{-# LANGUAGE BangPatterns #-} -- | -- Module : Data.ByteString.Search.KarpRabin -- Copyright : (c) 2010 Daniel Fischer -- Licence : BSD3 -- Maintainer : Daniel Fischer <daniel.is.fischer@googlemail.com> -- Stability : Provisional -- Portability : non-portable (BangPatterns) -- -- Simultaneous search for multiple patterns in a strict 'S.ByteString' -- using the Karp-Rabin algorithm. -- -- A description of the algorithm for a single pattern can be found at -- <http://www-igm.univ-mlv.fr/~lecroq/string/node5.html#SECTION0050>. module Data.ByteString.Search.KarpRabin ( -- * Overview -- $overview -- ** Caution -- $caution -- * Function indicesOfAny ) where import qualified Data.ByteString as S import Data.ByteString.Unsafe (unsafeIndex) import qualified Data.IntMap as IM import Data.Array import Data.Array.Base (unsafeAt) import Data.Word (Word8) import Data.Bits import Data.List (foldl') -- $overview -- -- The Karp-Rabin algorithm works by calculating a hash of the pattern and -- comparing that hash with the hash of a slice of the target string with -- the same length as the pattern. If the hashes are equal, the slice of the -- target is compared to the pattern byte for byte (since the hash -- function generally isn't injective). -- -- For a single pattern, this tends to be more efficient than the na&#239;ve -- algorithm, but it cannot compete with algorithms like -- Knuth-Morris-Pratt or Boyer-Moore. -- -- However, the algorithm can be generalised to search for multiple patterns -- simultaneously. If the shortest pattern has length @k@, hash the prefix of -- length @k@ of all patterns and compare the hash of the target's slices of -- length @k@ to them. If there's a match, check whether the slice is part -- of an occurrence of the corresponding pattern. -- -- With a hash-function that -- -- * allows to compute the hash of one slice in constant time from the hash -- of the previous slice, the new and the dropped character, and -- -- * produces few spurious matches, -- -- searching for occurrences of any of @n@ patterns has a best-case complexity -- of /O/(@targetLength@ * @lookup n@). The worst-case complexity is -- /O/(@targetLength@ * @lookup n@ * @sum patternLengths@), the average is -- not much worse than the best case. -- -- The functions in this module store the hashes of the patterns in an -- 'IM.IntMap', so the lookup is /O/(@log n@). Re-hashing is done in constant -- time and spurious matches of the hashes /should be/ sufficiently rare. -- The maximal length of the prefixes to be hashed is 32. -- $caution -- -- Unfortunately, the constant factors are high, so these functions are slow. -- Unless the number of patterns to search for is high (larger than 50 at -- least), repeated search for single patterns using Boyer-Moore or DFA and -- manual merging of the indices is faster. /Much/ faster for less than 40 -- or so patterns. -- -- In summary, this module is more of an interesting curiosity than anything -- else. -- | @'indicesOfAny'@ finds all occurrences of any of several non-empty patterns -- in a strict target string. If no non-empty patterns are given, -- the result is an empty list. Otherwise the result list contains -- the pairs of all indices where any of the (non-empty) patterns start -- and the list of all patterns starting at that index, the patterns being -- represented by their (zero-based) position in the pattern list. -- Empty patterns are filtered out before processing begins. {-# INLINE indicesOfAny #-} indicesOfAny :: [S.ByteString] -- ^ List of non-empty patterns -> S.ByteString -- ^ String to search -> [(Int,[Int])] -- ^ List of matches indicesOfAny pats | null nepats = const [] | otherwise = strictMatcher nepats where nepats = filter (not . S.null) pats ------------------------------------------------------------------------------ -- Workers -- ------------------------------------------------------------------------------ {-# INLINE rehash1 #-} rehash1 :: Int -> Int -> Word8 -> Word8 -> Int rehash1 out h o n = (h `shiftL` 1 - (fromIntegral o `shiftL` out)) + fromIntegral n {-# INLINE rehash2 #-} rehash2 :: Int -> Int -> Word8 -> Word8 -> Int rehash2 out h o n = (h `shiftL` 2 - (fromIntegral o `shiftL` out)) + fromIntegral n {-# INLINE rehash3 #-} rehash3 :: Int -> Int -> Word8 -> Word8 -> Int rehash3 out h o n = (h `shiftL` 3 - (fromIntegral o `shiftL` out)) + fromIntegral n {-# INLINE rehash4 #-} rehash4 :: Int -> Int -> Word8 -> Word8 -> Int rehash4 out h o n = (h `shiftL` 4 - (fromIntegral o `shiftL` out)) + fromIntegral n strictMatcher :: [S.ByteString] -> S.ByteString -> [(Int,[Int])] strictMatcher pats = search where !hLen = minimum (32 : map S.length pats) !shDi = case 32 `quot` hLen of q | q < 4 -> q | otherwise -> 4 !outS = shDi*hLen !patNum = length pats !patArr = listArray (0, patNum - 1) pats {-# INLINE rehash #-} rehash :: Int -> Word8 -> Word8 -> Int rehash = case shDi of 1 -> rehash1 hLen 2 -> rehash2 outS 3 -> rehash3 outS _ -> rehash4 outS hash :: S.ByteString -> Int hash = S.foldl' (\h w -> (h `shiftL` shDi) + fromIntegral w) 0 . S.take hLen !hashMap = foldl' (\mp (h,i) -> IM.insertWith (flip (++)) h [i] mp) IM.empty $ zip (map hash pats) [0 :: Int .. ] search str | strLen < hLen = [] | otherwise = go 0 shash where !strLen = S.length str !maxIdx = strLen - hLen {-# INLINE strAt #-} strAt !i = unsafeIndex str i !shash = hash str go !sI !h = case IM.lookup h hashMap of Nothing -> if sI == maxIdx then [] else go (sI + 1) (rehash h (strAt sI) (strAt (sI + hLen))) Just ps -> let !rst = S.drop sI str {-# INLINE hd #-} hd = strAt sI {-# INLINE more #-} more = if sI == maxIdx then [] else go (sI + 1) (rehash h hd (strAt (sI + hLen))) {-# INLINE okay #-} okay bs = S.isPrefixOf bs rst in case filter (okay . (patArr `unsafeAt`)) ps of [] -> more qs -> seq (length qs) $ (sI,qs) : more