -8,17 +8,15 @@ -- Portability : portable -- -- This Haskell library provides an efficient lazy wheel sieve for --- prime generation ispired by "Lazy wheel sieves and spirals of --- primes" [1] by Colin Runciman and "The Genuine Sieve of --- Eratosthenes" [2] by Melissa O'Neil. --- --- [1]: --- --- [2]: +-- prime generation inspired by /Lazy wheel sieves and spirals of/ +-- /primes/ by Colin Runciman +-- () and +-- /The Genuine Sieve of Eratosthenes/ by Melissa O'Neil +-- (). -- module Data.Numbers.Primes ( primes, wheelSieve ) where --- | +-- | -- This global constant is an infinite list of prime numbers. It is -- generated by a lazy wheel sieve and shared among different -- applications. If you are concerned about the memory requirements of @@ -37,7 +35,7 @@ -- wheelSieve :: Int -- ^ number of primes canceled by the wheel -> [Integer] -- ^ infinite list of primes -wheelSieve k = reverse ps ++ sieve (spin p (cycle ns)) Empty +wheelSieve k = reverse ps ++ sieve (spin p (cycle ns)) Empty where (p:ps,ns) = wheel k spin n (x:xs) = n : spin (n+x) xs @@ -47,13 +45,13 @@ -- Sieves a list of prime candidates using a lazy priority queue. -- -sieve :: [Integer] -> Queue -> [Integer] -sieve (n:ns) Empty = n : sieve ns (enqueue (map (n*) (n:ns)) Empty) -sieve (n:ns) queue - | m == n = sieve ns (enqueue ms q) - | m < n = sieve (n:ns) (enqueue ms q) - | otherwise = n : sieve ns (enqueue (map (n*) (n:ns)) queue) - where (m:ms,q) = dequeue queue +sieve :: [Integer] -> Queue -> [Integer] +sieve (n:ns) Empty = n : sieve ns (enqueue (map (n*) (n:ns)) Empty) +sieve (n:ns) queue + | m == n = sieve ns (enqueue ms q) + | m < n = sieve (n:ns) (enqueue ms q) + | otherwise = n : sieve ns (enqueue (map (n*) (n:ns)) queue) + where (m:ms,q) = dequeue queue -- A wheel consists of a list of primes whose multiples are canceled -- and the actual wheel that is rolled for canceling. @@ -65,9 +63,9 @@ -- -- For example: -- --- wheel 0 = ([2],[1]) --- wheel 1 = ([3,2],[2]) --- wheel 2 = ([5,3,2],[2,4]) +-- wheel 0 = ([2],[1]) +-- wheel 1 = ([3,2],[2]) +-- wheel 2 = ([5,3,2],[2,4]) -- wheel 3 = ([7,5,3,2],[4,2,4,2,4,6,2,6]) -- wheel :: Int -> Wheel @@ -75,9 +73,8 @@ next :: Wheel -> Wheel next (ps@(p:_),xs) = (py:ps,cancel (product ps) p py ys) - where - (y:ys) = cycle xs - py = p + y + where (y:ys) = cycle xs + py = p + y cancel :: Integer -> Integer -> Integer -> [Integer] -> [Integer] cancel 0 _ _ _ = [] @@ -87,28 +84,27 @@ where nx = n + x --- We use a special version of priority queues implemented as "pairing --- heaps" ((see "Purely functional datastructures by Chris Okasaki). +-- We use a special version of priority queues implemented as /pairing/ +-- /heaps/ (see /Purely Functional Data Structures/ by Chris Okasaki). -- -- The queue stores non-empty lists of multiples; the first element is -- used as priority. -- -data Queue = Empty | Fork [Integer] [Queue] +data Queue = Empty | Fork [Integer] [Queue] enqueue :: [Integer] -> Queue -> Queue -enqueue ns = merge (Fork ns []) +enqueue ns = merge (Fork ns []) merge :: Queue -> Queue -> Queue -merge Empty y = y; merge x Empty = x -merge x y | prio x <= prio y = join x y - | otherwise = join y x - where prio (Fork (n:_) _) = n - join (Fork ns qs) q = Fork ns (q:qs) +merge Empty y = y; merge x Empty = x +merge x y | prio x <= prio y = join x y + | otherwise = join y x + where prio (Fork (n:_) _) = n + join (Fork ns qs) q = Fork ns (q:qs) dequeue :: Queue -> ([Integer], Queue) -dequeue (Fork ns qs) = (ns,mergeAll qs) +dequeue (Fork ns qs) = (ns,mergeAll qs) mergeAll :: [Queue] -> Queue -mergeAll [] = Empty; mergeAll [x] = x +mergeAll [] = Empty; mergeAll [x] = x mergeAll (x:y:qs) = merge (merge x y) (mergeAll qs) - diff --git a/README b/README --- a/README +++ b/README @@ -1,7 +1,7 @@ This Haskell library provides an efficient lazy wheel sieve for prime -generation ispired by "Lazy wheel sieves and spirals of primes" [1] by -Colin Runciman and "The Genuine Sieve of Eratosthenes" [2] by Melissa -O'Neil. +generation inspired by "Lazy wheel sieves and spirals of primes" [1] +by Colin Runciman and "The Genuine Sieve of Eratosthenes" [2] by +Melissa O'Neil. [1]: [2]: diff --git a/primes.cabal b/primes.cabal --- a/primes.cabal +++ b/primes.cabal @@ -1,20 +1,20 @@ Name: primes -Version: 0.1 +Version: 0.1.1 Cabal-Version: >= 1.6 Synopsis: Efficient, purely functional generation of prime numbers -Description: +Description: This Haskell library provides an efficient lazy wheel sieve for - prime generation ispired by "Lazy wheel sieves and spirals of - primes" by Colin Runciman and "The Genuine Sieve of Eratosthenes" by - Melissa O'Neil. + prime generation inspired by /Lazy wheel sieves and spirals of/ + /primes/ by Colin Runciman and /The Genuine Sieve of Eratosthenes/ + by Melissa O'Neil. Category: Algorithms, Numerical License: PublicDomain License-File: LICENSE Author: Sebastian Fischer Maintainer: Sebastian Fischer -Bug-Reports: mailto:sebf@informatik.uni-kiel.de +Bug-Reports: http://github.com/sebfisch/primes/issues Homepage: http://github.com/sebfisch/primes Build-Type: Simple Stability: experimental