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{-# LANGUAGE BangPatterns, CPP, GeneralizedNewtypeDeriving, MagicHash,
TypeFamilies #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.EnumMapSet
-- Copyright : (c) Daan Leijen 2002
-- (c) Joachim Breitner 2011
-- (c) Matthew West 2012
-- License : BSD-style
-- Stability : experimental
-- Portability : Uses GHC extensions
--
-- Based on Data.IntSet.Base
--
-----------------------------------------------------------------------------
module Data.EnumMapSet.Base (
EnumMapSet,
S(..), (:&)(..),
-- * Query
null,
size,
member,
-- * Construction
empty,
singleton,
insert,
delete,
-- * Combine
union,
difference,
intersection,
-- * Map
map,
-- * Folds
foldr,
-- * Lists
toList,
fromList,
keys,
-- * Internals
EMS(..),
EnumMapMap(KSC),
suffixBitMask,
prefixBitMask,
bitmapOf,
prefixOf
) where
import Prelude hiding (lookup,
map,
filter,
foldr, foldl,
null, init,
head, tail)
import Data.Bits
import qualified Data.List as List
import GHC.Exts (Word(..), Int(..))
import GHC.Prim (indexInt8OffAddr#)
#include "MachDeps.h"
import Data.EnumMapMap.Base ((:&)(..),
IsEmm,
EnumMapMap,
Prefix, Nat, Mask,
branchMask, mask,
intFromNat,
shiftRL, shiftLL,
nomatch, zero,
shorter,
foldlStrict)
import qualified Data.EnumMapMap.Base as EMM
type EnumMapSet k = EnumMapMap k ()
type BitMap = Word
-- | Keys are terminated with the 'S' type.
--
-- > singleKey :: S Int
-- > singleKey = S 5
--
newtype S k = S k
deriving (Show, Eq)
-- This is used instead of @EMM k BitMap@ in order to unpack the 'BitMap' in
-- 'Tip'. Hopefully this will lead to much optimisation by GHC.
data EMS k = Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask
!(EMS k) !(EMS k)
| Tip {-# UNPACK #-} !Int {-# UNPACK #-} !BitMap
| Nil
deriving (Show)
instance (Enum k, Eq k) => IsEmm (S k) where
data EnumMapMap (S k) v = KSC (EMS k)
emptySubTrees e@(KSC emm) =
case emm of
Nil -> False
_ -> EMM.emptySubTrees_ e
emptySubTrees_ (KSC emm) = go emm
where
go t = case t of
Bin _ _ l r -> go l || go r
Tip _ _ -> False
Nil -> True
removeEmpties = id
unsafeJoinKey (KSC _) = undefined
empty = KSC Nil
null (KSC ems) = case ems of
Nil -> True
_ -> False
size (KSC ems) = go ems
where
go (Bin _ _ l r) = go l + go r
go (Tip _ bm) = bitcount 0 bm
go Nil = 0
member !(S key') (KSC ems) = key `seq` go ems
where
go (Bin p m l r)
| nomatch key p m = False
| zero key m = go l
| otherwise = go r
go (Tip y bm) = prefixOf key == y && bitmapOf key .&. bm /= 0
go Nil = False
key = fromEnum key'
singleton (S key') _
= key `seq` KSC $ Tip (prefixOf key) (bitmapOf key)
where key = fromEnum key'
insert (S key') _ (KSC ems)
= key `seq` KSC $ insertBM (prefixOf key) (bitmapOf key) ems
where key = fromEnum key'
delete (S key') (KSC ems)
= key `seq` KSC $ deleteBM (prefixOf key) (bitmapOf key) ems
where key = fromEnum key'
foldrWithKey f init (KSC ems)
= case ems of Bin _ m l r | m < 0 -> go (go init l) r
| otherwise -> go (go init r) l
_ -> go init ems
where
go init' Nil = init'
go init' (Tip kx bm) = foldrBits kx f' init' bm
go init' (Bin _ _ l r) = go (go init' r) l
f' !k t = f (S $ toEnum k) undefined t
union (KSC ems1) (KSC ems2) = KSC $ go ems1 ems2
where
go t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
| shorter m1 m2 = union1
| shorter m2 m1 = union2
| p1 == p2 = Bin p1 m1 (go l1 l2) (go r1 r2)
| otherwise = join p1 t1 p2 t2
where
union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
| zero p2 m1 = Bin p1 m1 (go l1 t2) r1
| otherwise = Bin p1 m1 l1 (go r1 t2)
union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
| zero p1 m2 = Bin p2 m2 (go t1 l2) r2
| otherwise = Bin p2 m2 l2 (go t1 r2)
go t@(Bin _ _ _ _) (Tip kx bm) = insertBM kx bm t
go t@(Bin _ _ _ _) Nil = t
go (Tip kx bm) t = insertBM kx bm t
go Nil t = t
difference (KSC ems1) (KSC ems2) = KSC $ go ems1 ems2
where
go t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
| shorter m1 m2 = difference1
| shorter m2 m1 = difference2
| p1 == p2 = bin p1 m1 (go l1 l2) (go r1 r2)
| otherwise = t1
where
difference1 | nomatch p2 p1 m1 = t1
| zero p2 m1 = bin p1 m1 (go l1 t2) r1
| otherwise = bin p1 m1 l1 (go r1 t2)
difference2 | nomatch p1 p2 m2 = t1
| zero p1 m2 = go t1 l2
| otherwise = go t1 r2
go t@(Bin _ _ _ _) (Tip kx bm) = deleteBM kx bm t
go t@(Bin _ _ _ _) Nil = t
go t1@(Tip kx bm) t2 = differenceTip t2
where differenceTip (Bin p2 m2 l2 r2)
| nomatch kx p2 m2 = t1
| zero kx m2 = differenceTip l2
| otherwise = differenceTip r2
differenceTip (Tip kx2 bm2)
| kx == kx2 = tip kx (bm .&. complement bm2)
| otherwise = t1
differenceTip Nil = t1
go Nil _ = Nil
intersection (KSC ems1) (KSC ems2) = KSC $ go ems1 ems2
where
go t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
| shorter m1 m2 = intersection1
| shorter m2 m1 = intersection2
| p1 == p2 = bin p1 m1 (go l1 l2) (go r1 r2)
| otherwise = Nil
where
intersection1 | nomatch p2 p1 m1 = Nil
| zero p2 m1 = go l1 t2
| otherwise = go r1 t2
intersection2 | nomatch p1 p2 m2 = Nil
| zero p1 m2 = go t1 l2
| otherwise = go t1 r2
go t1@(Bin _ _ _ _) (Tip kx2 bm2) = intersectBM t1
where intersectBM (Bin p1 m1 l1 r1)
| nomatch kx2 p1 m1 = Nil
| zero kx2 m1 = intersectBM l1
| otherwise = intersectBM r1
intersectBM (Tip kx1 bm1)
| kx1 == kx2 = tip kx1 (bm1 .&. bm2)
| otherwise = Nil
intersectBM Nil = Nil
go (Bin _ _ _ _) Nil = Nil
go (Tip kx1 bm1) t2 = intersectBM t2
where intersectBM (Bin p2 m2 l2 r2)
| nomatch kx1 p2 m2 = Nil
| zero kx1 m2 = intersectBM l2
| otherwise = intersectBM r2
intersectBM (Tip kx2 bm2)
| kx1 == kx2 = tip kx1 (bm1 .&. bm2)
| otherwise = Nil
intersectBM Nil = Nil
go Nil _ = Nil
equal (KSC ems1) (KSC ems2) = go ems1 ems2
where
go (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
= (m1 == m2) && (p1 == p2) && (go l1 l2) && (go r1 r2)
go (Tip kx1 bm1) (Tip kx2 bm2)
= kx1 == kx2 && bm1 == bm2
go Nil Nil = True
go _ _ = False
nequal (KSC ems1) (KSC ems2) = go ems1 ems2
where
go (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
= (m1 /= m2) || (p1 /= p2) || (go l1 l2) || (go r1 r2)
go (Tip kx1 bm1) (Tip kx2 bm2)
= kx1 /= kx2 || bm1 /= bm2
go Nil Nil = False
go _ _ = True
insertWith = undefined
insertWithKey = undefined
lookup = undefined
alter = undefined
foldr = undefined
map = undefined
mapWithKey = undefined
unionWith = undefined
unionWithKey = undefined
differenceWith = undefined
differenceWithKey = undefined
intersectionWith = undefined
intersectionWithKey = undefined
fromList = undefined
toList = undefined
elems = undefined
keysSet = undefined
{---------------------------------------------------------------------
Exported API
The Set API is somewhat different to the Map API so we define the following
functions to call the IsEMM functions with the type of 'v' as (), hoping that
GHC will inline away all the empty parameters.
---------------------------------------------------------------------}
null :: (IsEmm k) => EnumMapSet k -> Bool
null = EMM.null
size :: (IsEmm k) => EnumMapSet k -> Int
size = EMM.size
member ::(IsEmm k) => k -> EnumMapSet k -> Bool
member = EMM.member
empty :: (IsEmm k) => EnumMapSet k
empty = EMM.empty
singleton :: (IsEmm k) => k -> EnumMapSet k
singleton !key = EMM.singleton key ()
insert :: (IsEmm k) => k -> EnumMapSet k -> EnumMapSet k
insert !key = EMM.insert key ()
delete :: (IsEmm k) => k -> EnumMapSet k -> EnumMapSet k
delete = EMM.delete
-- This function has not been optimised in any way.
foldr :: (IsEmm k) => (k -> t -> t) -> t -> EnumMapSet k -> t
foldr f = EMM.foldrWithKey go
where
go k _ z = f k z
-- | @'map' f s@ is the set obtained by applying @f@ to each element of @s@.
--
-- It's worth noting that the size of the result may be smaller if,
-- for some @(x,y)@, @x \/= y && f x == f y@
map :: (IsEmm k1, IsEmm k2) =>
(k1 -> k2) -> EnumMapSet k1 -> EnumMapSet k2
map f = fromList . List.map f . toList
union :: (IsEmm k) => EnumMapSet k -> EnumMapSet k -> EnumMapSet k
union = EMM.union
difference :: (IsEmm k) => EnumMapSet k -> EnumMapSet k -> EnumMapSet k
difference = EMM.difference
intersection :: (IsEmm k) => EnumMapSet k -> EnumMapSet k -> EnumMapSet k
intersection = EMM.intersection
{---------------------------------------------------------------------
Lists
---------------------------------------------------------------------}
fromList :: IsEmm k => [k] -> EnumMapSet k
fromList xs
= foldlStrict (\t x -> insert x t) empty xs
toList :: IsEmm k => EnumMapSet k -> [k]
toList = foldr (:) []
keys :: IsEmm k => EnumMapSet k -> [k]
keys = toList
{---------------------------------------------------------------------
Instances
---------------------------------------------------------------------}
instance EMM.HasSKey (S k) where
type Skey (S k) = S k
toS (S _) = undefined
toK (S _) = undefined
{---------------------------------------------------------------------
Helper functions
---------------------------------------------------------------------}
insertBM :: Prefix -> BitMap -> EMS k -> EMS k
insertBM !kx !bm t
= case t of
Bin p m l r
| nomatch kx p m -> join kx (Tip kx bm) p t
| zero kx m -> Bin p m (insertBM kx bm l) r
| otherwise -> Bin p m l (insertBM kx bm r)
Tip kx' bm'
| kx' == kx -> Tip kx' (bm .|. bm')
| otherwise -> join kx (Tip kx bm) kx' t
Nil -> Tip kx bm
deleteBM :: Prefix -> BitMap -> EMS k -> EMS k
deleteBM !kx !bm t
= case t of
Bin p m l r
| nomatch kx p m -> t
| zero kx m -> bin p m (deleteBM kx bm l) r
| otherwise -> bin p m l (deleteBM kx bm r)
Tip kx' bm'
| kx' == kx -> tip kx (bm' .&. complement bm)
| otherwise -> t
Nil -> Nil
join :: Prefix -> EMS k -> Prefix -> EMS k -> EMS k
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
{-# INLINE join #-}
bin :: Prefix -> Mask -> EMS k -> EMS k -> EMS k
bin _ _ l Nil = l
bin _ _ Nil r = r
bin p m l r = Bin p m l r
{-# INLINE bin #-}
{--------------------------------------------------------------------
@tip@ assures that we never have empty bitmaps within a tree.
--------------------------------------------------------------------}
tip :: Prefix -> BitMap -> EMS k
tip _ 0 = Nil
tip kx bm = Tip kx bm
{-# INLINE tip #-}
{----------------------------------------------------------------------
Functions that generate Prefix and BitMap of a Key or a Suffix.
Commentary and credits can be found with the original code in
Data/IntSet/Base.hs in 'containers 5.0'.
----------------------------------------------------------------------}
suffixBitMask :: Int
suffixBitMask = bitSize (undefined::Word) - 1
{-# INLINE suffixBitMask #-}
prefixBitMask :: Int
prefixBitMask = complement suffixBitMask
{-# INLINE prefixBitMask #-}
prefixOf :: Int -> Prefix
prefixOf x = x .&. prefixBitMask
{-# INLINE prefixOf #-}
suffixOf :: Int -> Int
suffixOf x = x .&. suffixBitMask
{-# INLINE suffixOf #-}
bitmapOfSuffix :: Int -> BitMap
bitmapOfSuffix s = 1 `shiftLL` s
{-# INLINE bitmapOfSuffix #-}
bitmapOf :: Int -> BitMap
bitmapOf x = bitmapOfSuffix (suffixOf x)
{-# INLINE bitmapOf #-}
bitcount :: Int -> Word -> Int
bitcount a0 x0 = go a0 x0
where go a 0 = a
go a x = go (a + 1) (x .&. (x-1))
{-# INLINE bitcount #-}
{----------------------------------------------------------------------
Folds over a BitMap.
Commentary and credits can be found with the original code in
Data/IntSet/Base.hs in 'containers 5.0'.
----------------------------------------------------------------------}
foldrBits :: Int -> (Int -> a -> a) -> a -> Nat -> a
{-# INLINE foldrBits #-}
indexOfTheOnlyBit :: Nat -> Int
{-# INLINE indexOfTheOnlyBit #-}
indexOfTheOnlyBit bitmask =
I# (lsbArray `indexInt8OffAddr#` unboxInt
(intFromNat ((bitmask * magic) `shiftRL` offset)))
where unboxInt (I# i) = i
#if WORD_SIZE_IN_BITS==32
magic = 0x077CB531
offset = 27
!lsbArray = "\0\1\28\2\29\14\24\3\30\22\20\15\25\17\4\8\31\27\13\23\21\19\16\7\26\12\18\6\11\5\10\9"#
#else
magic = 0x07EDD5E59A4E28C2
offset = 58
!lsbArray = "\63\0\58\1\59\47\53\2\60\39\48\27\54\33\42\3\61\51\37\40\49\18\28\20\55\30\34\11\43\14\22\4\62\57\46\52\38\26\32\41\50\36\17\19\29\10\13\21\56\45\25\31\35\16\9\12\44\24\15\8\23\7\6\5"#
#endif
lowestBitMask :: Nat -> Nat
lowestBitMask x = x .&. negate x
{-# INLINE lowestBitMask #-}
revNat :: Nat -> Nat
#if WORD_SIZE_IN_BITS==32
revNat x1 = case ((x1 `shiftRL` 1) .&. 0x55555555) .|. ((x1 .&. 0x55555555) `shiftLL` 1) of
x2 -> case ((x2 `shiftRL` 2) .&. 0x33333333) .|. ((x2 .&. 0x33333333) `shiftLL` 2) of
x3 -> case ((x3 `shiftRL` 4) .&. 0x0F0F0F0F) .|. ((x3 .&. 0x0F0F0F0F) `shiftLL` 4) of
x4 -> case ((x4 `shiftRL` 8) .&. 0x00FF00FF) .|. ((x4 .&. 0x00FF00FF) `shiftLL` 8) of
x5 -> ( x5 `shiftRL` 16 ) .|. ( x5 `shiftLL` 16);
#else
revNat x1 = case ((x1 `shiftRL` 1) .&. 0x5555555555555555) .|. ((x1 .&. 0x5555555555555555) `shiftLL` 1) of
x2 -> case ((x2 `shiftRL` 2) .&. 0x3333333333333333) .|. ((x2 .&. 0x3333333333333333) `shiftLL` 2) of
x3 -> case ((x3 `shiftRL` 4) .&. 0x0F0F0F0F0F0F0F0F) .|. ((x3 .&. 0x0F0F0F0F0F0F0F0F) `shiftLL` 4) of
x4 -> case ((x4 `shiftRL` 8) .&. 0x00FF00FF00FF00FF) .|. ((x4 .&. 0x00FF00FF00FF00FF) `shiftLL` 8) of
x5 -> case ((x5 `shiftRL` 16) .&. 0x0000FFFF0000FFFF) .|. ((x5 .&. 0x0000FFFF0000FFFF) `shiftLL` 16) of
x6 -> ( x6 `shiftRL` 32 ) .|. ( x6 `shiftLL` 32);
#endif
foldrBits prefix f z bitmap = go (revNat bitmap) z
where go bm acc | bm == 0 = acc
| otherwise = case lowestBitMask bm of
bitmask -> bitmask `seq` case indexOfTheOnlyBit bitmask of
bi -> bi `seq` go (bm `xor` bitmask) ((f $! (prefix+(WORD_SIZE_IN_BITS-1)-bi)) acc)
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