1 {-# OPTIONS_GHC -XNoImplicitPrelude -funbox-strict-fields -fno-warn-name-shadowing #-}
3 -----------------------------------------------------------------------------
5 -- Module : Data.HashTable
6 -- Copyright : (c) The University of Glasgow 2003
7 -- License : BSD-style (see the file libraries/base/LICENSE)
9 -- Maintainer : libraries@haskell.org
10 -- Stability : provisional
11 -- Portability : portable
13 -- An implementation of extensible hash tables, as described in
14 -- Per-Ake Larson, /Dynamic Hash Tables/, CACM 31(4), April 1988,
15 -- pp. 446--457. The implementation is also derived from the one
16 -- in GHC's runtime system (@ghc\/rts\/Hash.{c,h}@).
18 -----------------------------------------------------------------------------
20 module Data.HashTable (
21 -- * Basic hash table operations
22 HashTable, new, newHint, insert, delete, lookup, update,
23 -- * Converting to and from lists
33 -- This module is imported by Data.Dynamic, which is pretty low down in the
34 -- module hierarchy, so don't import "high-level" modules
36 #ifdef __GLASGOW_HASKELL__
39 import Prelude hiding ( lookup )
41 import Data.Tuple ( fst )
44 import Data.List ( maximumBy, length, concat, foldl', partition )
45 import Data.Int ( Int32 )
47 #if defined(__GLASGOW_HASKELL__)
49 import GHC.Real ( fromIntegral )
50 import GHC.Show ( Show(..) )
51 import GHC.Int ( Int64 )
57 import Data.Char ( ord )
58 import Data.IORef ( IORef, newIORef, readIORef, writeIORef )
59 import System.IO.Unsafe ( unsafePerformIO )
60 import Data.Int ( Int64 )
61 # if defined(__HUGS__)
62 import Hugs.IOArray ( IOArray, newIOArray,
63 unsafeReadIOArray, unsafeWriteIOArray )
64 # elif defined(__NHC__)
65 import NHC.IOExtras ( IOArray, newIOArray, readIOArray, writeIOArray )
68 import Control.Monad ( mapM, mapM_, sequence_ )
71 -----------------------------------------------------------------------
76 -----------------------------------------------------------------------
78 readHTArray :: HTArray a -> Int32 -> IO a
79 writeMutArray :: MutArray a -> Int32 -> a -> IO ()
80 newMutArray :: (Int32, Int32) -> a -> IO (MutArray a)
81 newMutArray = newIOArray
82 type MutArray a = IOArray Int32 a
83 type HTArray a = MutArray a
84 #if defined(DEBUG) || defined(__NHC__)
85 readHTArray = readIOArray
86 writeMutArray = writeIOArray
88 readHTArray arr i = unsafeReadIOArray arr (fromIntegral i)
89 writeMutArray arr i x = unsafeWriteIOArray arr (fromIntegral i) x
92 data HashTable key val = HashTable {
93 cmp :: !(key -> key -> Bool),
94 hash_fn :: !(key -> Int32),
95 tab :: !(IORef (HT key val))
97 -- TODO: the IORef should really be an MVar.
101 kcount :: !Int32, -- Total number of keys.
103 buckets :: !(HTArray [(key,val)])
106 -- ------------------------------------------------------------
107 -- Instrumentation for performance tuning
109 -- This ought to be roundly ignored after optimization when
110 -- iNSTRUMENTED=False.
112 -- STRICT version of modifyIORef!
113 modifyIORef :: IORef a -> (a -> a) -> IO ()
116 let z = f v in z `seq` writeIORef r z
120 insertions :: !Integer,
122 totBuckets :: !Integer,
123 maxEntries :: !Int32,
126 } deriving (Eq, Show)
128 {-# NOINLINE hashData #-}
129 hashData :: IORef HashData
130 hashData = unsafePerformIO (newIORef (HD { tables=0, insertions=0, lookups=0,
131 totBuckets=0, maxEntries=0,
132 maxChain=0, maxBuckets=tABLE_MIN } ))
134 instrument :: (HashData -> HashData) -> IO ()
135 instrument i | iNSTRUMENTED = modifyIORef hashData i
136 | otherwise = return ()
139 recordNew = instrument rec
140 where rec hd@HD{ tables=t, totBuckets=b } =
141 hd{ tables=t+1, totBuckets=b+fromIntegral tABLE_MIN }
143 recordIns :: Int32 -> Int32 -> [a] -> IO ()
144 recordIns i sz bkt = instrument rec
145 where rec hd@HD{ insertions=ins, maxEntries=mx, maxChain=mc } =
146 hd{ insertions=ins+fromIntegral i, maxEntries=mx `max` sz,
147 maxChain=mc `max` length bkt }
149 recordResize :: Int32 -> Int32 -> IO ()
150 recordResize older newer = instrument rec
151 where rec hd@HD{ totBuckets=b, maxBuckets=mx } =
152 hd{ totBuckets=b+fromIntegral (newer-older),
153 maxBuckets=mx `max` newer }
155 recordLookup :: IO ()
156 recordLookup = instrument lkup
157 where lkup hd@HD{ lookups=l } = hd{ lookups=l+1 }
159 -- stats :: IO String
160 -- stats = fmap show $ readIORef hashData
162 -- ----------------------------------------------------------------------------
163 -- Sample hash functions
167 -- This implementation of hash tables uses the low-order /n/ bits of the hash
168 -- value for a key, where /n/ varies as the hash table grows. A good hash
169 -- function therefore will give an even distribution regardless of /n/.
171 -- If your keyspace is integrals such that the low-order bits between
172 -- keys are highly variable, then you could get away with using 'fromIntegral'
173 -- as the hash function.
175 -- We provide some sample hash functions for 'Int' and 'String' below.
178 golden = 1013904242 -- = round ((sqrt 5 - 1) * 2^32) :: Int32
179 -- was -1640531527 = round ((sqrt 5 - 1) * 2^31) :: Int32
180 -- but that has bad mulHi properties (even adding 2^32 to get its inverse)
181 -- Whereas the above works well and contains no hash duplications for
184 hashInt32 :: Int32 -> Int32
185 hashInt32 x = mulHi x golden + x
187 -- | A sample (and useful) hash function for Int and Int32,
188 -- implemented by extracting the uppermost 32 bits of the 64-bit
189 -- result of multiplying by a 33-bit constant. The constant is from
190 -- Knuth, derived from the golden ratio:
192 -- > golden = round ((sqrt 5 - 1) * 2^32)
194 -- We get good key uniqueness on small inputs
195 -- (a problem with previous versions):
196 -- (length $ group $ sort $ map hashInt [-32767..65536]) == 65536 + 32768
198 hashInt :: Int -> Int32
199 hashInt x = hashInt32 (fromIntegral x)
201 -- hi 32 bits of a x-bit * 32 bit -> 64-bit multiply
202 mulHi :: Int32 -> Int32 -> Int32
203 mulHi a b = fromIntegral (r `shiftR` 32)
205 r = fromIntegral a * fromIntegral b
207 -- | A sample hash function for Strings. We keep multiplying by the
208 -- golden ratio and adding. The implementation is:
210 -- > hashString = foldl' f golden
211 -- > where f m c = fromIntegral (ord c) * magic + hashInt32 m
212 -- > magic = 0xdeadbeef
214 -- Where hashInt32 works just as hashInt shown above.
216 -- Knuth argues that repeated multiplication by the golden ratio
217 -- will minimize gaps in the hash space, and thus it's a good choice
218 -- for combining together multiple keys to form one.
220 -- Here we know that individual characters c are often small, and this
221 -- produces frequent collisions if we use ord c alone. A
222 -- particular problem are the shorter low ASCII and ISO-8859-1
223 -- character strings. We pre-multiply by a magic twiddle factor to
224 -- obtain a good distribution. In fact, given the following test:
226 -- > testp :: Int32 -> Int
227 -- > testp k = (n - ) . length . group . sort . map hs . take n $ ls
228 -- > where ls = [] : [c : l | l <- ls, c <- ['\0'..'\xff']]
229 -- > hs = foldl' f golden
230 -- > f m c = fromIntegral (ord c) * k + hashInt32 m
233 -- We discover that testp magic = 0.
235 hashString :: String -> Int32
236 hashString = foldl' f golden
237 where f m c = fromIntegral (ord c) * magic + hashInt32 m
240 -- | A prime larger than the maximum hash table size
244 -- -----------------------------------------------------------------------------
248 tABLE_MAX = 32 * 1024 * 1024 -- Maximum size of hash table
253 hLOAD = 7 -- Maximum average load of a single hash bucket
256 hYSTERESIS = 64 -- entries to ignore in load computation
258 {- Hysteresis favors long association-list-like behavior for small tables. -}
260 -- -----------------------------------------------------------------------------
261 -- Creating a new hash table
263 -- | Creates a new hash table. The following property should hold for the @eq@
264 -- and @hash@ functions passed to 'new':
266 -- > eq A B => hash A == hash B
269 :: (key -> key -> Bool) -- ^ @eq@: An equality comparison on keys
270 -> (key -> Int32) -- ^ @hash@: A hash function on keys
271 -> IO (HashTable key val) -- ^ Returns: an empty hash table
275 -- make a new hash table with a single, empty, segment
276 let mask = tABLE_MIN-1
277 bkts <- newMutArray (0,mask) []
281 ht = HT { buckets=bkts, kcount=kcnt, bmask=mask }
284 return (HashTable { tab=table, hash_fn=hash, cmp=cmpr })
287 bitTwiddleSameAs takes as arguments positive Int32s less than maxBound/2 and
288 returns the smallest power of 2 that is greater than or equal to the
290 http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2
292 bitTwiddleSameAs :: Int32 -> Int32
293 bitTwiddleSameAs v0 =
295 v2 = v1 .|. (v1`shiftR`1)
296 v3 = v2 .|. (v2`shiftR`2)
297 v4 = v3 .|. (v3`shiftR`4)
298 v5 = v4 .|. (v4`shiftR`8)
299 v6 = v5 .|. (v5`shiftR`16)
303 powerOver takes as arguments Int32s and returns the smallest power of 2
304 that is greater than or equal to the argument if that power of 2 is
305 within [tABLE_MIN,tABLE_MAX]
307 powerOver :: Int32 -> Int32
311 else if n >= tABLE_MAX
313 else bitTwiddleSameAs n
315 -- | Creates a new hash table with the given minimum size.
317 :: (key -> key -> Bool) -- ^ @eq@: An equality comparison on keys
318 -> (key -> Int32) -- ^ @hash@: A hash function on keys
319 -> Int -- ^ @minSize@: initial table size
320 -> IO (HashTable key val) -- ^ Returns: an empty hash table
322 newHint cmpr hash minSize = do
324 -- make a new hash table with a single, empty, segment
325 let mask = powerOver $ fromIntegral minSize
326 bkts <- newMutArray (0,mask) []
330 ht = HT { buckets=bkts, kcount=kcnt, bmask=mask }
333 return (HashTable { tab=table, hash_fn=hash, cmp=cmpr })
335 -- -----------------------------------------------------------------------------
336 -- Inserting a key\/value pair into the hash table
338 -- | Inserts a key\/value mapping into the hash table.
340 -- Note that 'insert' doesn't remove the old entry from the table -
341 -- the behaviour is like an association list, where 'lookup' returns
342 -- the most-recently-inserted mapping for a key in the table. The
343 -- reason for this is to keep 'insert' as efficient as possible. If
344 -- you need to update a mapping, then we provide 'update'.
346 insert :: HashTable key val -> key -> val -> IO ()
349 updatingBucket CanInsert (\bucket -> ((key,val):bucket, 1, ())) ht key
352 -- ------------------------------------------------------------
353 -- The core of the implementation is lurking down here, in findBucket,
354 -- updatingBucket, and expandHashTable.
356 tooBig :: Int32 -> Int32 -> Bool
357 tooBig k b = k-hYSTERESIS > hLOAD * b
359 -- index of bucket within table.
360 bucketIndex :: Int32 -> Int32 -> Int32
361 bucketIndex mask h = h .&. mask
363 -- find the bucket in which the key belongs.
364 -- returns (key equality, bucket index, bucket)
366 -- This rather grab-bag approach gives enough power to do pretty much
367 -- any bucket-finding thing you might want to do. We rely on inlining
368 -- to throw away the stuff we don't want. I'm proud to say that this
369 -- plus updatingBucket below reduce most of the other definitions to a
370 -- few lines of code, while actually speeding up the hashtable
371 -- implementation when compared with a version which does everything
373 {-# INLINE findBucket #-}
374 findBucket :: HashTable key val -> key -> IO (HT key val, Int32, [(key,val)])
375 findBucket HashTable{ tab=ref, hash_fn=hash} key = do
376 table@HT{ buckets=bkts, bmask=b } <- readIORef ref
377 let indx = bucketIndex b (hash key)
378 bucket <- readHTArray bkts indx
379 return (table, indx, bucket)
381 data Inserts = CanInsert
385 -- updatingBucket is the real workhorse of all single-element table
386 -- updates. It takes a hashtable and a key, along with a function
387 -- describing what to do with the bucket in which that key belongs. A
388 -- flag indicates whether this function may perform table insertions.
389 -- The function returns the new contents of the bucket, the number of
390 -- bucket entries inserted (negative if entries were deleted), and a
391 -- value which becomes the return value for the function as a whole.
392 -- The table sizing is enforced here, calling out to expandSubTable as
395 -- This function is intended to be inlined and specialized for every
396 -- calling context (eg every provided bucketFn).
397 {-# INLINE updatingBucket #-}
399 updatingBucket :: Inserts -> ([(key,val)] -> ([(key,val)], Int32, a)) ->
400 HashTable key val -> key ->
402 updatingBucket canEnlarge bucketFn
403 ht@HashTable{ tab=ref, hash_fn=hash } key = do
404 (table@HT{ kcount=k, buckets=bkts, bmask=b },
405 indx, bckt) <- findBucket ht key
406 (bckt', inserts, result) <- return $ bucketFn bckt
408 table1 = table { kcount=k' }
409 writeMutArray bkts indx bckt'
410 table2 <- if canEnlarge == CanInsert && inserts > 0 then do
411 recordIns inserts k' bckt'
413 then expandHashTable hash table1
416 writeIORef ref table2
419 expandHashTable :: (key -> Int32) -> HT key val -> IO (HT key val)
420 expandHashTable hash table@HT{ buckets=bkts, bmask=mask } = do
423 newmask = mask + mask + 1
424 recordResize oldsize (newmask+1)
426 if newmask > tABLE_MAX-1
430 newbkts <- newMutArray (0,newmask) []
433 splitBucket oldindex = do
434 bucket <- readHTArray bkts oldindex
436 partition ((oldindex==). bucketIndex newmask . hash . fst) bucket
437 writeMutArray newbkts oldindex oldb
438 writeMutArray newbkts (oldindex + oldsize) newb
439 mapM_ splitBucket [0..mask]
441 return ( table{ buckets=newbkts, bmask=newmask } )
443 -- -----------------------------------------------------------------------------
444 -- Deleting a mapping from the hash table
446 -- Remove a key from a bucket
447 deleteBucket :: (key -> Bool) -> [(key,val)] -> ([(key, val)], Int32, ())
448 deleteBucket _ [] = ([],0,())
449 deleteBucket del (pair@(k,_):bucket) =
450 case deleteBucket del bucket of
451 (bucket', dels, _) | del k -> dels' `seq` (bucket', dels', ())
452 | otherwise -> (pair:bucket', dels, ())
453 where dels' = dels - 1
455 -- | Remove an entry from the hash table.
456 delete :: HashTable key val -> key -> IO ()
458 delete ht@HashTable{ cmp=eq } key =
459 updatingBucket Can'tInsert (deleteBucket (eq key)) ht key
461 -- -----------------------------------------------------------------------------
462 -- Updating a mapping in the hash table
464 -- | Updates an entry in the hash table, returning 'True' if there was
465 -- already an entry for this key, or 'False' otherwise. After 'update'
466 -- there will always be exactly one entry for the given key in the table.
468 -- 'insert' is more efficient than 'update' if you don't care about
469 -- multiple entries, or you know for sure that multiple entries can't
470 -- occur. However, 'update' is more efficient than 'delete' followed
472 update :: HashTable key val -> key -> val -> IO Bool
474 update ht@HashTable{ cmp=eq } key val =
475 updatingBucket CanInsert
476 (\bucket -> let (bucket', dels, _) = deleteBucket (eq key) bucket
477 in ((key,val):bucket', 1+dels, dels/=0))
480 -- -----------------------------------------------------------------------------
481 -- Looking up an entry in the hash table
483 -- | Looks up the value of a key in the hash table.
484 lookup :: HashTable key val -> key -> IO (Maybe val)
486 lookup ht@HashTable{ cmp=eq } key = do
488 (_, _, bucket) <- findBucket ht key
489 let firstHit (k,v) r | eq key k = Just v
491 return (foldr firstHit Nothing bucket)
493 -- -----------------------------------------------------------------------------
494 -- Converting to/from lists
496 -- | Convert a list of key\/value pairs into a hash table. Equality on keys
497 -- is taken from the Eq instance for the key type.
499 fromList :: (Eq key) => (key -> Int32) -> [(key,val)] -> IO (HashTable key val)
500 fromList hash list = do
501 table <- new (==) hash
502 sequence_ [ insert table k v | (k,v) <- list ]
505 -- | Converts a hash table to a list of key\/value pairs.
507 toList :: HashTable key val -> IO [(key,val)]
508 toList = mapReduce id concat
510 {-# INLINE mapReduce #-}
511 mapReduce :: ([(key,val)] -> r) -> ([r] -> r) -> HashTable key val -> IO r
512 mapReduce m r HashTable{ tab=ref } = do
513 HT{ buckets=bckts, bmask=b } <- readIORef ref
514 fmap r (mapM (fmap m . readHTArray bckts) [0..b])
516 -- -----------------------------------------------------------------------------
519 -- | This function is useful for determining whether your hash
520 -- function is working well for your data set. It returns the longest
521 -- chain of key\/value pairs in the hash table for which all the keys
522 -- hash to the same bucket. If this chain is particularly long (say,
523 -- longer than 14 elements or so), then it might be a good idea to try
524 -- a different hash function.
526 longestChain :: HashTable key val -> IO [(key,val)]
527 longestChain = mapReduce id (maximumBy lengthCmp)
528 where lengthCmp (_:x)(_:y) = lengthCmp x y