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Factor Data.IntSet into Data.IntSet.Base and Data.IntSet.

Similarly to Map and IntMap, the whole functionality is in
Data.IntSet.Base. The Data.IntSet module just reexports methods from
Data.IntSet.

The only difference between Data.IntSet.Base and Data.IntSet is that
Data.IntSet.Base exports the constructors of IntSet data type. This will
be used in IntMap to define efficient versions of keysSet and fromSet.
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commit 57042dc65cdedfc64d5f63e144b87c98443438f9 1 parent ea8688f
@foxik foxik authored
Showing with 1,490 additions and 1,360 deletions.
  1. +7 −1,360 Data/IntSet.hs
  2. +1,482 −0 Data/IntSet/Base.hs
  3. +1 −0  containers.cabal
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1,367 Data/IntSet.hs
@@ -1,9 +1,6 @@
{-# LANGUAGE CPP #-}
-#if __GLASGOW_HASKELL__
-{-# LANGUAGE MagicHash, BangPatterns, DeriveDataTypeable, StandaloneDeriving #-}
-#endif
#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703
-{-# LANGUAGE Trustworthy #-}
+{-# LANGUAGE Safe #-}
#endif
-----------------------------------------------------------------------------
-- |
@@ -49,32 +46,6 @@
-- (32 or 64).
-----------------------------------------------------------------------------
--- [Note: INLINE bit fiddling]
--- ~~~~~~~~~~~~~~~~~~~~~~~~~~~
--- It is essential that the bit fiddling functions like mask, zero, branchMask
--- etc are inlined. If they do not, the memory allocation skyrockets. The GHC
--- usually gets it right, but it is disastrous if it does not. Therefore we
--- explicitly mark these functions INLINE.
-
-
--- [Note: Local 'go' functions and capturing]
--- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--- Care must be taken when using 'go' function which captures an argument.
--- Sometimes (for example when the argument is passed to a data constructor,
--- as in insert), GHC heap-allocates more than necessary. Therefore C-- code
--- must be checked for increased allocation when creating and modifying such
--- functions.
-
-
--- [Note: Order of constructors]
--- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--- The order of constructors of IntSet matters when considering performance.
--- Currently in GHC 7.0, when type has 3 constructors, they are matched from
--- the first to the last -- the best performance is achieved when the
--- constructors are ordered by frequency.
--- On GHC 7.0, reordering constructors from Nil | Tip | Bin to Bin | Tip | Nil
--- improves the benchmark by circa 10%.
-
module Data.IntSet (
-- * Strictness properties
-- $strictness
@@ -90,7 +61,7 @@ module Data.IntSet (
, (\\)
-- * Query
- , null
+ , IS.null
, size
, member
, notMember
@@ -114,17 +85,17 @@ module Data.IntSet (
, intersection
-- * Filter
- , filter
+ , IS.filter
, partition
, split
, splitMember
-- * Map
- , map
+ , IS.map
-- * Folds
- , foldr
- , foldl
+ , IS.foldr
+ , IS.foldl
-- ** Strict folds
, foldr'
, foldl'
@@ -164,41 +135,7 @@ module Data.IntSet (
#endif
) where
-
-import Prelude hiding (filter,foldr,foldl,null,map)
-import Data.Bits
-
-import qualified Data.List as List
-import Data.Monoid (Monoid(..))
-import Data.Maybe (fromMaybe)
-import Data.Typeable
-import Control.DeepSeq (NFData)
-
-#if __GLASGOW_HASKELL__
-import Text.Read
-import Data.Data (Data(..), mkNoRepType)
-#endif
-
-#if __GLASGOW_HASKELL__
-import GHC.Exts ( Word(..), Int(..), build )
-import GHC.Prim ( uncheckedShiftL#, uncheckedShiftRL#, indexInt8OffAddr# )
-#else
-import Data.Word
-#endif
-
--- On GHC, include MachDeps.h to get WORD_SIZE_IN_BITS macro.
-#if defined(__GLASGOW_HASKELL__)
-#include "MachDeps.h"
-#endif
-
--- Use macros to define strictness of functions.
--- STRICT_x_OF_y denotes an y-ary function strict in the x-th parameter.
--- We do not use BangPatterns, because they are not in any standard and we
--- want the compilers to be compiled by as many compilers as possible.
-#define STRICT_1_OF_2(fn) fn arg _ | arg `seq` False = undefined
-#define STRICT_2_OF_2(fn) fn _ arg | arg `seq` False = undefined
-#define STRICT_1_OF_3(fn) fn arg _ _ | arg `seq` False = undefined
-#define STRICT_2_OF_3(fn) fn _ arg _ | arg `seq` False = undefined
+import Data.IntSet.Base as IS
-- $strictness
--
@@ -209,1293 +146,3 @@ import Data.Word
-- Here are some examples that illustrate the property:
--
-- > delete undefined s == undefined
-
-infixl 9 \\{-This comment teaches CPP correct behaviour -}
-
--- A "Nat" is a natural machine word (an unsigned Int)
-type Nat = Word
-
-natFromInt :: Int -> Nat
-natFromInt i = fromIntegral i
-{-# INLINE natFromInt #-}
-
-intFromNat :: Nat -> Int
-intFromNat w = fromIntegral w
-{-# INLINE intFromNat #-}
-
--- Right and left logical shifts.
-shiftRL, shiftLL :: Nat -> Int -> Nat
-#if __GLASGOW_HASKELL__
-{--------------------------------------------------------------------
- GHC: use unboxing to get @shiftRL@ and @shiftLL@ inlined.
---------------------------------------------------------------------}
-shiftRL (W# x) (I# i) = W# (uncheckedShiftRL# x i)
-shiftLL (W# x) (I# i) = W# (uncheckedShiftL# x i)
-#else
-shiftRL x i = shiftR x i
-shiftLL x i = shiftL x i
-#endif
-{-# INLINE shiftRL #-}
-{-# INLINE shiftLL #-}
-
-{--------------------------------------------------------------------
- Operators
---------------------------------------------------------------------}
--- | /O(n+m)/. See 'difference'.
-(\\) :: IntSet -> IntSet -> IntSet
-m1 \\ m2 = difference m1 m2
-
-{--------------------------------------------------------------------
- Types
---------------------------------------------------------------------}
-
--- | A set of integers.
-
--- See Note: Order of constructors
-data IntSet = Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !IntSet !IntSet
--- Invariant: Nil is never found as a child of Bin.
--- Invariant: The Mask is a power of 2. It is the largest bit position at which
--- two elements of the set differ.
--- Invariant: Prefix is the common high-order bits that all elements share to
--- the left of the Mask bit.
--- Invariant: In Bin prefix mask left right, left consists of the elements that
--- don't have the mask bit set; right is all the elements that do.
- | Tip {-# UNPACK #-} !Prefix {-# UNPACK #-} !BitMap
--- Invariant: The Prefix is zero for all but the last 5 (on 32 bit arches) or 6
--- bits (on 64 bit arches). The values of the map represented by a tip
--- are the prefix plus the indices of the set bits in the bit map.
- | Nil
-
--- A number stored in a set is stored as
--- * Prefix (all but last 5-6 bits) and
--- * BitMap (last 5-6 bits stored as a bitmask)
--- Last 5-6 bits are called a Suffix.
-
-type Prefix = Int
-type Mask = Int
-type BitMap = Word
-
-instance Monoid IntSet where
- mempty = empty
- mappend = union
- mconcat = unions
-
-#if __GLASGOW_HASKELL__
-
-{--------------------------------------------------------------------
- A Data instance
---------------------------------------------------------------------}
-
--- This instance preserves data abstraction at the cost of inefficiency.
--- We omit reflection services for the sake of data abstraction.
-
-instance Data IntSet where
- gfoldl f z is = z fromList `f` (toList is)
- toConstr _ = error "toConstr"
- gunfold _ _ = error "gunfold"
- dataTypeOf _ = mkNoRepType "Data.IntSet.IntSet"
-
-#endif
-
-{--------------------------------------------------------------------
- Query
---------------------------------------------------------------------}
--- | /O(1)/. Is the set empty?
-null :: IntSet -> Bool
-null Nil = True
-null _ = False
-{-# INLINE null #-}
-
--- | /O(n)/. Cardinality of the set.
-size :: IntSet -> Int
-size t
- = case t of
- Bin _ _ l r -> size l + size r
- Tip _ bm -> bitcount 0 bm
- Nil -> 0
-
--- | /O(min(n,W))/. Is the value a member of the set?
-
--- See Note: Local 'go' functions and capturing]
-member :: Int -> IntSet -> Bool
-member x = x `seq` go
- where
- go (Bin p m l r)
- | nomatch x p m = False
- | zero x m = go l
- | otherwise = go r
- go (Tip y bm) = prefixOf x == y && bitmapOf x .&. bm /= 0
- go Nil = False
-
--- | /O(min(n,W))/. Is the element not in the set?
-notMember :: Int -> IntSet -> Bool
-notMember k = not . member k
-
--- | /O(log n)/. Find largest element smaller than the given one.
---
--- > lookupLT 3 (fromList [3, 5]) == Nothing
--- > lookupLT 5 (fromList [3, 5]) == Just 3
-
--- See Note: Local 'go' functions and capturing.
-lookupLT :: Int -> IntSet -> Maybe Int
-lookupLT x t = x `seq` case t of
- Bin _ m l r | m < 0 -> if x >= 0 then go r l else go Nil r
- _ -> go Nil t
- where
- go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMax def else unsafeFindMax r
- | zero x m = go def l
- | otherwise = go l r
- go def (Tip kx bm) | prefixOf x > kx = Just $ kx + highestBitSet bm
- | prefixOf x == kx && maskLT /= 0 = Just $ kx + highestBitSet maskLT
- | otherwise = unsafeFindMax def
- where maskLT = (bitmapOf x - 1) .&. bm
- go def Nil = unsafeFindMax def
-
-
--- | /O(log n)/. Find smallest element greater than the given one.
---
--- > lookupGT 4 (fromList [3, 5]) == Just 5
--- > lookupGT 5 (fromList [3, 5]) == Nothing
-
--- See Note: Local 'go' functions and capturing.
-lookupGT :: Int -> IntSet -> Maybe Int
-lookupGT x t = x `seq` case t of
- Bin _ m l r | m < 0 -> if x >= 0 then go Nil l else go l r
- _ -> go Nil t
- where
- go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMin l else unsafeFindMin def
- | zero x m = go r l
- | otherwise = go def r
- go def (Tip kx bm) | prefixOf x < kx = Just $ kx + lowestBitSet bm
- | prefixOf x == kx && maskGT /= 0 = Just $ kx + lowestBitSet maskGT
- | otherwise = unsafeFindMin def
- where maskGT = (- ((bitmapOf x) `shiftLL` 1)) .&. bm
- go def Nil = unsafeFindMin def
-
-
--- | /O(log n)/. Find largest element smaller or equal to the given one.
---
--- > lookupLE 2 (fromList [3, 5]) == Nothing
--- > lookupLE 4 (fromList [3, 5]) == Just 3
--- > lookupLE 5 (fromList [3, 5]) == Just 5
-
--- See Note: Local 'go' functions and capturing.
-lookupLE :: Int -> IntSet -> Maybe Int
-lookupLE x t = x `seq` case t of
- Bin _ m l r | m < 0 -> if x >= 0 then go r l else go Nil r
- _ -> go Nil t
- where
- go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMax def else unsafeFindMax r
- | zero x m = go def l
- | otherwise = go l r
- go def (Tip kx bm) | prefixOf x > kx = Just $ kx + highestBitSet bm
- | prefixOf x == kx && maskLE /= 0 = Just $ kx + highestBitSet maskLE
- | otherwise = unsafeFindMax def
- where maskLE = (((bitmapOf x) `shiftLL` 1) - 1) .&. bm
- go def Nil = unsafeFindMax def
-
-
--- | /O(log n)/. Find smallest element greater or equal to the given one.
---
--- > lookupGE 3 (fromList [3, 5]) == Just 3
--- > lookupGE 4 (fromList [3, 5]) == Just 5
--- > lookupGE 6 (fromList [3, 5]) == Nothing
-
--- See Note: Local 'go' functions and capturing.
-lookupGE :: Int -> IntSet -> Maybe Int
-lookupGE x t = x `seq` case t of
- Bin _ m l r | m < 0 -> if x >= 0 then go Nil l else go l r
- _ -> go Nil t
- where
- go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMin l else unsafeFindMin def
- | zero x m = go r l
- | otherwise = go def r
- go def (Tip kx bm) | prefixOf x < kx = Just $ kx + lowestBitSet bm
- | prefixOf x == kx && maskGE /= 0 = Just $ kx + lowestBitSet maskGE
- | otherwise = unsafeFindMin def
- where maskGE = (- (bitmapOf x)) .&. bm
- go def Nil = unsafeFindMin def
-
-
-
--- Helper function for lookupGE and lookupGT. It assumes that if a Bin node is
--- given, it has m > 0.
-unsafeFindMin :: IntSet -> Maybe Int
-unsafeFindMin Nil = Nothing
-unsafeFindMin (Tip kx bm) = Just $ kx + lowestBitSet bm
-unsafeFindMin (Bin _ _ l _) = unsafeFindMin l
-
--- Helper function for lookupLE and lookupLT. It assumes that if a Bin node is
--- given, it has m > 0.
-unsafeFindMax :: IntSet -> Maybe Int
-unsafeFindMax Nil = Nothing
-unsafeFindMax (Tip kx bm) = Just $ kx + highestBitSet bm
-unsafeFindMax (Bin _ _ _ r) = unsafeFindMax r
-
-{--------------------------------------------------------------------
- Construction
---------------------------------------------------------------------}
--- | /O(1)/. The empty set.
-empty :: IntSet
-empty
- = Nil
-{-# INLINE empty #-}
-
--- | /O(1)/. A set of one element.
-singleton :: Int -> IntSet
-singleton x
- = Tip (prefixOf x) (bitmapOf x)
-{-# INLINE singleton #-}
-
-{--------------------------------------------------------------------
- Insert
---------------------------------------------------------------------}
--- | /O(min(n,W))/. Add a value to the set. There is no left- or right bias for
--- IntSets.
-insert :: Int -> IntSet -> IntSet
-insert x = x `seq` insertBM (prefixOf x) (bitmapOf x)
-
--- Helper function for insert and union.
-insertBM :: Prefix -> BitMap -> IntSet -> IntSet
-insertBM kx bm t = kx `seq` bm `seq`
- 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
-
--- | /O(min(n,W))/. Delete a value in the set. Returns the
--- original set when the value was not present.
-delete :: Int -> IntSet -> IntSet
-delete x = x `seq` deleteBM (prefixOf x) (bitmapOf x)
-
--- Deletes all values mentioned in the BitMap from the set.
--- Helper function for delete and difference.
-deleteBM :: Prefix -> BitMap -> IntSet -> IntSet
-deleteBM kx bm t = kx `seq` bm `seq`
- 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
-
-
-{--------------------------------------------------------------------
- Union
---------------------------------------------------------------------}
--- | The union of a list of sets.
-unions :: [IntSet] -> IntSet
-unions xs
- = foldlStrict union empty xs
-
-
--- | /O(n+m)/. The union of two sets.
-union :: IntSet -> IntSet -> IntSet
-union 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 (union l1 l2) (union 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 (union l1 t2) r1
- | otherwise = Bin p1 m1 l1 (union r1 t2)
-
- union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
- | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
- | otherwise = Bin p2 m2 l2 (union t1 r2)
-
-union t@(Bin _ _ _ _) (Tip kx bm) = insertBM kx bm t
-union t@(Bin _ _ _ _) Nil = t
-union (Tip kx bm) t = insertBM kx bm t
-union Nil t = t
-
-
-{--------------------------------------------------------------------
- Difference
---------------------------------------------------------------------}
--- | /O(n+m)/. Difference between two sets.
-difference :: IntSet -> IntSet -> IntSet
-difference 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 (difference l1 l2) (difference r1 r2)
- | otherwise = t1
- where
- difference1 | nomatch p2 p1 m1 = t1
- | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
- | otherwise = bin p1 m1 l1 (difference r1 t2)
-
- difference2 | nomatch p1 p2 m2 = t1
- | zero p1 m2 = difference t1 l2
- | otherwise = difference t1 r2
-
-difference t@(Bin _ _ _ _) (Tip kx bm) = deleteBM kx bm t
-difference t@(Bin _ _ _ _) Nil = t
-
-difference 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
-
-difference Nil _ = Nil
-
-
-
-{--------------------------------------------------------------------
- Intersection
---------------------------------------------------------------------}
--- | /O(n+m)/. The intersection of two sets.
-intersection :: IntSet -> IntSet -> IntSet
-intersection 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 (intersection l1 l2) (intersection r1 r2)
- | otherwise = Nil
- where
- intersection1 | nomatch p2 p1 m1 = Nil
- | zero p2 m1 = intersection l1 t2
- | otherwise = intersection r1 t2
-
- intersection2 | nomatch p1 p2 m2 = Nil
- | zero p1 m2 = intersection t1 l2
- | otherwise = intersection t1 r2
-
-intersection 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
-
-intersection (Bin _ _ _ _) Nil = Nil
-
-intersection (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
-
-intersection Nil _ = Nil
-
-{--------------------------------------------------------------------
- Subset
---------------------------------------------------------------------}
--- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
-isProperSubsetOf :: IntSet -> IntSet -> Bool
-isProperSubsetOf t1 t2
- = case subsetCmp t1 t2 of
- LT -> True
- _ -> False
-
-subsetCmp :: IntSet -> IntSet -> Ordering
-subsetCmp t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
- | shorter m1 m2 = GT
- | shorter m2 m1 = case subsetCmpLt of
- GT -> GT
- _ -> LT
- | p1 == p2 = subsetCmpEq
- | otherwise = GT -- disjoint
- where
- subsetCmpLt | nomatch p1 p2 m2 = GT
- | zero p1 m2 = subsetCmp t1 l2
- | otherwise = subsetCmp t1 r2
- subsetCmpEq = case (subsetCmp l1 l2, subsetCmp r1 r2) of
- (GT,_ ) -> GT
- (_ ,GT) -> GT
- (EQ,EQ) -> EQ
- _ -> LT
-
-subsetCmp (Bin _ _ _ _) _ = GT
-subsetCmp (Tip kx1 bm1) (Tip kx2 bm2)
- | kx1 /= kx2 = GT -- disjoint
- | bm1 == bm2 = EQ
- | bm1 .&. complement bm2 == 0 = LT
- | otherwise = GT
-subsetCmp t1@(Tip kx _) (Bin p m l r)
- | nomatch kx p m = GT
- | zero kx m = case subsetCmp t1 l of GT -> GT ; _ -> LT
- | otherwise = case subsetCmp t1 r of GT -> GT ; _ -> LT
-subsetCmp (Tip _ _) Nil = GT -- disjoint
-subsetCmp Nil Nil = EQ
-subsetCmp Nil _ = LT
-
--- | /O(n+m)/. Is this a subset?
--- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@.
-
-isSubsetOf :: IntSet -> IntSet -> Bool
-isSubsetOf t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
- | shorter m1 m2 = False
- | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubsetOf t1 l2
- else isSubsetOf t1 r2)
- | otherwise = (p1==p2) && isSubsetOf l1 l2 && isSubsetOf r1 r2
-isSubsetOf (Bin _ _ _ _) _ = False
-isSubsetOf (Tip kx1 bm1) (Tip kx2 bm2) = kx1 == kx2 && bm1 .&. complement bm2 == 0
-isSubsetOf t1@(Tip kx _) (Bin p m l r)
- | nomatch kx p m = False
- | zero kx m = isSubsetOf t1 l
- | otherwise = isSubsetOf t1 r
-isSubsetOf (Tip _ _) Nil = False
-isSubsetOf Nil _ = True
-
-
-{--------------------------------------------------------------------
- Filter
---------------------------------------------------------------------}
--- | /O(n)/. Filter all elements that satisfy some predicate.
-filter :: (Int -> Bool) -> IntSet -> IntSet
-filter predicate t
- = case t of
- Bin p m l r
- -> bin p m (filter predicate l) (filter predicate r)
- Tip kx bm
- -> tip kx (foldl'Bits 0 (bitPred kx) 0 bm)
- Nil -> Nil
- where bitPred kx bm bi | predicate (kx + bi) = bm .|. bitmapOfSuffix bi
- | otherwise = bm
- {-# INLINE bitPred #-}
-
--- | /O(n)/. partition the set according to some predicate.
-partition :: (Int -> Bool) -> IntSet -> (IntSet,IntSet)
-partition predicate t
- = case t of
- Bin p m l r
- -> let (l1,l2) = partition predicate l
- (r1,r2) = partition predicate r
- in (bin p m l1 r1, bin p m l2 r2)
- Tip kx bm
- -> let bm1 = foldl'Bits 0 (bitPred kx) 0 bm
- in (tip kx bm1, tip kx (bm `xor` bm1))
- Nil -> (Nil,Nil)
- where bitPred kx bm bi | predicate (kx + bi) = bm .|. bitmapOfSuffix bi
- | otherwise = bm
- {-# INLINE bitPred #-}
-
-
--- | /O(min(n,W))/. The expression (@'split' x set@) is a pair @(set1,set2)@
--- where @set1@ comprises the elements of @set@ less than @x@ and @set2@
--- comprises the elements of @set@ greater than @x@.
---
--- > split 3 (fromList [1..5]) == (fromList [1,2], fromList [4,5])
-split :: Int -> IntSet -> (IntSet,IntSet)
-split x t =
- case t of Bin _ m l r | m < 0 -> if x >= 0 then case go x l of (lt, gt) -> (union lt r, gt)
- else case go x r of (lt, gt) -> (lt, union gt l)
- _ -> go x t
- where
- go x' t'@(Bin p m l r) | match x' p m = if zero x' m then case go x' l of (lt, gt) -> (lt, union gt r)
- else case go x' r of (lt, gt) -> (union lt l, gt)
- | otherwise = if x' < p then (Nil, t')
- else (t', Nil)
- go x' t'@(Tip kx' bm) | kx' > x' = (Nil, t')
- -- equivalent to kx' > prefixOf x'
- | kx' < prefixOf x' = (t', Nil)
- | otherwise = (tip kx' (bm .&. lowerBitmap), tip kx' (bm .&. higherBitmap))
- where lowerBitmap = bitmapOf x' - 1
- higherBitmap = complement (lowerBitmap + bitmapOf x')
- go _ Nil = (Nil, Nil)
-
--- | /O(min(n,W))/. Performs a 'split' but also returns whether the pivot
--- element was found in the original set.
-splitMember :: Int -> IntSet -> (IntSet,Bool,IntSet)
-splitMember x t =
- case t of Bin _ m l r | m < 0 -> if x >= 0 then case go x l of (lt, fnd, gt) -> (union lt r, fnd, gt)
- else case go x r of (lt, fnd, gt) -> (lt, fnd, union gt l)
- _ -> go x t
- where
- go x' t'@(Bin p m l r) | match x' p m = if zero x' m then case go x' l of (lt, fnd, gt) -> (lt, fnd, union gt r)
- else case go x' r of (lt, fnd, gt) -> (union lt l, fnd, gt)
- | otherwise = if x' < p then (Nil, False, t')
- else (t', False, Nil)
- go x' t'@(Tip kx' bm) | kx' > x' = (Nil, False, t')
- -- equivalent to kx' > prefixOf x'
- | kx' < prefixOf x' = (t', False, Nil)
- | otherwise = (tip kx' (bm .&. lowerBitmap), (bm .&. bitmapOfx') /= 0, tip kx' (bm .&. higherBitmap))
- where bitmapOfx' = bitmapOf x'
- lowerBitmap = bitmapOfx' - 1
- higherBitmap = complement (lowerBitmap + bitmapOfx')
- go _ Nil = (Nil, False, Nil)
-
-
-{----------------------------------------------------------------------
- Min/Max
-----------------------------------------------------------------------}
-
--- | /O(min(n,W))/. Retrieves the maximal key of the set, and the set
--- stripped of that element, or 'Nothing' if passed an empty set.
-maxView :: IntSet -> Maybe (Int, IntSet)
-maxView t =
- case t of Nil -> Nothing
- Bin p m l r | m < 0 -> case go l of (result, l') -> Just (result, bin p m l' r)
- _ -> Just (go t)
- where
- go (Bin p m l r) = case go r of (result, r') -> (result, bin p m l r')
- go (Tip kx bm) = case highestBitSet bm of bi -> (kx + bi, tip kx (bm .&. complement (bitmapOfSuffix bi)))
- go Nil = error "maxView Nil"
-
--- | /O(min(n,W))/. Retrieves the minimal key of the set, and the set
--- stripped of that element, or 'Nothing' if passed an empty set.
-minView :: IntSet -> Maybe (Int, IntSet)
-minView t =
- case t of Nil -> Nothing
- Bin p m l r | m < 0 -> case go r of (result, r') -> Just (result, bin p m l r')
- _ -> Just (go t)
- where
- go (Bin p m l r) = case go l of (result, l') -> (result, bin p m l' r)
- go (Tip kx bm) = case lowestBitSet bm of bi -> (kx + bi, tip kx (bm .&. complement (bitmapOfSuffix bi)))
- go Nil = error "minView Nil"
-
--- | /O(min(n,W))/. Delete and find the minimal element.
---
--- > deleteFindMin set = (findMin set, deleteMin set)
-deleteFindMin :: IntSet -> (Int, IntSet)
-deleteFindMin = fromMaybe (error "deleteFindMin: empty set has no minimal element") . minView
-
--- | /O(min(n,W))/. Delete and find the maximal element.
---
--- > deleteFindMax set = (findMax set, deleteMax set)
-deleteFindMax :: IntSet -> (Int, IntSet)
-deleteFindMax = fromMaybe (error "deleteFindMax: empty set has no maximal element") . maxView
-
-
--- | /O(min(n,W))/. The minimal element of the set.
-findMin :: IntSet -> Int
-findMin Nil = error "findMin: empty set has no minimal element"
-findMin (Tip kx bm) = kx + lowestBitSet bm
-findMin (Bin _ m l r)
- | m < 0 = find r
- | otherwise = find l
- where find (Tip kx bm) = kx + lowestBitSet bm
- find (Bin _ _ l' _) = find l'
- find Nil = error "findMin Nil"
-
--- | /O(min(n,W))/. The maximal element of a set.
-findMax :: IntSet -> Int
-findMax Nil = error "findMax: empty set has no maximal element"
-findMax (Tip kx bm) = kx + highestBitSet bm
-findMax (Bin _ m l r)
- | m < 0 = find l
- | otherwise = find r
- where find (Tip kx bm) = kx + highestBitSet bm
- find (Bin _ _ _ r') = find r'
- find Nil = error "findMax Nil"
-
-
--- | /O(min(n,W))/. Delete the minimal element.
-deleteMin :: IntSet -> IntSet
-deleteMin = maybe Nil snd . minView
-
--- | /O(min(n,W))/. Delete the maximal element.
-deleteMax :: IntSet -> IntSet
-deleteMax = maybe Nil snd . maxView
-
-{----------------------------------------------------------------------
- Map
-----------------------------------------------------------------------}
-
--- | /O(n*min(n,W))/.
--- @'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 :: (Int->Int) -> IntSet -> IntSet
-map f = fromList . List.map f . toList
-
-{--------------------------------------------------------------------
- Fold
---------------------------------------------------------------------}
--- | /O(n)/. Fold the elements in the set using the given right-associative
--- binary operator. This function is an equivalent of 'foldr' and is present
--- for compatibility only.
---
--- /Please note that fold will be deprecated in the future and removed./
-fold :: (Int -> b -> b) -> b -> IntSet -> b
-fold = foldr
-{-# INLINE fold #-}
-
--- | /O(n)/. Fold the elements in the set using the given right-associative
--- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'toAscList'@.
---
--- For example,
---
--- > toAscList set = foldr (:) [] set
-foldr :: (Int -> b -> b) -> b -> IntSet -> b
-foldr f z = \t -> -- Use lambda t to be inlinable with two arguments only.
- case t of Bin _ m l r | m < 0 -> go (go z l) r -- put negative numbers before
- | otherwise -> go (go z r) l
- _ -> go z t
- where
- go z' Nil = z'
- go z' (Tip kx bm) = foldrBits kx f z' bm
- go z' (Bin _ _ l r) = go (go z' r) l
-{-# INLINE foldr #-}
-
--- | /O(n)/. A strict version of 'foldr'. Each application of the operator is
--- evaluated before using the result in the next application. This
--- function is strict in the starting value.
-foldr' :: (Int -> b -> b) -> b -> IntSet -> b
-foldr' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
- case t of Bin _ m l r | m < 0 -> go (go z l) r -- put negative numbers before
- | otherwise -> go (go z r) l
- _ -> go z t
- where
- STRICT_1_OF_2(go)
- go z' Nil = z'
- go z' (Tip kx bm) = foldr'Bits kx f z' bm
- go z' (Bin _ _ l r) = go (go z' r) l
-{-# INLINE foldr' #-}
-
--- | /O(n)/. Fold the elements in the set using the given left-associative
--- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'toAscList'@.
---
--- For example,
---
--- > toDescList set = foldl (flip (:)) [] set
-foldl :: (a -> Int -> a) -> a -> IntSet -> a
-foldl f z = \t -> -- Use lambda t to be inlinable with two arguments only.
- case t of Bin _ m l r | m < 0 -> go (go z r) l -- put negative numbers before
- | otherwise -> go (go z l) r
- _ -> go z t
- where
- STRICT_1_OF_2(go)
- go z' Nil = z'
- go z' (Tip kx bm) = foldlBits kx f z' bm
- go z' (Bin _ _ l r) = go (go z' l) r
-{-# INLINE foldl #-}
-
--- | /O(n)/. A strict version of 'foldl'. Each application of the operator is
--- evaluated before using the result in the next application. This
--- function is strict in the starting value.
-foldl' :: (a -> Int -> a) -> a -> IntSet -> a
-foldl' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
- case t of Bin _ m l r | m < 0 -> go (go z r) l -- put negative numbers before
- | otherwise -> go (go z l) r
- _ -> go z t
- where
- STRICT_1_OF_2(go)
- go z' Nil = z'
- go z' (Tip kx bm) = foldl'Bits kx f z' bm
- go z' (Bin _ _ l r) = go (go z' l) r
-{-# INLINE foldl' #-}
-
-{--------------------------------------------------------------------
- List variations
---------------------------------------------------------------------}
--- | /O(n)/. An alias of 'toAscList'. The elements of a set in ascending order.
--- Subject to list fusion.
-elems :: IntSet -> [Int]
-elems
- = toAscList
-
-{--------------------------------------------------------------------
- Lists
---------------------------------------------------------------------}
--- | /O(n)/. Convert the set to a list of elements. Subject to list fusion.
-toList :: IntSet -> [Int]
-toList
- = toAscList
-
--- | /O(n)/. Convert the set to an ascending list of elements. Subject to list
--- fusion.
-toAscList :: IntSet -> [Int]
-toAscList = foldr (:) []
-
--- | /O(n)/. Convert the set to a descending list of elements. Subject to list
--- fusion.
-toDescList :: IntSet -> [Int]
-toDescList = foldl (flip (:)) []
-
--- List fusion for the list generating functions.
-#if __GLASGOW_HASKELL__
--- The foldrFB and foldlFB are foldr and foldl equivalents, used for list fusion.
--- They are important to convert unfused to{Asc,Desc}List back, see mapFB in prelude.
-foldrFB :: (Int -> b -> b) -> b -> IntSet -> b
-foldrFB = foldr
-{-# INLINE[0] foldrFB #-}
-foldlFB :: (a -> Int -> a) -> a -> IntSet -> a
-foldlFB = foldl
-{-# INLINE[0] foldlFB #-}
-
--- Inline elems and toList, so that we need to fuse only toAscList.
-{-# INLINE elems #-}
-{-# INLINE toList #-}
-
--- The fusion is enabled up to phase 2 included. If it does not succeed,
--- convert in phase 1 the expanded to{Asc,Desc}List calls back to
--- to{Asc,Desc}List. In phase 0, we inline fold{lr}FB (which were used in
--- a list fusion, otherwise it would go away in phase 1), and let compiler do
--- whatever it wants with to{Asc,Desc}List -- it was forbidden to inline it
--- before phase 0, otherwise the fusion rules would not fire at all.
-{-# NOINLINE[0] toAscList #-}
-{-# NOINLINE[0] toDescList #-}
-{-# RULES "IntSet.toAscList" [~1] forall s . toAscList s = build (\c n -> foldrFB c n s) #-}
-{-# RULES "IntSet.toAscListBack" [1] foldrFB (:) [] = toAscList #-}
-{-# RULES "IntSet.toDescList" [~1] forall s . toDescList s = build (\c n -> foldlFB (\xs x -> c x xs) n s) #-}
-{-# RULES "IntSet.toDescListBack" [1] foldlFB (\xs x -> x : xs) [] = toDescList #-}
-#endif
-
-
--- | /O(n*min(n,W))/. Create a set from a list of integers.
-fromList :: [Int] -> IntSet
-fromList xs
- = foldlStrict ins empty xs
- where
- ins t x = insert x t
-
--- | /O(n)/. Build a set from an ascending list of elements.
--- /The precondition (input list is ascending) is not checked./
-fromAscList :: [Int] -> IntSet
-fromAscList [] = Nil
-fromAscList (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0)
- where
- combineEq x' [] = [x']
- combineEq x' (x:xs)
- | x==x' = combineEq x' xs
- | otherwise = x' : combineEq x xs
-
--- | /O(n)/. Build a set from an ascending list of distinct elements.
--- /The precondition (input list is strictly ascending) is not checked./
-fromDistinctAscList :: [Int] -> IntSet
-fromDistinctAscList [] = Nil
-fromDistinctAscList (z0 : zs0) = work (prefixOf z0) (bitmapOf z0) zs0 Nada
- where
- -- 'work' accumulates all values that go into one tip, before passing this Tip
- -- to 'reduce'
- work kx bm [] stk = finish kx (Tip kx bm) stk
- work kx bm (z:zs) stk | kx == prefixOf z = work kx (bm .|. bitmapOf z) zs stk
- work kx bm (z:zs) stk = reduce z zs (branchMask z kx) kx (Tip kx bm) stk
-
- reduce z zs _ px tx Nada = work (prefixOf z) (bitmapOf z) zs (Push px tx Nada)
- reduce z zs m px tx stk@(Push py ty stk') =
- let mxy = branchMask px py
- pxy = mask px mxy
- in if shorter m mxy
- then reduce z zs m pxy (Bin pxy mxy ty tx) stk'
- else work (prefixOf z) (bitmapOf z) zs (Push px tx stk)
-
- finish _ t Nada = t
- finish px tx (Push py ty stk) = finish p (join py ty px tx) stk
- where m = branchMask px py
- p = mask px m
-
-data Stack = Push {-# UNPACK #-} !Prefix !IntSet !Stack | Nada
-
-
-{--------------------------------------------------------------------
- Eq
---------------------------------------------------------------------}
-instance Eq IntSet where
- t1 == t2 = equal t1 t2
- t1 /= t2 = nequal t1 t2
-
-equal :: IntSet -> IntSet -> Bool
-equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
- = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
-equal (Tip kx1 bm1) (Tip kx2 bm2)
- = kx1 == kx2 && bm1 == bm2
-equal Nil Nil = True
-equal _ _ = False
-
-nequal :: IntSet -> IntSet -> Bool
-nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
- = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
-nequal (Tip kx1 bm1) (Tip kx2 bm2)
- = kx1 /= kx2 || bm1 /= bm2
-nequal Nil Nil = False
-nequal _ _ = True
-
-{--------------------------------------------------------------------
- Ord
---------------------------------------------------------------------}
-
-instance Ord IntSet where
- compare s1 s2 = compare (toAscList s1) (toAscList s2)
- -- tentative implementation. See if more efficient exists.
-
-{--------------------------------------------------------------------
- Show
---------------------------------------------------------------------}
-instance Show IntSet where
- showsPrec p xs = showParen (p > 10) $
- showString "fromList " . shows (toList xs)
-
-{--------------------------------------------------------------------
- Read
---------------------------------------------------------------------}
-instance Read IntSet where
-#ifdef __GLASGOW_HASKELL__
- readPrec = parens $ prec 10 $ do
- Ident "fromList" <- lexP
- xs <- readPrec
- return (fromList xs)
-
- readListPrec = readListPrecDefault
-#else
- readsPrec p = readParen (p > 10) $ \ r -> do
- ("fromList",s) <- lex r
- (xs,t) <- reads s
- return (fromList xs,t)
-#endif
-
-{--------------------------------------------------------------------
- Typeable
---------------------------------------------------------------------}
-
-#include "Typeable.h"
-INSTANCE_TYPEABLE0(IntSet,intSetTc,"IntSet")
-
-{--------------------------------------------------------------------
- NFData
---------------------------------------------------------------------}
-
--- The IntSet constructors consist only of strict fields of Ints and
--- IntSets, thus the default NFData instance which evaluates to whnf
--- should suffice
-instance NFData IntSet
-
-{--------------------------------------------------------------------
- Debugging
---------------------------------------------------------------------}
--- | /O(n)/. Show the tree that implements the set. The tree is shown
--- in a compressed, hanging format.
-showTree :: IntSet -> String
-showTree s
- = showTreeWith True False s
-
-
-{- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
- the tree that implements the set. If @hang@ is
- 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
- @wide@ is 'True', an extra wide version is shown.
--}
-showTreeWith :: Bool -> Bool -> IntSet -> String
-showTreeWith hang wide t
- | hang = (showsTreeHang wide [] t) ""
- | otherwise = (showsTree wide [] [] t) ""
-
-showsTree :: Bool -> [String] -> [String] -> IntSet -> ShowS
-showsTree wide lbars rbars t
- = case t of
- Bin p m l r
- -> showsTree wide (withBar rbars) (withEmpty rbars) r .
- showWide wide rbars .
- showsBars lbars . showString (showBin p m) . showString "\n" .
- showWide wide lbars .
- showsTree wide (withEmpty lbars) (withBar lbars) l
- Tip kx bm
- -> showsBars lbars . showString " " . shows kx . showString " + " .
- showsBitMap bm . showString "\n"
- Nil -> showsBars lbars . showString "|\n"
-
-showsTreeHang :: Bool -> [String] -> IntSet -> ShowS
-showsTreeHang wide bars t
- = case t of
- Bin p m l r
- -> showsBars bars . showString (showBin p m) . showString "\n" .
- showWide wide bars .
- showsTreeHang wide (withBar bars) l .
- showWide wide bars .
- showsTreeHang wide (withEmpty bars) r
- Tip kx bm
- -> showsBars bars . showString " " . shows kx . showString " + " .
- showsBitMap bm . showString "\n"
- Nil -> showsBars bars . showString "|\n"
-
-showBin :: Prefix -> Mask -> String
-showBin _ _
- = "*" -- ++ show (p,m)
-
-showWide :: Bool -> [String] -> String -> String
-showWide wide bars
- | wide = showString (concat (reverse bars)) . showString "|\n"
- | otherwise = id
-
-showsBars :: [String] -> ShowS
-showsBars bars
- = case bars of
- [] -> id
- _ -> showString (concat (reverse (tail bars))) . showString node
-
-showsBitMap :: Word -> ShowS
-showsBitMap = showString . showBitMap
-
-showBitMap :: Word -> String
-showBitMap w = show $ foldrBits 0 (:) [] w
-
-node :: String
-node = "+--"
-
-withBar, withEmpty :: [String] -> [String]
-withBar bars = "| ":bars
-withEmpty bars = " ":bars
-
-
-{--------------------------------------------------------------------
- Helpers
---------------------------------------------------------------------}
-{--------------------------------------------------------------------
- Join
---------------------------------------------------------------------}
-join :: Prefix -> IntSet -> Prefix -> IntSet -> IntSet
-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@ assures that we never have empty trees within a tree.
---------------------------------------------------------------------}
-bin :: Prefix -> Mask -> IntSet -> IntSet -> IntSet
-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 -> IntSet
-tip _ 0 = Nil
-tip kx bm = Tip kx bm
-{-# INLINE tip #-}
-
-
-{----------------------------------------------------------------------
- Functions that generate Prefix and BitMap of a Key or a Suffix.
-----------------------------------------------------------------------}
-
-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 #-}
-
-
-{--------------------------------------------------------------------
- Endian independent bit twiddling
---------------------------------------------------------------------}
-zero :: Int -> Mask -> Bool
-zero i m
- = (natFromInt i) .&. (natFromInt m) == 0
-{-# INLINE zero #-}
-
-nomatch,match :: Int -> Prefix -> Mask -> Bool
-nomatch i p m
- = (mask i m) /= p
-{-# INLINE nomatch #-}
-
-match i p m
- = (mask i m) == p
-{-# INLINE match #-}
-
--- Suppose a is largest such that 2^a divides 2*m.
--- Then mask i m is i with the low a bits zeroed out.
-mask :: Int -> Mask -> Prefix
-mask i m
- = maskW (natFromInt i) (natFromInt m)
-{-# INLINE mask #-}
-
-{--------------------------------------------------------------------
- Big endian operations
---------------------------------------------------------------------}
-maskW :: Nat -> Nat -> Prefix
-maskW i m
- = intFromNat (i .&. (complement (m-1) `xor` m))
-{-# INLINE maskW #-}
-
-shorter :: Mask -> Mask -> Bool
-shorter m1 m2
- = (natFromInt m1) > (natFromInt m2)
-{-# INLINE shorter #-}
-
-branchMask :: Prefix -> Prefix -> Mask
-branchMask p1 p2
- = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
-{-# INLINE branchMask #-}
-
-{----------------------------------------------------------------------
- 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
-
- highestBit: method cycles
- --------------
- frexp 195
- float 33
- bit 11
- asm 11
-
- 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
-#if !(defined(__GLASGOW_HASKELL__) && WORD_SIZE_IN_BITS==32)
- x5 -> case (x5 .|. shiftRL x5 32) of -- for 64 bit platforms
-#endif
- x6 -> (x6 `xor` (shiftRL x6 1))
-{-# INLINE highestBitMask #-}
-
-{----------------------------------------------------------------------
- To get best performance, we provide fast implementations of
- lowestBitSet, highestBitSet and fold[lr][l]Bits for GHC.
- If the intel bsf and bsr instructions ever become GHC primops,
- this code should be reimplemented using these.
-
- Performance of this code is crucial for folds, toList, filter, partition.
-
- The signatures of methods in question are placed after this comment.
-----------------------------------------------------------------------}
-
-lowestBitSet :: Nat -> Int
-highestBitSet :: Nat -> Int
-foldlBits :: Int -> (a -> Int -> a) -> a -> Nat -> a
-foldl'Bits :: Int -> (a -> Int -> a) -> a -> Nat -> a
-foldrBits :: Int -> (Int -> a -> a) -> a -> Nat -> a
-foldr'Bits :: Int -> (Int -> a -> a) -> a -> Nat -> a
-
-{-# INLINE lowestBitSet #-}
-{-# INLINE highestBitSet #-}
-{-# INLINE foldlBits #-}
-{-# INLINE foldl'Bits #-}
-{-# INLINE foldrBits #-}
-{-# INLINE foldr'Bits #-}
-
-#if defined(__GLASGOW_HASKELL__) && (WORD_SIZE_IN_BITS==32 || WORD_SIZE_IN_BITS==64)
-{----------------------------------------------------------------------
- For lowestBitSet we use wordsize-dependant implementation based on
- multiplication and DeBrujn indeces, which was proposed by Edward Kmett
- <http://haskell.org/pipermail/libraries/2011-September/016749.html>
-
- The core of this implementation is fast indexOfTheOnlyBit,
- which is given a Nat with exactly one bit set, and returns
- its index.
-
- Lot of effort was put in these implementations, please benchmark carefully
- before changing this code.
-----------------------------------------------------------------------}
-
-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
--- The lsbArray gets inlined to every call site of indexOfTheOnlyBit.
--- That cannot be easily avoided, as GHC forbids top-level Addr# literal.
--- One could go around that by supplying getLsbArray :: () -> Addr# marked
--- as NOINLINE. But the code size of calling it and processing the result
--- is 48B on 32-bit and 56B on 64-bit architectures -- so the 32B and 64B array
--- is actually improvement on 32-bit and only a 8B size increase on 64-bit.
-
-lowestBitMask :: Nat -> Nat
-lowestBitMask x = x .&. negate x
-{-# INLINE lowestBitMask #-}
-
--- Reverse the order of bits in the Nat.
-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
-
-lowestBitSet x = indexOfTheOnlyBit (lowestBitMask x)
-
-highestBitSet x = indexOfTheOnlyBit (highestBitMask x)
-
-foldlBits prefix f z bitmap = go 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 acc) $! (prefix+bi))
-
-foldl'Bits prefix f z bitmap = go bitmap z
- where STRICT_2_OF_2(go)
- 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 acc) $! (prefix+bi))
-
-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)
-
-foldr'Bits prefix f z bitmap = go (revNat bitmap) z
- where STRICT_2_OF_2(go)
- 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)
-
-#else
-{----------------------------------------------------------------------
- In general case we use logarithmic implementation of
- lowestBitSet and highestBitSet, which works up to bit sizes of 64.
-
- Folds are linear scans.
-----------------------------------------------------------------------}
-
-lowestBitSet n0 =
- let (n1,b1) = if n0 .&. 0xFFFFFFFF /= 0 then (n0,0) else (n0 `shiftRL` 32, 32)
- (n2,b2) = if n1 .&. 0xFFFF /= 0 then (n1,b1) else (n1 `shiftRL` 16, 16+b1)
- (n3,b3) = if n2 .&. 0xFF /= 0 then (n2,b2) else (n2 `shiftRL` 8, 8+b2)
- (n4,b4) = if n3 .&. 0xF /= 0 then (n3,b3) else (n3 `shiftRL` 4, 4+b3)
- (n5,b5) = if n4 .&. 0x3 /= 0 then (n4,b4) else (n4 `shiftRL` 2, 2+b4)
- b6 = if n5 .&. 0x1 /= 0 then b5 else 1+b5
- in b6
-
-highestBitSet n0 =
- let (n1,b1) = if n0 .&. 0xFFFFFFFF00000000 /= 0 then (n0 `shiftRL` 32, 32) else (n0,0)
- (n2,b2) = if n1 .&. 0xFFFF0000 /= 0 then (n1 `shiftRL` 16, 16+b1) else (n1,b1)
- (n3,b3) = if n2 .&. 0xFF00 /= 0 then (n2 `shiftRL` 8, 8+b2) else (n2,b2)
- (n4,b4) = if n3 .&. 0xF0 /= 0 then (n3 `shiftRL` 4, 4+b3) else (n3,b3)
- (n5,b5) = if n4 .&. 0xC /= 0 then (n4 `shiftRL` 2, 2+b4) else (n4,b4)
- b6 = if n5 .&. 0x2 /= 0 then 1+b5 else b5
- in b6
-
-foldlBits prefix f z bm = let lb = lowestBitSet bm
- in go (prefix+lb) z (bm `shiftRL` lb)
- where STRICT_1_OF_3(go)
- go _ acc 0 = acc
- go bi acc n | n `testBit` 0 = go (bi + 1) (f acc bi) (n `shiftRL` 1)
- | otherwise = go (bi + 1) acc (n `shiftRL` 1)
-
-foldl'Bits prefix f z bm = let lb = lowestBitSet bm
- in go (prefix+lb) z (bm `shiftRL` lb)
- where STRICT_1_OF_3(go)
- STRICT_2_OF_3(go)
- go _ acc 0 = acc
- go bi acc n | n `testBit` 0 = go (bi + 1) (f acc bi) (n `shiftRL` 1)
- | otherwise = go (bi + 1) acc (n `shiftRL` 1)
-
-foldrBits prefix f z bm = let lb = lowestBitSet bm
- in go (prefix+lb) (bm `shiftRL` lb)
- where STRICT_1_OF_2(go)
- go _ 0 = z
- go bi n | n `testBit` 0 = f bi (go (bi + 1) (n `shiftRL` 1))
- | otherwise = go (bi + 1) (n `shiftRL` 1)
-
-foldr'Bits prefix f z bm = let lb = lowestBitSet bm
- in go (prefix+lb) (bm `shiftRL` lb)
- where STRICT_1_OF_2(go)
- go _ 0 = z
- go bi n | n `testBit` 0 = f bi $! go (bi + 1) (n `shiftRL` 1)
- | otherwise = go (bi + 1) (n `shiftRL` 1)
-
-#endif
-
-{----------------------------------------------------------------------
- [bitcount] as posted by David F. Place to haskell-cafe on April 11, 2006,
- based on the code on
- http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetKernighan,
- where the following source is given:
- Published in 1988, the C Programming Language 2nd Ed. (by Brian W.
- Kernighan and Dennis M. Ritchie) mentions this in exercise 2-9. On April
- 19, 2006 Don Knuth pointed out to me that this method "was first published
- by Peter Wegner in CACM 3 (1960), 322. (Also discovered independently by
- Derrick Lehmer and published in 1964 in a book edited by Beckenbach.)"
-----------------------------------------------------------------------}
-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 #-}
-
-
-{--------------------------------------------------------------------
- Utilities
---------------------------------------------------------------------}
-foldlStrict :: (a -> b -> a) -> a -> [b] -> a
-foldlStrict f = go
- where
- go z [] = z
- go z (x:xs) = let z' = f z x in z' `seq` go z' xs
-{-# INLINE foldlStrict #-}
View
1,482 Data/IntSet/Base.hs
@@ -0,0 +1,1482 @@
+{-# LANGUAGE CPP #-}
+#if __GLASGOW_HASKELL__
+{-# LANGUAGE MagicHash, BangPatterns, DeriveDataTypeable, StandaloneDeriving #-}
+#endif
+#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703
+{-# LANGUAGE Trustworthy #-}
+#endif
+-----------------------------------------------------------------------------
+-- |
+-- Module : Data.IntSet.Base
+-- Copyright : (c) Daan Leijen 2002
+-- (c) Joachim Breitner 2011
+-- License : BSD-style
+-- Maintainer : libraries@haskell.org
+-- Stability : provisional
+-- Portability : portable
+--
+-- An efficient implementation of integer sets.
+--
+-- These modules are intended to be imported qualified, to avoid name
+-- clashes with Prelude functions, e.g.
+--
+-- > import Data.IntSet (IntSet)
+-- > import qualified Data.IntSet as IntSet
+--
+-- 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 set implementation (see "Data.Set").
+--
+-- * 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.
+--
+-- Additionally, this implementation places bitmaps in the leaves of the tree.
+-- Their size is the natural size of a machine word (32 or 64 bits) and greatly
+-- reduce memory footprint and execution times for dense sets, e.g. sets where
+-- it is likely that many values lie close to each other. The asymptotics are
+-- not affected by this optimization.
+--
+-- 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).
+-----------------------------------------------------------------------------
+
+-- [Note: INLINE bit fiddling]
+-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~
+-- It is essential that the bit fiddling functions like mask, zero, branchMask
+-- etc are inlined. If they do not, the memory allocation skyrockets. The GHC
+-- usually gets it right, but it is disastrous if it does not. Therefore we
+-- explicitly mark these functions INLINE.
+
+
+-- [Note: Local 'go' functions and capturing]
+-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+-- Care must be taken when using 'go' function which captures an argument.
+-- Sometimes (for example when the argument is passed to a data constructor,
+-- as in insert), GHC heap-allocates more than necessary. Therefore C-- code
+-- must be checked for increased allocation when creating and modifying such
+-- functions.
+
+
+-- [Note: Order of constructors]
+-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+-- The order of constructors of IntSet matters when considering performance.
+-- Currently in GHC 7.0, when type has 3 constructors, they are matched from
+-- the first to the last -- the best performance is achieved when the
+-- constructors are ordered by frequency.
+-- On GHC 7.0, reordering constructors from Nil | Tip | Bin to Bin | Tip | Nil
+-- improves the benchmark by circa 10%.
+
+module Data.IntSet.Base (
+ -- * Set type
+ IntSet(..) -- instance Eq,Show
+
+ -- * Operators
+ , (\\)
+
+ -- * Query
+ , null
+ , size
+ , member
+ , notMember
+ , lookupLT
+ , lookupGT
+ , lookupLE
+ , lookupGE
+ , isSubsetOf
+ , isProperSubsetOf
+
+ -- * Construction
+ , empty
+ , singleton
+ , insert
+ , delete
+
+ -- * Combine
+ , union
+ , unions
+ , difference
+ , intersection
+
+ -- * Filter
+ , filter
+ , partition
+ , split
+ , splitMember
+
+ -- * Map
+ , map
+
+ -- * Folds
+ , foldr
+ , foldl
+ -- ** Strict folds
+ , foldr'
+ , foldl'
+ -- ** Legacy folds
+ , fold
+
+ -- * Min\/Max
+ , findMin
+ , findMax
+ , deleteMin
+ , deleteMax
+ , deleteFindMin
+ , deleteFindMax
+ , maxView
+ , minView
+
+ -- * Conversion
+
+ -- ** List
+ , elems
+ , toList
+ , fromList
+
+ -- ** Ordered list
+ , toAscList
+ , toDescList
+ , fromAscList
+ , fromDistinctAscList
+
+ -- * Debugging
+ , showTree
+ , showTreeWith
+
+ -- * Internals
+ , match
+ ) where
+
+
+import Prelude hiding (filter,foldr,foldl,null,map)
+import Data.Bits
+
+import qualified Data.List as List
+import Data.Monoid (Monoid(..))
+import Data.Maybe (fromMaybe)
+import Data.Typeable
+import Control.DeepSeq (NFData)
+
+#if __GLASGOW_HASKELL__
+import Text.Read
+import Data.Data (Data(..), mkNoRepType)
+#endif
+
+#if __GLASGOW_HASKELL__
+import GHC.Exts ( Word(..), Int(..), build )
+import GHC.Prim ( uncheckedShiftL#, uncheckedShiftRL#, indexInt8OffAddr# )
+#else
+import Data.Word
+#endif
+
+-- On GHC, include MachDeps.h to get WORD_SIZE_IN_BITS macro.
+#if defined(__GLASGOW_HASKELL__)
+#include "MachDeps.h"
+#endif
+
+-- Use macros to define strictness of functions.
+-- STRICT_x_OF_y denotes an y-ary function strict in the x-th parameter.
+-- We do not use BangPatterns, because they are not in any standard and we
+-- want the compilers to be compiled by as many compilers as possible.
+#define STRICT_1_OF_2(fn) fn arg _ | arg `seq` False = undefined
+#define STRICT_2_OF_2(fn) fn _ arg | arg `seq` False = undefined
+#define STRICT_1_OF_3(fn) fn arg _ _ | arg `seq` False = undefined
+#define STRICT_2_OF_3(fn) fn _ arg _ | arg `seq` False = undefined
+
+infixl 9 \\{-This comment teaches CPP correct behaviour -}
+
+-- A "Nat" is a natural machine word (an unsigned Int)
+type Nat = Word
+
+natFromInt :: Int -> Nat
+natFromInt i = fromIntegral i
+{-# INLINE natFromInt #-}
+
+intFromNat :: Nat -> Int
+intFromNat w = fromIntegral w
+{-# INLINE intFromNat #-}
+
+-- Right and left logical shifts.
+shiftRL, shiftLL :: Nat -> Int -> Nat
+#if __GLASGOW_HASKELL__
+{--------------------------------------------------------------------
+ GHC: use unboxing to get @shiftRL@ and @shiftLL@ inlined.
+--------------------------------------------------------------------}
+shiftRL (W# x) (I# i) = W# (uncheckedShiftRL# x i)
+shiftLL (W# x) (I# i) = W# (uncheckedShiftL# x i)
+#else
+shiftRL x i = shiftR x i
+shiftLL x i = shiftL x i
+#endif
+{-# INLINE shiftRL #-}
+{-# INLINE shiftLL #-}
+
+{--------------------------------------------------------------------
+ Operators
+--------------------------------------------------------------------}
+-- | /O(n+m)/. See 'difference'.
+(\\) :: IntSet -> IntSet -> IntSet
+m1 \\ m2 = difference m1 m2
+
+{--------------------------------------------------------------------
+ Types
+--------------------------------------------------------------------}
+
+-- | A set of integers.
+
+-- See Note: Order of constructors
+data IntSet = Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !IntSet !IntSet
+-- Invariant: Nil is never found as a child of Bin.
+-- Invariant: The Mask is a power of 2. It is the largest bit position at which
+-- two elements of the set differ.
+-- Invariant: Prefix is the common high-order bits that all elements share to
+-- the left of the Mask bit.
+-- Invariant: In Bin prefix mask left right, left consists of the elements that
+-- don't have the mask bit set; right is all the elements that do.
+ | Tip {-# UNPACK #-} !Prefix {-# UNPACK #-} !BitMap
+-- Invariant: The Prefix is zero for all but the last 5 (on 32 bit arches) or 6
+-- bits (on 64 bit arches). The values of the map represented by a tip
+-- are the prefix plus the indices of the set bits in the bit map.
+ | Nil
+
+-- A number stored in a set is stored as
+-- * Prefix (all but last 5-6 bits) and
+-- * BitMap (last 5-6 bits stored as a bitmask)
+-- Last 5-6 bits are called a Suffix.
+
+type Prefix = Int
+type Mask = Int
+type BitMap = Word
+
+instance Monoid IntSet where
+ mempty = empty
+ mappend = union
+ mconcat = unions
+
+#if __GLASGOW_HASKELL__
+
+{--------------------------------------------------------------------
+ A Data instance
+--------------------------------------------------------------------}
+
+-- This instance preserves data abstraction at the cost of inefficiency.
+-- We omit reflection services for the sake of data abstraction.
+
+instance Data IntSet where
+ gfoldl f z is = z fromList `f` (toList is)
+ toConstr _ = error "toConstr"
+ gunfold _ _ = error "gunfold"
+ dataTypeOf _ = mkNoRepType "Data.IntSet.IntSet"
+
+#endif
+
+{--------------------------------------------------------------------
+ Query
+--------------------------------------------------------------------}
+-- | /O(1)/. Is the set empty?
+null :: IntSet -> Bool
+null Nil = True
+null _ = False
+{-# INLINE null #-}
+
+-- | /O(n)/. Cardinality of the set.
+size :: IntSet -> Int
+size t
+ = case t of
+ Bin _ _ l r -> size l + size r
+ Tip _ bm -> bitcount 0 bm
+ Nil -> 0
+
+-- | /O(min(n,W))/. Is the value a member of the set?
+
+-- See Note: Local 'go' functions and capturing]
+member :: Int -> IntSet -> Bool
+member x = x `seq` go
+ where
+ go (Bin p m l r)
+ | nomatch x p m = False
+ | zero x m = go l
+ | otherwise = go r
+ go (Tip y bm) = prefixOf x == y && bitmapOf x .&. bm /= 0
+ go Nil = False
+
+-- | /O(min(n,W))/. Is the element not in the set?
+notMember :: Int -> IntSet -> Bool
+notMember k = not . member k
+
+-- | /O(log n)/. Find largest element smaller than the given one.
+--
+-- > lookupLT 3 (fromList [3, 5]) == Nothing
+-- > lookupLT 5 (fromList [3, 5]) == Just 3
+
+-- See Note: Local 'go' functions and capturing.
+lookupLT :: Int -> IntSet -> Maybe Int
+lookupLT x t = x `seq` case t of
+ Bin _ m l r | m < 0 -> if x >= 0 then go r l else go Nil r
+ _ -> go Nil t
+ where
+ go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMax def else unsafeFindMax r
+ | zero x m = go def l
+ | otherwise = go l r
+ go def (Tip kx bm) | prefixOf x > kx = Just $ kx + highestBitSet bm
+ | prefixOf x == kx && maskLT /= 0 = Just $ kx + highestBitSet maskLT
+ | otherwise = unsafeFindMax def
+ where maskLT = (bitmapOf x - 1) .&. bm
+ go def Nil = unsafeFindMax def
+
+
+-- | /O(log n)/. Find smallest element greater than the given one.
+--
+-- > lookupGT 4 (fromList [3, 5]) == Just 5
+-- > lookupGT 5 (fromList [3, 5]) == Nothing
+
+-- See Note: Local 'go' functions and capturing.
+lookupGT :: Int -> IntSet -> Maybe Int
+lookupGT x t = x `seq` case t of
+ Bin _ m l r | m < 0 -> if x >= 0 then go Nil l else go l r
+ _ -> go Nil t
+ where
+ go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMin l else unsafeFindMin def
+ | zero x m = go r l
+ | otherwise = go def r
+ go def (Tip kx bm) | prefixOf x < kx = Just $ kx + lowestBitSet bm
+ | prefixOf x == kx && maskGT /= 0 = Just $ kx + lowestBitSet maskGT
+ | otherwise = unsafeFindMin def
+ where maskGT = (- ((bitmapOf x) `shiftLL` 1)) .&. bm
+ go def Nil = unsafeFindMin def
+
+
+-- | /O(log n)/. Find largest element smaller or equal to the given one.
+--
+-- > lookupLE 2 (fromList [3, 5]) == Nothing
+-- > lookupLE 4 (fromList [3, 5]) == Just 3
+-- > lookupLE 5 (fromList [3, 5]) == Just 5
+
+-- See Note: Local 'go' functions and capturing.
+lookupLE :: Int -> IntSet -> Maybe Int
+lookupLE x t = x `seq` case t of
+ Bin _ m l r | m < 0 -> if x >= 0 then go r l else go Nil r
+ _ -> go Nil t
+ where
+ go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMax def else unsafeFindMax r
+ | zero x m = go def l
+ | otherwise = go l r
+ go def (Tip kx bm) | prefixOf x > kx = Just $ kx + highestBitSet bm
+ | prefixOf x == kx && maskLE /= 0 = Just $ kx + highestBitSet maskLE
+ | otherwise = unsafeFindMax def
+ where maskLE = (((bitmapOf x) `shiftLL` 1) - 1) .&. bm
+ go def Nil = unsafeFindMax def
+
+
+-- | /O(log n)/. Find smallest element greater or equal to the given one.
+--
+-- > lookupGE 3 (fromList [3, 5]) == Just 3
+-- > lookupGE 4 (fromList [3, 5]) == Just 5
+-- > lookupGE 6 (fromList [3, 5]) == Nothing
+
+-- See Note: Local 'go' functions and capturing.
+lookupGE :: Int -> IntSet -> Maybe Int
+lookupGE x t = x `seq` case t of
+ Bin _ m l r | m < 0 -> if x >= 0 then go Nil l else go l r
+ _ -> go Nil t
+ where
+ go def (Bin p m l r) | nomatch x p m = if x < p then unsafeFindMin l else unsafeFindMin def
+ | zero x m = go r l
+ | otherwise = go def r
+ go def (Tip kx bm) | prefixOf x < kx = Just $ kx + lowestBitSet bm
+ | prefixOf x == kx && maskGE /= 0 = Just $ kx + lowestBitSet maskGE
+ | otherwise = unsafeFindMin def
+ where maskGE = (- (bitmapOf x)) .&. bm
+ go def Nil = unsafeFindMin def
+
+
+
+-- Helper function for lookupGE and lookupGT. It assumes that if a Bin node is
+-- given, it has m > 0.
+unsafeFindMin :: IntSet -> Maybe Int
+unsafeFindMin Nil = Nothing
+unsafeFindMin (Tip kx bm) = Just $ kx + lowestBitSet bm
+unsafeFindMin (Bin _ _ l _) = unsafeFindMin l
+
+-- Helper function for lookupLE and lookupLT. It assumes that if a Bin node is
+-- given, it has m > 0.
+unsafeFindMax :: IntSet -> Maybe Int
+unsafeFindMax Nil = Nothing
+unsafeFindMax (Tip kx bm) = Just $ kx + highestBitSet bm
+unsafeFindMax (Bin _ _ _ r) = unsafeFindMax r
+
+{--------------------------------------------------------------------
+ Construction
+--------------------------------------------------------------------}
+-- | /O(1)/. The empty set.
+empty :: IntSet
+empty
+ = Nil
+{-# INLINE empty #-}
+
+-- | /O(1)/. A set of one element.
+singleton :: Int -> IntSet
+singleton x
+ = Tip (prefixOf x) (bitmapOf x)
+{-# INLINE singleton #-}
+
+{--------------------------------------------------------------------
+ Insert
+--------------------------------------------------------------------}
+-- | /O(min(n,W))/. Add a value to the set. There is no left- or right bias for
+-- IntSets.
+insert :: Int -> IntSet -> IntSet
+insert x = x `seq` insertBM (prefixOf x) (bitmapOf x)
+
+-- Helper function for insert and union.
+insertBM :: Prefix -> BitMap -> IntSet -> IntSet
+insertBM kx bm t = kx `seq` bm `seq`
+ 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
+
+-- | /O(min(n,W))/. Delete a value in the set. Returns the
+-- original set when the value was not present.
+delete :: Int -> IntSet -> IntSet
+delete x = x `seq` deleteBM (prefixOf x) (bitmapOf x)
+
+-- Deletes all values mentioned in the BitMap from the set.
+-- Helper function for delete and difference.
+deleteBM :: Prefix -> BitMap -> IntSet -> IntSet
+deleteBM kx bm t = kx `seq` bm `seq`
+ 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
+
+
+{--------------------------------------------------------------------
+ Union
+--------------------------------------------------------------------}
+-- | The union of a list of sets.
+unions :: [IntSet] -> IntSet
+unions xs
+ = foldlStrict union empty xs
+
+
+-- | /O(n+m)/. The union of two sets.
+union :: IntSet -> IntSet -> IntSet
+union 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 (union l1 l2) (union 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 (union l1 t2) r1
+ | otherwise = Bin p1 m1 l1 (union r1 t2)
+
+ union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
+ | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
+ | otherwise = Bin p2 m2 l2 (union t1 r2)
+
+union t@(Bin _ _ _ _) (Tip kx bm) = insertBM kx bm t
+union t@(Bin _ _ _ _) Nil = t
+union (Tip kx bm) t = insertBM kx bm t
+union Nil t = t
+
+
+{--------------------------------------------------------------------
+ Difference
+--------------------------------------------------------------------}
+-- | /O(n+m)/. Difference between two sets.
+difference :: IntSet -> IntSet -> IntSet
+difference 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 (difference l1 l2) (difference r1 r2)
+ | otherwise = t1
+ where
+ difference1 | nomatch p2 p1 m1 = t1
+ | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
+ | otherwise = bin p1 m1 l1 (difference r1 t2)
+
+ difference2 | nomatch p1 p2 m2 = t1
+ | zero p1 m2 = difference t1 l2
+ | otherwise = difference t1 r2
+
+difference t@(Bin _ _ _ _) (Tip kx bm) = deleteBM kx bm t
+difference t@(Bin _ _ _ _) Nil = t
+
+difference 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
+
+difference Nil _ = Nil
+
+
+
+{--------------------------------------------------------------------
+ Intersection
+--------------------------------------------------------------------}
+-- | /O(n+m)/. The intersection of two sets.
+intersection :: IntSet -> IntSet -> IntSet
+intersection 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 (intersection l1 l2) (intersection r1 r2)
+ | otherwise = Nil
+ where
+ intersection1 | nomatch p2 p1 m1 = Nil
+ | zero p2 m1 = intersection l1 t2
+ | otherwise = intersection r1 t2
+
+ intersection2 | nomatch p1 p2 m2 = Nil
+ | zero p1 m2 = intersection t1 l2
+ | otherwise = intersection t1 r2
+
+intersection 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
+
+intersection (Bin _ _ _ _) Nil = Nil
+
+intersection (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
+
+intersection Nil _ = Nil
+
+{--------------------------------------------------------------------
+ Subset
+--------------------------------------------------------------------}
+-- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
+isProperSubsetOf :: IntSet -> IntSet -> Bool
+isProperSubsetOf t1 t2
+ = case subsetCmp t1 t2 of
+ LT -> True
+ _ -> False
+
+subsetCmp :: IntSet -> IntSet -> Ordering
+subsetCmp t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
+ | shorter m1 m2 = GT
+ | shorter m2 m1 = case subsetCmpLt of
+ GT -> GT
+ _ -> LT
+ | p1 == p2 = subsetCmpEq
+ | otherwise = GT -- disjoint
+ where
+ subsetCmpLt | nomatch p1 p2 m2 = GT
+ | zero p1 m2 = subsetCmp t1 l2
+ | otherwise = subsetCmp t1 r2
+ subsetCmpEq = case (subsetCmp l1 l2, subsetCmp r1 r2) of
+ (GT,_ ) -> GT
+ (_ ,GT) -> GT
+ (EQ,EQ) -> EQ
+ _ -> LT
+
+subsetCmp (Bin _ _ _ _) _ = GT
+subsetCmp (Tip kx1 bm1) (Tip kx2 bm2)
+ | kx1 /= kx2 = GT -- disjoint
+ | bm1 == bm2 = EQ
+ | bm1 .&. complement bm2 == 0 = LT
+ | otherwise = GT
+subsetCmp t1@(Tip kx _) (Bin p m l r)
+ | nomatch kx p m = GT
+ | zero kx m = case subsetCmp t1 l of GT -> GT ; _ -> LT
+ | otherwise = case subsetCmp t1 r of GT -> GT ; _ -> LT
+subsetCmp (Tip _ _) Nil = GT -- disjoint
+subsetCmp Nil Nil = EQ
+subsetCmp Nil _ = LT
+
+-- | /O(n+m)/. Is this a subset?
+-- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@.
+
+isSubsetOf :: IntSet -> IntSet -> Bool
+isSubsetOf t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
+ | shorter m1 m2 = False
+ | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubsetOf t1 l2
+ else isSubsetOf t1 r2)
+ | otherwise = (p1==p2) && isSubsetOf l1 l2 && isSubsetOf r1 r2
+isSubsetOf (Bin _ _ _ _) _ = False
+isSubsetOf (Tip kx1 bm1) (Tip kx2 bm2) = kx1 == kx2 && bm1 .&. complement bm2 == 0
+isSubsetOf t1@(Tip kx _) (Bin p m l r)
+ | nomatch kx p m = False
+ | zero kx m = isSubsetOf t1 l
+ | otherwise = isSubsetOf t1 r
+isSubsetOf (Tip _ _) Nil = False
+isSubsetOf Nil _ = True
+
+
+{--------------------------------------------------------------------
+ Filter
+--------------------------------------------------------------------}
+-- | /O(n)/. Filter all elements that satisfy some predicate.
+filter :: (Int -> Bool) -> IntSet -> IntSet
+filter predicate t
+ = case t of
+ Bin p m l r
+ -> bin p m (filter predicate l) (filter predicate r)
+ Tip kx bm
+ -> tip kx (foldl'Bits 0 (bitPred kx) 0 bm)
+ Nil -> Nil
+ where bitPred kx bm bi | predicate (kx + bi) = bm .|. bitmapOfSuffix bi
+ | otherwise = bm
+ {-# INLINE bitPred #-}
+
+-- | /O(n)/. partition the set according to some predicate.
+partition :: (Int -> Bool) -> IntSet -> (IntSet,IntSet)
+partition predicate t
+ = case t of
+ Bin p m l r
+ -> let (l1,l2) = partition predicate l
+ (r1,r2) = partition predicate r
+ in (bin p m l1 r1, bin p m l2 r2)
+ Tip kx bm
+ -> let bm1 = foldl'Bits 0 (bitPred kx) 0 bm
+ in (tip kx bm1, tip kx (bm `xor` bm1))
+ Nil -> (Nil,Nil)
+ where bitPred kx bm bi | predicate (kx + bi) = bm .|. bitmapOfSuffix bi
+ | otherwise = bm
+ {-# INLINE bitPred #-}
+
+
+-- | /O(min(n,W))/. The expression (@'split' x set@) is a pair @(set1,set2)@
+-- where @set1@ comprises the elements of @set@ less than @x@ and @set2@
+-- comprises the elements of @set@ greater than @x@.
+--
+-- > split 3 (fromList [1..5]) == (fromList [1,2], fromList [4,5])
+split :: Int -> IntSet -> (IntSet,IntSet)
+split x t =
+ case t of Bin _ m l r | m < 0 -> if x >= 0 then case go x l of (lt, gt) -> (union lt r, gt)
+ else case go x r of (lt, gt) -> (lt, union gt l)
+ _ -> go x t
+ where
+ go x' t'@(Bin p m l r) | match x' p m = if zero x' m then case go x' l of (lt, gt) -> (lt, union gt r)
+ else case go x' r of (lt, gt) -> (union lt l, gt)
+ | otherwise = if x' < p then (Nil, t')
+ else (t', Nil)
+ go x' t'@(Tip kx' bm) | kx' > x' = (Nil, t')
+ -- equivalent to kx' > prefixOf x'
+ | kx' < prefixOf x' = (t', Nil)
+ | otherwise = (tip kx' (bm .&. lowerBitmap), tip kx' (bm .&. higherBitmap))
+ where lowerBitmap = bitmapOf x' - 1
+ higherBitmap = complement (lowerBitmap + bitmapOf x')
+ go _ Nil = (Nil, Nil)
+
+-- | /O(min(n,W))/. Performs a 'split' but also returns whether the pivot
+-- element was found in the original set.
+splitMember :: Int -> IntSet -> (IntSet,Bool,IntSet)
+splitMember x t =
+ case t of Bin _ m l r | m < 0 -> if x >= 0 then case go x l of (lt, fnd, gt) -> (union lt r, fnd, gt)
+ else case go x r of (lt, fnd, gt) -> (lt, fnd, union gt l)
+ _ -> go x t
+ where
+ go x' t'@(Bin p m l r) | match x' p m = if zero x' m then case go x' l of (lt, fnd, gt) -> (lt, fnd, union gt r)
+ else case go x' r of (lt, fnd, gt) -> (union lt l, fnd, gt)
+ | otherwise = if x' < p then (Nil, False, t')
+ else (t', False, Nil)
+ go x' t'@(Tip kx' bm) | kx' > x' = (Nil, False, t')
+ -- equivalent to kx' > prefixOf x'
+ | kx' < prefixOf x' = (t', False, Nil)
+ | otherwise = (tip kx' (bm .&. lowerBitmap), (bm .&. bitmapOfx') /= 0, tip kx' (bm .&. higherBitmap))
+ where bitmapOfx' = bitmapOf x'
+ lowerBitmap = bitmapOfx' - 1
+ higherBitmap = complement (lowerBitmap + bitmapOfx')
+ go _ Nil = (Nil, False, Nil)
+
+
+{----------------------------------------------------------------------
+ Min/Max
+----------------------------------------------------------------------}
+
+-- | /O(min(n,W))/. Retrieves the maximal key of the set, and the set
+-- stripped of that element, or 'Nothing' if passed an empty set.
+maxView :: IntSet -> Maybe (Int, IntSet)
+maxView t =
+ case t of Nil -> Nothing
+ Bin p m l r | m < 0 -> case go l of (result, l') -> Just (result, bin p m l' r)
+ _ -> Just (go t)
+ where
+ go (Bin p m l r) = case go r of (result, r') -> (result, bin p m l r')
+ go (Tip kx bm) = case highestBitSet bm of bi -> (kx + bi, tip kx (bm .&. complement (bitmapOfSuffix bi)))
+ go Nil = error "maxView Nil"
+
+-- | /O(min(n,W))/. Retrieves the minimal key of the set, and the set
+-- stripped of that element, or 'Nothing' if passed an empty set.
+minView :: IntSet -> Maybe (Int, IntSet)
+minView t =
+ case t of Nil -> Nothing
+ Bin p m l r | m < 0 -> case go r of (result, r') -> Just (result, bin p m l r')
+ _ -> Just (go t)
+ where
+ go (Bin p m l r) = case go l of (result, l') -> (result, bin p m l' r)
+ go (Tip kx bm) = case lowestBitSet bm of bi -> (kx + bi, tip kx (bm .&. complement (bitmapOfSuffix bi)))
+ go Nil = error "minView Nil"
+
+-- | /O(min(n,W))/. Delete and find the minimal element.
+--
+-- > deleteFindMin set = (findMin set, deleteMin set)
+deleteFindMin :: IntSet -> (Int, IntSet)
+deleteFindMin = fromMaybe (error "deleteFindMin: empty set has no minimal element") . minView
+
+-- | /O(min(n,W))/. Delete and find the maximal element.
+--
+-- > deleteFindMax set = (findMax set, deleteMax set)
+deleteFindMax :: IntSet -> (Int, IntSet)
+deleteFindMax = fromMaybe (error "deleteFindMax: empty set has no maximal element") . maxView
+
+
+-- | /O(min(n,W))/. The minimal element of the set.
+findMin :: IntSet -> Int
+findMin Nil = error "findMin: empty set has no minimal element"
+findMin (Tip kx bm) = kx + lowestBitSet bm
+findMin (Bin _ m l r)
+ | m < 0 = find r
+ | otherwise = find l
+ where find (Tip kx bm) = kx + lowestBitSet bm
+ find (Bin _ _ l' _) = find l'
+ find Nil = error "findMin Nil"
+
+-- | /O(min(n,W))/. The maximal element of a set.
+findMax :: IntSet -> Int
+findMax Nil = error "findMax: empty set has no maximal element"
+findMax (Tip kx bm) = kx + highestBitSet bm
+findMax (Bin _ m l r)
+ | m < 0 = find l
+ | otherwise = find r
+ where find (Tip kx bm) = kx + highestBitSet bm
+ find (Bin _ _ _ r') = find r'
+ find Nil = error "findMax Nil"
+
+
+-- | /O(min(n,W))/. Delete the minimal element.
+deleteMin :: IntSet -> IntSet
+deleteMin = maybe Nil snd . minView
+
+-- | /O(min(n,W))/. Delete the maximal element.
+deleteMax :: IntSet -> IntSet
+deleteMax = maybe Nil snd . maxView
+
+{----------------------------------------------------------------------
+ Map
+----------------------------------------------------------------------}
+
+-- | /O(n*min(n,W))/.
+-- @'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 :: (Int->Int) -> IntSet -> IntSet
+map f = fromList . List.map f . toList
+
+{--------------------------------------------------------------------
+ Fold
+--------------------------------------------------------------------}
+-- | /O(n)/. Fold the elements in the set using the given right-associative
+-- binary operator. This function is an equivalent of 'foldr' and is present
+-- for compatibility only.
+--
+-- /Please note that fold will be deprecated in the future and removed./
+fold :: (Int -> b -> b) -> b -> IntSet -> b
+fold = foldr
+{-# INLINE fold #-}
+
+-- | /O(n)/. Fold the elements in the set using the given right-associative
+-- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'toAscList'@.
+--
+-- For example,
+--
+-- > toAscList set = foldr (:) [] set
+foldr :: (Int -> b -> b) -> b -> IntSet -> b
+foldr f z = \t -> -- Use lambda t to be inlinable with two arguments only.
+ case t of Bin _ m l r | m < 0 -> go (go z l) r -- put negative numbers before
+ | otherwise -> go (go z r) l
+ _ -> go z t
+ where
+ go z' Nil = z'
+ go z' (Tip kx bm) = foldrBits kx f z' bm
+ go z' (Bin _ _ l r) = go (go z' r) l
+{-# INLINE foldr #-}
+
+-- | /O(n)/. A strict version of 'foldr'. Each application of the operator is
+-- evaluated before using the result in the next application. This
+-- function is strict in the starting value.
+foldr' :: (Int -> b -> b) -> b -> IntSet -> b
+foldr' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
+ case t of Bin _ m l r | m < 0 -> go (go z l) r -- put negative numbers before
+ | otherwise -> go (go z r) l
+ _ -> go z t
+ where
+ STRICT_1_OF_2(go)
+ go z' Nil = z'
+ go z' (Tip kx bm) = foldr'Bits kx f z' bm
+ go z' (Bin _ _ l r) = go (go z' r) l
+{-# INLINE foldr' #-}
+
+-- | /O(n)/. Fold the elements in the set using the given left-associative
+-- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'toAscList'@.
+--
+-- For example,
+--
+-- > toDescList set = foldl (flip (:)) [] set
+foldl :: (a -> Int -> a) -> a -> IntSet -> a
+foldl f z = \t -> -- Use lambda t to be inlinable with two arguments only.
+ case t of Bin _ m l r | m < 0 -> go (go z r) l -- put negative numbers before
+ | otherwise -> go (go z l) r
+ _ -> go z t
+ where
+ STRICT_1_OF_2(go)
+ go z' Nil = z'
+ go z' (Tip kx bm) = foldlBits kx f z' bm
+ go z' (Bin _ _ l r) = go (go z' l) r
+{-# INLINE foldl #-}
+
+-- | /O(n)/. A strict version of 'foldl'. Each application of the operator is
+-- evaluated before using the result in the next application. This
+-- function is strict in the starting value.
+foldl' :: (a -> Int -> a) -> a -> IntSet -> a
+foldl' f z = \t -> -- Use lambda t to be inlinable with two arguments only.
+ case t of Bin _ m l r | m < 0 -> go (go z r) l -- put negative numbers before
+ | otherwise -> go (go z l) r
+ _ -> go z t
+ where
+ STRICT_1_OF_2(go)
+ go z' Nil = z'
+ go z' (Tip kx bm) = foldl'Bits kx f z' bm
+ go z' (Bin _ _ l r) = go (go z' l) r
+{-# INLINE foldl' #-}
+
+{--------------------------------------------------------------------
+ List variations
+--------------------------------------------------------------------}
+-- | /O(n)/. An alias of 'toAscList'. The elements of a set in ascending order.
+-- Subject to list fusion.
+elems :: IntSet -> [Int]
+elems
+ = toAscList
+
+{--------------------------------------------------------------------
+ Lists
+--------------------------------------------------------------------}
+-- | /O(n)/. Convert the set to a list of elements. Subject to list fusion.
+toList :: IntSet -> [Int]
+toList
+ = toAscList
+
+-- | /O(n)/. Convert the set to an ascending list of elements. Subject to list
+-- fusion.
+toAscList :: IntSet -> [Int]
+toAscList = foldr (:) []
+
+-- | /O(n)/. Convert the set to a descending list of elements. Subject to list
+-- fusion.
+toDescList :: IntSet -> [Int]
+toDescList = foldl (flip (:)) []
+
+-- List fusion for the list generating functions.
+#if __GLASGOW_HASKELL__
+-- The foldrFB and foldlFB are foldr and foldl equivalents, used for list fusion.
+-- They are important to convert unfused to{Asc,Desc}List back, see mapFB in prelude.
+foldrFB :: (Int -> b -> b) -> b -> IntSet -> b
+foldrFB = foldr
+{-# INLINE[0] foldrFB #-}
+foldlFB :: (a -> Int -> a) -> a -> IntSet -> a
+foldlFB = foldl
+{-# INLINE[0] foldlFB #-}
+
+-- Inline elems and toList, so that we need to fuse only toAscList.
+{-# INLINE elems #-}
+{-# INLINE toList #-}
+
+-- The fusion is enabled up to phase 2 included. If it does not succeed,
+-- convert in phase 1 the expanded to{Asc,Desc}List calls back to
+-- to{Asc,Desc}List. In phase 0, we inline fold{lr}FB (which were used in
+-- a list fusion, otherwise it would go away in phase 1), and let compiler do
+-- whatever it wants with to{Asc,Desc}List -- it was forbidden to inline it
+-- before phase 0, otherwise the fusion rules would not fire at all.
+{-# NOINLINE[0] toAscList #-}
+{-# NOINLINE[0] toDescList #-}
+{-# RULES "IntSet.toAscList" [~1] forall s . toAscList s = build (\c n -> foldrFB c n s) #-}
+{-# RULES "IntSet.toAscListBack" [1] foldrFB (:) [] = toAscList #-}
+{-# RULES "IntSet.toDescList" [~1] forall s . toDescList s = build (\c n -> foldlFB (\xs x -> c x xs) n s) #-}
+{-# RULES "IntSet.toDescListBack" [1] foldlFB (\xs x -> x : xs) [] = toDescList #-}
+#endif
+
+
+-- | /O(n*min(n,W))/. Create a set from a list of integers.
+fromList :: [Int] -> IntSet
+fromList xs
+ = foldlStrict ins empty xs
+ where
+ ins t x = insert x t
+
+-- | /O(n)/. Build a set from an ascending list of elements.
+-- /The precondition (input list is ascending) is not checked./
+fromAscList :: [Int] -> IntSet
+fromAscList [] = Nil
+fromAscList (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0)
+ where
+ combineEq x' [] = [x']
+ combineEq x' (x:xs)
+ | x==x' = combineEq x' xs
+ | otherwise = x' : combineEq x xs
+
+-- | /O(n)/. Build a set from an ascending list of distinct elements.
+-- /The precondition (input list is strictly ascending) is not checked./
+fromDistinctAscList :: [Int] -> IntSet
+fromDistinctAscList [] = Nil
+fromDistinctAscList (z0 : zs0) = work (prefixOf z0) (bitmapOf z0) zs0 Nada
+ where
+ -- 'work' accumulates all values that go into one tip, before passing this Tip
+ -- to 'reduce'
+ work kx bm [] stk = finish kx (Tip kx bm) stk
+ work kx bm (z:zs) stk | kx == prefixOf z = work kx (bm .|. bitmapOf z) zs stk
+ work kx bm (z:zs) stk = reduce z zs (branchMask z kx) kx (Tip kx bm) stk
+
+ reduce z zs _ px tx Nada = work (prefixOf z) (bitmapOf z) zs (Push px tx Nada)
+ reduce z zs m px tx stk@(Push py ty stk') =
+ let mxy = branchMask px py
+ pxy = mask px mxy
+ in if shorter m mxy
+ then reduce z zs m pxy (Bin pxy mxy ty tx) stk'
+ else work (prefixOf z) (bitmapOf z) zs (Push px tx stk)
+
+ finish _ t Nada = t
+ finish px tx (Push py ty stk) = finish p (join py ty px tx) stk
+ where m = branchMask px py
+ p = mask px m
+
+data Stack = Push {-# UNPACK #-} !Prefix !IntSet !Stack | Nada
+
+
+{--------------------------------------------------------------------
+ Eq
+--------------------------------------------------------------------}
+instance Eq IntSet where
+ t1 == t2 = equal t1 t2
+ t1 /= t2 = nequal t1 t2
+
+equal :: IntSet -> IntSet -> Bool
+equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
+ = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
+equal (Tip kx1 bm1) (Tip kx2 bm2)
+ = kx1 == kx2 && bm1 == bm2
+equal Nil Nil = True
+equal _ _ = False
+
+nequal :: IntSet -> IntSet -> Bool
+nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
+ = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
+nequal (Tip kx1 bm1) (Tip kx2 bm2)
+ = kx1 /= kx2 || bm1 /= bm2
+nequal Nil Nil = False
+nequal _ _ = True
+
+{--------------------------------------------------------------------
+ Ord
+--------------------------------------------------------------------}
+
+instance Ord IntSet where
+ compare s1 s2 = compare (toAscList s1) (toAscList s2)
+ -- tentative implementation. See if more efficient exists.
+
+{--------------------------------------------------------------------
+ Show
+--------------------------------------------------------------------}
+instance Show IntSet where
+ showsPrec p xs = showParen (p > 10) $
+ showString "fromList " . shows (toList xs)
+
+{--------------------------------------------------------------------
+ Read
+--------------------------------------------------------------------}
+instance Read IntSet where
+#ifdef __GLASGOW_HASKELL__
+ readPrec = parens $ prec 10 $ do
+ Ident "fromList" <- lexP
+ xs <- readPrec
+ return (fromList xs)
+
+ readListPrec = readListPrecDefault
+#else
+ readsPrec p = readParen (p > 10) $ \ r -> do
+ ("fromList",s) <- lex r
+ (xs,t) <- reads s
+ return (fromList xs,t)
+#endif
+
+{--------------------------------------------------------------------
+ Typeable
+--------------------------------------------------------------------}
+
+#include "Typeable.h"
+INSTANCE_TYPEABLE0(IntSet,intSetTc,"IntSet")
+
+{--------------------------------------------------------------------
+ NFData
+--------------------------------------------------------------------}
+
+-- The IntSet constructors consist only of strict fields of Ints and
+-- IntSets, thus the default NFData instance which evaluates to whnf
+-- should suffice
+instance NFData IntSet
+
+{--------------------------------------------------------------------
+ Debugging
+--------------------------------------------------------------------}
+-- | /O(n)/. Show the tree that implements the set. The tree is shown
+-- in a compressed, hanging format.