    {-# LANGUAGE CPP, MagicHash, NoImplicitPrelude #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  System.Event.IntMap
    -- Copyright   :  (c) Daan Leijen 2002
    --                (c) Andriy Palamarchuk 2008
    -- License     :  BSD-style
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- An efficient implementation of maps from integer keys to values.
    --
    -- Since many function names (but not the type name) clash with
    -- "Prelude" names, this module is usually imported @qualified@, e.g.
    --
    -- >  import Data.IntMap (IntMap)
    -- >  import qualified Data.IntMap as IntMap
    --
    -- The implementation is based on /big-endian patricia trees/.  This data
    -- structure performs especially well on binary operations like 'union'
    -- and 'intersection'.  However, my benchmarks show that it is also
    -- (much) faster on insertions and deletions when compared to a generic
    -- size-balanced map implementation (see "Data.Map").
    --
    --    * Chris Okasaki and Andy Gill,  \"/Fast Mergeable Integer Maps/\",
    --      Workshop on ML, September 1998, pages 77-86,
    --      <http://citeseer.ist.psu.edu/okasaki98fast.html>
    --
    --    * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
    --      Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
    --      October 1968, pages 514-534.
    --
    -- Operation comments contain the operation time complexity in
    -- the Big-O notation <http://en.wikipedia.org/wiki/Big_O_notation>.
    -- Many operations have a worst-case complexity of /O(min(n,W))/.
    -- This means that the operation can become linear in the number of
    -- elements with a maximum of /W/ -- the number of bits in an 'Int'
    -- (32 or 64).
    -----------------------------------------------------------------------------

    module System.Event.IntMap
        (
        -- * Map type
        IntMap
        , Key

        -- * Query
        , lookup
        , member

        -- * Construction
        , empty

        -- * Insertion
        , insertWith

        -- * Delete\/Update
        , delete
        , updateWith

        -- * Traversal
        -- ** Fold
        , foldWithKey

        -- * Conversion
        , keys
        ) where

    import Data.Bits

    import Data.Maybe (Maybe(..))
    import GHC.Base hiding (foldr)
    import GHC.Num (Num(..))
    import GHC.Real (fromIntegral)
    import GHC.Show (Show(showsPrec), showParen, shows, showString)

    #if __GLASGOW_HASKELL__
    import GHC.Word (Word(..))
    #else
    import Data.Word
    #endif

    -- | A @Nat@ is a natural machine word (an unsigned Int)
    type Nat = Word

    natFromInt :: Key -> Nat
    natFromInt i = fromIntegral i

    intFromNat :: Nat -> Key
    intFromNat w = fromIntegral w

    shiftRL :: Nat -> Key -> Nat
    #if __GLASGOW_HASKELL__
    -- GHC: use unboxing to get @shiftRL@ inlined.
    shiftRL (W# x) (I# i) = W# (shiftRL# x i)
    #else
    shiftRL x i = shiftR x i
    #endif

    ------------------------------------------------------------------------
    -- Types

    -- | A map of integers to values @a@.
    data IntMap a = Nil
                  | Tip {-# UNPACK #-} !Key !a
                  | Bin {-# UNPACK #-} !Prefix
                        {-# UNPACK #-} !Mask
                        !(IntMap a)
                        !(IntMap a)

    type Prefix = Int
    type Mask   = Int
    type Key    = Int

    ------------------------------------------------------------------------
    -- Query

    -- | /O(min(n,W))/ Lookup the value at a key in the map.  See also
    -- 'Data.Map.lookup'.
    lookup :: Key -> IntMap a -> Maybe a
    lookup k t = let nk = natFromInt k in seq nk (lookupN nk t)

    lookupN :: Nat -> IntMap a -> Maybe a
    lookupN k t
      = case t of
          Bin _ m l r
            | zeroN k (natFromInt m) -> lookupN k l
            | otherwise              -> lookupN k r
          Tip kx x
            | (k == natFromInt kx)  -> Just x
            | otherwise             -> Nothing
          Nil -> Nothing

    -- | /O(min(n,W))/. Is the key a member of the map?
    --
    -- > member 5 (fromList [(5,'a'), (3,'b')]) == True
    -- > member 1 (fromList [(5,'a'), (3,'b')]) == False

    member :: Key -> IntMap a -> Bool
    member k m
      = case lookup k m of
          Nothing -> False
          Just _  -> True

    ------------------------------------------------------------------------
    -- Construction

    -- | /O(1)/ The empty map.
    --
    -- > empty      == fromList []
    -- > size empty == 0
    empty :: IntMap a
    empty = Nil

    ------------------------------------------------------------------------
    -- Insert

    -- | /O(min(n,W))/ Insert with a function, combining new value and old
    -- value.  @insertWith f key value mp@ will insert the pair (key,
    -- value) into @mp@ if key does not exist in the map.  If the key does
    -- exist, the function will insert the pair (key, f new_value
    -- old_value).  The result is a pair where the first element is the
    -- old value, if one was present, and the second is the modified map.
    insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
    insertWith f k x t = case t of
        Bin p m l r
            | nomatch k p m -> (Nothing, join k (Tip k x) p t)
            | zero k m      -> let (found, l') = insertWith f k x l
                               in (found, Bin p m l' r)
            | otherwise     -> let (found, r') = insertWith f k x r
                               in (found, Bin p m l r')
        Tip ky y
            | k == ky       -> (Just y, Tip k (f x y))
            | otherwise     -> (Nothing, join k (Tip k x) ky t)
        Nil                 -> (Nothing, Tip k x)

    ------------------------------------------------------------------------
    -- Delete/Update

    -- | /O(min(n,W))/. Delete a key and its value from the map.  When the
    -- key is not a member of the map, the original map is returned.  The
    -- result is a pair where the first element is the value associated
    -- with the deleted key, if one existed, and the second element is the
    -- modified map.
    delete :: Key -> IntMap a -> (Maybe a, IntMap a)
    delete k t = case t of
       Bin p m l r
            | nomatch k p m -> (Nothing, t)
            | zero k m      -> let (found, l') = delete k l
                               in (found, bin p m l' r)
            | otherwise     -> let (found, r') = delete k r
                               in (found, bin p m l r')
       Tip ky y
            | k == ky       -> (Just y, Nil)
            | otherwise     -> (Nothing, t)
       Nil                  -> (Nothing, Nil)

    updateWith :: (a -> Maybe a) -> Key -> IntMap a -> (Maybe a, IntMap a)
    updateWith f k t = case t of
        Bin p m l r
            | nomatch k p m -> (Nothing, t)
            | zero k m      -> let (found, l') = updateWith f k l
                               in (found, bin p m l' r)
            | otherwise     -> let (found, r') = updateWith f k r
                               in (found, bin p m l r')
        Tip ky y
            | k == ky       -> case (f y) of
                                   Just y' -> (Just y, Tip ky y')
                                   Nothing -> (Just y, Nil)
            | otherwise     -> (Nothing, t)
        Nil                 -> (Nothing, Nil)
    -- | /O(n)/. Fold the keys and values in the map, such that
    -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
    -- For example,
    --
    -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
    --
    -- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
    -- > foldWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"

    foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
    foldWithKey f z t
      = foldr f z t

    -- | /O(n)/. Convert the map to a list of key\/value pairs.
    --
    -- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
    -- > toList empty == []

    toList :: IntMap a -> [(Key,a)]
    toList t
      = foldWithKey (\k x xs -> (k,x):xs) [] t

    foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
    foldr f z t
      = case t of
          Bin 0 m l r | m < 0 -> foldr' f (foldr' f z l) r  -- put negative numbers before.
          Bin _ _ _ _ -> foldr' f z t
          Tip k x     -> f k x z
          Nil         -> z

    foldr' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
    foldr' f z t
      = case t of
          Bin _ _ l r -> foldr' f (foldr' f z r) l
          Tip k x     -> f k x z
          Nil         -> z

    -- | /O(n)/. Return all keys of the map in ascending order.
    --
    -- > keys (fromList [(5,"a"), (3,"b")]) == [3,5]
    -- > keys empty == []

    keys  :: IntMap a -> [Key]
    keys m
      = foldWithKey (\k _ ks -> k:ks) [] m

    ------------------------------------------------------------------------
    -- Eq

    instance Eq a => Eq (IntMap a) where
        t1 == t2 = equal t1 t2
        t1 /= t2 = nequal t1 t2

    equal :: Eq a => IntMap a -> IntMap a -> Bool
    equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
        = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
    equal (Tip kx x) (Tip ky y)
        = (kx == ky) && (x==y)
    equal Nil Nil = True
    equal _   _   = False

    nequal :: Eq a => IntMap a -> IntMap a -> Bool
    nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
        = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
    nequal (Tip kx x) (Tip ky y)
        = (kx /= ky) || (x/=y)
    nequal Nil Nil = False
    nequal _   _   = True

    instance Show a => Show (IntMap a) where
      showsPrec d m   = showParen (d > 10) $
        showString "fromList " . shows (toList m)

    ------------------------------------------------------------------------
    -- Utility functions

    join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
    join p1 t1 p2 t2
      | zero p1 m = Bin p m t1 t2
      | otherwise = Bin p m t2 t1
      where
        m = branchMask p1 p2
        p = mask p1 m

    -- | @bin@ assures that we never have empty trees within a tree.
    bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
    bin _ _ l Nil = l
    bin _ _ Nil r = r
    bin p m l r   = Bin p m l r

    ------------------------------------------------------------------------
    -- Endian independent bit twiddling

    zero :: Key -> Mask -> Bool
    zero i m = (natFromInt i) .&. (natFromInt m) == 0

    nomatch :: Key -> Prefix -> Mask -> Bool
    nomatch i p m = (mask i m) /= p

    mask :: Key -> Mask -> Prefix
    mask i m = maskW (natFromInt i) (natFromInt m)

    zeroN :: Nat -> Nat -> Bool
    zeroN i m = (i .&. m) == 0

    ------------------------------------------------------------------------
    -- Big endian operations

    maskW :: Nat -> Nat -> Prefix
    maskW i m = intFromNat (i .&. (complement (m-1) `xor` m))

    branchMask :: Prefix -> Prefix -> Mask
    branchMask p1 p2
        = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))

    {-
    Finding the highest bit mask in a word [x] can be done efficiently in
    three ways:

    * convert to a floating point value and the mantissa tells us the
      [log2(x)] that corresponds with the highest bit position. The mantissa
      is retrieved either via the standard C function [frexp] or by some bit
      twiddling on IEEE compatible numbers (float). Note that one needs to
      use at least [double] precision for an accurate mantissa of 32 bit
      numbers.

    * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).

    * use processor specific assembler instruction (asm).

    The most portable way would be [bit], but is it efficient enough?
    I have measured the cycle counts of the different methods on an AMD
    Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:

    highestBitMask: method  cycles
                    --------------
                     frexp   200
                     float    33
                     bit      11
                     asm      12

    Wow, the bit twiddling is on today's RISC like machines even faster
    than a single CISC instruction (BSR)!
    -}

    -- | @highestBitMask@ returns a word where only the highest bit is
    -- set.  It is found by first setting all bits in lower positions than
    -- the highest bit and than taking an exclusive or with the original
    -- value.  Allthough the function may look expensive, GHC compiles
    -- this into excellent C code that subsequently compiled into highly
    -- efficient machine code. The algorithm is derived from Jorg Arndt's
    -- FXT library.
    highestBitMask :: Nat -> Nat
    highestBitMask x0
      = case (x0 .|. shiftRL x0 1) of
         x1 -> case (x1 .|. shiftRL x1 2) of
          x2 -> case (x2 .|. shiftRL x2 4) of
           x3 -> case (x3 .|. shiftRL x3 8) of
            x4 -> case (x4 .|. shiftRL x4 16) of
             x5 -> case (x5 .|. shiftRL x5 32) of   -- for 64 bit platforms
              x6 -> (x6 `xor` (shiftRL x6 1))