base- Basic libraries





An implementation of extensible hash tables, as described in Per-Ake Larson, Dynamic Hash Tables, CACM 31(4), April 1988, pp. 446--457. The implementation is also derived from the one in GHC's runtime system (ghc/rts/Hash.{c,h}).


Basic hash table operations

data HashTable key val Source



:: (key -> key -> Bool)

eq: An equality comparison on keys

-> (key -> Int32)

hash: A hash function on keys

-> IO (HashTable key val)

Returns: an empty hash table

Creates a new hash table. The following property should hold for the eq and hash functions passed to new:

   eq A B  =>  hash A == hash B



:: (key -> key -> Bool)

eq: An equality comparison on keys

-> (key -> Int32)

hash: A hash function on keys

-> Int

minSize: initial table size

-> IO (HashTable key val)

Returns: an empty hash table

Creates a new hash table with the given minimum size.

insert :: HashTable key val -> key -> val -> IO ()Source

Inserts a key/value mapping into the hash table.

Note that insert doesn't remove the old entry from the table - the behaviour is like an association list, where lookup returns the most-recently-inserted mapping for a key in the table. The reason for this is to keep insert as efficient as possible. If you need to update a mapping, then we provide update.

delete :: HashTable key val -> key -> IO ()Source

Remove an entry from the hash table.

lookup :: HashTable key val -> key -> IO (Maybe val)Source

Looks up the value of a key in the hash table.

update :: HashTable key val -> key -> val -> IO BoolSource

Updates an entry in the hash table, returning True if there was already an entry for this key, or False otherwise. After update there will always be exactly one entry for the given key in the table.

insert is more efficient than update if you don't care about multiple entries, or you know for sure that multiple entries can't occur. However, update is more efficient than delete followed by insert.

Converting to and from lists

fromList :: Eq key => (key -> Int32) -> [(key, val)] -> IO (HashTable key val)Source

Convert a list of key/value pairs into a hash table. Equality on keys is taken from the Eq instance for the key type.

toList :: HashTable key val -> IO [(key, val)]Source

Converts a hash table to a list of key/value pairs.

Hash functions

This implementation of hash tables uses the low-order n bits of the hash value for a key, where n varies as the hash table grows. A good hash function therefore will give an even distribution regardless of n.

If your keyspace is integrals such that the low-order bits between keys are highly variable, then you could get away with using fromIntegral as the hash function.

We provide some sample hash functions for Int and String below.

hashInt :: Int -> Int32Source

A sample (and useful) hash function for Int and Int32, implemented by extracting the uppermost 32 bits of the 64-bit result of multiplying by a 33-bit constant. The constant is from Knuth, derived from the golden ratio:

 golden = round ((sqrt 5 - 1) * 2^32)

We get good key uniqueness on small inputs (a problem with previous versions): (length $ group $ sort $ map hashInt [-32767..65536]) == 65536 + 32768

hashString :: String -> Int32Source

A sample hash function for Strings. We keep multiplying by the golden ratio and adding. The implementation is:

 hashString = foldl' f golden
   where f m c = fromIntegral (ord c) * magic + hashInt32 m
         magic = 0xdeadbeef

Where hashInt32 works just as hashInt shown above.

Knuth argues that repeated multiplication by the golden ratio will minimize gaps in the hash space, and thus it's a good choice for combining together multiple keys to form one.

Here we know that individual characters c are often small, and this produces frequent collisions if we use ord c alone. A particular problem are the shorter low ASCII and ISO-8859-1 character strings. We pre-multiply by a magic twiddle factor to obtain a good distribution. In fact, given the following test:

 testp :: Int32 -> Int
 testp k = (n - ) . length . group . sort . map hs . take n $ ls
   where ls = [] : [c : l | l <- ls, c <- ['\0'..'\xff']]
         hs = foldl' f golden
         f m c = fromIntegral (ord c) * k + hashInt32 m
         n = 100000

We discover that testp magic = 0.

prime :: Int32Source

A prime larger than the maximum hash table size


longestChain :: HashTable key val -> IO [(key, val)]Source

This function is useful for determining whether your hash function is working well for your data set. It returns the longest chain of key/value pairs in the hash table for which all the keys hash to the same bucket. If this chain is particularly long (say, longer than 14 elements or so), then it might be a good idea to try a different hash function.