diff --git a/Data/Graph.hs b/Data/Graph.hs --- a/Data/Graph.hs +++ b/Data/Graph.hs @@ -1,10 +1,16 @@ {-# LANGUAGE CPP #-} #if __GLASGOW_HASKELL__ {-# LANGUAGE Rank2Types #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE StandaloneDeriving #-} #endif #if __GLASGOW_HASKELL__ >= 703 {-# LANGUAGE Trustworthy #-} #endif +#if __GLASGOW_HASKELL__ >= 702 +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE StandaloneDeriving #-} +#endif #include "containers.h" @@ -77,12 +83,30 @@ -- std interfaces #if !MIN_VERSION_base(4,8,0) import Control.Applicative +import qualified Data.Foldable as F +import Data.Traversable +#else +import Data.Foldable as F #endif import Control.DeepSeq (NFData(rnf)) import Data.Maybe import Data.Array import Data.List +#if MIN_VERSION_base(4,9,0) +import Data.Functor.Classes +import Data.Semigroup (Semigroup (..)) +#endif +#if __GLASGOW_HASKELL__ >= 706 +import GHC.Generics (Generic, Generic1) +#elif __GLASGOW_HASKELL__ >= 702 +import GHC.Generics (Generic) +#endif +#ifdef __GLASGOW_HASKELL__ +import Data.Data (Data) +#endif +import Data.Typeable + ------------------------------------------------------------------------- -- - -- External interface @@ -94,6 +118,47 @@ -- in any cycle. | CyclicSCC [vertex] -- ^ A maximal set of mutually -- reachable vertices. + deriving (Eq, Show, Read) + +INSTANCE_TYPEABLE1(SCC) + +#ifdef __GLASGOW_HASKELL__ +deriving instance Data vertex => Data (SCC vertex) +#endif + +#if __GLASGOW_HASKELL__ >= 706 +deriving instance Generic1 SCC +#endif + +#if __GLASGOW_HASKELL__ >= 702 +deriving instance Generic (SCC vertex) +#endif + +#if MIN_VERSION_base(4,9,0) +instance Eq1 SCC where + liftEq eq (AcyclicSCC v1) (AcyclicSCC v2) = eq v1 v2 + liftEq eq (CyclicSCC vs1) (CyclicSCC vs2) = liftEq eq vs1 vs2 + liftEq _ _ _ = False +instance Show1 SCC where + liftShowsPrec sp _sl d (AcyclicSCC v) = showsUnaryWith sp "AcyclicSCC" d v + liftShowsPrec _sp sl d (CyclicSCC vs) = showsUnaryWith (const sl) "CyclicSCC" d vs +instance Read1 SCC where + liftReadsPrec rp rl = readsData $ + readsUnaryWith rp "AcyclicSCC" AcyclicSCC <> + readsUnaryWith (const rl) "CyclicSCC" CyclicSCC +#endif + +instance F.Foldable SCC where + foldr c n (AcyclicSCC v) = c v n + foldr c n (CyclicSCC vs) = foldr c n vs + +instance Traversable SCC where + -- We treat the non-empty cyclic case specially to cut one + -- fmap application. + traverse f (AcyclicSCC vertex) = AcyclicSCC <$> f vertex + traverse _f (CyclicSCC []) = pure (CyclicSCC []) + traverse f (CyclicSCC (x : xs)) = + (\x' xs' -> CyclicSCC (x' : xs')) <$> f x <*> traverse f xs instance NFData a => NFData (SCC a) where rnf (AcyclicSCC v) = rnf v diff --git a/Data/IntMap.hs b/Data/IntMap.hs --- a/Data/IntMap.hs +++ b/Data/IntMap.hs @@ -65,38 +65,33 @@ import qualified Data.IntMap.Strict as Strict import Data.IntMap.Lazy --- | /Deprecated./ As of version 0.5, replaced by --- 'Data.IntMap.Strict.insertWith'. --- --- /O(log n)/. Same as 'insertWith', but the result of the combining function +-- | /O(log n)/. Same as 'insertWith', but the result of the combining function -- is evaluated to WHNF before inserted to the map. +{-# DEPRECATED insertWith' "As of version 0.5, replaced by 'Data.IntMap.Strict.insertWith'." #-} insertWith' :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a insertWith' = Strict.insertWith --- | /Deprecated./ As of version 0.5, replaced by --- 'Data.IntMap.Strict.insertWithKey'. --- --- /O(log n)/. Same as 'insertWithKey', but the result of the combining +-- | /O(log n)/. Same as 'insertWithKey', but the result of the combining -- function is evaluated to WHNF before inserted to the map. +{-# DEPRECATED insertWithKey' "As of version 0.5, replaced by 'Data.IntMap.Strict.insertWithKey'." #-} insertWithKey' :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a insertWithKey' = Strict.insertWithKey --- | /Deprecated./ As of version 0.5, replaced by 'foldr'. --- --- /O(n)/. Fold the values in the map using the given +-- | /O(n)/. Fold the values in the map using the given -- right-associative binary operator. This function is an equivalent -- of 'foldr' and is present for compatibility only. +{-# DEPRECATED fold "As of version 0.5, replaced by 'foldr'." #-} fold :: (a -> b -> b) -> b -> IntMap a -> b fold = foldr {-# INLINE fold #-} --- | /Deprecated./ As of version 0.5, replaced by 'foldrWithKey'. --- --- /O(n)/. Fold the keys and values in the map using the given +-- | /O(n)/. Fold the keys and values in the map using the given -- right-associative binary operator. This function is an equivalent -- of 'foldrWithKey' and is present for compatibility only. + +{-# DEPRECATED foldWithKey "As of version 0.5, replaced by 'foldrWithKey'." #-} foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b foldWithKey = foldrWithKey {-# INLINE foldWithKey #-} diff --git a/Data/IntMap/Base.hs b/Data/IntMap/Base.hs deleted file mode 100644 --- a/Data/IntMap/Base.hs +++ /dev/null @@ -1,2397 +0,0 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE MagicHash, DeriveDataTypeable, StandaloneDeriving #-} -{-# LANGUAGE ScopedTypeVariables #-} -#endif -#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Trustworthy #-} -#endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE TypeFamilies #-} -#endif - -#include "containers.h" -{-# OPTIONS_HADDOCK hide #-} - ------------------------------------------------------------------------------ --- | --- Module : Data.IntMap.Base --- Copyright : (c) Daan Leijen 2002 --- (c) Andriy Palamarchuk 2008 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : provisional --- Portability : portable --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. --- --- = Description --- --- This defines the data structures and core (hidden) manipulations --- on representations. ------------------------------------------------------------------------------ - --- [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 IntMap 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.IntMap.Base ( - -- * Map type - IntMap(..), Key -- instance Eq,Show - - -- * Operators - , (!), (\\) - - -- * Query - , null - , size - , member - , notMember - , lookup - , findWithDefault - , lookupLT - , lookupGT - , lookupLE - , lookupGE - - -- * Construction - , empty - , singleton - - -- ** Insertion - , insert - , insertWith - , insertWithKey - , insertLookupWithKey - - -- ** Delete\/Update - , delete - , adjust - , adjustWithKey - , update - , updateWithKey - , updateLookupWithKey - , alter - , alterF - - -- * Combine - - -- ** Union - , union - , unionWith - , unionWithKey - , unions - , unionsWith - - -- ** Difference - , difference - , differenceWith - , differenceWithKey - - -- ** Intersection - , intersection - , intersectionWith - , intersectionWithKey - - -- ** Universal combining function - , mergeWithKey - , mergeWithKey' - - -- * Traversal - -- ** Map - , map - , mapWithKey - , traverseWithKey - , mapAccum - , mapAccumWithKey - , mapAccumRWithKey - , mapKeys - , mapKeysWith - , mapKeysMonotonic - - -- * Folds - , foldr - , foldl - , foldrWithKey - , foldlWithKey - , foldMapWithKey - - -- ** Strict folds - , foldr' - , foldl' - , foldrWithKey' - , foldlWithKey' - - -- * Conversion - , elems - , keys - , assocs - , keysSet - , fromSet - - -- ** Lists - , toList - , fromList - , fromListWith - , fromListWithKey - - -- ** Ordered lists - , toAscList - , toDescList - , fromAscList - , fromAscListWith - , fromAscListWithKey - , fromDistinctAscList - - -- * Filter - , filter - , filterWithKey - , restrictKeys - , withoutKeys - , partition - , partitionWithKey - - , mapMaybe - , mapMaybeWithKey - , mapEither - , mapEitherWithKey - - , split - , splitLookup - , splitRoot - - -- * Submap - , isSubmapOf, isSubmapOfBy - , isProperSubmapOf, isProperSubmapOfBy - - -- * Min\/Max - , findMin - , findMax - , deleteMin - , deleteMax - , deleteFindMin - , deleteFindMax - , updateMin - , updateMax - , updateMinWithKey - , updateMaxWithKey - , minView - , maxView - , minViewWithKey - , maxViewWithKey - - -- * Debugging - , showTree - , showTreeWith - - -- * Internal types - , Mask, Prefix, Nat - - -- * Utility - , natFromInt - , intFromNat - , link - , bin - , binCheckLeft - , binCheckRight - , zero - , nomatch - , match - , mask - , maskW - , shorter - , branchMask - , highestBitMask - ) where - -#if !(MIN_VERSION_base(4,8,0)) -import Control.Applicative (Applicative(pure, (<*>)), (<$>)) -import Data.Monoid (Monoid(..)) -import Data.Traversable (Traversable(traverse)) -import Data.Word (Word) -#endif -#if MIN_VERSION_base(4,9,0) -import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) -#endif - -import Control.DeepSeq (NFData(rnf)) -import Control.Monad (liftM) -import Data.Bits -import qualified Data.Foldable as Foldable -import Data.Maybe (fromMaybe) -import Data.Typeable -import Prelude hiding (lookup, map, filter, foldr, foldl, null) - -import Data.IntSet.Base (Key) -import qualified Data.IntSet.Base as IntSet -import Data.Utils.BitUtil -import Data.Utils.StrictFold -import Data.Utils.StrictPair - -#if __GLASGOW_HASKELL__ -import Data.Data (Data(..), Constr, mkConstr, constrIndex, Fixity(Prefix), - DataType, mkDataType) -import GHC.Exts (build) -#if !MIN_VERSION_base(4,8,0) -import Data.Functor ((<$)) -#endif -#if __GLASGOW_HASKELL__ >= 708 -import qualified GHC.Exts as GHCExts -#endif -import Text.Read -#endif -#if __GLASGOW_HASKELL__ >= 709 -import Data.Coerce -#endif - - --- A "Nat" is a natural machine word (an unsigned Int) -type Nat = Word - -natFromInt :: Key -> Nat -natFromInt = fromIntegral -{-# INLINE natFromInt #-} - -intFromNat :: Nat -> Key -intFromNat = fromIntegral -{-# INLINE intFromNat #-} - -{-------------------------------------------------------------------- - Types ---------------------------------------------------------------------} - - --- | A map of integers to values @a@. - --- See Note: Order of constructors -data IntMap a = Bin {-# UNPACK #-} !Prefix - {-# UNPACK #-} !Mask - !(IntMap a) - !(IntMap a) - | Tip {-# UNPACK #-} !Key a - | Nil - -type Prefix = Int -type Mask = Int - -{-------------------------------------------------------------------- - Operators ---------------------------------------------------------------------} - --- | /O(min(n,W))/. Find the value at a key. --- Calls 'error' when the element can not be found. --- --- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map --- > fromList [(5,'a'), (3,'b')] ! 5 == 'a' - -(!) :: IntMap a -> Key -> a -(!) m k = find k m - --- | Same as 'difference'. -(\\) :: IntMap a -> IntMap b -> IntMap a -m1 \\ m2 = difference m1 m2 - -infixl 9 \\{-This comment teaches CPP correct behaviour -} - -{-------------------------------------------------------------------- - Types ---------------------------------------------------------------------} - -instance Monoid (IntMap a) where - mempty = empty - mconcat = unions -#if !(MIN_VERSION_base(4,9,0)) - mappend = union -#else - mappend = (<>) - -instance Semigroup (IntMap a) where - (<>) = union - stimes = stimesIdempotentMonoid -#endif - -instance Foldable.Foldable IntMap where - fold = go - where go Nil = mempty - go (Tip _ v) = v - go (Bin _ _ l r) = go l `mappend` go r - {-# INLINABLE fold #-} - foldr = foldr - {-# INLINE foldr #-} - foldl = foldl - {-# INLINE foldl #-} - foldMap f t = go t - where go Nil = mempty - go (Tip _ v) = f v - go (Bin _ _ l r) = go l `mappend` go r - {-# INLINE foldMap #-} - -#if MIN_VERSION_base(4,6,0) - foldl' = foldl' - {-# INLINE foldl' #-} - foldr' = foldr' - {-# INLINE foldr' #-} -#endif -#if MIN_VERSION_base(4,8,0) - length = size - {-# INLINE length #-} - null = null - {-# INLINE null #-} - toList = elems -- NB: Foldable.toList /= IntMap.toList - {-# INLINE toList #-} - elem = go - where go !_ Nil = False - go x (Tip _ y) = x == y - go x (Bin _ _ l r) = go x l || go x r - {-# INLINABLE elem #-} - maximum = start - where start Nil = error "IntMap.Foldable.maximum: called with empty map" - start (Tip _ y) = y - start (Bin _ _ l r) = go (start l) r - - go !m Nil = m - go m (Tip _ y) = max m y - go m (Bin _ _ l r) = go (go m l) r - {-# INLINABLE maximum #-} - minimum = start - where start Nil = error "IntMap.Foldable.minimum: called with empty map" - start (Tip _ y) = y - start (Bin _ _ l r) = go (start l) r - - go !m Nil = m - go m (Tip _ y) = min m y - go m (Bin _ _ l r) = go (go m l) r - {-# INLINABLE minimum #-} - sum = foldl' (+) 0 - {-# INLINABLE sum #-} - product = foldl' (*) 1 - {-# INLINABLE product #-} -#endif - -instance Traversable IntMap where - traverse f = traverseWithKey (\_ -> f) - {-# INLINE traverse #-} - -instance NFData a => NFData (IntMap a) where - rnf Nil = () - rnf (Tip _ v) = rnf v - rnf (Bin _ _ l r) = rnf l `seq` rnf r - -#if __GLASGOW_HASKELL__ - -{-------------------------------------------------------------------- - A Data instance ---------------------------------------------------------------------} - --- This instance preserves data abstraction at the cost of inefficiency. --- We provide limited reflection services for the sake of data abstraction. - -instance Data a => Data (IntMap a) where - gfoldl f z im = z fromList `f` (toList im) - toConstr _ = fromListConstr - gunfold k z c = case constrIndex c of - 1 -> k (z fromList) - _ -> error "gunfold" - dataTypeOf _ = intMapDataType - dataCast1 f = gcast1 f - -fromListConstr :: Constr -fromListConstr = mkConstr intMapDataType "fromList" [] Prefix - -intMapDataType :: DataType -intMapDataType = mkDataType "Data.IntMap.Base.IntMap" [fromListConstr] - -#endif - -{-------------------------------------------------------------------- - Query ---------------------------------------------------------------------} --- | /O(1)/. Is the map empty? --- --- > Data.IntMap.null (empty) == True --- > Data.IntMap.null (singleton 1 'a') == False - -null :: IntMap a -> Bool -null Nil = True -null _ = False -{-# INLINE null #-} - --- | /O(n)/. Number of elements in the map. --- --- > size empty == 0 --- > size (singleton 1 'a') == 1 --- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3 -size :: IntMap a -> Int -size (Bin _ _ l r) = size l + size r -size (Tip _ _) = 1 -size Nil = 0 - --- | /O(min(n,W))/. Is the key a member of the map? --- --- > member 5 (fromList [(5,'a'), (3,'b')]) == True --- > member 1 (fromList [(5,'a'), (3,'b')]) == False - --- See Note: Local 'go' functions and capturing] -member :: Key -> IntMap a -> Bool -member !k = go - where - go (Bin p m l r) | nomatch k p m = False - | zero k m = go l - | otherwise = go r - go (Tip kx _) = k == kx - go Nil = False - --- | /O(min(n,W))/. Is the key not a member of the map? --- --- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False --- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True - -notMember :: Key -> IntMap a -> Bool -notMember k m = not $ member k m - --- | /O(min(n,W))/. Lookup the value at a key in the map. See also 'Data.Map.lookup'. - --- See Note: Local 'go' functions and capturing] -lookup :: Key -> IntMap a -> Maybe a -lookup !k = go - where - go (Bin p m l r) | nomatch k p m = Nothing - | zero k m = go l - | otherwise = go r - go (Tip kx x) | k == kx = Just x - | otherwise = Nothing - go Nil = Nothing - - --- See Note: Local 'go' functions and capturing] -find :: Key -> IntMap a -> a -find !k = go - where - go (Bin p m l r) | nomatch k p m = not_found - | zero k m = go l - | otherwise = go r - go (Tip kx x) | k == kx = x - | otherwise = not_found - go Nil = not_found - - not_found = error ("IntMap.!: key " ++ show k ++ " is not an element of the map") - --- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@ --- returns the value at key @k@ or returns @def@ when the key is not an --- element of the map. --- --- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' --- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' - --- See Note: Local 'go' functions and capturing] -findWithDefault :: a -> Key -> IntMap a -> a -findWithDefault def !k = go - where - go (Bin p m l r) | nomatch k p m = def - | zero k m = go l - | otherwise = go r - go (Tip kx x) | k == kx = x - | otherwise = def - go Nil = def - --- | /O(log n)/. Find largest key smaller than the given one and return the --- corresponding (key, value) pair. --- --- > lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing --- > lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') - --- See Note: Local 'go' functions and capturing. -lookupLT :: Key -> IntMap a -> Maybe (Key, a) -lookupLT !k t = case t of - Bin _ m l r | m < 0 -> if k >= 0 then go r l else go Nil r - _ -> go Nil t - where - go def (Bin p m l r) | nomatch k p m = if k < p then unsafeFindMax def else unsafeFindMax r - | zero k m = go def l - | otherwise = go l r - go def (Tip ky y) | k <= ky = unsafeFindMax def - | otherwise = Just (ky, y) - go def Nil = unsafeFindMax def - --- | /O(log n)/. Find smallest key greater than the given one and return the --- corresponding (key, value) pair. --- --- > lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') --- > lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing - --- See Note: Local 'go' functions and capturing. -lookupGT :: Key -> IntMap a -> Maybe (Key, a) -lookupGT !k t = case t of - Bin _ m l r | m < 0 -> if k >= 0 then go Nil l else go l r - _ -> go Nil t - where - go def (Bin p m l r) | nomatch k p m = if k < p then unsafeFindMin l else unsafeFindMin def - | zero k m = go r l - | otherwise = go def r - go def (Tip ky y) | k >= ky = unsafeFindMin def - | otherwise = Just (ky, y) - go def Nil = unsafeFindMin def - --- | /O(log n)/. Find largest key smaller or equal to the given one and return --- the corresponding (key, value) pair. --- --- > lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing --- > lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') --- > lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') - --- See Note: Local 'go' functions and capturing. -lookupLE :: Key -> IntMap a -> Maybe (Key, a) -lookupLE !k t = case t of - Bin _ m l r | m < 0 -> if k >= 0 then go r l else go Nil r - _ -> go Nil t - where - go def (Bin p m l r) | nomatch k p m = if k < p then unsafeFindMax def else unsafeFindMax r - | zero k m = go def l - | otherwise = go l r - go def (Tip ky y) | k < ky = unsafeFindMax def - | otherwise = Just (ky, y) - go def Nil = unsafeFindMax def - --- | /O(log n)/. Find smallest key greater or equal to the given one and return --- the corresponding (key, value) pair. --- --- > lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') --- > lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') --- > lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing - --- See Note: Local 'go' functions and capturing. -lookupGE :: Key -> IntMap a -> Maybe (Key, a) -lookupGE !k t = case t of - Bin _ m l r | m < 0 -> if k >= 0 then go Nil l else go l r - _ -> go Nil t - where - go def (Bin p m l r) | nomatch k p m = if k < p then unsafeFindMin l else unsafeFindMin def - | zero k m = go r l - | otherwise = go def r - go def (Tip ky y) | k > ky = unsafeFindMin def - | otherwise = Just (ky, y) - 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 :: IntMap a -> Maybe (Key, a) -unsafeFindMin Nil = Nothing -unsafeFindMin (Tip ky y) = Just (ky, y) -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 :: IntMap a -> Maybe (Key, a) -unsafeFindMax Nil = Nothing -unsafeFindMax (Tip ky y) = Just (ky, y) -unsafeFindMax (Bin _ _ _ r) = unsafeFindMax r - -{-------------------------------------------------------------------- - Construction ---------------------------------------------------------------------} --- | /O(1)/. The empty map. --- --- > empty == fromList [] --- > size empty == 0 - -empty :: IntMap a -empty - = Nil -{-# INLINE empty #-} - --- | /O(1)/. A map of one element. --- --- > singleton 1 'a' == fromList [(1, 'a')] --- > size (singleton 1 'a') == 1 - -singleton :: Key -> a -> IntMap a -singleton k x - = Tip k x -{-# INLINE singleton #-} - -{-------------------------------------------------------------------- - Insert ---------------------------------------------------------------------} --- | /O(min(n,W))/. Insert a new key\/value pair in the map. --- If the key is already present in the map, the associated value is --- replaced with the supplied value, i.e. 'insert' is equivalent to --- @'insertWith' 'const'@. --- --- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')] --- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] --- > insert 5 'x' empty == singleton 5 'x' - -insert :: Key -> a -> IntMap a -> IntMap a -insert !k x t@(Bin p m l r) - | nomatch k p m = link k (Tip k x) p t - | zero k m = Bin p m (insert k x l) r - | otherwise = Bin p m l (insert k x r) -insert k x t@(Tip ky _) - | k==ky = Tip k x - | otherwise = link k (Tip k x) ky t -insert k x Nil = Tip k x - --- right-biased insertion, used by 'union' --- | /O(min(n,W))/. Insert with a combining function. --- @'insertWith' f key value mp@ --- will insert the pair (key, value) into @mp@ if key does --- not exist in the map. If the key does exist, the function will --- insert @f new_value old_value@. --- --- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] --- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] --- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx" - -insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a -insertWith f k x t - = insertWithKey (\_ x' y' -> f x' y') k x t - --- | /O(min(n,W))/. Insert with a combining function. --- @'insertWithKey' f key value mp@ --- will insert the pair (key, value) into @mp@ if key does --- not exist in the map. If the key does exist, the function will --- insert @f key new_value old_value@. --- --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value --- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] --- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] --- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx" - -insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a -insertWithKey f !k x t@(Bin p m l r) - | nomatch k p m = link k (Tip k x) p t - | zero k m = Bin p m (insertWithKey f k x l) r - | otherwise = Bin p m l (insertWithKey f k x r) -insertWithKey f k x t@(Tip ky y) - | k == ky = Tip k (f k x y) - | otherwise = link k (Tip k x) ky t -insertWithKey _ k x Nil = Tip k x - --- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@) --- is a pair where the first element is equal to (@'lookup' k map@) --- and the second element equal to (@'insertWithKey' f k x map@). --- --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value --- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) --- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) --- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx") --- --- This is how to define @insertLookup@ using @insertLookupWithKey@: --- --- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t --- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) --- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) - -insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a) -insertLookupWithKey f !k x t@(Bin p m l r) - | nomatch k p m = (Nothing,link k (Tip k x) p t) - | zero k m = let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r) - | otherwise = let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r') -insertLookupWithKey f k x t@(Tip ky y) - | k == ky = (Just y,Tip k (f k x y)) - | otherwise = (Nothing,link k (Tip k x) ky t) -insertLookupWithKey _ k x Nil = (Nothing,Tip k x) - - -{-------------------------------------------------------------------- - Deletion ---------------------------------------------------------------------} --- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not --- a member of the map, the original map is returned. --- --- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > delete 5 empty == empty - -delete :: Key -> IntMap a -> IntMap a -delete !k t@(Bin p m l r) - | nomatch k p m = t - | zero k m = binCheckLeft p m (delete k l) r - | otherwise = binCheckRight p m l (delete k r) -delete k t@(Tip ky _) - | k == ky = Nil - | otherwise = t -delete _k Nil = Nil - --- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not --- a member of the map, the original map is returned. --- --- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] --- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > adjust ("new " ++) 7 empty == empty - -adjust :: (a -> a) -> Key -> IntMap a -> IntMap a -adjust f k m - = adjustWithKey (\_ x -> f x) k m - --- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not --- a member of the map, the original map is returned. --- --- > let f key x = (show key) ++ ":new " ++ x --- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] --- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > adjustWithKey f 7 empty == empty - -adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a -adjustWithKey f !k t@(Bin p m l r) - | nomatch k p m = t - | zero k m = Bin p m (adjustWithKey f k l) r - | otherwise = Bin p m l (adjustWithKey f k r) -adjustWithKey f k t@(Tip ky y) - | k == ky = Tip ky (f k y) - | otherwise = t -adjustWithKey _ _ Nil = Nil - - --- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@ --- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is --- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. --- --- > let f x = if x == "a" then Just "new a" else Nothing --- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] --- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a -update f - = updateWithKey (\_ x -> f x) - --- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@ --- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is --- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. --- --- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing --- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] --- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a -updateWithKey f !k t@(Bin p m l r) - | nomatch k p m = t - | zero k m = binCheckLeft p m (updateWithKey f k l) r - | otherwise = binCheckRight p m l (updateWithKey f k r) -updateWithKey f k t@(Tip ky y) - | k == ky = case (f k y) of - Just y' -> Tip ky y' - Nothing -> Nil - | otherwise = t -updateWithKey _ _ Nil = Nil - --- | /O(min(n,W))/. Lookup and update. --- The function returns original value, if it is updated. --- This is different behavior than 'Data.Map.updateLookupWithKey'. --- Returns the original key value if the map entry is deleted. --- --- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing --- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")]) --- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) --- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a") - -updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a) -updateLookupWithKey f !k t@(Bin p m l r) - | nomatch k p m = (Nothing,t) - | zero k m = let !(found,l') = updateLookupWithKey f k l in (found,binCheckLeft p m l' r) - | otherwise = let !(found,r') = updateLookupWithKey f k r in (found,binCheckRight p m l r') -updateLookupWithKey f k t@(Tip ky y) - | k==ky = case (f k y) of - Just y' -> (Just y,Tip ky y') - Nothing -> (Just y,Nil) - | otherwise = (Nothing,t) -updateLookupWithKey _ _ Nil = (Nothing,Nil) - - - --- | /O(min(n,W))/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof. --- 'alter' can be used to insert, delete, or update a value in an 'IntMap'. --- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@. -alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a -alter f !k t@(Bin p m l r) - | nomatch k p m = case f Nothing of - Nothing -> t - Just x -> link k (Tip k x) p t - | zero k m = binCheckLeft p m (alter f k l) r - | otherwise = binCheckRight p m l (alter f k r) -alter f k t@(Tip ky y) - | k==ky = case f (Just y) of - Just x -> Tip ky x - Nothing -> Nil - | otherwise = case f Nothing of - Just x -> link k (Tip k x) ky t - Nothing -> Tip ky y -alter f k Nil = case f Nothing of - Just x -> Tip k x - Nothing -> Nil - --- | /O(log n)/. The expression (@'alterF' f k map@) alters the value @x@ at --- @k@, or absence thereof. 'alterF' can be used to inspect, insert, delete, --- or update a value in an 'IntMap'. In short : @'lookup' k <$> 'alterF' f k m = f --- ('lookup' k m)@. --- --- Example: --- --- @ --- interactiveAlter :: Int -> IntMap String -> IO (IntMap String) --- interactiveAlter k m = alterF f k m where --- f Nothing -> do --- putStrLn $ show k ++ --- " was not found in the map. Would you like to add it?" --- getUserResponse1 :: IO (Maybe String) --- f (Just old) -> do --- putStrLn "The key is currently bound to " ++ show old ++ --- ". Would you like to change or delete it?" --- getUserresponse2 :: IO (Maybe String) --- @ --- --- 'alterF' is the most general operation for working with an individual --- key that may or may not be in a given map. --- --- Note: 'alterF' is a flipped version of the 'at' combinator from --- 'Control.Lens.At'. --- --- @since 0.5.8 - -alterF :: Functor f - => (Maybe a -> f (Maybe a)) -> Key -> IntMap a -> f (IntMap a) --- This implementation was stolen from 'Control.Lens.At'. -alterF f k m = (<$> f mv) $ \fres -> - case fres of - Nothing -> maybe m (const (delete k m)) mv - Just v' -> insert k v' m - where mv = lookup k m - -{-------------------------------------------------------------------- - Union ---------------------------------------------------------------------} --- | The union of a list of maps. --- --- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] --- > == fromList [(3, "b"), (5, "a"), (7, "C")] --- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])] --- > == fromList [(3, "B3"), (5, "A3"), (7, "C")] - -unions :: [IntMap a] -> IntMap a -unions xs - = foldlStrict union empty xs - --- | The union of a list of maps, with a combining operation. --- --- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] --- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")] - -unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a -unionsWith f ts - = foldlStrict (unionWith f) empty ts - --- | /O(n+m)/. The (left-biased) union of two maps. --- It prefers the first map when duplicate keys are encountered, --- i.e. (@'union' == 'unionWith' 'const'@). --- --- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")] - -union :: IntMap a -> IntMap a -> IntMap a -union m1 m2 - = mergeWithKey' Bin const id id m1 m2 - --- | /O(n+m)/. The union with a combining function. --- --- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")] - -unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a -unionWith f m1 m2 - = unionWithKey (\_ x y -> f x y) m1 m2 - --- | /O(n+m)/. The union with a combining function. --- --- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value --- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")] - -unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a -unionWithKey f m1 m2 - = mergeWithKey' Bin (\(Tip k1 x1) (Tip _k2 x2) -> Tip k1 (f k1 x1 x2)) id id m1 m2 - -{-------------------------------------------------------------------- - Difference ---------------------------------------------------------------------} --- | /O(n+m)/. Difference between two maps (based on keys). --- --- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b" - -difference :: IntMap a -> IntMap b -> IntMap a -difference m1 m2 - = mergeWithKey (\_ _ _ -> Nothing) id (const Nil) m1 m2 - --- | /O(n+m)/. Difference with a combining function. --- --- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing --- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")]) --- > == singleton 3 "b:B" - -differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a -differenceWith f m1 m2 - = differenceWithKey (\_ x y -> f x y) m1 m2 - --- | /O(n+m)/. Difference with a combining function. When two equal keys are --- encountered, the combining function is applied to the key and both values. --- If it returns 'Nothing', the element is discarded (proper set difference). --- If it returns (@'Just' y@), the element is updated with a new value @y@. --- --- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing --- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")]) --- > == singleton 3 "3:b|B" - -differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a -differenceWithKey f m1 m2 - = mergeWithKey f id (const Nil) m1 m2 - --- | Remove all the keys in a given set from a map. --- --- @ --- m `withoutKeys` s = 'filterWithKey' (\k _ -> k `'IntSet.notMember'` s) m --- @ --- --- @since 0.5.8 -withoutKeys :: IntMap a -> IntSet.IntSet -> IntMap a -withoutKeys = go - where - go t1@(Bin p1 m1 l1 r1) t2@(IntSet.Bin p2 m2 l2 r2) - | shorter m1 m2 = merge1 - | shorter m2 m1 = merge2 - | p1 == p2 = bin p1 m1 (go l1 l2) (go r1 r2) - | otherwise = t1 - where - merge1 | nomatch p2 p1 m1 = t1 - | zero p2 m1 = binCheckLeft p1 m1 (go l1 t2) r1 - | otherwise = binCheckRight p1 m1 l1 (go r1 t2) - merge2 | nomatch p1 p2 m2 = t1 - | zero p1 m2 = bin p2 m2 (go t1 l2) Nil - | otherwise = bin p2 m2 Nil (go t1 r2) - - go t1'@(Bin _ _ _ _) t2'@(IntSet.Tip _ _) = - filterWithKey (\k _ -> k `IntSet.notMember` t2') t1' - - go t1@(Bin _ _ _ _) IntSet.Nil = t1 - - go t1'@(Tip k1' _) t2' - | k1' `IntSet.member` t2' = Nil - | otherwise = t1' - go Nil _ = Nil - - -{-------------------------------------------------------------------- - Intersection ---------------------------------------------------------------------} --- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys). --- --- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a" - -intersection :: IntMap a -> IntMap b -> IntMap a -intersection m1 m2 - = mergeWithKey' bin const (const Nil) (const Nil) m1 m2 - --- | /O(n+m)/. The restriction of a map to the keys in a set. --- --- @ --- m `restrictKeys` s = 'filterWithKey' (\k _ -> k `'IntSet.member'` s) m --- @ --- --- @since 0.5.8 -restrictKeys :: IntMap a -> IntSet.IntSet -> IntMap a -restrictKeys = go - where - go t1@(Bin p1 m1 l1 r1) t2@(IntSet.Bin p2 m2 l2 r2) - | shorter m1 m2 = merge1 - | shorter m2 m1 = merge2 - | p1 == p2 = bin p1 m1 (go l1 l2) (go r1 r2) - | otherwise = Nil - where - merge1 | nomatch p2 p1 m1 = Nil - | zero p2 m1 = bin p1 m1 (go l1 t2) Nil - | otherwise = bin p1 m1 Nil (go r1 t2) - merge2 | nomatch p1 p2 m2 = Nil - | zero p1 m2 = bin p2 m2 (go t1 l2) Nil - | otherwise = bin p2 m2 Nil (go t1 r2) - - go t1'@(Bin _ _ _ _) t2'@(IntSet.Tip _ _) = - filterWithKey (\k _ -> k `IntSet.member` t2') t1' - go (Bin _ _ _ _) IntSet.Nil = Nil - - go t1'@(Tip k1' _) t2' - | k1' `IntSet.member` t2' = t1' - | otherwise = Nil - go Nil _ = Nil - --- | /O(n+m)/. The intersection with a combining function. --- --- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA" - -intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c -intersectionWith f m1 m2 - = intersectionWithKey (\_ x y -> f x y) m1 m2 - --- | /O(n+m)/. The intersection with a combining function. --- --- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar --- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A" - -intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c -intersectionWithKey f m1 m2 - = mergeWithKey' bin (\(Tip k1 x1) (Tip _k2 x2) -> Tip k1 (f k1 x1 x2)) (const Nil) (const Nil) m1 m2 - -{-------------------------------------------------------------------- - MergeWithKey ---------------------------------------------------------------------} - --- | /O(n+m)/. A high-performance universal combining function. Using --- 'mergeWithKey', all combining functions can be defined without any loss of --- efficiency (with exception of 'union', 'difference' and 'intersection', --- where sharing of some nodes is lost with 'mergeWithKey'). --- --- Please make sure you know what is going on when using 'mergeWithKey', --- otherwise you can be surprised by unexpected code growth or even --- corruption of the data structure. --- --- When 'mergeWithKey' is given three arguments, it is inlined to the call --- site. You should therefore use 'mergeWithKey' only to define your custom --- combining functions. For example, you could define 'unionWithKey', --- 'differenceWithKey' and 'intersectionWithKey' as --- --- > myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2 --- > myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2 --- > myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2 --- --- When calling @'mergeWithKey' combine only1 only2@, a function combining two --- 'IntMap's is created, such that --- --- * if a key is present in both maps, it is passed with both corresponding --- values to the @combine@ function. Depending on the result, the key is either --- present in the result with specified value, or is left out; --- --- * a nonempty subtree present only in the first map is passed to @only1@ and --- the output is added to the result; --- --- * a nonempty subtree present only in the second map is passed to @only2@ and --- the output is added to the result. --- --- The @only1@ and @only2@ methods /must return a map with a subset (possibly empty) of the keys of the given map/. --- The values can be modified arbitrarily. Most common variants of @only1@ and --- @only2@ are 'id' and @'const' 'empty'@, but for example @'map' f@ or --- @'filterWithKey' f@ could be used for any @f@. - -mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) - -> IntMap a -> IntMap b -> IntMap c -mergeWithKey f g1 g2 = mergeWithKey' bin combine g1 g2 - where -- We use the lambda form to avoid non-exhaustive pattern matches warning. - combine = \(Tip k1 x1) (Tip _k2 x2) -> case f k1 x1 x2 of Nothing -> Nil - Just x -> Tip k1 x - {-# INLINE combine #-} -{-# INLINE mergeWithKey #-} - --- Slightly more general version of mergeWithKey. It differs in the following: --- --- * the combining function operates on maps instead of keys and values. The --- reason is to enable sharing in union, difference and intersection. --- --- * mergeWithKey' is given an equivalent of bin. The reason is that in union*, --- Bin constructor can be used, because we know both subtrees are nonempty. - -mergeWithKey' :: (Prefix -> Mask -> IntMap c -> IntMap c -> IntMap c) - -> (IntMap a -> IntMap b -> IntMap c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) - -> IntMap a -> IntMap b -> IntMap c -mergeWithKey' bin' f g1 g2 = go - where - go t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) - | shorter m1 m2 = merge1 - | shorter m2 m1 = merge2 - | p1 == p2 = bin' p1 m1 (go l1 l2) (go r1 r2) - | otherwise = maybe_link p1 (g1 t1) p2 (g2 t2) - where - merge1 | nomatch p2 p1 m1 = maybe_link p1 (g1 t1) p2 (g2 t2) - | zero p2 m1 = bin' p1 m1 (go l1 t2) (g1 r1) - | otherwise = bin' p1 m1 (g1 l1) (go r1 t2) - merge2 | nomatch p1 p2 m2 = maybe_link p1 (g1 t1) p2 (g2 t2) - | zero p1 m2 = bin' p2 m2 (go t1 l2) (g2 r2) - | otherwise = bin' p2 m2 (g2 l2) (go t1 r2) - - go t1'@(Bin _ _ _ _) t2'@(Tip k2' _) = merge t2' k2' t1' - where merge t2 k2 t1@(Bin p1 m1 l1 r1) | nomatch k2 p1 m1 = maybe_link p1 (g1 t1) k2 (g2 t2) - | zero k2 m1 = bin' p1 m1 (merge t2 k2 l1) (g1 r1) - | otherwise = bin' p1 m1 (g1 l1) (merge t2 k2 r1) - merge t2 k2 t1@(Tip k1 _) | k1 == k2 = f t1 t2 - | otherwise = maybe_link k1 (g1 t1) k2 (g2 t2) - merge t2 _ Nil = g2 t2 - - go t1@(Bin _ _ _ _) Nil = g1 t1 - - go t1'@(Tip k1' _) t2' = merge t1' k1' t2' - where merge t1 k1 t2@(Bin p2 m2 l2 r2) | nomatch k1 p2 m2 = maybe_link k1 (g1 t1) p2 (g2 t2) - | zero k1 m2 = bin' p2 m2 (merge t1 k1 l2) (g2 r2) - | otherwise = bin' p2 m2 (g2 l2) (merge t1 k1 r2) - merge t1 k1 t2@(Tip k2 _) | k1 == k2 = f t1 t2 - | otherwise = maybe_link k1 (g1 t1) k2 (g2 t2) - merge t1 _ Nil = g1 t1 - - go Nil t2 = g2 t2 - - maybe_link _ Nil _ t2 = t2 - maybe_link _ t1 _ Nil = t1 - maybe_link p1 t1 p2 t2 = link p1 t1 p2 t2 - {-# INLINE maybe_link #-} -{-# INLINE mergeWithKey' #-} - -{-------------------------------------------------------------------- - Min\/Max ---------------------------------------------------------------------} - --- | /O(min(n,W))/. Update the value at the minimal key. --- --- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")] --- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -updateMinWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a -updateMinWithKey f t = - case t of Bin p m l r | m < 0 -> binCheckRight p m l (go f r) - _ -> go f t - where - go f' (Bin p m l r) = binCheckLeft p m (go f' l) r - go f' (Tip k y) = case f' k y of - Just y' -> Tip k y' - Nothing -> Nil - go _ Nil = error "updateMinWithKey Nil" - --- | /O(min(n,W))/. Update the value at the maximal key. --- --- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")] --- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" - -updateMaxWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a -updateMaxWithKey f t = - case t of Bin p m l r | m < 0 -> binCheckLeft p m (go f l) r - _ -> go f t - where - go f' (Bin p m l r) = binCheckRight p m l (go f' r) - go f' (Tip k y) = case f' k y of - Just y' -> Tip k y' - Nothing -> Nil - go _ Nil = error "updateMaxWithKey Nil" - --- | /O(min(n,W))/. Retrieves the maximal (key,value) pair of the map, and --- the map stripped of that element, or 'Nothing' if passed an empty map. --- --- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b") --- > maxViewWithKey empty == Nothing - -maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) -maxViewWithKey t = - case t of Nil -> Nothing - Bin p m l r | m < 0 -> case go l of (result, l') -> Just (result, binCheckLeft p m l' r) - _ -> Just (go t) - where - go (Bin p m l r) = case go r of (result, r') -> (result, binCheckRight p m l r') - go (Tip k y) = ((k, y), Nil) - go Nil = error "maxViewWithKey Nil" - --- | /O(min(n,W))/. Retrieves the minimal (key,value) pair of the map, and --- the map stripped of that element, or 'Nothing' if passed an empty map. --- --- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") --- > minViewWithKey empty == Nothing - -minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) -minViewWithKey t = - case t of Nil -> Nothing - Bin p m l r | m < 0 -> case go r of (result, r') -> Just (result, binCheckRight p m l r') - _ -> Just (go t) - where - go (Bin p m l r) = case go l of (result, l') -> (result, binCheckLeft p m l' r) - go (Tip k y) = ((k, y), Nil) - go Nil = error "minViewWithKey Nil" - --- | /O(min(n,W))/. Update the value at the maximal key. --- --- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")] --- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" - -updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a -updateMax f = updateMaxWithKey (const f) - --- | /O(min(n,W))/. Update the value at the minimal key. --- --- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")] --- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a -updateMin f = updateMinWithKey (const f) - --- Similar to the Arrow instance. -first :: (a -> c) -> (a, b) -> (c, b) -first f (x,y) = (f x,y) - --- | /O(min(n,W))/. Retrieves the maximal key of the map, and the map --- stripped of that element, or 'Nothing' if passed an empty map. -maxView :: IntMap a -> Maybe (a, IntMap a) -maxView t = liftM (first snd) (maxViewWithKey t) - --- | /O(min(n,W))/. Retrieves the minimal key of the map, and the map --- stripped of that element, or 'Nothing' if passed an empty map. -minView :: IntMap a -> Maybe (a, IntMap a) -minView t = liftM (first snd) (minViewWithKey t) - --- | /O(min(n,W))/. Delete and find the maximal element. -deleteFindMax :: IntMap a -> ((Key, a), IntMap a) -deleteFindMax = fromMaybe (error "deleteFindMax: empty map has no maximal element") . maxViewWithKey - --- | /O(min(n,W))/. Delete and find the minimal element. -deleteFindMin :: IntMap a -> ((Key, a), IntMap a) -deleteFindMin = fromMaybe (error "deleteFindMin: empty map has no minimal element") . minViewWithKey - --- | /O(min(n,W))/. The minimal key of the map. -findMin :: IntMap a -> (Key, a) -findMin Nil = error $ "findMin: empty map has no minimal element" -findMin (Tip k v) = (k,v) -findMin (Bin _ m l r) - | m < 0 = go r - | otherwise = go l - where go (Tip k v) = (k,v) - go (Bin _ _ l' _) = go l' - go Nil = error "findMax Nil" - --- | /O(min(n,W))/. The maximal key of the map. -findMax :: IntMap a -> (Key, a) -findMax Nil = error $ "findMax: empty map has no maximal element" -findMax (Tip k v) = (k,v) -findMax (Bin _ m l r) - | m < 0 = go l - | otherwise = go r - where go (Tip k v) = (k,v) - go (Bin _ _ _ r') = go r' - go Nil = error "findMax Nil" - --- | /O(min(n,W))/. Delete the minimal key. Returns an empty map if the map is empty. --- --- Note that this is a change of behaviour for consistency with 'Data.Map.Map' – --- versions prior to 0.5 threw an error if the 'IntMap' was already empty. -deleteMin :: IntMap a -> IntMap a -deleteMin = maybe Nil snd . minView - --- | /O(min(n,W))/. Delete the maximal key. Returns an empty map if the map is empty. --- --- Note that this is a change of behaviour for consistency with 'Data.Map.Map' – --- versions prior to 0.5 threw an error if the 'IntMap' was already empty. -deleteMax :: IntMap a -> IntMap a -deleteMax = maybe Nil snd . maxView - - -{-------------------------------------------------------------------- - Submap ---------------------------------------------------------------------} --- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). --- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@). -isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool -isProperSubmapOf m1 m2 - = isProperSubmapOfBy (==) m1 m2 - -{- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). - The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when - @m1@ and @m2@ are not equal, - all keys in @m1@ are in @m2@, and when @f@ returns 'True' when - applied to their respective values. For example, the following - expressions are all 'True': - - > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - - But the following are all 'False': - - > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) - > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) - > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) --} -isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool -isProperSubmapOfBy predicate t1 t2 - = case submapCmp predicate t1 t2 of - LT -> True - _ -> False - -submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering -submapCmp predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) - | shorter m1 m2 = GT - | shorter m2 m1 = submapCmpLt - | p1 == p2 = submapCmpEq - | otherwise = GT -- disjoint - where - submapCmpLt | nomatch p1 p2 m2 = GT - | zero p1 m2 = submapCmp predicate t1 l2 - | otherwise = submapCmp predicate t1 r2 - submapCmpEq = case (submapCmp predicate l1 l2, submapCmp predicate r1 r2) of - (GT,_ ) -> GT - (_ ,GT) -> GT - (EQ,EQ) -> EQ - _ -> LT - -submapCmp _ (Bin _ _ _ _) _ = GT -submapCmp predicate (Tip kx x) (Tip ky y) - | (kx == ky) && predicate x y = EQ - | otherwise = GT -- disjoint -submapCmp predicate (Tip k x) t - = case lookup k t of - Just y | predicate x y -> LT - _ -> GT -- disjoint -submapCmp _ Nil Nil = EQ -submapCmp _ Nil _ = LT - --- | /O(n+m)/. Is this a submap? --- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@). -isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool -isSubmapOf m1 m2 - = isSubmapOfBy (==) m1 m2 - -{- | /O(n+m)/. - The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if - all keys in @m1@ are in @m2@, and when @f@ returns 'True' when - applied to their respective values. For example, the following - expressions are all 'True': - - > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) - - But the following are all 'False': - - > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)]) - > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) --} -isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool -isSubmapOfBy predicate 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 isSubmapOfBy predicate t1 l2 - else isSubmapOfBy predicate t1 r2) - | otherwise = (p1==p2) && isSubmapOfBy predicate l1 l2 && isSubmapOfBy predicate r1 r2 -isSubmapOfBy _ (Bin _ _ _ _) _ = False -isSubmapOfBy predicate (Tip k x) t = case lookup k t of - Just y -> predicate x y - Nothing -> False -isSubmapOfBy _ Nil _ = True - -{-------------------------------------------------------------------- - Mapping ---------------------------------------------------------------------} --- | /O(n)/. Map a function over all values in the map. --- --- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")] - -map :: (a -> b) -> IntMap a -> IntMap b -map f = go - where - go (Bin p m l r) = Bin p m (go l) (go r) - go (Tip k x) = Tip k (f x) - go Nil = Nil - -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] map #-} -{-# RULES -"map/map" forall f g xs . map f (map g xs) = map (f . g) xs - #-} -#endif -#if __GLASGOW_HASKELL__ >= 709 --- Safe coercions were introduced in 7.8, but did not play well with RULES yet. -{-# RULES -"map/coerce" map coerce = coerce - #-} -#endif - --- | /O(n)/. Map a function over all values in the map. --- --- > let f key x = (show key) ++ ":" ++ x --- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")] - -mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b -mapWithKey f t - = case t of - Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r) - Tip k x -> Tip k (f k x) - Nil -> Nil - -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] mapWithKey #-} -{-# RULES -"mapWithKey/mapWithKey" forall f g xs . mapWithKey f (mapWithKey g xs) = - mapWithKey (\k a -> f k (g k a)) xs -"mapWithKey/map" forall f g xs . mapWithKey f (map g xs) = - mapWithKey (\k a -> f k (g a)) xs -"map/mapWithKey" forall f g xs . map f (mapWithKey g xs) = - mapWithKey (\k a -> f (g k a)) xs - #-} -#endif - --- | /O(n)/. --- @'traverseWithKey' f s == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@ --- That is, behaves exactly like a regular 'traverse' except that the traversing --- function also has access to the key associated with a value. --- --- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')]) --- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing -traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b) -traverseWithKey f = go - where - go Nil = pure Nil - go (Tip k v) = Tip k <$> f k v - go (Bin p m l r) = Bin p m <$> go l <*> go r -{-# INLINE traverseWithKey #-} - --- | /O(n)/. The function @'mapAccum'@ threads an accumulating --- argument through the map in ascending order of keys. --- --- > let f a b = (a ++ b, b ++ "X") --- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")]) - -mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) -mapAccum f = mapAccumWithKey (\a' _ x -> f a' x) - --- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating --- argument through the map in ascending order of keys. --- --- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X") --- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")]) - -mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) -mapAccumWithKey f a t - = mapAccumL f a t - --- | /O(n)/. The function @'mapAccumL'@ threads an accumulating --- argument through the map in ascending order of keys. -mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) -mapAccumL f a t - = case t of - Bin p m l r -> let (a1,l') = mapAccumL f a l - (a2,r') = mapAccumL f a1 r - in (a2,Bin p m l' r') - Tip k x -> let (a',x') = f a k x in (a',Tip k x') - Nil -> (a,Nil) - --- | /O(n)/. The function @'mapAccumR'@ threads an accumulating --- argument through the map in descending order of keys. -mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) -mapAccumRWithKey f a t - = case t of - Bin p m l r -> let (a1,r') = mapAccumRWithKey f a r - (a2,l') = mapAccumRWithKey f a1 l - in (a2,Bin p m l' r') - Tip k x -> let (a',x') = f a k x in (a',Tip k x') - Nil -> (a,Nil) - --- | /O(n*min(n,W))/. --- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@. --- --- The size of the result may be smaller if @f@ maps two or more distinct --- keys to the same new key. In this case the value at the greatest of the --- original keys is retained. --- --- > mapKeys (+ 1) (fromList [(5,"a"), (3,"b")]) == fromList [(4, "b"), (6, "a")] --- > mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c" --- > mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c" - -mapKeys :: (Key->Key) -> IntMap a -> IntMap a -mapKeys f = fromList . foldrWithKey (\k x xs -> (f k, x) : xs) [] - --- | /O(n*min(n,W))/. --- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@. --- --- The size of the result may be smaller if @f@ maps two or more distinct --- keys to the same new key. In this case the associated values will be --- combined using @c@. --- --- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab" --- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab" - -mapKeysWith :: (a -> a -> a) -> (Key->Key) -> IntMap a -> IntMap a -mapKeysWith c f = fromListWith c . foldrWithKey (\k x xs -> (f k, x) : xs) [] - --- | /O(n*min(n,W))/. --- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@ --- is strictly monotonic. --- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@. --- /The precondition is not checked./ --- Semi-formally, we have: --- --- > and [x < y ==> f x < f y | x <- ls, y <- ls] --- > ==> mapKeysMonotonic f s == mapKeys f s --- > where ls = keys s --- --- This means that @f@ maps distinct original keys to distinct resulting keys. --- This function has slightly better performance than 'mapKeys'. --- --- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")] - -mapKeysMonotonic :: (Key->Key) -> IntMap a -> IntMap a -mapKeysMonotonic f = fromDistinctAscList . foldrWithKey (\k x xs -> (f k, x) : xs) [] - -{-------------------------------------------------------------------- - Filter ---------------------------------------------------------------------} --- | /O(n)/. Filter all values that satisfy some predicate. --- --- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty --- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty - -filter :: (a -> Bool) -> IntMap a -> IntMap a -filter p m - = filterWithKey (\_ x -> p x) m - --- | /O(n)/. Filter all keys\/values that satisfy some predicate. --- --- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a -filterWithKey predicate t - = case t of - Bin p m l r - -> bin p m (filterWithKey predicate l) (filterWithKey predicate r) - Tip k x - | predicate k x -> t - | otherwise -> Nil - Nil -> Nil - --- | /O(n)/. Partition the map according to some predicate. The first --- map contains all elements that satisfy the predicate, the second all --- elements that fail the predicate. See also 'split'. --- --- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") --- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) --- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) - -partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a) -partition p m - = partitionWithKey (\_ x -> p x) m - --- | /O(n)/. Partition the map according to some predicate. The first --- map contains all elements that satisfy the predicate, the second all --- elements that fail the predicate. See also 'split'. --- --- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b") --- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) --- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) - -partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a) -partitionWithKey predicate0 t0 = toPair $ go predicate0 t0 - where - go predicate t - = case t of - Bin p m l r - -> let (l1 :*: l2) = go predicate l - (r1 :*: r2) = go predicate r - in bin p m l1 r1 :*: bin p m l2 r2 - Tip k x - | predicate k x -> (t :*: Nil) - | otherwise -> (Nil :*: t) - Nil -> (Nil :*: Nil) - --- | /O(n)/. Map values and collect the 'Just' results. --- --- > let f x = if x == "a" then Just "new a" else Nothing --- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a" - -mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b -mapMaybe f = mapMaybeWithKey (\_ x -> f x) - --- | /O(n)/. Map keys\/values and collect the 'Just' results. --- --- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing --- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3" - -mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b -mapMaybeWithKey f (Bin p m l r) - = bin p m (mapMaybeWithKey f l) (mapMaybeWithKey f r) -mapMaybeWithKey f (Tip k x) = case f k x of - Just y -> Tip k y - Nothing -> Nil -mapMaybeWithKey _ Nil = Nil - --- | /O(n)/. Map values and separate the 'Left' and 'Right' results. --- --- > let f a = if a < "c" then Left a else Right a --- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")]) --- > --- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) - -mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) -mapEither f m - = mapEitherWithKey (\_ x -> f x) m - --- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results. --- --- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a) --- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")]) --- > --- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")]) - -mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) -mapEitherWithKey f0 t0 = toPair $ go f0 t0 - where - go f (Bin p m l r) - = bin p m l1 r1 :*: bin p m l2 r2 - where - (l1 :*: l2) = go f l - (r1 :*: r2) = go f r - go f (Tip k x) = case f k x of - Left y -> (Tip k y :*: Nil) - Right z -> (Nil :*: Tip k z) - go _ Nil = (Nil :*: Nil) - --- | /O(min(n,W))/. The expression (@'split' k map@) is a pair @(map1,map2)@ --- where all keys in @map1@ are lower than @k@ and all keys in --- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@. --- --- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")]) --- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a") --- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") --- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty) --- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty) - -split :: Key -> IntMap a -> (IntMap a, IntMap a) -split k t = - case t of - Bin _ m l r - | m < 0 -> if k >= 0 -- handle negative numbers. - then case go k l of (lt :*: gt) -> let !lt' = union r lt - in (lt', gt) - else case go k r of (lt :*: gt) -> let !gt' = union gt l - in (lt, gt') - _ -> case go k t of - (lt :*: gt) -> (lt, gt) - where - go k' t'@(Bin p m l r) | nomatch k' p m = if k' > p then t' :*: Nil else Nil :*: t' - | zero k' m = case go k' l of (lt :*: gt) -> lt :*: union gt r - | otherwise = case go k' r of (lt :*: gt) -> union l lt :*: gt - go k' t'@(Tip ky _) | k' > ky = (t' :*: Nil) - | k' < ky = (Nil :*: t') - | otherwise = (Nil :*: Nil) - go _ Nil = (Nil :*: Nil) - --- | /O(min(n,W))/. Performs a 'split' but also returns whether the pivot --- key was found in the original map. --- --- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")]) --- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a") --- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a") --- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty) --- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty) - -splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a) -splitLookup k t = - case t of - Bin _ m l r - | m < 0 -> if k >= 0 -- handle negative numbers. - then case go k l of - (lt, fnd, gt) -> let !lt' = union r lt - in (lt', fnd, gt) - else case go k r of - (lt, fnd, gt) -> let !gt' = union gt l - in (lt, fnd, gt') - _ -> go k t - where - go k' t'@(Bin p m l r) - | nomatch k' p m = if k' > p then (t', Nothing, Nil) else (Nil, Nothing, t') - | zero k' m = case go k' l of - (lt, fnd, gt) -> let !gt' = union gt r in (lt, fnd, gt') - | otherwise = case go k' r of - (lt, fnd, gt) -> let !lt' = union l lt in (lt', fnd, gt) - go k' t'@(Tip ky y) | k' > ky = (t', Nothing, Nil) - | k' < ky = (Nil, Nothing, t') - | otherwise = (Nil, Just y, Nil) - go _ Nil = (Nil, Nothing, Nil) - -{-------------------------------------------------------------------- - Fold ---------------------------------------------------------------------} --- | /O(n)/. Fold the values in the map using the given right-associative --- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@. --- --- For example, --- --- > elems map = foldr (:) [] map --- --- > let f a len = len + (length a) --- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 -foldr :: (a -> b -> b) -> b -> IntMap a -> 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 _ x) = f x z' - 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' :: (a -> b -> b) -> b -> IntMap a -> 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 _ x) = f x z' - go z' (Bin _ _ l r) = go (go z' r) l -{-# INLINE foldr' #-} - --- | /O(n)/. Fold the values in the map using the given left-associative --- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@. --- --- For example, --- --- > elems = reverse . foldl (flip (:)) [] --- --- > let f len a = len + (length a) --- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 -foldl :: (a -> b -> a) -> a -> IntMap b -> 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 - go z' Nil = z' - go z' (Tip _ x) = f z' x - 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 -> b -> a) -> a -> IntMap b -> 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 - go !z' Nil = z' - go z' (Tip _ x) = f z' x - go z' (Bin _ _ l r) = go (go z' l) r -{-# INLINE foldl' #-} - --- | /O(n)/. Fold the keys and values in the map using the given right-associative --- binary operator, such that --- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@. --- --- For example, --- --- > keys map = foldrWithKey (\k x ks -> k:ks) [] map --- --- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" --- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)" -foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b -foldrWithKey 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 x) = f kx x z' - go z' (Bin _ _ l r) = go (go z' r) l -{-# INLINE foldrWithKey #-} - --- | /O(n)/. A strict version of 'foldrWithKey'. Each application of the operator is --- evaluated before using the result in the next application. This --- function is strict in the starting value. -foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b -foldrWithKey' 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 x) = f kx x z' - go z' (Bin _ _ l r) = go (go z' r) l -{-# INLINE foldrWithKey' #-} - --- | /O(n)/. Fold the keys and values in the map using the given left-associative --- binary operator, such that --- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@. --- --- For example, --- --- > keys = reverse . foldlWithKey (\ks k x -> k:ks) [] --- --- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" --- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)" -foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a -foldlWithKey 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 - go z' Nil = z' - go z' (Tip kx x) = f z' kx x - go z' (Bin _ _ l r) = go (go z' l) r -{-# INLINE foldlWithKey #-} - --- | /O(n)/. A strict version of 'foldlWithKey'. Each application of the operator is --- evaluated before using the result in the next application. This --- function is strict in the starting value. -foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a -foldlWithKey' 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 - go !z' Nil = z' - go z' (Tip kx x) = f z' kx x - go z' (Bin _ _ l r) = go (go z' l) r -{-# INLINE foldlWithKey' #-} - --- | /O(n)/. Fold the keys and values in the map using the given monoid, such that --- --- @'foldMapWithKey' f = 'Prelude.fold' . 'mapWithKey' f@ --- --- This can be an asymptotically faster than 'foldrWithKey' or 'foldlWithKey' for some monoids. -foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m -foldMapWithKey f = go - where - go Nil = mempty - go (Tip kx x) = f kx x - go (Bin _ _ l r) = go l `mappend` go r -{-# INLINE foldMapWithKey #-} - -{-------------------------------------------------------------------- - List variations ---------------------------------------------------------------------} --- | /O(n)/. --- Return all elements of the map in the ascending order of their keys. --- Subject to list fusion. --- --- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"] --- > elems empty == [] - -elems :: IntMap a -> [a] -elems = foldr (:) [] - --- | /O(n)/. Return all keys of the map in ascending order. Subject to list --- fusion. --- --- > keys (fromList [(5,"a"), (3,"b")]) == [3,5] --- > keys empty == [] - -keys :: IntMap a -> [Key] -keys = foldrWithKey (\k _ ks -> k : ks) [] - --- | /O(n)/. An alias for 'toAscList'. Returns all key\/value pairs in the --- map in ascending key order. Subject to list fusion. --- --- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] --- > assocs empty == [] - -assocs :: IntMap a -> [(Key,a)] -assocs = toAscList - --- | /O(n*min(n,W))/. The set of all keys of the map. --- --- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5] --- > keysSet empty == Data.IntSet.empty - -keysSet :: IntMap a -> IntSet.IntSet -keysSet Nil = IntSet.Nil -keysSet (Tip kx _) = IntSet.singleton kx -keysSet (Bin p m l r) - | m .&. IntSet.suffixBitMask == 0 = IntSet.Bin p m (keysSet l) (keysSet r) - | otherwise = IntSet.Tip (p .&. IntSet.prefixBitMask) (computeBm (computeBm 0 l) r) - where computeBm !acc (Bin _ _ l' r') = computeBm (computeBm acc l') r' - computeBm acc (Tip kx _) = acc .|. IntSet.bitmapOf kx - computeBm _ Nil = error "Data.IntSet.keysSet: Nil" - --- | /O(n)/. Build a map from a set of keys and a function which for each key --- computes its value. --- --- > fromSet (\k -> replicate k 'a') (Data.IntSet.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")] --- > fromSet undefined Data.IntSet.empty == empty - -fromSet :: (Key -> a) -> IntSet.IntSet -> IntMap a -fromSet _ IntSet.Nil = Nil -fromSet f (IntSet.Bin p m l r) = Bin p m (fromSet f l) (fromSet f r) -fromSet f (IntSet.Tip kx bm) = buildTree f kx bm (IntSet.suffixBitMask + 1) - where -- This is slightly complicated, as we to convert the dense - -- representation of IntSet into tree representation of IntMap. - -- - -- We are given a nonzero bit mask 'bmask' of 'bits' bits with prefix 'prefix'. - -- We split bmask into halves corresponding to left and right subtree. - -- If they are both nonempty, we create a Bin node, otherwise exactly - -- one of them is nonempty and we construct the IntMap from that half. - buildTree g !prefix !bmask bits = case bits of - 0 -> Tip prefix (g prefix) - _ -> case intFromNat ((natFromInt bits) `shiftRL` 1) of - bits2 | bmask .&. ((1 `shiftLL` bits2) - 1) == 0 -> - buildTree g (prefix + bits2) (bmask `shiftRL` bits2) bits2 - | (bmask `shiftRL` bits2) .&. ((1 `shiftLL` bits2) - 1) == 0 -> - buildTree g prefix bmask bits2 - | otherwise -> - Bin prefix bits2 (buildTree g prefix bmask bits2) (buildTree g (prefix + bits2) (bmask `shiftRL` bits2) bits2) - -{-------------------------------------------------------------------- - Lists ---------------------------------------------------------------------} -#if __GLASGOW_HASKELL__ >= 708 -instance GHCExts.IsList (IntMap a) where - type Item (IntMap a) = (Key,a) - fromList = fromList - toList = toList -#endif - --- | /O(n)/. Convert the map to a list of key\/value pairs. Subject to list --- fusion. --- --- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] --- > toList empty == [] - -toList :: IntMap a -> [(Key,a)] -toList = toAscList - --- | /O(n)/. Convert the map to a list of key\/value pairs where the --- keys are in ascending order. Subject to list fusion. --- --- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] - -toAscList :: IntMap a -> [(Key,a)] -toAscList = foldrWithKey (\k x xs -> (k,x):xs) [] - --- | /O(n)/. Convert the map to a list of key\/value pairs where the keys --- are in descending order. Subject to list fusion. --- --- > toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")] - -toDescList :: IntMap a -> [(Key,a)] -toDescList = foldlWithKey (\xs k x -> (k,x):xs) [] - --- List fusion for the list generating functions. -#if __GLASGOW_HASKELL__ --- The foldrFB and foldlFB are fold{r,l}WithKey equivalents, used for list fusion. --- They are important to convert unfused methods back, see mapFB in prelude. -foldrFB :: (Key -> a -> b -> b) -> b -> IntMap a -> b -foldrFB = foldrWithKey -{-# INLINE[0] foldrFB #-} -foldlFB :: (a -> Key -> b -> a) -> a -> IntMap b -> a -foldlFB = foldlWithKey -{-# INLINE[0] foldlFB #-} - --- Inline assocs and toList, so that we need to fuse only toAscList. -{-# INLINE assocs #-} -{-# INLINE toList #-} - --- The fusion is enabled up to phase 2 included. If it does not succeed, --- convert in phase 1 the expanded elems,keys,to{Asc,Desc}List calls back to --- elems,keys,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 elems,keys,to{Asc,Desc}List -- it was forbidden to --- inline it before phase 0, otherwise the fusion rules would not fire at all. -{-# NOINLINE[0] elems #-} -{-# NOINLINE[0] keys #-} -{-# NOINLINE[0] toAscList #-} -{-# NOINLINE[0] toDescList #-} -{-# RULES "IntMap.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-} -{-# RULES "IntMap.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-} -{-# RULES "IntMap.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-} -{-# RULES "IntMap.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-} -{-# RULES "IntMap.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-} -{-# RULES "IntMap.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-} -{-# RULES "IntMap.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-} -{-# RULES "IntMap.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-} -#endif - - --- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs. --- --- > fromList [] == empty --- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] --- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")] - -fromList :: [(Key,a)] -> IntMap a -fromList xs - = foldlStrict ins empty xs - where - ins t (k,x) = insert k x t - --- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'. --- --- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "ab"), (5, "cba")] --- > fromListWith (++) [] == empty - -fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a -fromListWith f xs - = fromListWithKey (\_ x y -> f x y) xs - --- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'. --- --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value --- > fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "3:a|b"), (5, "5:c|5:b|a")] --- > fromListWithKey f [] == empty - -fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a -fromListWithKey f xs - = foldlStrict ins empty xs - where - ins t (k,x) = insertWithKey f k x t - --- | /O(n)/. Build a map from a list of key\/value pairs where --- the keys are in ascending order. --- --- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] --- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")] - -fromAscList :: [(Key,a)] -> IntMap a -fromAscList xs - = fromAscListWithKey (\_ x _ -> x) xs - --- | /O(n)/. Build a map from a list of key\/value pairs where --- the keys are in ascending order, with a combining function on equal keys. --- /The precondition (input list is ascending) is not checked./ --- --- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] - -fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a -fromAscListWith f xs - = fromAscListWithKey (\_ x y -> f x y) xs - --- | /O(n)/. Build a map from a list of key\/value pairs where --- the keys are in ascending order, with a combining function on equal keys. --- /The precondition (input list is ascending) is not checked./ --- --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value --- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "5:b|a")] - -fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a -fromAscListWithKey _ [] = Nil -fromAscListWithKey f (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0) - where - -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] - combineEq z [] = [z] - combineEq z@(kz,zz) (x@(kx,xx):xs) - | kx==kz = let yy = f kx xx zz in combineEq (kx,yy) xs - | otherwise = z:combineEq x xs - --- | /O(n)/. Build a map from a list of key\/value pairs where --- the keys are in ascending order and all distinct. --- /The precondition (input list is strictly ascending) is not checked./ --- --- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] - -#if __GLASGOW_HASKELL__ -fromDistinctAscList :: forall a. [(Key,a)] -> IntMap a -#else -fromDistinctAscList :: [(Key,a)] -> IntMap a -#endif -fromDistinctAscList [] = Nil -fromDistinctAscList (z0 : zs0) = work z0 zs0 Nada - where - work (kx,vx) [] stk = finish kx (Tip kx vx) stk - work (kx,vx) (z@(kz,_):zs) stk = reduce z zs (branchMask kx kz) kx (Tip kx vx) stk - -#if __GLASGOW_HASKELL__ - reduce :: (Key,a) -> [(Key,a)] -> Mask -> Prefix -> IntMap a -> Stack a -> IntMap a -#endif - reduce z zs _ px tx Nada = work 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 z zs (Push px tx stk) - - finish _ t Nada = t - finish px tx (Push py ty stk) = finish p (link py ty px tx) stk - where m = branchMask px py - p = mask px m - -data Stack a = Push {-# UNPACK #-} !Prefix !(IntMap a) !(Stack a) | Nada - - -{-------------------------------------------------------------------- - Eq ---------------------------------------------------------------------} -instance Eq a => Eq (IntMap a) where - t1 == t2 = equal t1 t2 - t1 /= t2 = nequal t1 t2 - -equal :: Eq a => IntMap a -> IntMap a -> Bool -equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) - = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2) -equal (Tip kx x) (Tip ky y) - = (kx == ky) && (x==y) -equal Nil Nil = True -equal _ _ = False - -nequal :: Eq a => IntMap a -> IntMap a -> Bool -nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) - = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2) -nequal (Tip kx x) (Tip ky y) - = (kx /= ky) || (x/=y) -nequal Nil Nil = False -nequal _ _ = True - -{-------------------------------------------------------------------- - Ord ---------------------------------------------------------------------} - -instance Ord a => Ord (IntMap a) where - compare m1 m2 = compare (toList m1) (toList m2) - -{-------------------------------------------------------------------- - Functor ---------------------------------------------------------------------} - -instance Functor IntMap where - fmap = map - -#ifdef __GLASGOW_HASKELL__ - a <$ Bin p m l r = Bin p m (a <$ l) (a <$ r) - a <$ Tip k _ = Tip k a - _ <$ Nil = Nil -#endif - -{-------------------------------------------------------------------- - Show ---------------------------------------------------------------------} - -instance Show a => Show (IntMap a) where - showsPrec d m = showParen (d > 10) $ - showString "fromList " . shows (toList m) - -{-------------------------------------------------------------------- - Read ---------------------------------------------------------------------} -instance (Read e) => Read (IntMap e) 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 ---------------------------------------------------------------------} - -INSTANCE_TYPEABLE1(IntMap) - -{-------------------------------------------------------------------- - Helpers ---------------------------------------------------------------------} -{-------------------------------------------------------------------- - Link ---------------------------------------------------------------------} -link :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a -link 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 link #-} - -{-------------------------------------------------------------------- - @bin@ assures that we never have empty trees within a tree. ---------------------------------------------------------------------} -bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a -bin _ _ l Nil = l -bin _ _ Nil r = r -bin p m l r = Bin p m l r -{-# INLINE bin #-} - --- binCheckLeft only checks that the left subtree is non-empty -binCheckLeft :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a -binCheckLeft _ _ Nil r = r -binCheckLeft p m l r = Bin p m l r -{-# INLINE binCheckLeft #-} - --- binCheckRight only checks that the right subtree is non-empty -binCheckRight :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a -binCheckRight _ _ l Nil = l -binCheckRight p m l r = Bin p m l r -{-# INLINE binCheckRight #-} - -{-------------------------------------------------------------------- - Endian independent bit twiddling ---------------------------------------------------------------------} -zero :: Key -> Mask -> Bool -zero i m - = (natFromInt i) .&. (natFromInt m) == 0 -{-# INLINE zero #-} - -nomatch,match :: Key -> Prefix -> Mask -> Bool -nomatch i p m - = (mask i m) /= p -{-# INLINE nomatch #-} - -match i p m - = (mask i m) == p -{-# INLINE match #-} - -mask :: Key -> 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 #-} - -{-------------------------------------------------------------------- - Utilities ---------------------------------------------------------------------} - --- | /O(1)/. Decompose a map into pieces based on the structure of the underlying --- tree. This function is useful for consuming a map in parallel. --- --- No guarantee is made as to the sizes of the pieces; an internal, but --- deterministic process determines this. However, it is guaranteed that the --- pieces returned will be in ascending order (all elements in the first submap --- less than all elements in the second, and so on). --- --- Examples: --- --- > splitRoot (fromList (zip [1..6::Int] ['a'..])) == --- > [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d'),(5,'e'),(6,'f')]] --- --- > splitRoot empty == [] --- --- Note that the current implementation does not return more than two submaps, --- but you should not depend on this behaviour because it can change in the --- future without notice. -splitRoot :: IntMap a -> [IntMap a] -splitRoot orig = - case orig of - Nil -> [] - x@(Tip _ _) -> [x] - Bin _ m l r | m < 0 -> [r, l] - | otherwise -> [l, r] -{-# INLINE splitRoot #-} - - -{-------------------------------------------------------------------- - Debugging ---------------------------------------------------------------------} --- | /O(n)/. Show the tree that implements the map. The tree is shown --- in a compressed, hanging format. -showTree :: Show a => IntMap a -> String -showTree s - = showTreeWith True False s - - -{- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows - the tree that implements the map. 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 :: Show a => Bool -> Bool -> IntMap a -> String -showTreeWith hang wide t - | hang = (showsTreeHang wide [] t) "" - | otherwise = (showsTree wide [] [] t) "" - -showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> 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 k x - -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n" - Nil -> showsBars lbars . showString "|\n" - -showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> 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 k x - -> showsBars bars . showString " " . shows k . showString ":=" . shows x . 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 - -node :: String -node = "+--" - -withBar, withEmpty :: [String] -> [String] -withBar bars = "| ":bars -withEmpty bars = " ":bars diff --git a/Data/IntMap/Internal.hs b/Data/IntMap/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/IntMap/Internal.hs @@ -0,0 +1,3243 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE MagicHash, DeriveDataTypeable, StandaloneDeriving #-} +{-# LANGUAGE ScopedTypeVariables #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Trustworthy #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE TypeFamilies #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.IntMap.Internal +-- Copyright : (c) Daan Leijen 2002 +-- (c) Andriy Palamarchuk 2008 +-- (c) wren romano 2016 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. +-- +-- = Description +-- +-- This defines the data structures and core (hidden) manipulations +-- on representations. +----------------------------------------------------------------------------- + +-- [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 IntMap 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.IntMap.Internal ( + -- * Map type + IntMap(..), Key -- instance Eq,Show + + -- * Operators + , (!), (\\) + + -- * Query + , null + , size + , member + , notMember + , lookup + , findWithDefault + , lookupLT + , lookupGT + , lookupLE + , lookupGE + + -- * Construction + , empty + , singleton + + -- ** Insertion + , insert + , insertWith + , insertWithKey + , insertLookupWithKey + + -- ** Delete\/Update + , delete + , adjust + , adjustWithKey + , update + , updateWithKey + , updateLookupWithKey + , alter + , alterF + + -- * Combine + + -- ** Union + , union + , unionWith + , unionWithKey + , unions + , unionsWith + + -- ** Difference + , difference + , differenceWith + , differenceWithKey + + -- ** Intersection + , intersection + , intersectionWith + , intersectionWithKey + + -- ** General combining function + , SimpleWhenMissing + , SimpleWhenMatched + , runWhenMatched + , runWhenMissing + , merge + -- *** @WhenMatched@ tactics + , zipWithMaybeMatched + , zipWithMatched + -- *** @WhenMissing@ tactics + , mapMaybeMissing + , dropMissing + , preserveMissing + , mapMissing + , filterMissing + + -- ** Applicative general combining function + , WhenMissing (..) + , WhenMatched (..) + , mergeA + -- *** @WhenMatched@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , zipWithMaybeAMatched + , zipWithAMatched + -- *** @WhenMissing@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , traverseMaybeMissing + , traverseMissing + , filterAMissing + + -- ** Deprecated general combining function + , mergeWithKey + , mergeWithKey' + + -- * Traversal + -- ** Map + , map + , mapWithKey + , traverseWithKey + , mapAccum + , mapAccumWithKey + , mapAccumRWithKey + , mapKeys + , mapKeysWith + , mapKeysMonotonic + + -- * Folds + , foldr + , foldl + , foldrWithKey + , foldlWithKey + , foldMapWithKey + + -- ** Strict folds + , foldr' + , foldl' + , foldrWithKey' + , foldlWithKey' + + -- * Conversion + , elems + , keys + , assocs + , keysSet + , fromSet + + -- ** Lists + , toList + , fromList + , fromListWith + , fromListWithKey + + -- ** Ordered lists + , toAscList + , toDescList + , fromAscList + , fromAscListWith + , fromAscListWithKey + , fromDistinctAscList + + -- * Filter + , filter + , filterWithKey + , restrictKeys + , withoutKeys + , partition + , partitionWithKey + + , mapMaybe + , mapMaybeWithKey + , mapEither + , mapEitherWithKey + + , split + , splitLookup + , splitRoot + + -- * Submap + , isSubmapOf, isSubmapOfBy + , isProperSubmapOf, isProperSubmapOfBy + + -- * Min\/Max + , findMin + , findMax + , deleteMin + , deleteMax + , deleteFindMin + , deleteFindMax + , updateMin + , updateMax + , updateMinWithKey + , updateMaxWithKey + , minView + , maxView + , minViewWithKey + , maxViewWithKey + + -- * Debugging + , showTree + , showTreeWith + + -- * Internal types + , Mask, Prefix, Nat + + -- * Utility + , natFromInt + , intFromNat + , link + , bin + , binCheckLeft + , binCheckRight + , zero + , nomatch + , match + , mask + , maskW + , shorter + , branchMask + , highestBitMask + + -- * Used by "IntMap.Merge.Lazy" and "IntMap.Merge.Strict" + , mapWhenMissing + , mapWhenMatched + , lmapWhenMissing + , contramapFirstWhenMatched + , contramapSecondWhenMatched + , mapGentlyWhenMissing + , mapGentlyWhenMatched + ) where + +#if MIN_VERSION_base(4,8,0) +import Data.Functor.Identity (Identity (..)) +#else +import Control.Applicative (Applicative(pure, (<*>)), (<$>)) +import Data.Monoid (Monoid(..)) +import Data.Traversable (Traversable(traverse)) +import Data.Word (Word) +#endif +#if MIN_VERSION_base(4,9,0) +import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) +import Data.Functor.Classes +#endif + +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (liftM) +import Data.Bits +import qualified Data.Foldable as Foldable +import Data.Maybe (fromMaybe) +import Data.Typeable +import Prelude hiding (lookup, map, filter, foldr, foldl, null) + +import Data.IntSet.Internal (Key) +import qualified Data.IntSet.Internal as IntSet +import Utils.Containers.Internal.BitUtil +import Utils.Containers.Internal.StrictFold +import Utils.Containers.Internal.StrictPair + +#if __GLASGOW_HASKELL__ +import Data.Data (Data(..), Constr, mkConstr, constrIndex, Fixity(Prefix), + DataType, mkDataType) +import GHC.Exts (build) +#if !MIN_VERSION_base(4,8,0) +import Data.Functor ((<$)) +#endif +#if __GLASGOW_HASKELL__ >= 708 +import qualified GHC.Exts as GHCExts +#endif +import Text.Read +#endif +import qualified Control.Category as Category +#if __GLASGOW_HASKELL__ >= 709 +import Data.Coerce +#endif + + +-- A "Nat" is a natural machine word (an unsigned Int) +type Nat = Word + +natFromInt :: Key -> Nat +natFromInt = fromIntegral +{-# INLINE natFromInt #-} + +intFromNat :: Nat -> Key +intFromNat = fromIntegral +{-# INLINE intFromNat #-} + +{-------------------------------------------------------------------- + Types +--------------------------------------------------------------------} + + +-- | A map of integers to values @a@. + +-- See Note: Order of constructors +data IntMap a = Bin {-# UNPACK #-} !Prefix + {-# UNPACK #-} !Mask + !(IntMap a) + !(IntMap a) + | Tip {-# UNPACK #-} !Key a + | Nil + +type Prefix = Int +type Mask = Int + +{-------------------------------------------------------------------- + Operators +--------------------------------------------------------------------} + +-- | /O(min(n,W))/. Find the value at a key. +-- Calls 'error' when the element can not be found. +-- +-- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map +-- > fromList [(5,'a'), (3,'b')] ! 5 == 'a' + +(!) :: IntMap a -> Key -> a +(!) m k = find k m + +-- | Same as 'difference'. +(\\) :: IntMap a -> IntMap b -> IntMap a +m1 \\ m2 = difference m1 m2 + +infixl 9 \\{-This comment teaches CPP correct behaviour -} + +{-------------------------------------------------------------------- + Types +--------------------------------------------------------------------} + +instance Monoid (IntMap a) where + mempty = empty + mconcat = unions +#if !(MIN_VERSION_base(4,9,0)) + mappend = union +#else + mappend = (<>) + +instance Semigroup (IntMap a) where + (<>) = union + stimes = stimesIdempotentMonoid +#endif + +instance Foldable.Foldable IntMap where + fold = go + where go Nil = mempty + go (Tip _ v) = v + go (Bin _ _ l r) = go l `mappend` go r + {-# INLINABLE fold #-} + foldr = foldr + {-# INLINE foldr #-} + foldl = foldl + {-# INLINE foldl #-} + foldMap f t = go t + where go Nil = mempty + go (Tip _ v) = f v + go (Bin _ _ l r) = go l `mappend` go r + {-# INLINE foldMap #-} + +#if MIN_VERSION_base(4,6,0) + foldl' = foldl' + {-# INLINE foldl' #-} + foldr' = foldr' + {-# INLINE foldr' #-} +#endif +#if MIN_VERSION_base(4,8,0) + length = size + {-# INLINE length #-} + null = null + {-# INLINE null #-} + toList = elems -- NB: Foldable.toList /= IntMap.toList + {-# INLINE toList #-} + elem = go + where go !_ Nil = False + go x (Tip _ y) = x == y + go x (Bin _ _ l r) = go x l || go x r + {-# INLINABLE elem #-} + maximum = start + where start Nil = error "IntMap.Foldable.maximum: called with empty map" + start (Tip _ y) = y + start (Bin _ _ l r) = go (start l) r + + go !m Nil = m + go m (Tip _ y) = max m y + go m (Bin _ _ l r) = go (go m l) r + {-# INLINABLE maximum #-} + minimum = start + where start Nil = error "IntMap.Foldable.minimum: called with empty map" + start (Tip _ y) = y + start (Bin _ _ l r) = go (start l) r + + go !m Nil = m + go m (Tip _ y) = min m y + go m (Bin _ _ l r) = go (go m l) r + {-# INLINABLE minimum #-} + sum = foldl' (+) 0 + {-# INLINABLE sum #-} + product = foldl' (*) 1 + {-# INLINABLE product #-} +#endif + +instance Traversable IntMap where + traverse f = traverseWithKey (\_ -> f) + {-# INLINE traverse #-} + +instance NFData a => NFData (IntMap a) where + rnf Nil = () + rnf (Tip _ v) = rnf v + rnf (Bin _ _ l r) = rnf l `seq` rnf r + +#if __GLASGOW_HASKELL__ + +{-------------------------------------------------------------------- + A Data instance +--------------------------------------------------------------------} + +-- This instance preserves data abstraction at the cost of inefficiency. +-- We provide limited reflection services for the sake of data abstraction. + +instance Data a => Data (IntMap a) where + gfoldl f z im = z fromList `f` (toList im) + toConstr _ = fromListConstr + gunfold k z c = case constrIndex c of + 1 -> k (z fromList) + _ -> error "gunfold" + dataTypeOf _ = intMapDataType + dataCast1 f = gcast1 f + +fromListConstr :: Constr +fromListConstr = mkConstr intMapDataType "fromList" [] Prefix + +intMapDataType :: DataType +intMapDataType = mkDataType "Data.IntMap.Internal.IntMap" [fromListConstr] + +#endif + +{-------------------------------------------------------------------- + Query +--------------------------------------------------------------------} +-- | /O(1)/. Is the map empty? +-- +-- > Data.IntMap.null (empty) == True +-- > Data.IntMap.null (singleton 1 'a') == False + +null :: IntMap a -> Bool +null Nil = True +null _ = False +{-# INLINE null #-} + +-- | /O(n)/. Number of elements in the map. +-- +-- > size empty == 0 +-- > size (singleton 1 'a') == 1 +-- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3 +size :: IntMap a -> Int +size (Bin _ _ l r) = size l + size r +size (Tip _ _) = 1 +size Nil = 0 + +-- | /O(min(n,W))/. Is the key a member of the map? +-- +-- > member 5 (fromList [(5,'a'), (3,'b')]) == True +-- > member 1 (fromList [(5,'a'), (3,'b')]) == False + +-- See Note: Local 'go' functions and capturing] +member :: Key -> IntMap a -> Bool +member !k = go + where + go (Bin p m l r) | nomatch k p m = False + | zero k m = go l + | otherwise = go r + go (Tip kx _) = k == kx + go Nil = False + +-- | /O(min(n,W))/. Is the key not a member of the map? +-- +-- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False +-- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True + +notMember :: Key -> IntMap a -> Bool +notMember k m = not $ member k m + +-- | /O(min(n,W))/. Lookup the value at a key in the map. See also 'Data.Map.lookup'. + +-- See Note: Local 'go' functions and capturing] +lookup :: Key -> IntMap a -> Maybe a +lookup !k = go + where + go (Bin p m l r) | nomatch k p m = Nothing + | zero k m = go l + | otherwise = go r + go (Tip kx x) | k == kx = Just x + | otherwise = Nothing + go Nil = Nothing + + +-- See Note: Local 'go' functions and capturing] +find :: Key -> IntMap a -> a +find !k = go + where + go (Bin p m l r) | nomatch k p m = not_found + | zero k m = go l + | otherwise = go r + go (Tip kx x) | k == kx = x + | otherwise = not_found + go Nil = not_found + + not_found = error ("IntMap.!: key " ++ show k ++ " is not an element of the map") + +-- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@ +-- returns the value at key @k@ or returns @def@ when the key is not an +-- element of the map. +-- +-- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' +-- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' + +-- See Note: Local 'go' functions and capturing] +findWithDefault :: a -> Key -> IntMap a -> a +findWithDefault def !k = go + where + go (Bin p m l r) | nomatch k p m = def + | zero k m = go l + | otherwise = go r + go (Tip kx x) | k == kx = x + | otherwise = def + go Nil = def + +-- | /O(log n)/. Find largest key smaller than the given one and return the +-- corresponding (key, value) pair. +-- +-- > lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing +-- > lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') + +-- See Note: Local 'go' functions and capturing. +lookupLT :: Key -> IntMap a -> Maybe (Key, a) +lookupLT !k t = case t of + Bin _ m l r | m < 0 -> if k >= 0 then go r l else go Nil r + _ -> go Nil t + where + go def (Bin p m l r) + | nomatch k p m = if k < p then unsafeFindMax def else unsafeFindMax r + | zero k m = go def l + | otherwise = go l r + go def (Tip ky y) + | k <= ky = unsafeFindMax def + | otherwise = Just (ky, y) + go def Nil = unsafeFindMax def + +-- | /O(log n)/. Find smallest key greater than the given one and return the +-- corresponding (key, value) pair. +-- +-- > lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') +-- > lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing + +-- See Note: Local 'go' functions and capturing. +lookupGT :: Key -> IntMap a -> Maybe (Key, a) +lookupGT !k t = case t of + Bin _ m l r | m < 0 -> if k >= 0 then go Nil l else go l r + _ -> go Nil t + where + go def (Bin p m l r) + | nomatch k p m = if k < p then unsafeFindMin l else unsafeFindMin def + | zero k m = go r l + | otherwise = go def r + go def (Tip ky y) + | k >= ky = unsafeFindMin def + | otherwise = Just (ky, y) + go def Nil = unsafeFindMin def + +-- | /O(log n)/. Find largest key smaller or equal to the given one and return +-- the corresponding (key, value) pair. +-- +-- > lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing +-- > lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') +-- > lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') + +-- See Note: Local 'go' functions and capturing. +lookupLE :: Key -> IntMap a -> Maybe (Key, a) +lookupLE !k t = case t of + Bin _ m l r | m < 0 -> if k >= 0 then go r l else go Nil r + _ -> go Nil t + where + go def (Bin p m l r) + | nomatch k p m = if k < p then unsafeFindMax def else unsafeFindMax r + | zero k m = go def l + | otherwise = go l r + go def (Tip ky y) + | k < ky = unsafeFindMax def + | otherwise = Just (ky, y) + go def Nil = unsafeFindMax def + +-- | /O(log n)/. Find smallest key greater or equal to the given one and return +-- the corresponding (key, value) pair. +-- +-- > lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') +-- > lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') +-- > lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing + +-- See Note: Local 'go' functions and capturing. +lookupGE :: Key -> IntMap a -> Maybe (Key, a) +lookupGE !k t = case t of + Bin _ m l r | m < 0 -> if k >= 0 then go Nil l else go l r + _ -> go Nil t + where + go def (Bin p m l r) + | nomatch k p m = if k < p then unsafeFindMin l else unsafeFindMin def + | zero k m = go r l + | otherwise = go def r + go def (Tip ky y) + | k > ky = unsafeFindMin def + | otherwise = Just (ky, y) + 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 :: IntMap a -> Maybe (Key, a) +unsafeFindMin Nil = Nothing +unsafeFindMin (Tip ky y) = Just (ky, y) +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 :: IntMap a -> Maybe (Key, a) +unsafeFindMax Nil = Nothing +unsafeFindMax (Tip ky y) = Just (ky, y) +unsafeFindMax (Bin _ _ _ r) = unsafeFindMax r + +{-------------------------------------------------------------------- + Construction +--------------------------------------------------------------------} +-- | /O(1)/. The empty map. +-- +-- > empty == fromList [] +-- > size empty == 0 + +empty :: IntMap a +empty + = Nil +{-# INLINE empty #-} + +-- | /O(1)/. A map of one element. +-- +-- > singleton 1 'a' == fromList [(1, 'a')] +-- > size (singleton 1 'a') == 1 + +singleton :: Key -> a -> IntMap a +singleton k x + = Tip k x +{-# INLINE singleton #-} + +{-------------------------------------------------------------------- + Insert +--------------------------------------------------------------------} +-- | /O(min(n,W))/. Insert a new key\/value pair in the map. +-- If the key is already present in the map, the associated value is +-- replaced with the supplied value, i.e. 'insert' is equivalent to +-- @'insertWith' 'const'@. +-- +-- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')] +-- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] +-- > insert 5 'x' empty == singleton 5 'x' + +insert :: Key -> a -> IntMap a -> IntMap a +insert !k x t@(Bin p m l r) + | nomatch k p m = link k (Tip k x) p t + | zero k m = Bin p m (insert k x l) r + | otherwise = Bin p m l (insert k x r) +insert k x t@(Tip ky _) + | k==ky = Tip k x + | otherwise = link k (Tip k x) ky t +insert k x Nil = Tip k x + +-- right-biased insertion, used by 'union' +-- | /O(min(n,W))/. Insert with a combining function. +-- @'insertWith' f key value mp@ +-- will insert the pair (key, value) into @mp@ if key does +-- not exist in the map. If the key does exist, the function will +-- insert @f new_value old_value@. +-- +-- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] +-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] +-- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx" + +insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a +insertWith f k x t + = insertWithKey (\_ x' y' -> f x' y') k x t + +-- | /O(min(n,W))/. Insert with a combining function. +-- @'insertWithKey' f key value mp@ +-- will insert the pair (key, value) into @mp@ if key does +-- not exist in the map. If the key does exist, the function will +-- insert @f key new_value old_value@. +-- +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value +-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] +-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] +-- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx" + +insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a +insertWithKey f !k x t@(Bin p m l r) + | nomatch k p m = link k (Tip k x) p t + | zero k m = Bin p m (insertWithKey f k x l) r + | otherwise = Bin p m l (insertWithKey f k x r) +insertWithKey f k x t@(Tip ky y) + | k == ky = Tip k (f k x y) + | otherwise = link k (Tip k x) ky t +insertWithKey _ k x Nil = Tip k x + +-- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@) +-- is a pair where the first element is equal to (@'lookup' k map@) +-- and the second element equal to (@'insertWithKey' f k x map@). +-- +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value +-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) +-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) +-- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx") +-- +-- This is how to define @insertLookup@ using @insertLookupWithKey@: +-- +-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t +-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) +-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) + +insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a) +insertLookupWithKey f !k x t@(Bin p m l r) + | nomatch k p m = (Nothing,link k (Tip k x) p t) + | zero k m = let (found,l') = insertLookupWithKey f k x l + in (found,Bin p m l' r) + | otherwise = let (found,r') = insertLookupWithKey f k x r + in (found,Bin p m l r') +insertLookupWithKey f k x t@(Tip ky y) + | k == ky = (Just y,Tip k (f k x y)) + | otherwise = (Nothing,link k (Tip k x) ky t) +insertLookupWithKey _ k x Nil = (Nothing,Tip k x) + + +{-------------------------------------------------------------------- + Deletion +--------------------------------------------------------------------} +-- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not +-- a member of the map, the original map is returned. +-- +-- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > delete 5 empty == empty + +delete :: Key -> IntMap a -> IntMap a +delete !k t@(Bin p m l r) + | nomatch k p m = t + | zero k m = binCheckLeft p m (delete k l) r + | otherwise = binCheckRight p m l (delete k r) +delete k t@(Tip ky _) + | k == ky = Nil + | otherwise = t +delete _k Nil = Nil + +-- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not +-- a member of the map, the original map is returned. +-- +-- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] +-- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > adjust ("new " ++) 7 empty == empty + +adjust :: (a -> a) -> Key -> IntMap a -> IntMap a +adjust f k m + = adjustWithKey (\_ x -> f x) k m + +-- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not +-- a member of the map, the original map is returned. +-- +-- > let f key x = (show key) ++ ":new " ++ x +-- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] +-- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > adjustWithKey f 7 empty == empty + +adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a +adjustWithKey f !k t@(Bin p m l r) + | nomatch k p m = t + | zero k m = Bin p m (adjustWithKey f k l) r + | otherwise = Bin p m l (adjustWithKey f k r) +adjustWithKey f k t@(Tip ky y) + | k == ky = Tip ky (f k y) + | otherwise = t +adjustWithKey _ _ Nil = Nil + + +-- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@ +-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. +-- +-- > let f x = if x == "a" then Just "new a" else Nothing +-- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] +-- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a +update f + = updateWithKey (\_ x -> f x) + +-- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@ +-- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. +-- +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing +-- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] +-- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a +updateWithKey f !k t@(Bin p m l r) + | nomatch k p m = t + | zero k m = binCheckLeft p m (updateWithKey f k l) r + | otherwise = binCheckRight p m l (updateWithKey f k r) +updateWithKey f k t@(Tip ky y) + | k == ky = case (f k y) of + Just y' -> Tip ky y' + Nothing -> Nil + | otherwise = t +updateWithKey _ _ Nil = Nil + +-- | /O(min(n,W))/. Lookup and update. +-- The function returns original value, if it is updated. +-- This is different behavior than 'Data.Map.updateLookupWithKey'. +-- Returns the original key value if the map entry is deleted. +-- +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing +-- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")]) +-- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) +-- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a") + +updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a) +updateLookupWithKey f !k t@(Bin p m l r) + | nomatch k p m = (Nothing,t) + | zero k m = let !(found,l') = updateLookupWithKey f k l + in (found,binCheckLeft p m l' r) + | otherwise = let !(found,r') = updateLookupWithKey f k r + in (found,binCheckRight p m l r') +updateLookupWithKey f k t@(Tip ky y) + | k==ky = case (f k y) of + Just y' -> (Just y,Tip ky y') + Nothing -> (Just y,Nil) + | otherwise = (Nothing,t) +updateLookupWithKey _ _ Nil = (Nothing,Nil) + + + +-- | /O(min(n,W))/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof. +-- 'alter' can be used to insert, delete, or update a value in an 'IntMap'. +-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@. +alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a +alter f !k t@(Bin p m l r) + | nomatch k p m = case f Nothing of + Nothing -> t + Just x -> link k (Tip k x) p t + | zero k m = binCheckLeft p m (alter f k l) r + | otherwise = binCheckRight p m l (alter f k r) +alter f k t@(Tip ky y) + | k==ky = case f (Just y) of + Just x -> Tip ky x + Nothing -> Nil + | otherwise = case f Nothing of + Just x -> link k (Tip k x) ky t + Nothing -> Tip ky y +alter f k Nil = case f Nothing of + Just x -> Tip k x + Nothing -> Nil + +-- | /O(log n)/. The expression (@'alterF' f k map@) alters the value @x@ at +-- @k@, or absence thereof. 'alterF' can be used to inspect, insert, delete, +-- or update a value in an 'IntMap'. In short : @'lookup' k <$> 'alterF' f k m = f +-- ('lookup' k m)@. +-- +-- Example: +-- +-- @ +-- interactiveAlter :: Int -> IntMap String -> IO (IntMap String) +-- interactiveAlter k m = alterF f k m where +-- f Nothing -> do +-- putStrLn $ show k ++ +-- " was not found in the map. Would you like to add it?" +-- getUserResponse1 :: IO (Maybe String) +-- f (Just old) -> do +-- putStrLn "The key is currently bound to " ++ show old ++ +-- ". Would you like to change or delete it?" +-- getUserresponse2 :: IO (Maybe String) +-- @ +-- +-- 'alterF' is the most general operation for working with an individual +-- key that may or may not be in a given map. +-- +-- Note: 'alterF' is a flipped version of the 'at' combinator from +-- 'Control.Lens.At'. +-- +-- @since 0.5.8 + +alterF :: Functor f + => (Maybe a -> f (Maybe a)) -> Key -> IntMap a -> f (IntMap a) +-- This implementation was stolen from 'Control.Lens.At'. +alterF f k m = (<$> f mv) $ \fres -> + case fres of + Nothing -> maybe m (const (delete k m)) mv + Just v' -> insert k v' m + where mv = lookup k m + +{-------------------------------------------------------------------- + Union +--------------------------------------------------------------------} +-- | The union of a list of maps. +-- +-- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] +-- > == fromList [(3, "b"), (5, "a"), (7, "C")] +-- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])] +-- > == fromList [(3, "B3"), (5, "A3"), (7, "C")] + +unions :: [IntMap a] -> IntMap a +unions xs + = foldlStrict union empty xs + +-- | The union of a list of maps, with a combining operation. +-- +-- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] +-- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")] + +unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a +unionsWith f ts + = foldlStrict (unionWith f) empty ts + +-- | /O(n+m)/. The (left-biased) union of two maps. +-- It prefers the first map when duplicate keys are encountered, +-- i.e. (@'union' == 'unionWith' 'const'@). +-- +-- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")] + +union :: IntMap a -> IntMap a -> IntMap a +union m1 m2 + = mergeWithKey' Bin const id id m1 m2 + +-- | /O(n+m)/. The union with a combining function. +-- +-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")] + +unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a +unionWith f m1 m2 + = unionWithKey (\_ x y -> f x y) m1 m2 + +-- | /O(n+m)/. The union with a combining function. +-- +-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value +-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")] + +unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a +unionWithKey f m1 m2 + = mergeWithKey' Bin (\(Tip k1 x1) (Tip _k2 x2) -> Tip k1 (f k1 x1 x2)) id id m1 m2 + +{-------------------------------------------------------------------- + Difference +--------------------------------------------------------------------} +-- | /O(n+m)/. Difference between two maps (based on keys). +-- +-- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b" + +difference :: IntMap a -> IntMap b -> IntMap a +difference m1 m2 + = mergeWithKey (\_ _ _ -> Nothing) id (const Nil) m1 m2 + +-- | /O(n+m)/. Difference with a combining function. +-- +-- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing +-- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")]) +-- > == singleton 3 "b:B" + +differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a +differenceWith f m1 m2 + = differenceWithKey (\_ x y -> f x y) m1 m2 + +-- | /O(n+m)/. Difference with a combining function. When two equal keys are +-- encountered, the combining function is applied to the key and both values. +-- If it returns 'Nothing', the element is discarded (proper set difference). +-- If it returns (@'Just' y@), the element is updated with a new value @y@. +-- +-- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing +-- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")]) +-- > == singleton 3 "3:b|B" + +differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a +differenceWithKey f m1 m2 + = mergeWithKey f id (const Nil) m1 m2 + +-- | Remove all the keys in a given set from a map. +-- +-- @ +-- m `withoutKeys` s = 'filterWithKey' (\k _ -> k `'IntSet.notMember'` s) m +-- @ +-- +-- @since 0.5.8 +withoutKeys :: IntMap a -> IntSet.IntSet -> IntMap a +withoutKeys = go + where + go t1@(Bin p1 m1 l1 r1) t2@(IntSet.Bin p2 m2 l2 r2) + | shorter m1 m2 = merge1 + | shorter m2 m1 = merge2 + | p1 == p2 = bin p1 m1 (go l1 l2) (go r1 r2) + | otherwise = t1 + where + merge1 | nomatch p2 p1 m1 = t1 + | zero p2 m1 = binCheckLeft p1 m1 (go l1 t2) r1 + | otherwise = binCheckRight p1 m1 l1 (go r1 t2) + merge2 | nomatch p1 p2 m2 = t1 + | zero p1 m2 = bin p2 m2 (go t1 l2) Nil + | otherwise = bin p2 m2 Nil (go t1 r2) + + go t1'@(Bin _ _ _ _) t2'@(IntSet.Tip k2' _) = merge0 t2' k2' t1' + where + merge0 t2 k2 t1@(Bin p1 m1 l1 r1) + | nomatch k2 p1 m1 = t1 + | zero k2 m1 = binCheckLeft p1 m1 (merge0 t2 k2 l1) r1 + | otherwise = binCheckRight p1 m1 l1 (merge0 t2 k2 r1) + merge0 _ k2 t1@(Tip k1 _) + | k1 == k2 = Nil + | otherwise = t1 + merge0 _ _ Nil = Nil + + go t1@(Bin _ _ _ _) IntSet.Nil = t1 + + go t1'@(Tip k1' _) t2' = merge0 t1' k1' t2' + where + merge0 t1 k1 (IntSet.Bin p2 m2 l2 r2) + | nomatch k1 p2 m2 = t1 + | zero k1 m2 = bin p2 m2 (merge0 t1 k1 l2) Nil + | otherwise = bin p2 m2 Nil (merge0 t1 k1 r2) + merge0 t1 k1 (IntSet.Tip k2 _) + | k1 == k2 = Nil + | otherwise = t1 + merge0 t1 _ IntSet.Nil = t1 + + go Nil _ = Nil + + +{-------------------------------------------------------------------- + Intersection +--------------------------------------------------------------------} +-- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys). +-- +-- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a" + +intersection :: IntMap a -> IntMap b -> IntMap a +intersection m1 m2 + = mergeWithKey' bin const (const Nil) (const Nil) m1 m2 + +-- | /O(n+m)/. The restriction of a map to the keys in a set. +-- +-- @ +-- m `restrictKeys` s = 'filterWithKey' (\k _ -> k `'IntSet.member'` s) m +-- @ +-- +-- @since 0.5.8 +restrictKeys :: IntMap a -> IntSet.IntSet -> IntMap a +restrictKeys = go + where + go t1@(Bin p1 m1 l1 r1) t2@(IntSet.Bin p2 m2 l2 r2) + | shorter m1 m2 = merge1 + | shorter m2 m1 = merge2 + | p1 == p2 = bin p1 m1 (go l1 l2) (go r1 r2) + | otherwise = Nil + where + merge1 | nomatch p2 p1 m1 = Nil + | zero p2 m1 = bin p1 m1 (go l1 t2) Nil + | otherwise = bin p1 m1 Nil (go r1 t2) + merge2 | nomatch p1 p2 m2 = Nil + | zero p1 m2 = bin p2 m2 (go t1 l2) Nil + | otherwise = bin p2 m2 Nil (go t1 r2) + + go t1'@(Bin _ _ _ _) t2'@(IntSet.Tip k2' _) = merge0 t2' k2' t1' + where + merge0 t2 k2 (Bin p1 m1 l1 r1) + | nomatch k2 p1 m1 = Nil + | zero k2 m1 = bin p1 m1 (merge0 t2 k2 l1) Nil + | otherwise = bin p1 m1 Nil (merge0 t2 k2 r1) + merge0 _ k2 t1@(Tip k1 _) + | k1 == k2 = t1 + | otherwise = Nil + merge0 _ _ Nil = Nil + + go (Bin _ _ _ _) IntSet.Nil = Nil + + go t1'@(Tip k1' _) t2' = merge0 t1' k1' t2' + where + merge0 t1 k1 (IntSet.Bin p2 m2 l2 r2) + | nomatch k1 p2 m2 = Nil + | zero k1 m2 = bin p2 m2 (merge0 t1 k1 l2) Nil + | otherwise = bin p2 m2 Nil (merge0 t1 k1 r2) + merge0 t1 k1 (IntSet.Tip k2 _) + | k1 == k2 = t1 + | otherwise = Nil + merge0 _ _ IntSet.Nil = Nil + + go Nil _ = Nil + +-- | /O(n+m)/. The intersection with a combining function. +-- +-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA" + +intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c +intersectionWith f m1 m2 + = intersectionWithKey (\_ x y -> f x y) m1 m2 + +-- | /O(n+m)/. The intersection with a combining function. +-- +-- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar +-- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A" + +intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c +intersectionWithKey f m1 m2 + = mergeWithKey' bin (\(Tip k1 x1) (Tip _k2 x2) -> Tip k1 (f k1 x1 x2)) (const Nil) (const Nil) m1 m2 + +{-------------------------------------------------------------------- + MergeWithKey +--------------------------------------------------------------------} + +-- | /O(n+m)/. A high-performance universal combining function. Using +-- 'mergeWithKey', all combining functions can be defined without any loss of +-- efficiency (with exception of 'union', 'difference' and 'intersection', +-- where sharing of some nodes is lost with 'mergeWithKey'). +-- +-- Please make sure you know what is going on when using 'mergeWithKey', +-- otherwise you can be surprised by unexpected code growth or even +-- corruption of the data structure. +-- +-- When 'mergeWithKey' is given three arguments, it is inlined to the call +-- site. You should therefore use 'mergeWithKey' only to define your custom +-- combining functions. For example, you could define 'unionWithKey', +-- 'differenceWithKey' and 'intersectionWithKey' as +-- +-- > myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2 +-- > myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2 +-- > myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2 +-- +-- When calling @'mergeWithKey' combine only1 only2@, a function combining two +-- 'IntMap's is created, such that +-- +-- * if a key is present in both maps, it is passed with both corresponding +-- values to the @combine@ function. Depending on the result, the key is either +-- present in the result with specified value, or is left out; +-- +-- * a nonempty subtree present only in the first map is passed to @only1@ and +-- the output is added to the result; +-- +-- * a nonempty subtree present only in the second map is passed to @only2@ and +-- the output is added to the result. +-- +-- The @only1@ and @only2@ methods /must return a map with a subset (possibly empty) of the keys of the given map/. +-- The values can be modified arbitrarily. Most common variants of @only1@ and +-- @only2@ are 'id' and @'const' 'empty'@, but for example @'map' f@ or +-- @'filterWithKey' f@ could be used for any @f@. + +mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) + -> IntMap a -> IntMap b -> IntMap c +mergeWithKey f g1 g2 = mergeWithKey' bin combine g1 g2 + where -- We use the lambda form to avoid non-exhaustive pattern matches warning. + combine = \(Tip k1 x1) (Tip _k2 x2) -> + case f k1 x1 x2 of + Nothing -> Nil + Just x -> Tip k1 x + {-# INLINE combine #-} +{-# INLINE mergeWithKey #-} + +-- Slightly more general version of mergeWithKey. It differs in the following: +-- +-- * the combining function operates on maps instead of keys and values. The +-- reason is to enable sharing in union, difference and intersection. +-- +-- * mergeWithKey' is given an equivalent of bin. The reason is that in union*, +-- Bin constructor can be used, because we know both subtrees are nonempty. + +mergeWithKey' :: (Prefix -> Mask -> IntMap c -> IntMap c -> IntMap c) + -> (IntMap a -> IntMap b -> IntMap c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c) + -> IntMap a -> IntMap b -> IntMap c +mergeWithKey' bin' f g1 g2 = go + where + go t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) + | shorter m1 m2 = merge1 + | shorter m2 m1 = merge2 + | p1 == p2 = bin' p1 m1 (go l1 l2) (go r1 r2) + | otherwise = maybe_link p1 (g1 t1) p2 (g2 t2) + where + merge1 | nomatch p2 p1 m1 = maybe_link p1 (g1 t1) p2 (g2 t2) + | zero p2 m1 = bin' p1 m1 (go l1 t2) (g1 r1) + | otherwise = bin' p1 m1 (g1 l1) (go r1 t2) + merge2 | nomatch p1 p2 m2 = maybe_link p1 (g1 t1) p2 (g2 t2) + | zero p1 m2 = bin' p2 m2 (go t1 l2) (g2 r2) + | otherwise = bin' p2 m2 (g2 l2) (go t1 r2) + + go t1'@(Bin _ _ _ _) t2'@(Tip k2' _) = merge0 t2' k2' t1' + where + merge0 t2 k2 t1@(Bin p1 m1 l1 r1) + | nomatch k2 p1 m1 = maybe_link p1 (g1 t1) k2 (g2 t2) + | zero k2 m1 = bin' p1 m1 (merge0 t2 k2 l1) (g1 r1) + | otherwise = bin' p1 m1 (g1 l1) (merge0 t2 k2 r1) + merge0 t2 k2 t1@(Tip k1 _) + | k1 == k2 = f t1 t2 + | otherwise = maybe_link k1 (g1 t1) k2 (g2 t2) + merge0 t2 _ Nil = g2 t2 + + go t1@(Bin _ _ _ _) Nil = g1 t1 + + go t1'@(Tip k1' _) t2' = merge0 t1' k1' t2' + where + merge0 t1 k1 t2@(Bin p2 m2 l2 r2) + | nomatch k1 p2 m2 = maybe_link k1 (g1 t1) p2 (g2 t2) + | zero k1 m2 = bin' p2 m2 (merge0 t1 k1 l2) (g2 r2) + | otherwise = bin' p2 m2 (g2 l2) (merge0 t1 k1 r2) + merge0 t1 k1 t2@(Tip k2 _) + | k1 == k2 = f t1 t2 + | otherwise = maybe_link k1 (g1 t1) k2 (g2 t2) + merge0 t1 _ Nil = g1 t1 + + go Nil t2 = g2 t2 + + maybe_link _ Nil _ t2 = t2 + maybe_link _ t1 _ Nil = t1 + maybe_link p1 t1 p2 t2 = link p1 t1 p2 t2 + {-# INLINE maybe_link #-} +{-# INLINE mergeWithKey' #-} + + +{-------------------------------------------------------------------- + mergeA +--------------------------------------------------------------------} + +-- | A tactic for dealing with keys present in one map but not the +-- other in 'merge' or 'mergeA'. +-- +-- A tactic of type @WhenMissing f k x z@ is an abstract representation +-- of a function of type @Key -> x -> f (Maybe z)@. + +data WhenMissing f x y = WhenMissing + { missingSubtree :: IntMap x -> f (IntMap y) + , missingKey :: Key -> x -> f (Maybe y)} + + +instance (Applicative f, Monad f) => Functor (WhenMissing f x) where + fmap = mapWhenMissing + {-# INLINE fmap #-} + + +instance (Applicative f, Monad f) => Category.Category (WhenMissing f) + where + id = preserveMissing + f . g = + traverseMaybeMissing $ \ k x -> do + y <- missingKey g k x + case y of + Nothing -> pure Nothing + Just q -> missingKey f k q + {-# INLINE id #-} + {-# INLINE (.) #-} + + +-- | Equivalent to @ReaderT k (ReaderT x (MaybeT f))@. +instance (Applicative f, Monad f) => Applicative (WhenMissing f x) where + pure x = mapMissing (\ _ _ -> x) + f <*> g = + traverseMaybeMissing $ \k x -> do + res1 <- missingKey f k x + case res1 of + Nothing -> pure Nothing + Just r -> (pure $!) . fmap r =<< missingKey g k x + {-# INLINE pure #-} + {-# INLINE (<*>) #-} + + +-- | Equivalent to @ReaderT k (ReaderT x (MaybeT f))@. +instance (Applicative f, Monad f) => Monad (WhenMissing f x) where +#if !MIN_VERSION_base(4,8,0) + return = pure +#endif + m >>= f = + traverseMaybeMissing $ \k x -> do + res1 <- missingKey m k x + case res1 of + Nothing -> pure Nothing + Just r -> missingKey (f r) k x + {-# INLINE (>>=) #-} + + +-- | Map covariantly over a @'WhenMissing' f x@. +mapWhenMissing + :: (Applicative f, Monad f) + => (a -> b) + -> WhenMissing f x a + -> WhenMissing f x b +mapWhenMissing f t = WhenMissing + { missingSubtree = \m -> missingSubtree t m >>= \m' -> pure $! fmap f m' + , missingKey = \k x -> missingKey t k x >>= \q -> (pure $! fmap f q) } +{-# INLINE mapWhenMissing #-} + + +-- | Map covariantly over a @'WhenMissing' f x@, using only a +-- 'Functor f' constraint. +mapGentlyWhenMissing + :: Functor f + => (a -> b) + -> WhenMissing f x a + -> WhenMissing f x b +mapGentlyWhenMissing f t = WhenMissing + { missingSubtree = \m -> fmap f <$> missingSubtree t m + , missingKey = \k x -> fmap f <$> missingKey t k x } +{-# INLINE mapGentlyWhenMissing #-} + + +-- | Map covariantly over a @'WhenMatched' f k x@, using only a +-- 'Functor f' constraint. +mapGentlyWhenMatched + :: Functor f + => (a -> b) + -> WhenMatched f x y a + -> WhenMatched f x y b +mapGentlyWhenMatched f t = + zipWithMaybeAMatched $ \k x y -> fmap f <$> runWhenMatched t k x y +{-# INLINE mapGentlyWhenMatched #-} + + +-- | Map contravariantly over a @'WhenMissing' f _ x@. +lmapWhenMissing :: (b -> a) -> WhenMissing f a x -> WhenMissing f b x +lmapWhenMissing f t = WhenMissing + { missingSubtree = \m -> missingSubtree t (fmap f m) + , missingKey = \k x -> missingKey t k (f x) } +{-# INLINE lmapWhenMissing #-} + + +-- | Map contravariantly over a @'WhenMatched' f _ y z@. +contramapFirstWhenMatched + :: (b -> a) + -> WhenMatched f a y z + -> WhenMatched f b y z +contramapFirstWhenMatched f t = + WhenMatched $ \k x y -> runWhenMatched t k (f x) y +{-# INLINE contramapFirstWhenMatched #-} + + +-- | Map contravariantly over a @'WhenMatched' f x _ z@. +contramapSecondWhenMatched + :: (b -> a) + -> WhenMatched f x a z + -> WhenMatched f x b z +contramapSecondWhenMatched f t = + WhenMatched $ \k x y -> runWhenMatched t k x (f y) +{-# INLINE contramapSecondWhenMatched #-} + + +#if !MIN_VERSION_base(4,8,0) +newtype Identity a = Identity {runIdentity :: a} + +instance Functor Identity where + fmap f (Identity x) = Identity (f x) + +instance Applicative Identity where + pure = Identity + Identity f <*> Identity x = Identity (f x) +#endif + +-- | A tactic for dealing with keys present in one map but not the +-- other in 'merge'. +-- +-- A tactic of type @SimpleWhenMissing x z@ is an abstract +-- representation of a function of type @Key -> x -> Maybe z@. +type SimpleWhenMissing = WhenMissing Identity + + +-- | A tactic for dealing with keys present in both maps in 'merge' +-- or 'mergeA'. +-- +-- A tactic of type @WhenMatched f x y z@ is an abstract representation +-- of a function of type @Key -> x -> y -> f (Maybe z)@. +newtype WhenMatched f x y z = WhenMatched + { matchedKey :: Key -> x -> y -> f (Maybe z) } + + +-- | Along with zipWithMaybeAMatched, witnesses the isomorphism +-- between @WhenMatched f x y z@ and @Key -> x -> y -> f (Maybe z)@. +runWhenMatched :: WhenMatched f x y z -> Key -> x -> y -> f (Maybe z) +runWhenMatched = matchedKey +{-# INLINE runWhenMatched #-} + + +-- | Along with traverseMaybeMissing, witnesses the isomorphism +-- between @WhenMissing f x y@ and @Key -> x -> f (Maybe y)@. +runWhenMissing :: WhenMissing f x y -> Key-> x -> f (Maybe y) +runWhenMissing = missingKey +{-# INLINE runWhenMissing #-} + + +instance Functor f => Functor (WhenMatched f x y) where + fmap = mapWhenMatched + {-# INLINE fmap #-} + + +instance (Monad f, Applicative f) => Category.Category (WhenMatched f x) + where + id = zipWithMatched (\_ _ y -> y) + f . g = + zipWithMaybeAMatched $ \k x y -> do + res <- runWhenMatched g k x y + case res of + Nothing -> pure Nothing + Just r -> runWhenMatched f k x r + {-# INLINE id #-} + {-# INLINE (.) #-} + + +-- | Equivalent to @ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))@ +instance (Monad f, Applicative f) => Applicative (WhenMatched f x y) where + pure x = zipWithMatched (\_ _ _ -> x) + fs <*> xs = + zipWithMaybeAMatched $ \k x y -> do + res <- runWhenMatched fs k x y + case res of + Nothing -> pure Nothing + Just r -> (pure $!) . fmap r =<< runWhenMatched xs k x y + {-# INLINE pure #-} + {-# INLINE (<*>) #-} + + +-- | Equivalent to @ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))@ +instance (Monad f, Applicative f) => Monad (WhenMatched f x y) where +#if !MIN_VERSION_base(4,8,0) + return = pure +#endif + m >>= f = + zipWithMaybeAMatched $ \k x y -> do + res <- runWhenMatched m k x y + case res of + Nothing -> pure Nothing + Just r -> runWhenMatched (f r) k x y + {-# INLINE (>>=) #-} + + +-- | Map covariantly over a @'WhenMatched' f x y@. +mapWhenMatched + :: Functor f + => (a -> b) + -> WhenMatched f x y a + -> WhenMatched f x y b +mapWhenMatched f (WhenMatched g) = + WhenMatched $ \k x y -> fmap (fmap f) (g k x y) +{-# INLINE mapWhenMatched #-} + + +-- | A tactic for dealing with keys present in both maps in 'merge'. +-- +-- A tactic of type @SimpleWhenMatched x y z@ is an abstract +-- representation of a function of type @Key -> x -> y -> Maybe z@. +type SimpleWhenMatched = WhenMatched Identity + + +-- | When a key is found in both maps, apply a function to the key +-- and values and use the result in the merged map. +-- +-- > zipWithMatched +-- > :: (Key -> x -> y -> z) +-- > -> SimpleWhenMatched x y z +zipWithMatched + :: Applicative f + => (Key -> x -> y -> z) + -> WhenMatched f x y z +zipWithMatched f = WhenMatched $ \ k x y -> pure . Just $ f k x y +{-# INLINE zipWithMatched #-} + + +-- | When a key is found in both maps, apply a function to the key +-- and values to produce an action and use its result in the merged +-- map. +zipWithAMatched + :: Applicative f + => (Key -> x -> y -> f z) + -> WhenMatched f x y z +zipWithAMatched f = WhenMatched $ \ k x y -> Just <$> f k x y +{-# INLINE zipWithAMatched #-} + + +-- | When a key is found in both maps, apply a function to the key +-- and values and maybe use the result in the merged map. +-- +-- > zipWithMaybeMatched +-- > :: (Key -> x -> y -> Maybe z) +-- > -> SimpleWhenMatched x y z +zipWithMaybeMatched + :: Applicative f + => (Key -> x -> y -> Maybe z) + -> WhenMatched f x y z +zipWithMaybeMatched f = WhenMatched $ \ k x y -> pure $ f k x y +{-# INLINE zipWithMaybeMatched #-} + + +-- | When a key is found in both maps, apply a function to the key +-- and values, perform the resulting action, and maybe use the +-- result in the merged map. +-- +-- This is the fundamental 'WhenMatched' tactic. +zipWithMaybeAMatched + :: (Key -> x -> y -> f (Maybe z)) + -> WhenMatched f x y z +zipWithMaybeAMatched f = WhenMatched $ \ k x y -> f k x y +{-# INLINE zipWithMaybeAMatched #-} + + +-- | Drop all the entries whose keys are missing from the other +-- map. +-- +-- > dropMissing :: SimpleWhenMissing x y +-- +-- prop> dropMissing = mapMaybeMissing (\_ _ -> Nothing) +-- +-- but @dropMissing@ is much faster. +dropMissing :: Applicative f => WhenMissing f x y +dropMissing = WhenMissing + { missingSubtree = const (pure Nil) + , missingKey = \_ _ -> pure Nothing } +{-# INLINE dropMissing #-} + + +-- | Preserve, unchanged, the entries whose keys are missing from +-- the other map. +-- +-- > preserveMissing :: SimpleWhenMissing x x +-- +-- prop> preserveMissing = Lazy.Merge.mapMaybeMissing (\_ x -> Just x) +-- +-- but @preserveMissing@ is much faster. +preserveMissing :: Applicative f => WhenMissing f x x +preserveMissing = WhenMissing + { missingSubtree = pure + , missingKey = \_ v -> pure (Just v) } +{-# INLINE preserveMissing #-} + + +-- | Map over the entries whose keys are missing from the other map. +-- +-- > mapMissing :: (k -> x -> y) -> SimpleWhenMissing x y +-- +-- prop> mapMissing f = mapMaybeMissing (\k x -> Just $ f k x) +-- +-- but @mapMissing@ is somewhat faster. +mapMissing :: Applicative f => (Key -> x -> y) -> WhenMissing f x y +mapMissing f = WhenMissing + { missingSubtree = \m -> pure $! mapWithKey f m + , missingKey = \k x -> pure $ Just (f k x) } +{-# INLINE mapMissing #-} + + +-- | Map over the entries whose keys are missing from the other +-- map, optionally removing some. This is the most powerful +-- 'SimpleWhenMissing' tactic, but others are usually more efficient. +-- +-- > mapMaybeMissing :: (Key -> x -> Maybe y) -> SimpleWhenMissing x y +-- +-- prop> mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x)) +-- +-- but @mapMaybeMissing@ uses fewer unnecessary 'Applicative' +-- operations. +mapMaybeMissing + :: Applicative f => (Key -> x -> Maybe y) -> WhenMissing f x y +mapMaybeMissing f = WhenMissing + { missingSubtree = \m -> pure $! mapMaybeWithKey f m + , missingKey = \k x -> pure $! f k x } +{-# INLINE mapMaybeMissing #-} + + +-- | Filter the entries whose keys are missing from the other map. +-- +-- > filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing x x +-- +-- prop> filterMissing f = Lazy.Merge.mapMaybeMissing $ \k x -> guard (f k x) *> Just x +-- +-- but this should be a little faster. +filterMissing + :: Applicative f => (Key -> x -> Bool) -> WhenMissing f x x +filterMissing f = WhenMissing + { missingSubtree = \m -> pure $! filterWithKey f m + , missingKey = \k x -> pure $! if f k x then Just x else Nothing } +{-# INLINE filterMissing #-} + + +-- | Filter the entries whose keys are missing from the other map +-- using some 'Applicative' action. +-- +-- > filterAMissing f = Lazy.Merge.traverseMaybeMissing $ +-- > \k x -> (\b -> guard b *> Just x) <$> f k x +-- +-- but this should be a little faster. +filterAMissing + :: Applicative f => (Key -> x -> f Bool) -> WhenMissing f x x +filterAMissing f = WhenMissing + { missingSubtree = \m -> filterWithKeyA f m + , missingKey = \k x -> bool Nothing (Just x) <$> f k x } +{-# INLINE filterAMissing #-} + + +-- | /O(n)/. Filter keys and values using an 'Applicative' predicate. +filterWithKeyA + :: Applicative f => (Key -> a -> f Bool) -> IntMap a -> f (IntMap a) +filterWithKeyA _ Nil = pure Nil +filterWithKeyA f t@(Tip k x) = (\b -> if b then t else Nil) <$> f k x +filterWithKeyA f (Bin p m l r) = + bin p m <$> filterWithKeyA f l <*> filterWithKeyA f r + +-- | This wasn't in Data.Bool until 4.7.0, so we define it here +bool :: a -> a -> Bool -> a +bool f _ False = f +bool _ t True = t + + +-- | Traverse over the entries whose keys are missing from the other +-- map. +traverseMissing + :: Applicative f => (Key -> x -> f y) -> WhenMissing f x y +traverseMissing f = WhenMissing + { missingSubtree = traverseWithKey f + , missingKey = \k x -> Just <$> f k x } +{-# INLINE traverseMissing #-} + + +-- | Traverse over the entries whose keys are missing from the other +-- map, optionally producing values to put in the result. This is +-- the most powerful 'WhenMissing' tactic, but others are usually +-- more efficient. +traverseMaybeMissing + :: Applicative f => (Key -> x -> f (Maybe y)) -> WhenMissing f x y +traverseMaybeMissing f = WhenMissing + { missingSubtree = traverseMaybeWithKey f + , missingKey = f } +{-# INLINE traverseMaybeMissing #-} + + +-- | /O(n)/. Traverse keys\/values and collect the 'Just' results. +traverseMaybeWithKey + :: Applicative f => (Key -> a -> f (Maybe b)) -> IntMap a -> f (IntMap b) +traverseMaybeWithKey f = go + where + go Nil = pure Nil + go (Tip k x) = maybe Nil (Tip k) <$> f k x + go (Bin p m l r) = bin p m <$> go l <*> go r + + +-- | Merge two maps. +-- +-- @merge@ takes two 'WhenMissing' tactics, a 'WhenMatched' tactic +-- and two maps. It uses the tactics to merge the maps. Its behavior +-- is best understood via its fundamental tactics, 'mapMaybeMissing' +-- and 'zipWithMaybeMatched'. +-- +-- Consider +-- +-- @ +-- merge (mapMaybeMissing g1) +-- (mapMaybeMissing g2) +-- (zipWithMaybeMatched f) +-- m1 m2 +-- @ +-- +-- Take, for example, +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- @merge@ will first ''align'' these maps by key: +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- It will then pass the individual entries and pairs of entries +-- to @g1@, @g2@, or @f@ as appropriate: +-- +-- @ +-- maybes = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"] +-- @ +-- +-- This produces a 'Maybe' for each key: +-- +-- @ +-- keys = 0 1 2 3 4 +-- results = [Nothing, Just True, Just False, Nothing, Just True] +-- @ +-- +-- Finally, the @Just@ results are collected into a map: +-- +-- @ +-- return value = [(1, True), (2, False), (4, True)] +-- @ +-- +-- The other tactics below are optimizations or simplifications of +-- 'mapMaybeMissing' for special cases. Most importantly, +-- +-- * 'dropMissing' drops all the keys. +-- * 'preserveMissing' leaves all the entries alone. +-- +-- When 'merge' is given three arguments, it is inlined at the call +-- site. To prevent excessive inlining, you should typically use +-- 'merge' to define your custom combining functions. +-- +-- +-- Examples: +-- +-- prop> unionWithKey f = merge preserveMissing preserveMissing (zipWithMatched f) +-- prop> intersectionWithKey f = merge dropMissing dropMissing (zipWithMatched f) +-- prop> differenceWith f = merge diffPreserve diffDrop f +-- prop> symmetricDifference = merge diffPreserve diffPreserve (\ _ _ _ -> Nothing) +-- prop> mapEachPiece f g h = merge (diffMapWithKey f) (diffMapWithKey g) +-- +-- @since 0.5.8 +merge + :: SimpleWhenMissing a c -- ^ What to do with keys in @m1@ but not @m2@ + -> SimpleWhenMissing b c -- ^ What to do with keys in @m2@ but not @m1@ + -> SimpleWhenMatched a b c -- ^ What to do with keys in both @m1@ and @m2@ + -> IntMap a -- ^ Map @m1@ + -> IntMap b -- ^ Map @m2@ + -> IntMap c +merge g1 g2 f m1 m2 = + runIdentity $ mergeA g1 g2 f m1 m2 +{-# INLINE merge #-} + + +-- | An applicative version of 'merge'. +-- +-- @mergeA@ takes two 'WhenMissing' tactics, a 'WhenMatched' +-- tactic and two maps. It uses the tactics to merge the maps. +-- Its behavior is best understood via its fundamental tactics, +-- 'traverseMaybeMissing' and 'zipWithMaybeAMatched'. +-- +-- Consider +-- +-- @ +-- mergeA (traverseMaybeMissing g1) +-- (traverseMaybeMissing g2) +-- (zipWithMaybeAMatched f) +-- m1 m2 +-- @ +-- +-- Take, for example, +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- @mergeA@ will first ''align'' these maps by key: +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- It will then pass the individual entries and pairs of entries +-- to @g1@, @g2@, or @f@ as appropriate: +-- +-- @ +-- actions = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"] +-- @ +-- +-- Next, it will perform the actions in the @actions@ list in order from +-- left to right. +-- +-- @ +-- keys = 0 1 2 3 4 +-- results = [Nothing, Just True, Just False, Nothing, Just True] +-- @ +-- +-- Finally, the @Just@ results are collected into a map: +-- +-- @ +-- return value = [(1, True), (2, False), (4, True)] +-- @ +-- +-- The other tactics below are optimizations or simplifications of +-- 'traverseMaybeMissing' for special cases. Most importantly, +-- +-- * 'dropMissing' drops all the keys. +-- * 'preserveMissing' leaves all the entries alone. +-- * 'mapMaybeMissing' does not use the 'Applicative' context. +-- +-- When 'mergeA' is given three arguments, it is inlined at the call +-- site. To prevent excessive inlining, you should generally only use +-- 'mergeA' to define custom combining functions. +-- +-- @since 0.5.8 +mergeA + :: (Applicative f) + => WhenMissing f a c -- ^ What to do with keys in @m1@ but not @m2@ + -> WhenMissing f b c -- ^ What to do with keys in @m2@ but not @m1@ + -> WhenMatched f a b c -- ^ What to do with keys in both @m1@ and @m2@ + -> IntMap a -- ^ Map @m1@ + -> IntMap b -- ^ Map @m2@ + -> f (IntMap c) +mergeA + WhenMissing{missingSubtree = g1t, missingKey = g1k} + WhenMissing{missingSubtree = g2t, missingKey = g2k} + WhenMatched{matchedKey = f} + = go + where + go t1 Nil = g1t t1 + go Nil t2 = g2t t2 + + -- This case is already covered below. + -- go (Tip k1 x1) (Tip k2 x2) = mergeTips k1 x1 k2 x2 + + go (Tip k1 x1) t2' = merge2 t2' + where + merge2 t2@(Bin p2 m2 l2 r2) + | nomatch k1 p2 m2 = linkA k1 (subsingletonBy g1k k1 x1) p2 (g2t t2) + | zero k1 m2 = bin p2 m2 <$> merge2 l2 <*> g2t r2 + | otherwise = bin p2 m2 <$> g2t l2 <*> merge2 r2 + merge2 (Tip k2 x2) = mergeTips k1 x1 k2 x2 + merge2 Nil = subsingletonBy g1k k1 x1 + + go t1' (Tip k2 x2) = merge1 t1' + where + merge1 t1@(Bin p1 m1 l1 r1) + | nomatch k2 p1 m1 = linkA p1 (g1t t1) k2 (subsingletonBy g2k k2 x2) + | zero k2 m1 = bin p1 m1 <$> merge1 l1 <*> g1t r1 + | otherwise = bin p1 m1 <$> g1t l1 <*> merge1 r1 + merge1 (Tip k1 x1) = mergeTips k1 x1 k2 x2 + merge1 Nil = subsingletonBy g2k k2 x2 + + go t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2) + | shorter m1 m2 = merge1 + | shorter m2 m1 = merge2 + | p1 == p2 = bin p1 m1 <$> go l1 l2 <*> go r1 r2 + | otherwise = link_ p1 p2 <$> g1t t1 <*> g2t t2 + where + merge1 | nomatch p2 p1 m1 = link_ p1 p2 <$> g1t t1 <*> g2t t2 + | zero p2 m1 = bin p1 m1 <$> go l1 t2 <*> g1t r1 + | otherwise = bin p1 m1 <$> g1t l1 <*> go r1 t2 + merge2 | nomatch p1 p2 m2 = link_ p1 p2 <$> g1t t1 <*> g2t t2 + | zero p1 m2 = bin p2 m2 <$> go t1 l2 <*> g2t r2 + | otherwise = bin p2 m2 <$> g2t l2 <*> go t1 r2 + + subsingletonBy gk k x = maybe Nil (Tip k) <$> gk k x + {-# INLINE subsingletonBy #-} + + mergeTips k1 x1 k2 x2 + | k1 == k2 = maybe Nil (Tip k1) <$> f k1 x1 x2 + | k1 < k2 = subdoubleton k1 k2 <$> g1k k1 x1 <*> g2k k2 x2 + {- + = link_ k1 k2 <$> subsingletonBy g1k k1 x1 <*> subsingletonBy g2k k2 x2 + -} + | otherwise = subdoubleton k2 k1 <$> g2k k2 x2 <*> g1k k1 x1 + {-# INLINE mergeTips #-} + + subdoubleton _ _ Nothing Nothing = Nil + subdoubleton _ k2 Nothing (Just y2) = Tip k2 y2 + subdoubleton k1 _ (Just y1) Nothing = Tip k1 y1 + subdoubleton k1 k2 (Just y1) (Just y2) = link k1 (Tip k1 y1) k2 (Tip k2 y2) + {-# INLINE subdoubleton #-} + + link_ _ _ Nil t2 = t2 + link_ _ _ t1 Nil = t1 + link_ p1 p2 t1 t2 = link p1 t1 p2 t2 + {-# INLINE link_ #-} + + -- | A variant of 'link_' which makes sure to execute side-effects + -- in the right order. + linkA + :: Applicative f + => Prefix -> f (IntMap a) + -> Prefix -> f (IntMap a) + -> f (IntMap a) + linkA p1 t1 p2 t2 + | zero p1 m = bin p m <$> t1 <*> t2 + | otherwise = bin p m <$> t2 <*> t1 + where + m = branchMask p1 p2 + p = mask p1 m + {-# INLINE linkA #-} +{-# INLINE mergeA #-} + + +{-------------------------------------------------------------------- + Min\/Max +--------------------------------------------------------------------} + +-- | /O(min(n,W))/. Update the value at the minimal key. +-- +-- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")] +-- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +updateMinWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a +updateMinWithKey f t = + case t of Bin p m l r | m < 0 -> binCheckRight p m l (go f r) + _ -> go f t + where + go f' (Bin p m l r) = binCheckLeft p m (go f' l) r + go f' (Tip k y) = case f' k y of + Just y' -> Tip k y' + Nothing -> Nil + go _ Nil = error "updateMinWithKey Nil" + +-- | /O(min(n,W))/. Update the value at the maximal key. +-- +-- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")] +-- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" + +updateMaxWithKey :: (Key -> a -> Maybe a) -> IntMap a -> IntMap a +updateMaxWithKey f t = + case t of Bin p m l r | m < 0 -> binCheckLeft p m (go f l) r + _ -> go f t + where + go f' (Bin p m l r) = binCheckRight p m l (go f' r) + go f' (Tip k y) = case f' k y of + Just y' -> Tip k y' + Nothing -> Nil + go _ Nil = error "updateMaxWithKey Nil" + + +data View a = View {-# UNPACK #-} !Key a !(IntMap a) + +-- | /O(min(n,W))/. Retrieves the maximal (key,value) pair of the map, and +-- the map stripped of that element, or 'Nothing' if passed an empty map. +-- +-- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b") +-- > maxViewWithKey empty == Nothing + +maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) +maxViewWithKey t = + case t of + Nil -> Nothing + Bin p m l r | m < 0 -> + Just $ case go l of View k a l' -> ((k, a), binCheckLeft p m l' r) + _ -> Just $ case go t of View k a t' -> ((k, a), t') + where + go (Bin p m l r) = + case go r of View k a r' -> View k a (binCheckRight p m l r') + go (Tip k y) = View k y Nil + go Nil = error "maxViewWithKey Nil" + +-- | /O(min(n,W))/. Retrieves the minimal (key,value) pair of the map, and +-- the map stripped of that element, or 'Nothing' if passed an empty map. +-- +-- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") +-- > minViewWithKey empty == Nothing + +minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a) +minViewWithKey t = + case t of + Nil -> Nothing + Bin p m l r | m < 0 -> + Just $ case go r of View k a r' -> ((k, a), binCheckRight p m l r') + _ -> Just $ case go t of View k a t' -> ((k, a), t') + where + go (Bin p m l r) = + case go l of View k a l' -> View k a (binCheckLeft p m l' r) + go (Tip k y) = View k y Nil + go Nil = error "minViewWithKey Nil" + +-- | /O(min(n,W))/. Update the value at the maximal key. +-- +-- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")] +-- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" + +updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a +updateMax f = updateMaxWithKey (const f) + +-- | /O(min(n,W))/. Update the value at the minimal key. +-- +-- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")] +-- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a +updateMin f = updateMinWithKey (const f) + +-- Similar to the Arrow instance. +first :: (a -> c) -> (a, b) -> (c, b) +first f (x,y) = (f x,y) + +-- | /O(min(n,W))/. Retrieves the maximal key of the map, and the map +-- stripped of that element, or 'Nothing' if passed an empty map. +maxView :: IntMap a -> Maybe (a, IntMap a) +maxView t = liftM (first snd) (maxViewWithKey t) + +-- | /O(min(n,W))/. Retrieves the minimal key of the map, and the map +-- stripped of that element, or 'Nothing' if passed an empty map. +minView :: IntMap a -> Maybe (a, IntMap a) +minView t = liftM (first snd) (minViewWithKey t) + +-- | /O(min(n,W))/. Delete and find the maximal element. +deleteFindMax :: IntMap a -> ((Key, a), IntMap a) +deleteFindMax = fromMaybe (error "deleteFindMax: empty map has no maximal element") . maxViewWithKey + +-- | /O(min(n,W))/. Delete and find the minimal element. +deleteFindMin :: IntMap a -> ((Key, a), IntMap a) +deleteFindMin = fromMaybe (error "deleteFindMin: empty map has no minimal element") . minViewWithKey + +-- | /O(min(n,W))/. The minimal key of the map. +findMin :: IntMap a -> (Key, a) +findMin Nil = error $ "findMin: empty map has no minimal element" +findMin (Tip k v) = (k,v) +findMin (Bin _ m l r) + | m < 0 = go r + | otherwise = go l + where go (Tip k v) = (k,v) + go (Bin _ _ l' _) = go l' + go Nil = error "findMax Nil" + +-- | /O(min(n,W))/. The maximal key of the map. +findMax :: IntMap a -> (Key, a) +findMax Nil = error $ "findMax: empty map has no maximal element" +findMax (Tip k v) = (k,v) +findMax (Bin _ m l r) + | m < 0 = go l + | otherwise = go r + where go (Tip k v) = (k,v) + go (Bin _ _ _ r') = go r' + go Nil = error "findMax Nil" + +-- | /O(min(n,W))/. Delete the minimal key. Returns an empty map if the map is empty. +-- +-- Note that this is a change of behaviour for consistency with 'Data.Map.Map' – +-- versions prior to 0.5 threw an error if the 'IntMap' was already empty. +deleteMin :: IntMap a -> IntMap a +deleteMin = maybe Nil snd . minView + +-- | /O(min(n,W))/. Delete the maximal key. Returns an empty map if the map is empty. +-- +-- Note that this is a change of behaviour for consistency with 'Data.Map.Map' – +-- versions prior to 0.5 threw an error if the 'IntMap' was already empty. +deleteMax :: IntMap a -> IntMap a +deleteMax = maybe Nil snd . maxView + + +{-------------------------------------------------------------------- + Submap +--------------------------------------------------------------------} +-- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). +-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@). +isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool +isProperSubmapOf m1 m2 + = isProperSubmapOfBy (==) m1 m2 + +{- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). + The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when + @m1@ and @m2@ are not equal, + all keys in @m1@ are in @m2@, and when @f@ returns 'True' when + applied to their respective values. For example, the following + expressions are all 'True': + + > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + + But the following are all 'False': + + > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) + > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) + > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) +-} +isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool +isProperSubmapOfBy predicate t1 t2 + = case submapCmp predicate t1 t2 of + LT -> True + _ -> False + +submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering +submapCmp predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) + | shorter m1 m2 = GT + | shorter m2 m1 = submapCmpLt + | p1 == p2 = submapCmpEq + | otherwise = GT -- disjoint + where + submapCmpLt | nomatch p1 p2 m2 = GT + | zero p1 m2 = submapCmp predicate t1 l2 + | otherwise = submapCmp predicate t1 r2 + submapCmpEq = case (submapCmp predicate l1 l2, submapCmp predicate r1 r2) of + (GT,_ ) -> GT + (_ ,GT) -> GT + (EQ,EQ) -> EQ + _ -> LT + +submapCmp _ (Bin _ _ _ _) _ = GT +submapCmp predicate (Tip kx x) (Tip ky y) + | (kx == ky) && predicate x y = EQ + | otherwise = GT -- disjoint +submapCmp predicate (Tip k x) t + = case lookup k t of + Just y | predicate x y -> LT + _ -> GT -- disjoint +submapCmp _ Nil Nil = EQ +submapCmp _ Nil _ = LT + +-- | /O(n+m)/. Is this a submap? +-- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@). +isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool +isSubmapOf m1 m2 + = isSubmapOfBy (==) m1 m2 + +{- | /O(n+m)/. + The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if + all keys in @m1@ are in @m2@, and when @f@ returns 'True' when + applied to their respective values. For example, the following + expressions are all 'True': + + > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) + + But the following are all 'False': + + > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)]) + > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) +-} +isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool +isSubmapOfBy predicate 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 isSubmapOfBy predicate t1 l2 + else isSubmapOfBy predicate t1 r2 + | otherwise = (p1==p2) && isSubmapOfBy predicate l1 l2 && isSubmapOfBy predicate r1 r2 +isSubmapOfBy _ (Bin _ _ _ _) _ = False +isSubmapOfBy predicate (Tip k x) t = case lookup k t of + Just y -> predicate x y + Nothing -> False +isSubmapOfBy _ Nil _ = True + +{-------------------------------------------------------------------- + Mapping +--------------------------------------------------------------------} +-- | /O(n)/. Map a function over all values in the map. +-- +-- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")] + +map :: (a -> b) -> IntMap a -> IntMap b +map f = go + where + go (Bin p m l r) = Bin p m (go l) (go r) + go (Tip k x) = Tip k (f x) + go Nil = Nil + +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] map #-} +{-# RULES +"map/map" forall f g xs . map f (map g xs) = map (f . g) xs + #-} +#endif +#if __GLASGOW_HASKELL__ >= 709 +-- Safe coercions were introduced in 7.8, but did not play well with RULES yet. +{-# RULES +"map/coerce" map coerce = coerce + #-} +#endif + +-- | /O(n)/. Map a function over all values in the map. +-- +-- > let f key x = (show key) ++ ":" ++ x +-- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")] + +mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b +mapWithKey f t + = case t of + Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r) + Tip k x -> Tip k (f k x) + Nil -> Nil + +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] mapWithKey #-} +{-# RULES +"mapWithKey/mapWithKey" forall f g xs . mapWithKey f (mapWithKey g xs) = + mapWithKey (\k a -> f k (g k a)) xs +"mapWithKey/map" forall f g xs . mapWithKey f (map g xs) = + mapWithKey (\k a -> f k (g a)) xs +"map/mapWithKey" forall f g xs . map f (mapWithKey g xs) = + mapWithKey (\k a -> f (g k a)) xs + #-} +#endif + +-- | /O(n)/. +-- @'traverseWithKey' f s == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@ +-- That is, behaves exactly like a regular 'traverse' except that the traversing +-- function also has access to the key associated with a value. +-- +-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')]) +-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing +traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b) +traverseWithKey f = go + where + go Nil = pure Nil + go (Tip k v) = Tip k <$> f k v + go (Bin p m l r) = Bin p m <$> go l <*> go r +{-# INLINE traverseWithKey #-} + +-- | /O(n)/. The function @'mapAccum'@ threads an accumulating +-- argument through the map in ascending order of keys. +-- +-- > let f a b = (a ++ b, b ++ "X") +-- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")]) + +mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) +mapAccum f = mapAccumWithKey (\a' _ x -> f a' x) + +-- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating +-- argument through the map in ascending order of keys. +-- +-- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X") +-- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")]) + +mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) +mapAccumWithKey f a t + = mapAccumL f a t + +-- | /O(n)/. The function @'mapAccumL'@ threads an accumulating +-- argument through the map in ascending order of keys. +mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) +mapAccumL f a t + = case t of + Bin p m l r -> let (a1,l') = mapAccumL f a l + (a2,r') = mapAccumL f a1 r + in (a2,Bin p m l' r') + Tip k x -> let (a',x') = f a k x in (a',Tip k x') + Nil -> (a,Nil) + +-- | /O(n)/. The function @'mapAccumR'@ threads an accumulating +-- argument through the map in descending order of keys. +mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c) +mapAccumRWithKey f a t + = case t of + Bin p m l r -> let (a1,r') = mapAccumRWithKey f a r + (a2,l') = mapAccumRWithKey f a1 l + in (a2,Bin p m l' r') + Tip k x -> let (a',x') = f a k x in (a',Tip k x') + Nil -> (a,Nil) + +-- | /O(n*min(n,W))/. +-- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@. +-- +-- The size of the result may be smaller if @f@ maps two or more distinct +-- keys to the same new key. In this case the value at the greatest of the +-- original keys is retained. +-- +-- > mapKeys (+ 1) (fromList [(5,"a"), (3,"b")]) == fromList [(4, "b"), (6, "a")] +-- > mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c" +-- > mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c" + +mapKeys :: (Key->Key) -> IntMap a -> IntMap a +mapKeys f = fromList . foldrWithKey (\k x xs -> (f k, x) : xs) [] + +-- | /O(n*min(n,W))/. +-- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@. +-- +-- The size of the result may be smaller if @f@ maps two or more distinct +-- keys to the same new key. In this case the associated values will be +-- combined using @c@. +-- +-- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab" +-- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab" + +mapKeysWith :: (a -> a -> a) -> (Key->Key) -> IntMap a -> IntMap a +mapKeysWith c f + = fromListWith c . foldrWithKey (\k x xs -> (f k, x) : xs) [] + +-- | /O(n*min(n,W))/. +-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@ +-- is strictly monotonic. +-- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@. +-- /The precondition is not checked./ +-- Semi-formally, we have: +-- +-- > and [x < y ==> f x < f y | x <- ls, y <- ls] +-- > ==> mapKeysMonotonic f s == mapKeys f s +-- > where ls = keys s +-- +-- This means that @f@ maps distinct original keys to distinct resulting keys. +-- This function has slightly better performance than 'mapKeys'. +-- +-- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")] + +mapKeysMonotonic :: (Key->Key) -> IntMap a -> IntMap a +mapKeysMonotonic f + = fromDistinctAscList . foldrWithKey (\k x xs -> (f k, x) : xs) [] + +{-------------------------------------------------------------------- + Filter +--------------------------------------------------------------------} +-- | /O(n)/. Filter all values that satisfy some predicate. +-- +-- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty +-- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty + +filter :: (a -> Bool) -> IntMap a -> IntMap a +filter p m + = filterWithKey (\_ x -> p x) m + +-- | /O(n)/. Filter all keys\/values that satisfy some predicate. +-- +-- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a +filterWithKey predicate = go + where + go Nil = Nil + go t@(Tip k x) = if predicate k x then t else Nil + go (Bin p m l r) = bin p m (go l) (go r) + +-- | /O(n)/. Partition the map according to some predicate. The first +-- map contains all elements that satisfy the predicate, the second all +-- elements that fail the predicate. See also 'split'. +-- +-- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") +-- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) +-- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) + +partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a) +partition p m + = partitionWithKey (\_ x -> p x) m + +-- | /O(n)/. Partition the map according to some predicate. The first +-- map contains all elements that satisfy the predicate, the second all +-- elements that fail the predicate. See also 'split'. +-- +-- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b") +-- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) +-- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) + +partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a) +partitionWithKey predicate0 t0 = toPair $ go predicate0 t0 + where + go predicate t = + case t of + Bin p m l r -> + let (l1 :*: l2) = go predicate l + (r1 :*: r2) = go predicate r + in bin p m l1 r1 :*: bin p m l2 r2 + Tip k x + | predicate k x -> (t :*: Nil) + | otherwise -> (Nil :*: t) + Nil -> (Nil :*: Nil) + +-- | /O(n)/. Map values and collect the 'Just' results. +-- +-- > let f x = if x == "a" then Just "new a" else Nothing +-- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a" + +mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b +mapMaybe f = mapMaybeWithKey (\_ x -> f x) + +-- | /O(n)/. Map keys\/values and collect the 'Just' results. +-- +-- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing +-- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3" + +mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b +mapMaybeWithKey f (Bin p m l r) + = bin p m (mapMaybeWithKey f l) (mapMaybeWithKey f r) +mapMaybeWithKey f (Tip k x) = case f k x of + Just y -> Tip k y + Nothing -> Nil +mapMaybeWithKey _ Nil = Nil + +-- | /O(n)/. Map values and separate the 'Left' and 'Right' results. +-- +-- > let f a = if a < "c" then Left a else Right a +-- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")]) +-- > +-- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) + +mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) +mapEither f m + = mapEitherWithKey (\_ x -> f x) m + +-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results. +-- +-- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a) +-- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")]) +-- > +-- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")]) + +mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c) +mapEitherWithKey f0 t0 = toPair $ go f0 t0 + where + go f (Bin p m l r) = + bin p m l1 r1 :*: bin p m l2 r2 + where + (l1 :*: l2) = go f l + (r1 :*: r2) = go f r + go f (Tip k x) = case f k x of + Left y -> (Tip k y :*: Nil) + Right z -> (Nil :*: Tip k z) + go _ Nil = (Nil :*: Nil) + +-- | /O(min(n,W))/. The expression (@'split' k map@) is a pair @(map1,map2)@ +-- where all keys in @map1@ are lower than @k@ and all keys in +-- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@. +-- +-- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")]) +-- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a") +-- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") +-- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty) +-- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty) + +split :: Key -> IntMap a -> (IntMap a, IntMap a) +split k t = + case t of + Bin _ m l r + | m < 0 -> + if k >= 0 -- handle negative numbers. + then + case go k l of + (lt :*: gt) -> + let !lt' = union r lt + in (lt', gt) + else + case go k r of + (lt :*: gt) -> + let !gt' = union gt l + in (lt, gt') + _ -> case go k t of + (lt :*: gt) -> (lt, gt) + where + go k' t'@(Bin p m l r) + | nomatch k' p m = if k' > p then t' :*: Nil else Nil :*: t' + | zero k' m = case go k' l of (lt :*: gt) -> lt :*: union gt r + | otherwise = case go k' r of (lt :*: gt) -> union l lt :*: gt + go k' t'@(Tip ky _) + | k' > ky = (t' :*: Nil) + | k' < ky = (Nil :*: t') + | otherwise = (Nil :*: Nil) + go _ Nil = (Nil :*: Nil) + + +data SplitLookup a = SplitLookup !(IntMap a) !(Maybe a) !(IntMap a) + +mapLT :: (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a +mapLT f (SplitLookup lt fnd gt) = SplitLookup (f lt) fnd gt +{-# INLINE mapLT #-} + +mapGT :: (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a +mapGT f (SplitLookup lt fnd gt) = SplitLookup lt fnd (f gt) +{-# INLINE mapGT #-} + +-- | /O(min(n,W))/. Performs a 'split' but also returns whether the pivot +-- key was found in the original map. +-- +-- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")]) +-- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a") +-- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a") +-- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty) +-- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty) + +splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a) +splitLookup k t = + case + case t of + Bin _ m l r + | m < 0 -> + if k >= 0 -- handle negative numbers. + then mapLT (union r) (go k l) + else mapGT (`union` l) (go k r) + _ -> go k t + of SplitLookup lt fnd gt -> (lt, fnd, gt) + where + go k' t'@(Bin p m l r) + | nomatch k' p m = + if k' > p + then SplitLookup t' Nothing Nil + else SplitLookup Nil Nothing t' + | zero k' m = mapGT (`union` r) (go k' l) + | otherwise = mapLT (union l) (go k' r) + go k' t'@(Tip ky y) + | k' > ky = SplitLookup t' Nothing Nil + | k' < ky = SplitLookup Nil Nothing t' + | otherwise = SplitLookup Nil (Just y) Nil + go _ Nil = SplitLookup Nil Nothing Nil + +{-------------------------------------------------------------------- + Fold +--------------------------------------------------------------------} +-- | /O(n)/. Fold the values in the map using the given right-associative +-- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@. +-- +-- For example, +-- +-- > elems map = foldr (:) [] map +-- +-- > let f a len = len + (length a) +-- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 +foldr :: (a -> b -> b) -> b -> IntMap a -> 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 _ x) = f x z' + 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' :: (a -> b -> b) -> b -> IntMap a -> 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 _ x) = f x z' + go z' (Bin _ _ l r) = go (go z' r) l +{-# INLINE foldr' #-} + +-- | /O(n)/. Fold the values in the map using the given left-associative +-- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@. +-- +-- For example, +-- +-- > elems = reverse . foldl (flip (:)) [] +-- +-- > let f len a = len + (length a) +-- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 +foldl :: (a -> b -> a) -> a -> IntMap b -> 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 + go z' Nil = z' + go z' (Tip _ x) = f z' x + 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 -> b -> a) -> a -> IntMap b -> 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 + go !z' Nil = z' + go z' (Tip _ x) = f z' x + go z' (Bin _ _ l r) = go (go z' l) r +{-# INLINE foldl' #-} + +-- | /O(n)/. Fold the keys and values in the map using the given right-associative +-- binary operator, such that +-- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@. +-- +-- For example, +-- +-- > keys map = foldrWithKey (\k x ks -> k:ks) [] map +-- +-- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" +-- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)" +foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b +foldrWithKey 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 x) = f kx x z' + go z' (Bin _ _ l r) = go (go z' r) l +{-# INLINE foldrWithKey #-} + +-- | /O(n)/. A strict version of 'foldrWithKey'. Each application of the operator is +-- evaluated before using the result in the next application. This +-- function is strict in the starting value. +foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b +foldrWithKey' 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 x) = f kx x z' + go z' (Bin _ _ l r) = go (go z' r) l +{-# INLINE foldrWithKey' #-} + +-- | /O(n)/. Fold the keys and values in the map using the given left-associative +-- binary operator, such that +-- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@. +-- +-- For example, +-- +-- > keys = reverse . foldlWithKey (\ks k x -> k:ks) [] +-- +-- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" +-- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)" +foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a +foldlWithKey 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 + go z' Nil = z' + go z' (Tip kx x) = f z' kx x + go z' (Bin _ _ l r) = go (go z' l) r +{-# INLINE foldlWithKey #-} + +-- | /O(n)/. A strict version of 'foldlWithKey'. Each application of the operator is +-- evaluated before using the result in the next application. This +-- function is strict in the starting value. +foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a +foldlWithKey' 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 + go !z' Nil = z' + go z' (Tip kx x) = f z' kx x + go z' (Bin _ _ l r) = go (go z' l) r +{-# INLINE foldlWithKey' #-} + +-- | /O(n)/. Fold the keys and values in the map using the given monoid, such that +-- +-- @'foldMapWithKey' f = 'Prelude.fold' . 'mapWithKey' f@ +-- +-- This can be an asymptotically faster than 'foldrWithKey' or 'foldlWithKey' for some monoids. +foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m +foldMapWithKey f = go + where + go Nil = mempty + go (Tip kx x) = f kx x + go (Bin _ _ l r) = go l `mappend` go r +{-# INLINE foldMapWithKey #-} + +{-------------------------------------------------------------------- + List variations +--------------------------------------------------------------------} +-- | /O(n)/. +-- Return all elements of the map in the ascending order of their keys. +-- Subject to list fusion. +-- +-- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"] +-- > elems empty == [] + +elems :: IntMap a -> [a] +elems = foldr (:) [] + +-- | /O(n)/. Return all keys of the map in ascending order. Subject to list +-- fusion. +-- +-- > keys (fromList [(5,"a"), (3,"b")]) == [3,5] +-- > keys empty == [] + +keys :: IntMap a -> [Key] +keys = foldrWithKey (\k _ ks -> k : ks) [] + +-- | /O(n)/. An alias for 'toAscList'. Returns all key\/value pairs in the +-- map in ascending key order. Subject to list fusion. +-- +-- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] +-- > assocs empty == [] + +assocs :: IntMap a -> [(Key,a)] +assocs = toAscList + +-- | /O(n*min(n,W))/. The set of all keys of the map. +-- +-- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5] +-- > keysSet empty == Data.IntSet.empty + +keysSet :: IntMap a -> IntSet.IntSet +keysSet Nil = IntSet.Nil +keysSet (Tip kx _) = IntSet.singleton kx +keysSet (Bin p m l r) + | m .&. IntSet.suffixBitMask == 0 = IntSet.Bin p m (keysSet l) (keysSet r) + | otherwise = IntSet.Tip (p .&. IntSet.prefixBitMask) (computeBm (computeBm 0 l) r) + where computeBm !acc (Bin _ _ l' r') = computeBm (computeBm acc l') r' + computeBm acc (Tip kx _) = acc .|. IntSet.bitmapOf kx + computeBm _ Nil = error "Data.IntSet.keysSet: Nil" + +-- | /O(n)/. Build a map from a set of keys and a function which for each key +-- computes its value. +-- +-- > fromSet (\k -> replicate k 'a') (Data.IntSet.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")] +-- > fromSet undefined Data.IntSet.empty == empty + +fromSet :: (Key -> a) -> IntSet.IntSet -> IntMap a +fromSet _ IntSet.Nil = Nil +fromSet f (IntSet.Bin p m l r) = Bin p m (fromSet f l) (fromSet f r) +fromSet f (IntSet.Tip kx bm) = buildTree f kx bm (IntSet.suffixBitMask + 1) + where + -- This is slightly complicated, as we to convert the dense + -- representation of IntSet into tree representation of IntMap. + -- + -- We are given a nonzero bit mask 'bmask' of 'bits' bits with + -- prefix 'prefix'. We split bmask into halves corresponding + -- to left and right subtree. If they are both nonempty, we + -- create a Bin node, otherwise exactly one of them is nonempty + -- and we construct the IntMap from that half. + buildTree g !prefix !bmask bits = case bits of + 0 -> Tip prefix (g prefix) + _ -> case intFromNat ((natFromInt bits) `shiftRL` 1) of + bits2 + | bmask .&. ((1 `shiftLL` bits2) - 1) == 0 -> + buildTree g (prefix + bits2) (bmask `shiftRL` bits2) bits2 + | (bmask `shiftRL` bits2) .&. ((1 `shiftLL` bits2) - 1) == 0 -> + buildTree g prefix bmask bits2 + | otherwise -> + Bin prefix bits2 + (buildTree g prefix bmask bits2) + (buildTree g (prefix + bits2) (bmask `shiftRL` bits2) bits2) + +{-------------------------------------------------------------------- + Lists +--------------------------------------------------------------------} +#if __GLASGOW_HASKELL__ >= 708 +instance GHCExts.IsList (IntMap a) where + type Item (IntMap a) = (Key,a) + fromList = fromList + toList = toList +#endif + +-- | /O(n)/. Convert the map to a list of key\/value pairs. Subject to list +-- fusion. +-- +-- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] +-- > toList empty == [] + +toList :: IntMap a -> [(Key,a)] +toList = toAscList + +-- | /O(n)/. Convert the map to a list of key\/value pairs where the +-- keys are in ascending order. Subject to list fusion. +-- +-- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] + +toAscList :: IntMap a -> [(Key,a)] +toAscList = foldrWithKey (\k x xs -> (k,x):xs) [] + +-- | /O(n)/. Convert the map to a list of key\/value pairs where the keys +-- are in descending order. Subject to list fusion. +-- +-- > toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")] + +toDescList :: IntMap a -> [(Key,a)] +toDescList = foldlWithKey (\xs k x -> (k,x):xs) [] + +-- List fusion for the list generating functions. +#if __GLASGOW_HASKELL__ +-- The foldrFB and foldlFB are fold{r,l}WithKey equivalents, used for list fusion. +-- They are important to convert unfused methods back, see mapFB in prelude. +foldrFB :: (Key -> a -> b -> b) -> b -> IntMap a -> b +foldrFB = foldrWithKey +{-# INLINE[0] foldrFB #-} +foldlFB :: (a -> Key -> b -> a) -> a -> IntMap b -> a +foldlFB = foldlWithKey +{-# INLINE[0] foldlFB #-} + +-- Inline assocs and toList, so that we need to fuse only toAscList. +{-# INLINE assocs #-} +{-# INLINE toList #-} + +-- The fusion is enabled up to phase 2 included. If it does not succeed, +-- convert in phase 1 the expanded elems,keys,to{Asc,Desc}List calls back to +-- elems,keys,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 elems,keys,to{Asc,Desc}List -- it was forbidden to +-- inline it before phase 0, otherwise the fusion rules would not fire at all. +{-# NOINLINE[0] elems #-} +{-# NOINLINE[0] keys #-} +{-# NOINLINE[0] toAscList #-} +{-# NOINLINE[0] toDescList #-} +{-# RULES "IntMap.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-} +{-# RULES "IntMap.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-} +{-# RULES "IntMap.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-} +{-# RULES "IntMap.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-} +{-# RULES "IntMap.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-} +{-# RULES "IntMap.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-} +{-# RULES "IntMap.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-} +{-# RULES "IntMap.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-} +#endif + + +-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs. +-- +-- > fromList [] == empty +-- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] +-- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")] + +fromList :: [(Key,a)] -> IntMap a +fromList xs + = foldlStrict ins empty xs + where + ins t (k,x) = insert k x t + +-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'. +-- +-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "ab"), (5, "cba")] +-- > fromListWith (++) [] == empty + +fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a +fromListWith f xs + = fromListWithKey (\_ x y -> f x y) xs + +-- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'. +-- +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value +-- > fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "3:a|b"), (5, "5:c|5:b|a")] +-- > fromListWithKey f [] == empty + +fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a +fromListWithKey f xs + = foldlStrict ins empty xs + where + ins t (k,x) = insertWithKey f k x t + +-- | /O(n)/. Build a map from a list of key\/value pairs where +-- the keys are in ascending order. +-- +-- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] +-- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")] + +fromAscList :: [(Key,a)] -> IntMap a +fromAscList xs + = fromAscListWithKey (\_ x _ -> x) xs + +-- | /O(n)/. Build a map from a list of key\/value pairs where +-- the keys are in ascending order, with a combining function on equal keys. +-- /The precondition (input list is ascending) is not checked./ +-- +-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] + +fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a +fromAscListWith f xs + = fromAscListWithKey (\_ x y -> f x y) xs + +-- | /O(n)/. Build a map from a list of key\/value pairs where +-- the keys are in ascending order, with a combining function on equal keys. +-- /The precondition (input list is ascending) is not checked./ +-- +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value +-- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "5:b|a")] + +fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a +fromAscListWithKey _ [] = Nil +fromAscListWithKey f (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0) + where + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] + combineEq z [] = [z] + combineEq z@(kz,zz) (x@(kx,xx):xs) + | kx==kz = let yy = f kx xx zz in combineEq (kx,yy) xs + | otherwise = z:combineEq x xs + +-- | /O(n)/. Build a map from a list of key\/value pairs where +-- the keys are in ascending order and all distinct. +-- /The precondition (input list is strictly ascending) is not checked./ +-- +-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] + +#if __GLASGOW_HASKELL__ +fromDistinctAscList :: forall a. [(Key,a)] -> IntMap a +#else +fromDistinctAscList :: [(Key,a)] -> IntMap a +#endif +fromDistinctAscList [] = Nil +fromDistinctAscList (z0 : zs0) = work z0 zs0 Nada + where + work (kx,vx) [] stk = finish kx (Tip kx vx) stk + work (kx,vx) (z@(kz,_):zs) stk = reduce z zs (branchMask kx kz) kx (Tip kx vx) stk + +#if __GLASGOW_HASKELL__ + reduce :: (Key,a) -> [(Key,a)] -> Mask -> Prefix -> IntMap a -> Stack a -> IntMap a +#endif + reduce z zs _ px tx Nada = work 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 z zs (Push px tx stk) + + finish _ t Nada = t + finish px tx (Push py ty stk) = finish p (link py ty px tx) stk + where m = branchMask px py + p = mask px m + +data Stack a = Push {-# UNPACK #-} !Prefix !(IntMap a) !(Stack a) | Nada + + +{-------------------------------------------------------------------- + Eq +--------------------------------------------------------------------} +instance Eq a => Eq (IntMap a) where + t1 == t2 = equal t1 t2 + t1 /= t2 = nequal t1 t2 + +equal :: Eq a => IntMap a -> IntMap a -> Bool +equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) + = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2) +equal (Tip kx x) (Tip ky y) + = (kx == ky) && (x==y) +equal Nil Nil = True +equal _ _ = False + +nequal :: Eq a => IntMap a -> IntMap a -> Bool +nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) + = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2) +nequal (Tip kx x) (Tip ky y) + = (kx /= ky) || (x/=y) +nequal Nil Nil = False +nequal _ _ = True + +#if MIN_VERSION_base(4,9,0) +instance Eq1 IntMap where + liftEq eq (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2) + = (m1 == m2) && (p1 == p2) && (liftEq eq l1 l2) && (liftEq eq r1 r2) + liftEq eq (Tip kx x) (Tip ky y) + = (kx == ky) && (eq x y) + liftEq _eq Nil Nil = True + liftEq _eq _ _ = False +#endif + +{-------------------------------------------------------------------- + Ord +--------------------------------------------------------------------} + +instance Ord a => Ord (IntMap a) where + compare m1 m2 = compare (toList m1) (toList m2) + +#if MIN_VERSION_base(4,9,0) +instance Ord1 IntMap where + liftCompare cmp m n = + liftCompare (liftCompare cmp) (toList m) (toList n) +#endif + +{-------------------------------------------------------------------- + Functor +--------------------------------------------------------------------} + +instance Functor IntMap where + fmap = map + +#ifdef __GLASGOW_HASKELL__ + a <$ Bin p m l r = Bin p m (a <$ l) (a <$ r) + a <$ Tip k _ = Tip k a + _ <$ Nil = Nil +#endif + +{-------------------------------------------------------------------- + Show +--------------------------------------------------------------------} + +instance Show a => Show (IntMap a) where + showsPrec d m = showParen (d > 10) $ + showString "fromList " . shows (toList m) + +#if MIN_VERSION_base(4,9,0) +instance Show1 IntMap where + liftShowsPrec sp sl d m = + showsUnaryWith (liftShowsPrec sp' sl') "fromList" d (toList m) + where + sp' = liftShowsPrec sp sl + sl' = liftShowList sp sl +#endif + +{-------------------------------------------------------------------- + Read +--------------------------------------------------------------------} +instance (Read e) => Read (IntMap e) 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 + +#if MIN_VERSION_base(4,9,0) +instance Read1 IntMap where + liftReadsPrec rp rl = readsData $ + readsUnaryWith (liftReadsPrec rp' rl') "fromList" fromList + where + rp' = liftReadsPrec rp rl + rl' = liftReadList rp rl +#endif + +{-------------------------------------------------------------------- + Typeable +--------------------------------------------------------------------} + +INSTANCE_TYPEABLE1(IntMap) + +{-------------------------------------------------------------------- + Helpers +--------------------------------------------------------------------} +{-------------------------------------------------------------------- + Link +--------------------------------------------------------------------} +link :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a +link 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 link #-} + +{-------------------------------------------------------------------- + @bin@ assures that we never have empty trees within a tree. +--------------------------------------------------------------------} +bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a +bin _ _ l Nil = l +bin _ _ Nil r = r +bin p m l r = Bin p m l r +{-# INLINE bin #-} + +-- binCheckLeft only checks that the left subtree is non-empty +binCheckLeft :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a +binCheckLeft _ _ Nil r = r +binCheckLeft p m l r = Bin p m l r +{-# INLINE binCheckLeft #-} + +-- binCheckRight only checks that the right subtree is non-empty +binCheckRight :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a +binCheckRight _ _ l Nil = l +binCheckRight p m l r = Bin p m l r +{-# INLINE binCheckRight #-} + +{-------------------------------------------------------------------- + Endian independent bit twiddling +--------------------------------------------------------------------} +zero :: Key -> Mask -> Bool +zero i m + = (natFromInt i) .&. (natFromInt m) == 0 +{-# INLINE zero #-} + +nomatch,match :: Key -> Prefix -> Mask -> Bool +nomatch i p m + = (mask i m) /= p +{-# INLINE nomatch #-} + +match i p m + = (mask i m) == p +{-# INLINE match #-} + +mask :: Key -> 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 #-} + +{-------------------------------------------------------------------- + Utilities +--------------------------------------------------------------------} + +-- | /O(1)/. Decompose a map into pieces based on the structure of the underlying +-- tree. This function is useful for consuming a map in parallel. +-- +-- No guarantee is made as to the sizes of the pieces; an internal, but +-- deterministic process determines this. However, it is guaranteed that the +-- pieces returned will be in ascending order (all elements in the first submap +-- less than all elements in the second, and so on). +-- +-- Examples: +-- +-- > splitRoot (fromList (zip [1..6::Int] ['a'..])) == +-- > [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d'),(5,'e'),(6,'f')]] +-- +-- > splitRoot empty == [] +-- +-- Note that the current implementation does not return more than two submaps, +-- but you should not depend on this behaviour because it can change in the +-- future without notice. +splitRoot :: IntMap a -> [IntMap a] +splitRoot orig = + case orig of + Nil -> [] + x@(Tip _ _) -> [x] + Bin _ m l r | m < 0 -> [r, l] + | otherwise -> [l, r] +{-# INLINE splitRoot #-} + + +{-------------------------------------------------------------------- + Debugging +--------------------------------------------------------------------} +{-# DEPRECATED showTree, showTreeWith + "These debugging functions will be moved to a separate module in future versions" + #-} + +-- | /O(n)/. Show the tree that implements the map. The tree is shown +-- in a compressed, hanging format. +showTree :: Show a => IntMap a -> String +showTree s + = showTreeWith True False s + + +{- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows + the tree that implements the map. 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 :: Show a => Bool -> Bool -> IntMap a -> String +showTreeWith hang wide t + | hang = (showsTreeHang wide [] t) "" + | otherwise = (showsTree wide [] [] t) "" + +showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> 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 k x -> + showsBars lbars . + showString " " . shows k . showString ":=" . shows x . showString "\n" + Nil -> showsBars lbars . showString "|\n" + +showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> 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 k x -> + showsBars bars . + showString " " . shows k . showString ":=" . shows x . 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 + +node :: String +node = "+--" + +withBar, withEmpty :: [String] -> [String] +withBar bars = "| ":bars +withEmpty bars = " ":bars diff --git a/Data/IntMap/Lazy.hs b/Data/IntMap/Lazy.hs --- a/Data/IntMap/Lazy.hs +++ b/Data/IntMap/Lazy.hs @@ -208,7 +208,7 @@ , showTreeWith ) where -import Data.IntMap.Base as IM +import Data.IntMap.Internal as IM -- $strictness -- diff --git a/Data/IntMap/Merge/Lazy.hs b/Data/IntMap/Merge/Lazy.hs new file mode 100644 --- /dev/null +++ b/Data/IntMap/Merge/Lazy.hs @@ -0,0 +1,103 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Safe #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE TypeFamilies #-} +#define USE_MAGIC_PROXY 1 +#endif + +#if USE_MAGIC_PROXY +{-# LANGUAGE MagicHash #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.IntMap.Merge.Lazy +-- Copyright : (c) wren romano 2016 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- This module defines an API for writing functions that merge two +-- maps. The key functions are 'merge' and 'mergeA'. +-- Each of these can be used with several different \"merge tactics\". +-- +-- The 'merge' and 'mergeA' functions are shared by +-- the lazy and strict modules. Only the choice of merge tactics +-- determines strictness. If you use 'Data.Map.Strict.Merge.mapMissing' +-- from "Data.Map.Strict.Merge" then the results will be forced before +-- they are inserted. If you use 'Data.Map.Lazy.Merge.mapMissing' from +-- this module then they will not. +-- +-- == Efficiency note +-- +-- The 'Category', 'Applicative', and 'Monad' instances for 'WhenMissing' +-- tactics are included because they are valid. However, they are +-- inefficient in many cases and should usually be avoided. The instances +-- for 'WhenMatched' tactics should not pose any major efficiency problems. + +module Data.IntMap.Merge.Lazy ( + -- ** Simple merge tactic types + SimpleWhenMissing + , SimpleWhenMatched + + -- ** General combining function + , merge + + -- *** @WhenMatched@ tactics + , zipWithMaybeMatched + , zipWithMatched + + -- *** @WhenMissing@ tactics + , mapMaybeMissing + , dropMissing + , preserveMissing + , mapMissing + , filterMissing + + -- ** Applicative merge tactic types + , WhenMissing + , WhenMatched + + -- ** Applicative general combining function + , mergeA + + -- *** @WhenMatched@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , zipWithMaybeAMatched + , zipWithAMatched + + -- *** @WhenMissing@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , traverseMaybeMissing + , traverseMissing + , filterAMissing + + -- *** Covariant maps for tactics + , mapWhenMissing + , mapWhenMatched + + -- *** Contravariant maps for tactics + , lmapWhenMissing + , contramapFirstWhenMatched + , contramapSecondWhenMatched + + -- *** Miscellaneous tactic functions + , runWhenMatched + , runWhenMissing + ) where + +import Data.IntMap.Internal diff --git a/Data/IntMap/Merge/Strict.hs b/Data/IntMap/Merge/Strict.hs new file mode 100644 --- /dev/null +++ b/Data/IntMap/Merge/Strict.hs @@ -0,0 +1,99 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Safe #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE TypeFamilies #-} +#define USE_MAGIC_PROXY 1 +#endif + +#if USE_MAGIC_PROXY +{-# LANGUAGE MagicHash #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.IntMap.Merge.Strict +-- Copyright : (c) wren romano 2016 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- This module defines an API for writing functions that merge two +-- maps. The key functions are 'merge' and 'mergeA'. +-- Each of these can be used with several different \"merge tactics\". +-- +-- The 'merge' and 'mergeA' functions are shared by +-- the lazy and strict modules. Only the choice of merge tactics +-- determines strictness. If you use 'Data.Map.Strict.Merge.mapMissing' +-- from this module then the results will be forced before they are +-- inserted. If you use 'Data.Map.Lazy.Merge.mapMissing' from +-- "Data.Map.Lazy.Merge" then they will not. +-- +-- == Efficiency note +-- +-- The 'Category', 'Applicative', and 'Monad' instances for 'WhenMissing' +-- tactics are included because they are valid. However, they are +-- inefficient in many cases and should usually be avoided. The instances +-- for 'WhenMatched' tactics should not pose any major efficiency problems. + +module Data.IntMap.Merge.Strict ( + -- ** Simple merge tactic types + SimpleWhenMissing + , SimpleWhenMatched + + -- ** General combining function + , merge + + -- *** @WhenMatched@ tactics + , zipWithMaybeMatched + , zipWithMatched + + -- *** @WhenMissing@ tactics + , mapMaybeMissing + , dropMissing + , preserveMissing + , mapMissing + , filterMissing + + -- ** Applicative merge tactic types + , WhenMissing + , WhenMatched + + -- ** Applicative general combining function + , mergeA + + -- *** @WhenMatched@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , zipWithMaybeAMatched + , zipWithAMatched + + -- *** @WhenMissing@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , traverseMaybeMissing + , traverseMissing + , filterAMissing + + -- ** Covariant maps for tactics + , mapWhenMissing + , mapWhenMatched + + -- ** Miscellaneous functions on tactics + + , runWhenMatched + , runWhenMissing + ) where + +import Data.IntMap.Internal diff --git a/Data/IntMap/Strict.hs b/Data/IntMap/Strict.hs --- a/Data/IntMap/Strict.hs +++ b/Data/IntMap/Strict.hs @@ -57,7 +57,7 @@ -- on strict maps, the resulting maps will be lazy. ----------------------------------------------------------------------------- --- See the notes at the beginning of Data.IntMap.Base. +-- See the notes at the beginning of Data.IntMap.Internal. module Data.IntMap.Strict ( -- * Strictness properties @@ -218,7 +218,7 @@ import Prelude hiding (lookup,map,filter,foldr,foldl,null) import Data.Bits -import Data.IntMap.Base hiding +import Data.IntMap.Internal hiding ( findWithDefault , singleton , insert @@ -264,10 +264,10 @@ , fromDistinctAscList ) -import qualified Data.IntSet.Base as IntSet -import Data.Utils.BitUtil -import Data.Utils.StrictFold -import Data.Utils.StrictPair +import qualified Data.IntSet.Internal as IntSet +import Utils.Containers.Internal.BitUtil +import Utils.Containers.Internal.StrictFold +import Utils.Containers.Internal.StrictPair #if __GLASGOW_HASKELL__ >= 709 import Data.Coerce #endif @@ -304,7 +304,7 @@ -- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' -- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' --- See IntMap.Base.Note: Local 'go' functions and capturing] +-- See IntMap.Internal.Note: Local 'go' functions and capturing] findWithDefault :: a -> Key -> IntMap a -> a findWithDefault def !k = go where diff --git a/Data/IntSet.hs b/Data/IntSet.hs --- a/Data/IntSet.hs +++ b/Data/IntSet.hs @@ -140,7 +140,7 @@ #endif ) where -import Data.IntSet.Base as IS +import Data.IntSet.Internal as IS -- $strictness -- diff --git a/Data/IntSet/Base.hs b/Data/IntSet/Base.hs deleted file mode 100644 --- a/Data/IntSet/Base.hs +++ /dev/null @@ -1,1502 +0,0 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE MagicHash, DeriveDataTypeable, StandaloneDeriving #-} -#endif -#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Trustworthy #-} -#endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE TypeFamilies #-} -#endif - -#include "containers.h" -{-# OPTIONS_HADDOCK hide #-} - ------------------------------------------------------------------------------ --- | --- Module : Data.IntSet.Base --- Copyright : (c) Daan Leijen 2002 --- (c) Joachim Breitner 2011 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : provisional --- Portability : portable --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. --- --- = Description --- --- 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, --- --- --- * 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(..), Key -- 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 - , splitRoot - - -- * 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 - , suffixBitMask - , prefixBitMask - , bitmapOf - ) where - -import Control.DeepSeq (NFData(rnf)) -import Data.Bits -import qualified Data.List as List -import Data.Maybe (fromMaybe) -#if !MIN_VERSION_base(4,8,0) -import Data.Monoid (Monoid(..)) -import Data.Word (Word) -#endif -#if MIN_VERSION_base(4,9,0) -import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) -#endif -import Data.Typeable -import Prelude hiding (filter, foldr, foldl, null, map) - -import Data.Utils.BitUtil -import Data.Utils.StrictFold -import Data.Utils.StrictPair - -#if __GLASGOW_HASKELL__ -import Data.Data (Data(..), Constr, mkConstr, constrIndex, Fixity(Prefix), DataType, mkDataType) -import Text.Read -#endif - -#if __GLASGOW_HASKELL__ -import GHC.Exts (Int(..), build) -#if __GLASGOW_HASKELL__ >= 708 -import qualified GHC.Exts as GHCExts -#endif -import GHC.Prim (indexInt8OffAddr#) -#endif - - -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 #-} - -{-------------------------------------------------------------------- - 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 -type Key = Int - -instance Monoid IntSet where - mempty = empty - mconcat = unions -#if !(MIN_VERSION_base(4,9,0)) - mappend = union -#else - mappend = (<>) - -instance Semigroup IntSet where - (<>) = union - stimes = stimesIdempotentMonoid -#endif - -#if __GLASGOW_HASKELL__ - -{-------------------------------------------------------------------- - A Data instance ---------------------------------------------------------------------} - --- This instance preserves data abstraction at the cost of inefficiency. --- We provide limited reflection services for the sake of data abstraction. - -instance Data IntSet where - gfoldl f z is = z fromList `f` (toList is) - toConstr _ = fromListConstr - gunfold k z c = case constrIndex c of - 1 -> k (z fromList) - _ -> error "gunfold" - dataTypeOf _ = intSetDataType - -fromListConstr :: Constr -fromListConstr = mkConstr intSetDataType "fromList" [] Prefix - -intSetDataType :: DataType -intSetDataType = mkDataType "Data.IntSet.Base.IntSet" [fromListConstr] - -#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 (Bin _ _ l r) = size l + size r -size (Tip _ bm) = bitcount 0 bm -size Nil = 0 - --- | /O(min(n,W))/. Is the value a member of the set? - --- See Note: Local 'go' functions and capturing] -member :: Key -> IntSet -> Bool -member !x = 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 :: Key -> 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 :: Key -> IntSet -> Maybe Key -lookupLT !x t = 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 :: Key -> IntSet -> Maybe Key -lookupGT !x t = 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 :: Key -> IntSet -> Maybe Key -lookupLE !x t = 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 :: Key -> IntSet -> Maybe Key -lookupGE !x t = 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 Key -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 Key -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 :: Key -> 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 :: Key -> IntSet -> IntSet -insert !x = insertBM (prefixOf x) (bitmapOf x) - --- Helper function for insert and union. -insertBM :: Prefix -> BitMap -> IntSet -> IntSet -insertBM !kx !bm t@(Bin p m l r) - | nomatch kx p m = link 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) -insertBM kx bm t@(Tip kx' bm') - | kx' == kx = Tip kx' (bm .|. bm') - | otherwise = link kx (Tip kx bm) kx' t -insertBM kx bm 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 :: Key -> IntSet -> IntSet -delete !x = 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@(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) -deleteBM kx bm t@(Tip kx' bm') - | kx' == kx = tip kx (bm' .&. complement bm) - | otherwise = t -deleteBM _ _ 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 = link p1 t1 p2 t2 - where - union1 | nomatch p2 p1 m1 = link 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 = link 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 :: (Key -> 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 :: (Key -> Bool) -> IntSet -> (IntSet,IntSet) -partition predicate0 t0 = toPair $ go predicate0 t0 - where - go predicate t - = case t of - Bin p m l r - -> let (l1 :*: l2) = go predicate l - (r1 :*: r2) = go 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 :: Key -> IntSet -> (IntSet,IntSet) -split x t = - case t of - Bin _ m l r - | m < 0 -> if x >= 0 -- handle negative numbers. - then case go x l of (lt :*: gt) -> let !lt' = union lt r - in (lt', gt) - else case go x r of (lt :*: gt) -> let !gt' = union gt l - in (lt, gt') - _ -> case go x t of - (lt :*: gt) -> (lt, gt) - 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 :: Key -> 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) -> let !lt' = union lt r - in (lt', fnd, gt) - else case go x r of - (lt, fnd, gt) -> let !gt' = union gt l - in (lt, fnd, gt') - _ -> 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 = let !lt = tip kx' (bm .&. lowerBitmap) - !found = (bm .&. bitmapOfx') /= 0 - !gt = tip kx' (bm .&. higherBitmap) - in (lt, found, gt) - 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 (Key, 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 (Key, 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 -> (Key, 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 -> (Key, IntSet) -deleteFindMax = fromMaybe (error "deleteFindMax: empty set has no maximal element") . maxView - - --- | /O(min(n,W))/. The minimal element of the set. -findMin :: IntSet -> Key -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 -> Key -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. Returns an empty set if the set is empty. --- --- Note that this is a change of behaviour for consistency with 'Data.Set.Set' – --- versions prior to 0.5 threw an error if the 'IntSet' was already empty. -deleteMin :: IntSet -> IntSet -deleteMin = maybe Nil snd . minView - --- | /O(min(n,W))/. Delete the maximal element. Returns an empty set if the set is empty. --- --- Note that this is a change of behaviour for consistency with 'Data.Set.Set' – --- versions prior to 0.5 threw an error if the 'IntSet' was already empty. -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 :: (Key -> Key) -> 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 :: (Key -> 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 :: (Key -> 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' :: (Key -> 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) = 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 -> Key -> 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 - 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 -> Key -> 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 - 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 -> [Key] -elems - = toAscList - -{-------------------------------------------------------------------- - Lists ---------------------------------------------------------------------} -#if __GLASGOW_HASKELL__ >= 708 -instance GHCExts.IsList IntSet where - type Item IntSet = Key - fromList = fromList - toList = toList -#endif - --- | /O(n)/. Convert the set to a list of elements. Subject to list fusion. -toList :: IntSet -> [Key] -toList - = toAscList - --- | /O(n)/. Convert the set to an ascending list of elements. Subject to list --- fusion. -toAscList :: IntSet -> [Key] -toAscList = foldr (:) [] - --- | /O(n)/. Convert the set to a descending list of elements. Subject to list --- fusion. -toDescList :: IntSet -> [Key] -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 :: (Key -> b -> b) -> b -> IntSet -> b -foldrFB = foldr -{-# INLINE[0] foldrFB #-} -foldlFB :: (a -> Key -> 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 :: [Key] -> 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 :: [Key] -> 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 :: [Key] -> 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 (link 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 ---------------------------------------------------------------------} - -INSTANCE_TYPEABLE0(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 where rnf x = seq x () - -{-------------------------------------------------------------------- - 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 [] = id -showsBars bars = 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 ---------------------------------------------------------------------} -{-------------------------------------------------------------------- - Link ---------------------------------------------------------------------} -link :: Prefix -> IntSet -> Prefix -> IntSet -> IntSet -link 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 link #-} - -{-------------------------------------------------------------------- - @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 -#if MIN_VERSION_base(4,7,0) -suffixBitMask = finiteBitSize (undefined::Word) - 1 -#else -suffixBitMask = bitSize (undefined::Word) - 1 -#endif -{-# 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 #-} - -{---------------------------------------------------------------------- - 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 - - - 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 0 acc = acc - go bm acc = go (bm `xor` bitmask) ((f acc) $! (prefix+bi)) - where - !bitmask = lowestBitMask bm - !bi = indexOfTheOnlyBit bitmask - -foldl'Bits prefix f z bitmap = go bitmap z - where go 0 acc = acc - go bm !acc = go (bm `xor` bitmask) ((f acc) $! (prefix+bi)) - where !bitmask = lowestBitMask bm - !bi = indexOfTheOnlyBit bitmask - -foldrBits prefix f z bitmap = go (revNat bitmap) z - where go 0 acc = acc - go bm acc = go (bm `xor` bitmask) ((f $! (prefix+(WORD_SIZE_IN_BITS-1)-bi)) acc) - where !bitmask = lowestBitMask bm - !bi = indexOfTheOnlyBit bitmask - - -foldr'Bits prefix f z bitmap = go (revNat bitmap) z - where go 0 acc = acc - go bm !acc = go (bm `xor` bitmask) ((f $! (prefix+(WORD_SIZE_IN_BITS-1)-bi)) acc) - where !bitmask = lowestBitMask bm - !bi = indexOfTheOnlyBit bitmask - -#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 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 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 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 - 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 -#if MIN_VERSION_base(4,5,0) -bitcount a x = a + popCount x -#else -bitcount a0 x0 = go a0 x0 - where go a 0 = a - go a x = go (a + 1) (x .&. (x-1)) -#endif -{-# INLINE bitcount #-} - - -{-------------------------------------------------------------------- - Utilities ---------------------------------------------------------------------} - --- | /O(1)/. Decompose a set into pieces based on the structure of the underlying --- tree. This function is useful for consuming a set in parallel. --- --- No guarantee is made as to the sizes of the pieces; an internal, but --- deterministic process determines this. However, it is guaranteed that the --- pieces returned will be in ascending order (all elements in the first submap --- less than all elements in the second, and so on). --- --- Examples: --- --- > splitRoot (fromList [1..120]) == [fromList [1..63],fromList [64..120]] --- > splitRoot empty == [] --- --- Note that the current implementation does not return more than two subsets, --- but you should not depend on this behaviour because it can change in the --- future without notice. Also, the current version does not continue --- splitting all the way to individual singleton sets -- it stops at some --- point. -splitRoot :: IntSet -> [IntSet] -splitRoot Nil = [] --- NOTE: we don't currently split below Tip, but we could. -splitRoot x@(Tip _ _) = [x] -splitRoot (Bin _ m l r) | m < 0 = [r, l] - | otherwise = [l, r] -{-# INLINE splitRoot #-} diff --git a/Data/IntSet/Internal.hs b/Data/IntSet/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/IntSet/Internal.hs @@ -0,0 +1,1501 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE MagicHash, DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Trustworthy #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE TypeFamilies #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.IntSet.Internal +-- Copyright : (c) Daan Leijen 2002 +-- (c) Joachim Breitner 2011 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. +-- +-- = Description +-- +-- 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, +-- +-- +-- * 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.Internal ( + -- * Set type + IntSet(..), Key -- 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 + , splitRoot + + -- * 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 + , suffixBitMask + , prefixBitMask + , bitmapOf + ) where + +import Control.DeepSeq (NFData(rnf)) +import Data.Bits +import qualified Data.List as List +import Data.Maybe (fromMaybe) +#if !MIN_VERSION_base(4,8,0) +import Data.Monoid (Monoid(..)) +import Data.Word (Word) +#endif +#if MIN_VERSION_base(4,9,0) +import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) +#endif +import Data.Typeable +import Prelude hiding (filter, foldr, foldl, null, map) + +import Utils.Containers.Internal.BitUtil +import Utils.Containers.Internal.StrictFold +import Utils.Containers.Internal.StrictPair + +#if __GLASGOW_HASKELL__ +import Data.Data (Data(..), Constr, mkConstr, constrIndex, Fixity(Prefix), DataType, mkDataType) +import Text.Read +#endif + +#if __GLASGOW_HASKELL__ +import GHC.Exts (Int(..), build) +#if __GLASGOW_HASKELL__ >= 708 +import qualified GHC.Exts as GHCExts +#endif +import GHC.Prim (indexInt8OffAddr#) +#endif + + +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 #-} + +{-------------------------------------------------------------------- + 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 +type Key = Int + +instance Monoid IntSet where + mempty = empty + mconcat = unions +#if !(MIN_VERSION_base(4,9,0)) + mappend = union +#else + mappend = (<>) + +instance Semigroup IntSet where + (<>) = union + stimes = stimesIdempotentMonoid +#endif + +#if __GLASGOW_HASKELL__ + +{-------------------------------------------------------------------- + A Data instance +--------------------------------------------------------------------} + +-- This instance preserves data abstraction at the cost of inefficiency. +-- We provide limited reflection services for the sake of data abstraction. + +instance Data IntSet where + gfoldl f z is = z fromList `f` (toList is) + toConstr _ = fromListConstr + gunfold k z c = case constrIndex c of + 1 -> k (z fromList) + _ -> error "gunfold" + dataTypeOf _ = intSetDataType + +fromListConstr :: Constr +fromListConstr = mkConstr intSetDataType "fromList" [] Prefix + +intSetDataType :: DataType +intSetDataType = mkDataType "Data.IntSet.Internal.IntSet" [fromListConstr] + +#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 (Bin _ _ l r) = size l + size r +size (Tip _ bm) = bitcount 0 bm +size Nil = 0 + +-- | /O(min(n,W))/. Is the value a member of the set? + +-- See Note: Local 'go' functions and capturing] +member :: Key -> IntSet -> Bool +member !x = 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 :: Key -> 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 :: Key -> IntSet -> Maybe Key +lookupLT !x t = 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 :: Key -> IntSet -> Maybe Key +lookupGT !x t = 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 :: Key -> IntSet -> Maybe Key +lookupLE !x t = 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 :: Key -> IntSet -> Maybe Key +lookupGE !x t = 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 Key +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 Key +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 :: Key -> 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 :: Key -> IntSet -> IntSet +insert !x = insertBM (prefixOf x) (bitmapOf x) + +-- Helper function for insert and union. +insertBM :: Prefix -> BitMap -> IntSet -> IntSet +insertBM !kx !bm t@(Bin p m l r) + | nomatch kx p m = link 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) +insertBM kx bm t@(Tip kx' bm') + | kx' == kx = Tip kx' (bm .|. bm') + | otherwise = link kx (Tip kx bm) kx' t +insertBM kx bm 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 :: Key -> IntSet -> IntSet +delete !x = 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@(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) +deleteBM kx bm t@(Tip kx' bm') + | kx' == kx = tip kx (bm' .&. complement bm) + | otherwise = t +deleteBM _ _ 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 = link p1 t1 p2 t2 + where + union1 | nomatch p2 p1 m1 = link 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 = link 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 :: (Key -> 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 :: (Key -> Bool) -> IntSet -> (IntSet,IntSet) +partition predicate0 t0 = toPair $ go predicate0 t0 + where + go predicate t + = case t of + Bin p m l r + -> let (l1 :*: l2) = go predicate l + (r1 :*: r2) = go 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 :: Key -> IntSet -> (IntSet,IntSet) +split x t = + case t of + Bin _ m l r + | m < 0 -> if x >= 0 -- handle negative numbers. + then case go x l of (lt :*: gt) -> let !lt' = union lt r + in (lt', gt) + else case go x r of (lt :*: gt) -> let !gt' = union gt l + in (lt, gt') + _ -> case go x t of + (lt :*: gt) -> (lt, gt) + 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 :: Key -> 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) -> let !lt' = union lt r + in (lt', fnd, gt) + else case go x r of + (lt, fnd, gt) -> let !gt' = union gt l + in (lt, fnd, gt') + _ -> 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 = let !lt = tip kx' (bm .&. lowerBitmap) + !found = (bm .&. bitmapOfx') /= 0 + !gt = tip kx' (bm .&. higherBitmap) + in (lt, found, gt) + 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 (Key, 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 (Key, 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 -> (Key, 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 -> (Key, IntSet) +deleteFindMax = fromMaybe (error "deleteFindMax: empty set has no maximal element") . maxView + + +-- | /O(min(n,W))/. The minimal element of the set. +findMin :: IntSet -> Key +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 -> Key +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. Returns an empty set if the set is empty. +-- +-- Note that this is a change of behaviour for consistency with 'Data.Set.Set' – +-- versions prior to 0.5 threw an error if the 'IntSet' was already empty. +deleteMin :: IntSet -> IntSet +deleteMin = maybe Nil snd . minView + +-- | /O(min(n,W))/. Delete the maximal element. Returns an empty set if the set is empty. +-- +-- Note that this is a change of behaviour for consistency with 'Data.Set.Set' – +-- versions prior to 0.5 threw an error if the 'IntSet' was already empty. +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 :: (Key -> Key) -> 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 :: (Key -> 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 :: (Key -> 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' :: (Key -> 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) = 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 -> Key -> 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 + 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 -> Key -> 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 + 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 -> [Key] +elems + = toAscList + +{-------------------------------------------------------------------- + Lists +--------------------------------------------------------------------} +#if __GLASGOW_HASKELL__ >= 708 +instance GHCExts.IsList IntSet where + type Item IntSet = Key + fromList = fromList + toList = toList +#endif + +-- | /O(n)/. Convert the set to a list of elements. Subject to list fusion. +toList :: IntSet -> [Key] +toList + = toAscList + +-- | /O(n)/. Convert the set to an ascending list of elements. Subject to list +-- fusion. +toAscList :: IntSet -> [Key] +toAscList = foldr (:) [] + +-- | /O(n)/. Convert the set to a descending list of elements. Subject to list +-- fusion. +toDescList :: IntSet -> [Key] +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 :: (Key -> b -> b) -> b -> IntSet -> b +foldrFB = foldr +{-# INLINE[0] foldrFB #-} +foldlFB :: (a -> Key -> 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 :: [Key] -> 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 :: [Key] -> 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 :: [Key] -> 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 (link 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 +--------------------------------------------------------------------} + +INSTANCE_TYPEABLE0(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 where rnf x = seq x () + +{-------------------------------------------------------------------- + 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 [] = id +showsBars bars = 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 +--------------------------------------------------------------------} +{-------------------------------------------------------------------- + Link +--------------------------------------------------------------------} +link :: Prefix -> IntSet -> Prefix -> IntSet -> IntSet +link 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 link #-} + +{-------------------------------------------------------------------- + @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 +#if MIN_VERSION_base(4,7,0) +suffixBitMask = finiteBitSize (undefined::Word) - 1 +#else +suffixBitMask = bitSize (undefined::Word) - 1 +#endif +{-# 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 #-} + +{---------------------------------------------------------------------- + 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 + + + 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 0 acc = acc + go bm acc = go (bm `xor` bitmask) ((f acc) $! (prefix+bi)) + where + !bitmask = lowestBitMask bm + !bi = indexOfTheOnlyBit bitmask + +foldl'Bits prefix f z bitmap = go bitmap z + where go 0 acc = acc + go bm !acc = go (bm `xor` bitmask) ((f acc) $! (prefix+bi)) + where !bitmask = lowestBitMask bm + !bi = indexOfTheOnlyBit bitmask + +foldrBits prefix f z bitmap = go (revNat bitmap) z + where go 0 acc = acc + go bm acc = go (bm `xor` bitmask) ((f $! (prefix+(WORD_SIZE_IN_BITS-1)-bi)) acc) + where !bitmask = lowestBitMask bm + !bi = indexOfTheOnlyBit bitmask + + +foldr'Bits prefix f z bitmap = go (revNat bitmap) z + where go 0 acc = acc + go bm !acc = go (bm `xor` bitmask) ((f $! (prefix+(WORD_SIZE_IN_BITS-1)-bi)) acc) + where !bitmask = lowestBitMask bm + !bi = indexOfTheOnlyBit bitmask + +#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 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 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 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 + 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 +#if MIN_VERSION_base(4,5,0) +bitcount a x = a + popCount x +#else +bitcount a0 x0 = go a0 x0 + where go a 0 = a + go a x = go (a + 1) (x .&. (x-1)) +#endif +{-# INLINE bitcount #-} + + +{-------------------------------------------------------------------- + Utilities +--------------------------------------------------------------------} + +-- | /O(1)/. Decompose a set into pieces based on the structure of the underlying +-- tree. This function is useful for consuming a set in parallel. +-- +-- No guarantee is made as to the sizes of the pieces; an internal, but +-- deterministic process determines this. However, it is guaranteed that the +-- pieces returned will be in ascending order (all elements in the first submap +-- less than all elements in the second, and so on). +-- +-- Examples: +-- +-- > splitRoot (fromList [1..120]) == [fromList [1..63],fromList [64..120]] +-- > splitRoot empty == [] +-- +-- Note that the current implementation does not return more than two subsets, +-- but you should not depend on this behaviour because it can change in the +-- future without notice. Also, the current version does not continue +-- splitting all the way to individual singleton sets -- it stops at some +-- point. +splitRoot :: IntSet -> [IntSet] +splitRoot Nil = [] +-- NOTE: we don't currently split below Tip, but we could. +splitRoot x@(Tip _ _) = [x] +splitRoot (Bin _ m l r) | m < 0 = [r, l] + | otherwise = [l, r] +{-# INLINE splitRoot #-} diff --git a/Data/Map/Base.hs b/Data/Map/Base.hs deleted file mode 100644 --- a/Data/Map/Base.hs +++ /dev/null @@ -1,4135 +0,0 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} -#endif -#if __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Trustworthy #-} -#endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE RoleAnnotations #-} -{-# LANGUAGE TypeFamilies #-} -#define USE_MAGIC_PROXY 1 -#endif - -#if USE_MAGIC_PROXY -{-# LANGUAGE MagicHash #-} -#endif - -#include "containers.h" - -#if !(WORD_SIZE_IN_BITS >= 61) -#define DEFINE_ALTERF_FALLBACK 1 -#endif - -{-# OPTIONS_HADDOCK hide #-} - ------------------------------------------------------------------------------ --- | --- Module : Data.Map.Base --- Copyright : (c) Daan Leijen 2002 --- (c) Andriy Palamarchuk 2008 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : provisional --- Portability : portable --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. --- --- = Description --- --- An efficient implementation of maps from keys to values (dictionaries). --- --- Since many function names (but not the type name) clash with --- "Prelude" names, this module is usually imported @qualified@, e.g. --- --- > import Data.Map (Map) --- > import qualified Data.Map as Map --- --- The implementation of 'Map' is based on /size balanced/ binary trees (or --- trees of /bounded balance/) as described by: --- --- * Stephen Adams, \"/Efficient sets: a balancing act/\", --- Journal of Functional Programming 3(4):553-562, October 1993, --- . --- * J. Nievergelt and E.M. Reingold, --- \"/Binary search trees of bounded balance/\", --- SIAM journal of computing 2(1), March 1973. --- --- Bounds for 'union', 'intersection', and 'difference' are as given --- by --- --- * Guy Blelloch, Daniel Ferizovic, and Yihan Sun, --- \"/Just Join for Parallel Ordered Sets/\", --- . --- --- Note that the implementation is /left-biased/ -- the elements of a --- first argument are always preferred to the second, for example in --- 'union' or 'insert'. --- --- Operation comments contain the operation time complexity in --- the Big-O notation . ------------------------------------------------------------------------------ - --- [Note: Using INLINABLE] --- ~~~~~~~~~~~~~~~~~~~~~~~ --- It is crucial to the performance that the functions specialize on the Ord --- type when possible. GHC 7.0 and higher does this by itself when it sees th --- unfolding of a function -- that is why all public functions are marked --- INLINABLE (that exposes the unfolding). - - --- [Note: Using INLINE] --- ~~~~~~~~~~~~~~~~~~~~ --- For other compilers and GHC pre 7.0, we mark some of the functions INLINE. --- We mark the functions that just navigate down the tree (lookup, insert, --- delete and similar). That navigation code gets inlined and thus specialized --- when possible. There is a price to pay -- code growth. The code INLINED is --- therefore only the tree navigation, all the real work (rebalancing) is not --- INLINED by using a NOINLINE. --- --- All methods marked INLINE have to be nonrecursive -- a 'go' function doing --- the real work is provided. - - --- [Note: Type of local 'go' function] --- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- If the local 'go' function uses an Ord class, it sometimes heap-allocates --- the Ord dictionary when the 'go' function does not have explicit type. --- In that case we give 'go' explicit type. But this slightly decrease --- performance, as the resulting 'go' function can float out to top level. - - --- [Note: Local 'go' functions and capturing] --- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- As opposed to Map, when 'go' function captures an argument, increased --- heap-allocation can occur: sometimes in a polymorphic function, the 'go' --- floats out of its enclosing function and then it heap-allocates the --- dictionary and the argument. Maybe it floats out too late and strictness --- analyzer cannot see that these could be passed on stack. --- - --- [Note: Order of constructors] --- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- The order of constructors of Map matters when considering performance. --- Currently in GHC 7.0, when type has 2 constructors, a forward conditional --- jump is made when successfully matching second constructor. Successful match --- of first constructor results in the forward jump not taken. --- On GHC 7.0, reordering constructors from Tip | Bin to Bin | Tip --- improves the benchmark by up to 10% on x86. - -module Data.Map.Base ( - -- * Map type - Map(..) -- instance Eq,Show,Read - - -- * Operators - , (!), (\\) - - -- * Query - , null - , size - , member - , notMember - , lookup - , findWithDefault - , lookupLT - , lookupGT - , lookupLE - , lookupGE - - -- * Construction - , empty - , singleton - - -- ** Insertion - , insert - , insertWith - , insertWithKey - , insertLookupWithKey - - -- ** Delete\/Update - , delete - , adjust - , adjustWithKey - , update - , updateWithKey - , updateLookupWithKey - , alter - , alterF - - -- * Combine - - -- ** Union - , union - , unionWith - , unionWithKey - , unions - , unionsWith - - -- ** Difference - , difference - , differenceWith - , differenceWithKey - - -- ** Intersection - , intersection - , intersectionWith - , intersectionWithKey - - -- ** General combining function - , SimpleWhenMissing - , SimpleWhenMatched - , runWhenMatched - , runWhenMissing - , merge - -- *** @WhenMatched@ tactics - , zipWithMaybeMatched - , zipWithMatched - -- *** @WhenMissing@ tactics - , mapMaybeMissing - , dropMissing - , preserveMissing - , mapMissing - , filterMissing - - -- ** Applicative general combining function - , WhenMissing (..) - , WhenMatched (..) - , mergeA - - -- *** @WhenMatched@ tactics - -- | The tactics described for 'merge' work for - -- 'mergeA' as well. Furthermore, the following - -- are available. - , zipWithMaybeAMatched - , zipWithAMatched - - -- *** @WhenMissing@ tactics - -- | The tactics described for 'merge' work for - -- 'mergeA' as well. Furthermore, the following - -- are available. - , traverseMaybeMissing - , traverseMissing - , filterAMissing - - -- ** Deprecated general combining function - - , mergeWithKey - - -- * Traversal - -- ** Map - , map - , mapWithKey - , traverseWithKey - , traverseMaybeWithKey - , mapAccum - , mapAccumWithKey - , mapAccumRWithKey - , mapKeys - , mapKeysWith - , mapKeysMonotonic - - -- * Folds - , foldr - , foldl - , foldrWithKey - , foldlWithKey - , foldMapWithKey - - -- ** Strict folds - , foldr' - , foldl' - , foldrWithKey' - , foldlWithKey' - - -- * Conversion - , elems - , keys - , assocs - , keysSet - , fromSet - - -- ** Lists - , toList - , fromList - , fromListWith - , fromListWithKey - - -- ** Ordered lists - , toAscList - , toDescList - , fromAscList - , fromAscListWith - , fromAscListWithKey - , fromDistinctAscList - , fromDescList - , fromDescListWith - , fromDescListWithKey - , fromDistinctDescList - - -- * Filter - , filter - , filterWithKey - - , takeWhileAntitone - , dropWhileAntitone - , spanAntitone - - , restrictKeys - , withoutKeys - , partition - , partitionWithKey - - , mapMaybe - , mapMaybeWithKey - , mapEither - , mapEitherWithKey - - , split - , splitLookup - , splitRoot - - -- * Submap - , isSubmapOf, isSubmapOfBy - , isProperSubmapOf, isProperSubmapOfBy - - -- * Indexed - , lookupIndex - , findIndex - , elemAt - , updateAt - , deleteAt - , take - , drop - , splitAt - - -- * Min\/Max - , findMin - , findMax - , deleteMin - , deleteMax - , deleteFindMin - , deleteFindMax - , updateMin - , updateMax - , updateMinWithKey - , updateMaxWithKey - , minView - , maxView - , minViewWithKey - , maxViewWithKey - - -- * Debugging - , showTree - , showTreeWith - , valid - - -- Used by the strict version - , AreWeStrict (..) - , atKeyImpl -#if __GLASGOW_HASKELL__ && MIN_VERSION_base(4,8,0) - , atKeyPlain -#endif - , bin - , balance - , balanced - , balanceL - , balanceR - , delta - , insertMax - , link - , link2 - , glue - , MaybeS(..) - , Identity(..) - - -- Used by Map.Lazy.Merge - , mapWhenMissing - , mapWhenMatched - , lmapWhenMissing - , contramapFirstWhenMatched - , contramapSecondWhenMatched - , mapGentlyWhenMissing - , mapGentlyWhenMatched - ) where - -#if MIN_VERSION_base(4,8,0) -import Data.Functor.Identity (Identity (..)) -#else -import Control.Applicative (Applicative(..), (<$>)) -import Data.Monoid (Monoid(..)) -import Data.Traversable (Traversable(traverse)) -#endif -#if MIN_VERSION_base(4,9,0) -import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) -#endif -import Control.Applicative (Const (..)) -import Control.DeepSeq (NFData(rnf)) -import Data.Bits (shiftL, shiftR) -import qualified Data.Foldable as Foldable -import Data.Typeable -import Prelude hiding (lookup, map, filter, foldr, foldl, null, splitAt, take, drop) - -import qualified Data.Set.Base as Set -import Data.Set.Base (Set) -import Data.Utils.PtrEquality (ptrEq) -import Data.Utils.StrictFold -import Data.Utils.StrictPair -import Data.Utils.StrictMaybe -import Data.Utils.BitQueue -#if DEFINE_ALTERF_FALLBACK -import Data.Utils.BitUtil (wordSize) -#endif - -#if __GLASGOW_HASKELL__ -import GHC.Exts (build) -#if !MIN_VERSION_base(4,8,0) -import Data.Functor ((<$)) -#endif -#if USE_MAGIC_PROXY -import GHC.Exts (Proxy#, proxy# ) -#endif -#if __GLASGOW_HASKELL__ >= 708 -import qualified GHC.Exts as GHCExts -#endif -import Text.Read hiding (lift) -import Data.Data -import qualified Control.Category as Category -#endif -#if __GLASGOW_HASKELL__ >= 708 -import Data.Coerce -#endif - - -{-------------------------------------------------------------------- - Operators ---------------------------------------------------------------------} -infixl 9 !,\\ -- - --- | /O(log n)/. Find the value at a key. --- Calls 'error' when the element can not be found. --- --- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map --- > fromList [(5,'a'), (3,'b')] ! 5 == 'a' - -(!) :: Ord k => Map k a -> k -> a -(!) m k = find k m -#if __GLASGOW_HASKELL__ -{-# INLINABLE (!) #-} -#endif - --- | Same as 'difference'. -(\\) :: Ord k => Map k a -> Map k b -> Map k a -m1 \\ m2 = difference m1 m2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE (\\) #-} -#endif - -{-------------------------------------------------------------------- - Size balanced trees. ---------------------------------------------------------------------} --- | A Map from keys @k@ to values @a@. - --- See Note: Order of constructors -data Map k a = Bin {-# UNPACK #-} !Size !k a !(Map k a) !(Map k a) - | Tip - -type Size = Int - -#if __GLASGOW_HASKELL__ >= 708 -type role Map nominal representational -#endif - -instance (Ord k) => Monoid (Map k v) where - mempty = empty - mconcat = unions -#if !(MIN_VERSION_base(4,9,0)) - mappend = union -#else - mappend = (<>) - -instance (Ord k) => Semigroup (Map k v) where - (<>) = union - stimes = stimesIdempotentMonoid -#endif - -#if __GLASGOW_HASKELL__ - -{-------------------------------------------------------------------- - A Data instance ---------------------------------------------------------------------} - --- This instance preserves data abstraction at the cost of inefficiency. --- We provide limited reflection services for the sake of data abstraction. - -instance (Data k, Data a, Ord k) => Data (Map k a) where - gfoldl f z m = z fromList `f` toList m - toConstr _ = fromListConstr - gunfold k z c = case constrIndex c of - 1 -> k (z fromList) - _ -> error "gunfold" - dataTypeOf _ = mapDataType - dataCast2 f = gcast2 f - -fromListConstr :: Constr -fromListConstr = mkConstr mapDataType "fromList" [] Prefix - -mapDataType :: DataType -mapDataType = mkDataType "Data.Map.Base.Map" [fromListConstr] - -#endif - -{-------------------------------------------------------------------- - Query ---------------------------------------------------------------------} --- | /O(1)/. Is the map empty? --- --- > Data.Map.null (empty) == True --- > Data.Map.null (singleton 1 'a') == False - -null :: Map k a -> Bool -null Tip = True -null (Bin {}) = False -{-# INLINE null #-} - --- | /O(1)/. The number of elements in the map. --- --- > size empty == 0 --- > size (singleton 1 'a') == 1 --- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3 - -size :: Map k a -> Int -size Tip = 0 -size (Bin sz _ _ _ _) = sz -{-# INLINE size #-} - - --- | /O(log n)/. Lookup the value at a key in the map. --- --- The function will return the corresponding value as @('Just' value)@, --- or 'Nothing' if the key isn't in the map. --- --- An example of using @lookup@: --- --- > import Prelude hiding (lookup) --- > import Data.Map --- > --- > employeeDept = fromList([("John","Sales"), ("Bob","IT")]) --- > deptCountry = fromList([("IT","USA"), ("Sales","France")]) --- > countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")]) --- > --- > employeeCurrency :: String -> Maybe String --- > employeeCurrency name = do --- > dept <- lookup name employeeDept --- > country <- lookup dept deptCountry --- > lookup country countryCurrency --- > --- > main = do --- > putStrLn $ "John's currency: " ++ (show (employeeCurrency "John")) --- > putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete")) --- --- The output of this program: --- --- > John's currency: Just "Euro" --- > Pete's currency: Nothing -lookup :: Ord k => k -> Map k a -> Maybe a -lookup = go - where - go !_ Tip = Nothing - go k (Bin _ kx x l r) = case compare k kx of - LT -> go k l - GT -> go k r - EQ -> Just x -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookup #-} -#else -{-# INLINE lookup #-} -#endif - --- | /O(log n)/. Is the key a member of the map? See also 'notMember'. --- --- > member 5 (fromList [(5,'a'), (3,'b')]) == True --- > member 1 (fromList [(5,'a'), (3,'b')]) == False -member :: Ord k => k -> Map k a -> Bool -member = go - where - go !_ Tip = False - go k (Bin _ kx _ l r) = case compare k kx of - LT -> go k l - GT -> go k r - EQ -> True -#if __GLASGOW_HASKELL__ -{-# INLINABLE member #-} -#else -{-# INLINE member #-} -#endif - --- | /O(log n)/. Is the key not a member of the map? See also 'member'. --- --- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False --- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True - -notMember :: Ord k => k -> Map k a -> Bool -notMember k m = not $ member k m -#if __GLASGOW_HASKELL__ -{-# INLINABLE notMember #-} -#else -{-# INLINE notMember #-} -#endif - --- | /O(log n)/. Find the value at a key. --- Calls 'error' when the element can not be found. -find :: Ord k => k -> Map k a -> a -find = go - where - go !_ Tip = error "Map.!: given key is not an element in the map" - go k (Bin _ kx x l r) = case compare k kx of - LT -> go k l - GT -> go k r - EQ -> x -#if __GLASGOW_HASKELL__ -{-# INLINABLE find #-} -#else -{-# INLINE find #-} -#endif - --- | /O(log n)/. The expression @('findWithDefault' def k map)@ returns --- the value at key @k@ or returns default value @def@ --- when the key is not in the map. --- --- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' --- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' -findWithDefault :: Ord k => a -> k -> Map k a -> a -findWithDefault = go - where - go def !_ Tip = def - go def k (Bin _ kx x l r) = case compare k kx of - LT -> go def k l - GT -> go def k r - EQ -> x -#if __GLASGOW_HASKELL__ -{-# INLINABLE findWithDefault #-} -#else -{-# INLINE findWithDefault #-} -#endif - --- | /O(log n)/. Find largest key smaller than the given one and return the --- corresponding (key, value) pair. --- --- > lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing --- > lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') -lookupLT :: Ord k => k -> Map k v -> Maybe (k, v) -lookupLT = goNothing - where - goNothing !_ Tip = Nothing - goNothing k (Bin _ kx x l r) | k <= kx = goNothing k l - | otherwise = goJust k kx x r - - goJust !_ kx' x' Tip = Just (kx', x') - goJust k kx' x' (Bin _ kx x l r) | k <= kx = goJust k kx' x' l - | otherwise = goJust k kx x r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupLT #-} -#else -{-# INLINE lookupLT #-} -#endif - --- | /O(log n)/. Find smallest key greater than the given one and return the --- corresponding (key, value) pair. --- --- > lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') --- > lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing -lookupGT :: Ord k => k -> Map k v -> Maybe (k, v) -lookupGT = goNothing - where - goNothing !_ Tip = Nothing - goNothing k (Bin _ kx x l r) | k < kx = goJust k kx x l - | otherwise = goNothing k r - - goJust !_ kx' x' Tip = Just (kx', x') - goJust k kx' x' (Bin _ kx x l r) | k < kx = goJust k kx x l - | otherwise = goJust k kx' x' r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupGT #-} -#else -{-# INLINE lookupGT #-} -#endif - --- | /O(log n)/. Find largest key smaller or equal to the given one and return --- the corresponding (key, value) pair. --- --- > lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing --- > lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') --- > lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') -lookupLE :: Ord k => k -> Map k v -> Maybe (k, v) -lookupLE = goNothing - where - goNothing !_ Tip = Nothing - goNothing k (Bin _ kx x l r) = case compare k kx of LT -> goNothing k l - EQ -> Just (kx, x) - GT -> goJust k kx x r - - goJust !_ kx' x' Tip = Just (kx', x') - goJust k kx' x' (Bin _ kx x l r) = case compare k kx of LT -> goJust k kx' x' l - EQ -> Just (kx, x) - GT -> goJust k kx x r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupLE #-} -#else -{-# INLINE lookupLE #-} -#endif - --- | /O(log n)/. Find smallest key greater or equal to the given one and return --- the corresponding (key, value) pair. --- --- > lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') --- > lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') --- > lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing -lookupGE :: Ord k => k -> Map k v -> Maybe (k, v) -lookupGE = goNothing - where - goNothing !_ Tip = Nothing - goNothing k (Bin _ kx x l r) = case compare k kx of LT -> goJust k kx x l - EQ -> Just (kx, x) - GT -> goNothing k r - - goJust !_ kx' x' Tip = Just (kx', x') - goJust k kx' x' (Bin _ kx x l r) = case compare k kx of LT -> goJust k kx x l - EQ -> Just (kx, x) - GT -> goJust k kx' x' r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupGE #-} -#else -{-# INLINE lookupGE #-} -#endif - -{-------------------------------------------------------------------- - Construction ---------------------------------------------------------------------} --- | /O(1)/. The empty map. --- --- > empty == fromList [] --- > size empty == 0 - -empty :: Map k a -empty = Tip -{-# INLINE empty #-} - --- | /O(1)/. A map with a single element. --- --- > singleton 1 'a' == fromList [(1, 'a')] --- > size (singleton 1 'a') == 1 - -singleton :: k -> a -> Map k a -singleton k x = Bin 1 k x Tip Tip -{-# INLINE singleton #-} - -{-------------------------------------------------------------------- - Insertion ---------------------------------------------------------------------} --- | /O(log n)/. Insert a new key and value in the map. --- If the key is already present in the map, the associated value is --- replaced with the supplied value. 'insert' is equivalent to --- @'insertWith' 'const'@. --- --- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')] --- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] --- > insert 5 'x' empty == singleton 5 'x' - --- See Note: Type of local 'go' function -insert :: Ord k => k -> a -> Map k a -> Map k a -insert = go - where - -- Unlike insertR, we only get sharing here - -- when the inserted value is at the same address - -- as the present value. We try anyway. If we decide - -- not to, then Data.Map.Strict should probably - -- get its own union implementation. - go :: Ord k => k -> a -> Map k a -> Map k a - go !kx x Tip = singleton kx x - go !kx x t@(Bin sz ky y l r) = - case compare kx ky of - LT | l' `ptrEq` l -> t - | otherwise -> balanceL ky y l' r - where !l' = go kx x l - GT | r' `ptrEq` r -> t - | otherwise -> balanceR ky y l r' - where !r' = go kx x r - EQ | kx `ptrEq` ky && x `ptrEq` y -> t - | otherwise -> Bin sz kx x l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE insert #-} -#else -{-# INLINE insert #-} -#endif - --- Insert a new key and value in the map if it is not already present. --- Used by `union`. - --- See Note: Type of local 'go' function -insertR :: Ord k => k -> a -> Map k a -> Map k a -insertR = go - where - go :: Ord k => k -> a -> Map k a -> Map k a - go !kx x Tip = singleton kx x - go kx x t@(Bin _ ky y l r) = - case compare kx ky of - LT | l' `ptrEq` l -> t - | otherwise -> balanceL ky y l' r - where !l' = go kx x l - GT | r' `ptrEq` r -> t - | otherwise -> balanceR ky y l r' - where !r' = go kx x r - EQ -> t -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertR #-} -#else -{-# INLINE insertR #-} -#endif - --- | /O(log n)/. Insert with a function, combining new value and old value. --- @'insertWith' f key value mp@ --- will insert the pair (key, value) into @mp@ if key does --- not exist in the map. If the key does exist, the function will --- insert the pair @(key, f new_value old_value)@. --- --- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] --- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] --- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx" - -insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a -insertWith = go - where - -- We have no hope of making pointer equality tricks work - -- here, because lazy insertWith *always* changes the tree, - -- either adding a new entry or replacing an element with a - -- thunk. - go :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a - go _ !kx x Tip = singleton kx x - go f !kx x (Bin sy ky y l r) = - case compare kx ky of - LT -> balanceL ky y (go f kx x l) r - GT -> balanceR ky y l (go f kx x r) - EQ -> Bin sy kx (f x y) l r - -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertWith #-} -#else -{-# INLINE insertWith #-} -#endif - --- | A helper function for 'unionWith'. When the key is already in --- the map, the key is left alone, not replaced. The combining --- function is flipped--it is applied to the old value and then the --- new value. - -insertWithR :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a -insertWithR = go - where - go :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a - go _ !kx x Tip = singleton kx x - go f !kx x (Bin sy ky y l r) = - case compare kx ky of - LT -> balanceL ky y (go f kx x l) r - GT -> balanceR ky y l (go f kx x r) - EQ -> Bin sy ky (f y x) l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertWithR #-} -#else -{-# INLINE insertWithR #-} -#endif - --- | /O(log n)/. Insert with a function, combining key, new value and old value. --- @'insertWithKey' f key value mp@ --- will insert the pair (key, value) into @mp@ if key does --- not exist in the map. If the key does exist, the function will --- insert the pair @(key,f key new_value old_value)@. --- Note that the key passed to f is the same key passed to 'insertWithKey'. --- --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value --- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] --- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] --- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx" - --- See Note: Type of local 'go' function -insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a -insertWithKey = go - where - go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a - go _ !kx x Tip = singleton kx x - go f kx x (Bin sy ky y l r) = - case compare kx ky of - LT -> balanceL ky y (go f kx x l) r - GT -> balanceR ky y l (go f kx x r) - EQ -> Bin sy kx (f kx x y) l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertWithKey #-} -#else -{-# INLINE insertWithKey #-} -#endif - --- | A helper function for 'unionWithKey'. When the key is already in --- the map, the key is left alone, not replaced. The combining --- function is flipped--it is applied to the old value and then the --- new value. -insertWithKeyR :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a -insertWithKeyR = go - where - go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a - go _ !kx x Tip = singleton kx x - go f kx x (Bin sy ky y l r) = - case compare kx ky of - LT -> balanceL ky y (go f kx x l) r - GT -> balanceR ky y l (go f kx x r) - EQ -> Bin sy ky (f ky y x) l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertWithKeyR #-} -#else -{-# INLINE insertWithKeyR #-} -#endif - --- | /O(log n)/. Combines insert operation with old value retrieval. --- The expression (@'insertLookupWithKey' f k x map@) --- is a pair where the first element is equal to (@'lookup' k map@) --- and the second element equal to (@'insertWithKey' f k x map@). --- --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value --- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) --- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) --- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx") --- --- This is how to define @insertLookup@ using @insertLookupWithKey@: --- --- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t --- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) --- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) - --- See Note: Type of local 'go' function -insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a - -> (Maybe a, Map k a) -insertLookupWithKey f0 k0 x0 = toPair . go f0 k0 x0 - where - go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a) - go _ !kx x Tip = (Nothing :*: singleton kx x) - go f kx x (Bin sy ky y l r) = - case compare kx ky of - LT -> let !(found :*: l') = go f kx x l - !t' = balanceL ky y l' r - in (found :*: t') - GT -> let !(found :*: r') = go f kx x r - !t' = balanceR ky y l r' - in (found :*: t') - EQ -> (Just y :*: Bin sy kx (f kx x y) l r) -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertLookupWithKey #-} -#else -{-# INLINE insertLookupWithKey #-} -#endif - -{-------------------------------------------------------------------- - Deletion ---------------------------------------------------------------------} --- | /O(log n)/. Delete a key and its value from the map. When the key is not --- a member of the map, the original map is returned. --- --- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > delete 5 empty == empty - --- See Note: Type of local 'go' function -delete :: Ord k => k -> Map k a -> Map k a -delete = go - where - go :: Ord k => k -> Map k a -> Map k a - go !_ Tip = Tip - go k t@(Bin _ kx x l r) = - case compare k kx of - LT | l' `ptrEq` l -> t - | otherwise -> balanceR kx x l' r - where !l' = go k l - GT | r' `ptrEq` r -> t - | otherwise -> balanceL kx x l r' - where !r' = go k r - EQ -> glue l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE delete #-} -#else -{-# INLINE delete #-} -#endif - --- | /O(log n)/. Update a value at a specific key with the result of the provided function. --- When the key is not --- a member of the map, the original map is returned. --- --- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] --- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > adjust ("new " ++) 7 empty == empty - -adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a -adjust f = adjustWithKey (\_ x -> f x) -#if __GLASGOW_HASKELL__ -{-# INLINABLE adjust #-} -#else -{-# INLINE adjust #-} -#endif - --- | /O(log n)/. Adjust a value at a specific key. When the key is not --- a member of the map, the original map is returned. --- --- > let f key x = (show key) ++ ":new " ++ x --- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] --- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > adjustWithKey f 7 empty == empty - -adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a -adjustWithKey = go - where - go :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a - go _ !_ Tip = Tip - go f k (Bin sx kx x l r) = - case compare k kx of - LT -> Bin sx kx x (go f k l) r - GT -> Bin sx kx x l (go f k r) - EQ -> Bin sx kx (f kx x) l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE adjustWithKey #-} -#else -{-# INLINE adjustWithKey #-} -#endif - --- | /O(log n)/. The expression (@'update' f k map@) updates the value @x@ --- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is --- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. --- --- > let f x = if x == "a" then Just "new a" else Nothing --- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] --- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a -update f = updateWithKey (\_ x -> f x) -#if __GLASGOW_HASKELL__ -{-# INLINABLE update #-} -#else -{-# INLINE update #-} -#endif - --- | /O(log n)/. The expression (@'updateWithKey' f k map@) updates the --- value @x@ at @k@ (if it is in the map). If (@f k x@) is 'Nothing', --- the element is deleted. If it is (@'Just' y@), the key @k@ is bound --- to the new value @y@. --- --- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing --- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] --- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - --- See Note: Type of local 'go' function -updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a -updateWithKey = go - where - go :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a - go _ !_ Tip = Tip - go f k(Bin sx kx x l r) = - case compare k kx of - LT -> balanceR kx x (go f k l) r - GT -> balanceL kx x l (go f k r) - EQ -> case f kx x of - Just x' -> Bin sx kx x' l r - Nothing -> glue l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE updateWithKey #-} -#else -{-# INLINE updateWithKey #-} -#endif - --- | /O(log n)/. Lookup and update. See also 'updateWithKey'. --- The function returns changed value, if it is updated. --- Returns the original key value if the map entry is deleted. --- --- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing --- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "5:new a", fromList [(3, "b"), (5, "5:new a")]) --- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) --- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a") - --- See Note: Type of local 'go' function -updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a,Map k a) -updateLookupWithKey f0 k0 = toPair . go f0 k0 - where - go :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> StrictPair (Maybe a) (Map k a) - go _ !_ Tip = (Nothing :*: Tip) - go f k (Bin sx kx x l r) = - case compare k kx of - LT -> let !(found :*: l') = go f k l - !t' = balanceR kx x l' r - in (found :*: t') - GT -> let !(found :*: r') = go f k r - !t' = balanceL kx x l r' - in (found :*: t') - EQ -> case f kx x of - Just x' -> (Just x' :*: Bin sx kx x' l r) - Nothing -> let !glued = glue l r - in (Just x :*: glued) -#if __GLASGOW_HASKELL__ -{-# INLINABLE updateLookupWithKey #-} -#else -{-# INLINE updateLookupWithKey #-} -#endif - --- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof. --- 'alter' can be used to insert, delete, or update a value in a 'Map'. --- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@. --- --- > let f _ = Nothing --- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] --- > alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > --- > let f _ = Just "c" --- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")] --- > alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")] - --- See Note: Type of local 'go' function -alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a -alter = go - where - go :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a - go f !k Tip = case f Nothing of - Nothing -> Tip - Just x -> singleton k x - - go f k (Bin sx kx x l r) = case compare k kx of - LT -> balance kx x (go f k l) r - GT -> balance kx x l (go f k r) - EQ -> case f (Just x) of - Just x' -> Bin sx kx x' l r - Nothing -> glue l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE alter #-} -#else -{-# INLINE alter #-} -#endif - --- Used to choose the appropriate alterF implementation. -data AreWeStrict = Strict | Lazy - --- | /O(log n)/. The expression (@'alterF' f k map@) alters the value @x@ at --- @k@, or absence thereof. 'alterF' can be used to inspect, insert, delete, --- or update a value in a 'Map'. In short: @'lookup' k \<$\> 'alterF' f k m = f --- ('lookup' k m)@. --- --- Example: --- --- @ --- interactiveAlter :: Int -> Map Int String -> IO (Map Int String) --- interactiveAlter k m = alterF f k m where --- f Nothing -> do --- putStrLn $ show k ++ --- " was not found in the map. Would you like to add it?" --- getUserResponse1 :: IO (Maybe String) --- f (Just old) -> do --- putStrLn "The key is currently bound to " ++ show old ++ --- ". Would you like to change or delete it?" --- getUserresponse2 :: IO (Maybe String) --- @ --- --- 'alterF' is the most general operation for working with an individual --- key that may or may not be in a given map. When used with trivial --- functors like 'Identity' and 'Const', it is often slightly slower than --- more specialized combinators like 'lookup' and 'insert'. However, when --- the functor is non-trivial and key comparison is not particularly cheap, --- it is the fastest way. --- --- Note on rewrite rules: --- --- This module includes GHC rewrite rules to optimize 'alterF' for --- the 'Const' and 'Identity' functors. In general, these rules --- improve performance. The sole exception is that when using --- 'Identity', deleting a key that is already absent takes longer --- than it would without the rules. If you expect this to occur --- a very large fraction of the time, you might consider using a --- private copy of the 'Identity' type. --- --- Note: 'alterF' is a flipped version of the 'at' combinator from --- 'Control.Lens.At'. --- --- @since 0.5.8 -alterF :: (Functor f, Ord k) - => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) -alterF f k m = atKeyImpl Lazy k f m - -#ifndef __GLASGOW_HASKELL__ -{-# INLINE alterF #-} -#else -{-# INLINABLE [2] alterF #-} - --- We can save a little time by recognizing the special case of --- `Control.Applicative.Const` and just doing a lookup. -{-# RULES -"alterF/Const" forall k (f :: Maybe a -> Const b (Maybe a)) . alterF f k = \m -> Const . getConst . f $ lookup k m - #-} - -#if MIN_VERSION_base(4,8,0) --- base 4.8 and above include Data.Functor.Identity, so we can --- save a pretty decent amount of time by handling it specially. -{-# RULES -"alterF/Identity" forall k f . alterF f k = atKeyIdentity k f - #-} -#endif -#endif - -atKeyImpl :: (Functor f, Ord k) => - AreWeStrict -> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a) -#if DEFINE_ALTERF_FALLBACK -atKeyImpl strict !k f m --- It doesn't seem sensible to worry about overflowing the queue --- if the word size is 61 or more. If I calculate it correctly, --- that would take a map with nearly a quadrillion entries. - | wordSize < 61 && size m >= alterFCutoff = alterFFallback strict k f m -#endif -atKeyImpl strict !k f m = case lookupTrace k m of - TraceResult mv q -> (<$> f mv) $ \ fres -> - case fres of - Nothing -> case mv of - Nothing -> m - Just old -> deleteAlong old q m - Just new -> case strict of - Strict -> new `seq` case mv of - Nothing -> insertAlong q k new m - Just _ -> replaceAlong q new m - Lazy -> case mv of - Nothing -> insertAlong q k new m - Just _ -> replaceAlong q new m - -{-# INLINE atKeyImpl #-} - -#if DEFINE_ALTERF_FALLBACK -alterFCutoff :: Int -#if WORD_SIZE_IN_BITS == 32 -alterFCutoff = 55744454 -#else -alterFCutoff = case wordSize of - 30 -> 17637893 - 31 -> 31356255 - 32 -> 55744454 - x -> (4^(x*2-2)) `quot` (3^(x*2-2)) -- Unlikely -#endif -#endif - -data TraceResult a = TraceResult (Maybe a) {-# UNPACK #-} !BitQueue - --- Look up a key and return a result indicating whether it was found --- and what path was taken. -lookupTrace :: Ord k => k -> Map k a -> TraceResult a -lookupTrace = go emptyQB - where - go :: Ord k => BitQueueB -> k -> Map k a -> TraceResult a - go !q !_ Tip = TraceResult Nothing (buildQ q) - go q k (Bin _ kx x l r) = case compare k kx of - LT -> (go $! q `snocQB` False) k l - GT -> (go $! q `snocQB` True) k r - EQ -> TraceResult (Just x) (buildQ q) - --- GHC 7.8 doesn't manage to unbox the queue properly --- unless we explicitly inline this function. This stuff --- is a bit touchy, unfortunately. -#if __GLASGOW_HASKELL__ >= 710 -{-# INLINABLE lookupTrace #-} -#else -{-# INLINE lookupTrace #-} -#endif - --- Insert at a location (which will always be a leaf) --- described by the path passed in. -insertAlong :: BitQueue -> k -> a -> Map k a -> Map k a -insertAlong !_ kx x Tip = singleton kx x -insertAlong q kx x (Bin sz ky y l r) = - case unconsQ q of - Just (False, tl) -> balanceL ky y (insertAlong tl kx x l) r - Just (True,tl) -> balanceR ky y l (insertAlong tl kx x r) - Nothing -> Bin sz kx x l r -- Shouldn't happen - --- Delete from a location (which will always be a node) --- described by the path passed in. --- --- This is fairly horrifying! We don't actually have any --- use for the old value we're deleting. But if GHC sees --- that, then it will allocate a thunk representing the --- Map with the key deleted before we have any reason to --- believe we'll actually want that. This transformation --- enhances sharing, but we don't care enough about that. --- So deleteAlong needs to take the old value, and we need --- to convince GHC somehow that it actually uses it. We --- can't NOINLINE deleteAlong, because that would prevent --- the BitQueue from being unboxed. So instead we pass the --- old value to a NOINLINE constant function and then --- convince GHC that we use the result throughout the --- computation. Doing the obvious thing and just passing --- the value itself through the recursion costs 3-4% time, --- so instead we convert the value to a magical zero-width --- proxy that's ultimately erased. -deleteAlong :: any -> BitQueue -> Map k a -> Map k a -deleteAlong old !q0 !m = go (bogus old) q0 m where -#if USE_MAGIC_PROXY - go :: Proxy# () -> BitQueue -> Map k a -> Map k a -#else - go :: any -> BitQueue -> Map k a -> Map k a -#endif - go !_ !_ Tip = Tip - go foom q (Bin _ ky y l r) = - case unconsQ q of - Just (False, tl) -> balanceR ky y (go foom tl l) r - Just (True, tl) -> balanceL ky y l (go foom tl r) - Nothing -> glue l r - -#if USE_MAGIC_PROXY -{-# NOINLINE bogus #-} -bogus :: a -> Proxy# () -bogus _ = proxy# -#else --- No point hiding in this case. -{-# INLINE bogus #-} -bogus :: a -> a -bogus a = a -#endif - --- Replace the value found in the node described --- by the given path with a new one. -replaceAlong :: BitQueue -> a -> Map k a -> Map k a -replaceAlong !_ _ Tip = Tip -- Should not happen -replaceAlong q x (Bin sz ky y l r) = - case unconsQ q of - Just (False, tl) -> Bin sz ky y (replaceAlong tl x l) r - Just (True,tl) -> Bin sz ky y l (replaceAlong tl x r) - Nothing -> Bin sz ky x l r - -#if __GLASGOW_HASKELL__ && MIN_VERSION_base(4,8,0) -atKeyIdentity :: Ord k => k -> (Maybe a -> Identity (Maybe a)) -> Map k a -> Identity (Map k a) -atKeyIdentity k f t = Identity $ atKeyPlain Lazy k (coerce f) t -{-# INLINABLE atKeyIdentity #-} - -atKeyPlain :: Ord k => AreWeStrict -> k -> (Maybe a -> Maybe a) -> Map k a -> Map k a -atKeyPlain strict k0 f0 t = case go k0 f0 t of - AltSmaller t' -> t' - AltBigger t' -> t' - AltAdj t' -> t' - AltSame -> t - where - go :: Ord k => k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a - go !k f Tip = case f Nothing of - Nothing -> AltSame - Just x -> case strict of - Lazy -> AltBigger $ singleton k x - Strict -> x `seq` (AltBigger $ singleton k x) - - go k f (Bin sx kx x l r) = case compare k kx of - LT -> case go k f l of - AltSmaller l' -> AltSmaller $ balanceR kx x l' r - AltBigger l' -> AltBigger $ balanceL kx x l' r - AltAdj l' -> AltAdj $ Bin sx kx x l' r - AltSame -> AltSame - GT -> case go k f r of - AltSmaller r' -> AltSmaller $ balanceL kx x l r' - AltBigger r' -> AltBigger $ balanceR kx x l r' - AltAdj r' -> AltAdj $ Bin sx kx x l r' - AltSame -> AltSame - EQ -> case f (Just x) of - Just x' -> case strict of - Lazy -> AltAdj $ Bin sx kx x' l r - Strict -> x' `seq` (AltAdj $ Bin sx kx x' l r) - Nothing -> AltSmaller $ glue l r -{-# INLINE atKeyPlain #-} - -data Altered k a = AltSmaller !(Map k a) | AltBigger !(Map k a) | AltAdj !(Map k a) | AltSame -#endif - -#if DEFINE_ALTERF_FALLBACK --- When the map is too large to use a bit queue, we fall back to --- this much slower version which uses a more "natural" implementation --- improved with Yoneda to avoid repeated fmaps. This works okayish for --- some operations, but it's pretty lousy for lookups. -alterFFallback :: (Functor f, Ord k) - => AreWeStrict -> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a) -alterFFallback Lazy k f t = alterFYoneda k (\m q -> q <$> f m) t id -alterFFallback Strict k f t = alterFYoneda k (\m q -> q . forceMaybe <$> f m) t id - where - forceMaybe Nothing = Nothing - forceMaybe may@(Just !_) = may -{-# NOINLINE alterFFallback #-} - -alterFYoneda :: Ord k => - k -> (Maybe a -> (Maybe a -> b) -> f b) -> Map k a -> (Map k a -> b) -> f b -alterFYoneda = go - where - go :: Ord k => - k -> (Maybe a -> (Maybe a -> b) -> f b) -> Map k a -> (Map k a -> b) -> f b - go !k f Tip g = f Nothing $ \ mx -> case mx of - Nothing -> g Tip - Just x -> g (singleton k x) - go k f (Bin sx kx x l r) g = case compare k kx of - LT -> go k f l (\m -> g (balance kx x m r)) - GT -> go k f r (\m -> g (balance kx x l m)) - EQ -> f (Just x) $ \ mx' -> case mx' of - Just x' -> g (Bin sx kx x' l r) - Nothing -> g (glue l r) -{-# INLINE alterFYoneda #-} -#endif - -{-------------------------------------------------------------------- - Indexing ---------------------------------------------------------------------} --- | /O(log n)/. Return the /index/ of a key, which is its zero-based index in --- the sequence sorted by keys. The index is a number from /0/ up to, but not --- including, the 'size' of the map. Calls 'error' when the key is not --- a 'member' of the map. --- --- > findIndex 2 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map --- > findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0 --- > findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1 --- > findIndex 6 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map - --- See Note: Type of local 'go' function -findIndex :: Ord k => k -> Map k a -> Int -findIndex = go 0 - where - go :: Ord k => Int -> k -> Map k a -> Int - go !_ !_ Tip = error "Map.findIndex: element is not in the map" - go idx k (Bin _ kx _ l r) = case compare k kx of - LT -> go idx k l - GT -> go (idx + size l + 1) k r - EQ -> idx + size l -#if __GLASGOW_HASKELL__ -{-# INLINABLE findIndex #-} -#endif - --- | /O(log n)/. Lookup the /index/ of a key, which is its zero-based index in --- the sequence sorted by keys. The index is a number from /0/ up to, but not --- including, the 'size' of the map. --- --- > isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")])) == False --- > fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0 --- > fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1 --- > isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")])) == False - --- See Note: Type of local 'go' function -lookupIndex :: Ord k => k -> Map k a -> Maybe Int -lookupIndex = go 0 - where - go :: Ord k => Int -> k -> Map k a -> Maybe Int - go !_ !_ Tip = Nothing - go idx k (Bin _ kx _ l r) = case compare k kx of - LT -> go idx k l - GT -> go (idx + size l + 1) k r - EQ -> Just $! idx + size l -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupIndex #-} -#endif - --- | /O(log n)/. Retrieve an element by its /index/, i.e. by its zero-based --- index in the sequence sorted by keys. If the /index/ is out of range (less --- than zero, greater or equal to 'size' of the map), 'error' is called. --- --- > elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b") --- > elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a") --- > elemAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range - -elemAt :: Int -> Map k a -> (k,a) -elemAt !_ Tip = error "Map.elemAt: index out of range" -elemAt i (Bin _ kx x l r) - = case compare i sizeL of - LT -> elemAt i l - GT -> elemAt (i-sizeL-1) r - EQ -> (kx,x) - where - sizeL = size l - --- | Take a given number of entries in key order, beginning --- with the smallest keys. --- --- @ --- take n = 'fromDistinctAscList' . 'Prelude.take' n . 'toAscList' --- @ - -take :: Int -> Map k a -> Map k a -take i m | i >= size m = m -take i0 m0 = go i0 m0 - where - go i !_ | i <= 0 = Tip - go !_ Tip = Tip - go i (Bin _ kx x l r) = - case compare i sizeL of - LT -> go i l - GT -> link kx x l (go (i - sizeL - 1) r) - EQ -> l - where sizeL = size l - --- | Drop a given number of entries in key order, beginning --- with the smallest keys. --- --- @ --- drop n = 'fromDistinctAscList' . 'Prelude.drop' n . 'toAscList' --- @ -drop :: Int -> Map k a -> Map k a -drop i m | i >= size m = Tip -drop i0 m0 = go i0 m0 - where - go i m | i <= 0 = m - go !_ Tip = Tip - go i (Bin _ kx x l r) = - case compare i sizeL of - LT -> link kx x (go i l) r - GT -> go (i - sizeL - 1) r - EQ -> insertMin kx x r - where sizeL = size l - --- | /O(log n)/. Split a map at a particular index. --- --- @ --- splitAt !n !xs = ('take' n xs, 'drop' n xs) --- @ -splitAt :: Int -> Map k a -> (Map k a, Map k a) -splitAt i0 m0 - | i0 >= size m0 = (m0, Tip) - | otherwise = toPair $ go i0 m0 - where - go i m | i <= 0 = Tip :*: m - go !_ Tip = Tip :*: Tip - go i (Bin _ kx x l r) - = case compare i sizeL of - LT -> case go i l of - ll :*: lr -> ll :*: link kx x lr r - GT -> case go (i - sizeL - 1) r of - rl :*: rr -> link kx x l rl :*: rr - EQ -> l :*: insertMin kx x r - where sizeL = size l - --- | /O(log n)/. Update the element at /index/, i.e. by its zero-based index in --- the sequence sorted by keys. If the /index/ is out of range (less than zero, --- greater or equal to 'size' of the map), 'error' is called. --- --- > updateAt (\ _ _ -> Just "x") 0 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")] --- > updateAt (\ _ _ -> Just "x") 1 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")] --- > updateAt (\ _ _ -> Just "x") 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range --- > updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range --- > updateAt (\_ _ -> Nothing) 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" --- > updateAt (\_ _ -> Nothing) 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > updateAt (\_ _ -> Nothing) 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range --- > updateAt (\_ _ -> Nothing) (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range - -updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a -updateAt f !i t = - case t of - Tip -> error "Map.updateAt: index out of range" - Bin sx kx x l r -> case compare i sizeL of - LT -> balanceR kx x (updateAt f i l) r - GT -> balanceL kx x l (updateAt f (i-sizeL-1) r) - EQ -> case f kx x of - Just x' -> Bin sx kx x' l r - Nothing -> glue l r - where - sizeL = size l - --- | /O(log n)/. Delete the element at /index/, i.e. by its zero-based index in --- the sequence sorted by keys. If the /index/ is out of range (less than zero, --- greater or equal to 'size' of the map), 'error' is called. --- --- > deleteAt 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" --- > deleteAt 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > deleteAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range --- > deleteAt (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range - -deleteAt :: Int -> Map k a -> Map k a -deleteAt !i t = - case t of - Tip -> error "Map.deleteAt: index out of range" - Bin _ kx x l r -> case compare i sizeL of - LT -> balanceR kx x (deleteAt i l) r - GT -> balanceL kx x l (deleteAt (i-sizeL-1) r) - EQ -> glue l r - where - sizeL = size l - - -{-------------------------------------------------------------------- - Minimal, Maximal ---------------------------------------------------------------------} --- | /O(log n)/. The minimal key of the map. Calls 'error' if the map is empty. --- --- > findMin (fromList [(5,"a"), (3,"b")]) == (3,"b") --- > findMin empty Error: empty map has no minimal element - -findMin :: Map k a -> (k,a) -findMin (Bin _ kx x Tip _) = (kx,x) -findMin (Bin _ _ _ l _) = findMin l -findMin Tip = error "Map.findMin: empty map has no minimal element" - --- | /O(log n)/. The maximal key of the map. Calls 'error' if the map is empty. --- --- > findMax (fromList [(5,"a"), (3,"b")]) == (5,"a") --- > findMax empty Error: empty map has no maximal element - -findMax :: Map k a -> (k,a) -findMax (Bin _ kx x _ Tip) = (kx,x) -findMax (Bin _ _ _ _ r) = findMax r -findMax Tip = error "Map.findMax: empty map has no maximal element" - --- | /O(log n)/. Delete the minimal key. Returns an empty map if the map is empty. --- --- > deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(5,"a"), (7,"c")] --- > deleteMin empty == empty - -deleteMin :: Map k a -> Map k a -deleteMin (Bin _ _ _ Tip r) = r -deleteMin (Bin _ kx x l r) = balanceR kx x (deleteMin l) r -deleteMin Tip = Tip - --- | /O(log n)/. Delete the maximal key. Returns an empty map if the map is empty. --- --- > deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(3,"b"), (5,"a")] --- > deleteMax empty == empty - -deleteMax :: Map k a -> Map k a -deleteMax (Bin _ _ _ l Tip) = l -deleteMax (Bin _ kx x l r) = balanceL kx x l (deleteMax r) -deleteMax Tip = Tip - --- | /O(log n)/. Update the value at the minimal key. --- --- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")] --- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -updateMin :: (a -> Maybe a) -> Map k a -> Map k a -updateMin f m - = updateMinWithKey (\_ x -> f x) m - --- | /O(log n)/. Update the value at the maximal key. --- --- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")] --- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" - -updateMax :: (a -> Maybe a) -> Map k a -> Map k a -updateMax f m - = updateMaxWithKey (\_ x -> f x) m - - --- | /O(log n)/. Update the value at the minimal key. --- --- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")] --- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a -updateMinWithKey _ Tip = Tip -updateMinWithKey f (Bin sx kx x Tip r) = case f kx x of - Nothing -> r - Just x' -> Bin sx kx x' Tip r -updateMinWithKey f (Bin _ kx x l r) = balanceR kx x (updateMinWithKey f l) r - --- | /O(log n)/. Update the value at the maximal key. --- --- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")] --- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" - -updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a -updateMaxWithKey _ Tip = Tip -updateMaxWithKey f (Bin sx kx x l Tip) = case f kx x of - Nothing -> l - Just x' -> Bin sx kx x' l Tip -updateMaxWithKey f (Bin _ kx x l r) = balanceL kx x l (updateMaxWithKey f r) - --- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and --- the map stripped of that element, or 'Nothing' if passed an empty map. --- --- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") --- > minViewWithKey empty == Nothing - -minViewWithKey :: Map k a -> Maybe ((k,a), Map k a) -minViewWithKey Tip = Nothing -minViewWithKey x = Just $! deleteFindMin x - --- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and --- the map stripped of that element, or 'Nothing' if passed an empty map. --- --- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b") --- > maxViewWithKey empty == Nothing - -maxViewWithKey :: Map k a -> Maybe ((k,a), Map k a) -maxViewWithKey Tip = Nothing -maxViewWithKey x = Just $! deleteFindMax x - --- | /O(log n)/. Retrieves the value associated with minimal key of the --- map, and the map stripped of that element, or 'Nothing' if passed an --- empty map. --- --- > minView (fromList [(5,"a"), (3,"b")]) == Just ("b", singleton 5 "a") --- > minView empty == Nothing - -minView :: Map k a -> Maybe (a, Map k a) -minView Tip = Nothing -minView x = Just $! (first snd $ deleteFindMin x) - --- | /O(log n)/. Retrieves the value associated with maximal key of the --- map, and the map stripped of that element, or 'Nothing' if passed an --- empty map. --- --- > maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b") --- > maxView empty == Nothing - -maxView :: Map k a -> Maybe (a, Map k a) -maxView Tip = Nothing -maxView x = Just $! (first snd $ deleteFindMax x) - --- Update the 1st component of a tuple (stricter version of --- Control.Arrow.first) -first :: (a -> b) -> (a,c) -> (b,c) -first f (x,y) = (f x, y) - -{-------------------------------------------------------------------- - Union. ---------------------------------------------------------------------} --- | The union of a list of maps: --- (@'unions' == 'Prelude.foldl' 'union' 'empty'@). --- --- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] --- > == fromList [(3, "b"), (5, "a"), (7, "C")] --- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])] --- > == fromList [(3, "B3"), (5, "A3"), (7, "C")] - -unions :: Ord k => [Map k a] -> Map k a -unions ts - = foldlStrict union empty ts -#if __GLASGOW_HASKELL__ -{-# INLINABLE unions #-} -#endif - --- | The union of a list of maps, with a combining operation: --- (@'unionsWith' f == 'Prelude.foldl' ('unionWith' f) 'empty'@). --- --- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] --- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")] - -unionsWith :: Ord k => (a->a->a) -> [Map k a] -> Map k a -unionsWith f ts - = foldlStrict (unionWith f) empty ts -#if __GLASGOW_HASKELL__ -{-# INLINABLE unionsWith #-} -#endif - --- | /O(m*log(n\/m + 1)), m <= n/. --- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@. --- It prefers @t1@ when duplicate keys are encountered, --- i.e. (@'union' == 'unionWith' 'const'@). --- --- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")] - -union :: Ord k => Map k a -> Map k a -> Map k a -union t1 Tip = t1 -union t1 (Bin _ k x Tip Tip) = insertR k x t1 -union (Bin _ k x Tip Tip) t2 = insert k x t2 -union Tip t2 = t2 -union t1@(Bin _ k1 x1 l1 r1) t2 = case split k1 t2 of - (l2, r2) | l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 -> t1 - | otherwise -> link k1 x1 l1l2 r1r2 - where !l1l2 = union l1 l2 - !r1r2 = union r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE union #-} -#endif - -{-------------------------------------------------------------------- - Union with a combining function ---------------------------------------------------------------------} --- | /O(m*log(n\/m + 1)), m <= n/. Union with a combining function. --- --- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")] - -unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a --- QuickCheck says pointer equality never happens here. -unionWith _f t1 Tip = t1 -unionWith f t1 (Bin _ k x Tip Tip) = insertWithR f k x t1 -unionWith f (Bin _ k x Tip Tip) t2 = insertWith f k x t2 -unionWith _f Tip t2 = t2 -unionWith f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of - (l2, mb, r2) -> case mb of - Nothing -> link k1 x1 l1l2 r1r2 - Just x2 -> link k1 (f x1 x2) l1l2 r1r2 - where !l1l2 = unionWith f l1 l2 - !r1r2 = unionWith f r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE unionWith #-} -#endif - --- | /O(m*log(n\/m + 1)), m <= n/. --- Union with a combining function. --- --- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value --- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")] - -unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a -unionWithKey _f t1 Tip = t1 -unionWithKey f t1 (Bin _ k x Tip Tip) = insertWithKeyR f k x t1 -unionWithKey f (Bin _ k x Tip Tip) t2 = insertWithKey f k x t2 -unionWithKey _f Tip t2 = t2 -unionWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of - (l2, mb, r2) -> case mb of - Nothing -> link k1 x1 l1l2 r1r2 - Just x2 -> link k1 (f k1 x1 x2) l1l2 r1r2 - where !l1l2 = unionWithKey f l1 l2 - !r1r2 = unionWithKey f r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE unionWithKey #-} -#endif - -{-------------------------------------------------------------------- - Difference ---------------------------------------------------------------------} - --- | /O(m*log(n\/m + 1)), m <= n/. Difference of two maps. --- Return elements of the first map not existing in the second map. --- --- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b" - -difference :: Ord k => Map k a -> Map k b -> Map k a -difference Tip _ = Tip -difference t1 Tip = t1 -difference t1 (Bin _ k _ l2 r2) = case split k t1 of - (l1, r1) - | size l1l2 + size r1r2 == size t1 -> t1 - | otherwise -> link2 l1l2 r1r2 - where - !l1l2 = difference l1 l2 - !r1r2 = difference r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE difference #-} -#endif - --- | /O(m*log(n/m + 1)), m <= n/. Remove all keys in a 'Set' from a 'Map'. --- --- @ --- m `withoutKeys` s = 'filterWithKey' (\k _ -> k `'Set.notMember'` s) m --- @ --- --- @since 0.5.8 - -withoutKeys :: Ord k => Map k a -> Set k -> Map k a -withoutKeys Tip _ = Tip -withoutKeys m Set.Tip = m -withoutKeys m (Set.Bin _ k ls rs) = case splitMember k m of - (lm, b, rm) - | not b && lm' `ptrEq` lm && rm' `ptrEq` rm -> m - | otherwise -> link2 lm' rm' - where - !lm' = withoutKeys lm ls - !rm' = withoutKeys rm rs -#if __GLASGOW_HASKELL__ -{-# INLINABLE withoutKeys #-} -#endif - --- | /O(n+m)/. Difference with a combining function. --- When two equal keys are --- encountered, the combining function is applied to the values of these keys. --- If it returns 'Nothing', the element is discarded (proper set difference). If --- it returns (@'Just' y@), the element is updated with a new value @y@. --- --- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing --- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")]) --- > == singleton 3 "b:B" -differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a -differenceWith f = merge preserveMissing dropMissing $ - zipWithMaybeMatched (\_ x y -> f x y) -#if __GLASGOW_HASKELL__ -{-# INLINABLE differenceWith #-} -#endif - --- | /O(n+m)/. Difference with a combining function. When two equal keys are --- encountered, the combining function is applied to the key and both values. --- If it returns 'Nothing', the element is discarded (proper set difference). If --- it returns (@'Just' y@), the element is updated with a new value @y@. --- --- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing --- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")]) --- > == singleton 3 "3:b|B" - -differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a -differenceWithKey f = - merge preserveMissing dropMissing (zipWithMaybeMatched f) -#if __GLASGOW_HASKELL__ -{-# INLINABLE differenceWithKey #-} -#endif - - -{-------------------------------------------------------------------- - Intersection ---------------------------------------------------------------------} --- | /O(m*log(n\/m + 1)), m <= n/. Intersection of two maps. --- Return data in the first map for the keys existing in both maps. --- (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@). --- --- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a" - -intersection :: Ord k => Map k a -> Map k b -> Map k a -intersection Tip _ = Tip -intersection _ Tip = Tip -intersection t1@(Bin _ k x l1 r1) t2 - | mb = if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 - then t1 - else link k x l1l2 r1r2 - | otherwise = link2 l1l2 r1r2 - where - !(l2, mb, r2) = splitMember k t2 - !l1l2 = intersection l1 l2 - !r1r2 = intersection r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE intersection #-} -#endif - --- | /O(m*log(n/m + 1)), m <= n/. Restrict a 'Map' to only those keys --- found in a 'Set'. --- --- @ --- m `restrictKeys` s = 'filterWithKey' (\k _ -> k `'Set.member'` s) m --- @ --- --- @since 0.5.8 -restrictKeys :: Ord k => Map k a -> Set k -> Map k a -restrictKeys Tip _ = Tip -restrictKeys _ Set.Tip = Tip -restrictKeys m@(Bin _ k x l1 r1) s - | b = if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 - then m - else link k x l1l2 r1r2 - | otherwise = link2 l1l2 r1r2 - where - !(l2, b, r2) = Set.splitMember k s - !l1l2 = restrictKeys l1 l2 - !r1r2 = restrictKeys r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE restrictKeys #-} -#endif - --- | /O(m*log(n\/m + 1)), m <= n/. Intersection with a combining function. --- --- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA" - -intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c --- We have no hope of pointer equality tricks here because every single --- element in the result will be a thunk. -intersectionWith _f Tip _ = Tip -intersectionWith _f _ Tip = Tip -intersectionWith f (Bin _ k x1 l1 r1) t2 = case mb of - Just x2 -> link k (f x1 x2) l1l2 r1r2 - Nothing -> link2 l1l2 r1r2 - where - !(l2, mb, r2) = splitLookup k t2 - !l1l2 = intersectionWith f l1 l2 - !r1r2 = intersectionWith f r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE intersectionWith #-} -#endif - --- | /O(m*log(n\/m + 1)), m <= n/. Intersection with a combining function. --- --- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar --- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A" - -intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c -intersectionWithKey _f Tip _ = Tip -intersectionWithKey _f _ Tip = Tip -intersectionWithKey f (Bin _ k x1 l1 r1) t2 = case mb of - Just x2 -> link k (f k x1 x2) l1l2 r1r2 - Nothing -> link2 l1l2 r1r2 - where - !(l2, mb, r2) = splitLookup k t2 - !l1l2 = intersectionWithKey f l1 l2 - !r1r2 = intersectionWithKey f r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE intersectionWithKey #-} -#endif - -#if !MIN_VERSION_base (4,8,0) --- | The identity type. -newtype Identity a = Identity { runIdentity :: a } -#if __GLASGOW_HASKELL__ == 708 -instance Functor Identity where - fmap = coerce -instance Applicative Identity where - (<*>) = coerce - pure = Identity -#else -instance Functor Identity where - fmap f (Identity a) = Identity (f a) -instance Applicative Identity where - Identity f <*> Identity x = Identity (f x) - pure = Identity -#endif -#endif - --- | A tactic for dealing with keys present in one map but not the other in --- 'merge' or 'mergeA'. --- --- A tactic of type @ WhenMissing f k x z @ is an abstract representation --- of a function of type @ k -> x -> f (Maybe z) @. - -data WhenMissing f k x y = WhenMissing - { missingSubtree :: Map k x -> f (Map k y) - , missingKey :: k -> x -> f (Maybe y)} - -instance (Applicative f, Monad f) => Functor (WhenMissing f k x) where - fmap = mapWhenMissing - {-# INLINE fmap #-} - -instance (Applicative f, Monad f) - => Category.Category (WhenMissing f k) where - id = preserveMissing - f . g = traverseMaybeMissing $ - \ k x -> missingKey g k x >>= \y -> - case y of - Nothing -> pure Nothing - Just q -> missingKey f k q - {-# INLINE id #-} - {-# INLINE (.) #-} - --- | Equivalent to @ ReaderT k (ReaderT x (MaybeT f)) @. -instance (Applicative f, Monad f) => Applicative (WhenMissing f k x) where - pure x = mapMissing (\ _ _ -> x) - f <*> g = traverseMaybeMissing $ \k x -> do - res1 <- missingKey f k x - case res1 of - Nothing -> pure Nothing - Just r -> (pure $!) . fmap r =<< missingKey g k x - {-# INLINE pure #-} - {-# INLINE (<*>) #-} - --- | Equivalent to @ ReaderT k (ReaderT x (MaybeT f)) @. -instance (Applicative f, Monad f) => Monad (WhenMissing f k x) where -#if !MIN_VERSION_base(4,8,0) - return = pure -#endif - m >>= f = traverseMaybeMissing $ \k x -> do - res1 <- missingKey m k x - case res1 of - Nothing -> pure Nothing - Just r -> missingKey (f r) k x - {-# INLINE (>>=) #-} - --- | Map covariantly over a @'WhenMissing' f k x@. -mapWhenMissing :: (Applicative f, Monad f) - => (a -> b) - -> WhenMissing f k x a -> WhenMissing f k x b -mapWhenMissing f t = WhenMissing - { missingSubtree = \m -> missingSubtree t m >>= \m' -> pure $! fmap f m' - , missingKey = \k x -> missingKey t k x >>= \q -> (pure $! fmap f q) } -{-# INLINE mapWhenMissing #-} - --- | Map covariantly over a @'WhenMissing' f k x@, using only a 'Functor f' --- constraint. -mapGentlyWhenMissing :: Functor f - => (a -> b) - -> WhenMissing f k x a -> WhenMissing f k x b -mapGentlyWhenMissing f t = WhenMissing - { missingSubtree = \m -> fmap f <$> missingSubtree t m - , missingKey = \k x -> fmap f <$> missingKey t k x } -{-# INLINE mapGentlyWhenMissing #-} - --- | Map covariantly over a @'WhenMatched' f k x@, using only a 'Functor f' --- constraint. -mapGentlyWhenMatched :: Functor f - => (a -> b) - -> WhenMatched f k x y a -> WhenMatched f k x y b -mapGentlyWhenMatched f t = zipWithMaybeAMatched $ - \k x y -> fmap f <$> runWhenMatched t k x y -{-# INLINE mapGentlyWhenMatched #-} - --- | Map contravariantly over a @'WhenMissing' f k _ x@. -lmapWhenMissing :: (b -> a) -> WhenMissing f k a x -> WhenMissing f k b x -lmapWhenMissing f t = WhenMissing - { missingSubtree = \m -> missingSubtree t (fmap f m) - , missingKey = \k x -> missingKey t k (f x) } -{-# INLINE lmapWhenMissing #-} - --- | Map contravariantly over a @'WhenMatched' f k _ y z@. -contramapFirstWhenMatched :: (b -> a) - -> WhenMatched f k a y z - -> WhenMatched f k b y z -contramapFirstWhenMatched f t = WhenMatched $ - \k x y -> runWhenMatched t k (f x) y -{-# INLINE contramapFirstWhenMatched #-} - --- | Map contravariantly over a @'WhenMatched' f k x _ z@. -contramapSecondWhenMatched :: (b -> a) - -> WhenMatched f k x a z - -> WhenMatched f k x b z -contramapSecondWhenMatched f t = WhenMatched $ - \k x y -> runWhenMatched t k x (f y) -{-# INLINE contramapSecondWhenMatched #-} - --- | A tactic for dealing with keys present in one map but not the other in --- 'merge'. --- --- A tactic of type @ SimpleWhenMissing k x z @ is an abstract representation --- of a function of type @ k -> x -> Maybe z @. -type SimpleWhenMissing = WhenMissing Identity - --- | A tactic for dealing with keys present in both --- maps in 'merge' or 'mergeA'. --- --- A tactic of type @ WhenMatched f k x y z @ is an abstract representation --- of a function of type @ k -> x -> y -> f (Maybe z) @. -newtype WhenMatched f k x y z = WhenMatched - { matchedKey :: k -> x -> y -> f (Maybe z) } - --- | Along with zipWithMaybeAMatched, witnesses the isomorphism between --- @WhenMatched f k x y z@ and @k -> x -> y -> f (Maybe z)@. -runWhenMatched :: WhenMatched f k x y z -> k -> x -> y -> f (Maybe z) -runWhenMatched = matchedKey -{-# INLINE runWhenMatched #-} - --- | Along with traverseMaybeMissing, witnesses the isomorphism between --- @WhenMissing f k x y@ and @k -> x -> f (Maybe y)@. -runWhenMissing :: WhenMissing f k x y -> k -> x -> f (Maybe y) -runWhenMissing = missingKey -{-# INLINE runWhenMissing #-} - -instance Functor f => Functor (WhenMatched f k x y) where - fmap = mapWhenMatched - {-# INLINE fmap #-} - -instance (Monad f, Applicative f) => Category.Category (WhenMatched f k x) where - id = zipWithMatched (\_ _ y -> y) - f . g = zipWithMaybeAMatched $ - \k x y -> do - res <- runWhenMatched g k x y - case res of - Nothing -> pure Nothing - Just r -> runWhenMatched f k x r - {-# INLINE id #-} - {-# INLINE (.) #-} - --- | Equivalent to @ ReaderT k (ReaderT x (ReaderT y (MaybeT f))) @ -instance (Monad f, Applicative f) => Applicative (WhenMatched f k x y) where - pure x = zipWithMatched (\_ _ _ -> x) - fs <*> xs = zipWithMaybeAMatched $ \k x y -> do - res <- runWhenMatched fs k x y - case res of - Nothing -> pure Nothing - Just r -> (pure $!) . fmap r =<< runWhenMatched xs k x y - {-# INLINE pure #-} - {-# INLINE (<*>) #-} - --- | Equivalent to @ ReaderT k (ReaderT x (ReaderT y (MaybeT f))) @ -instance (Monad f, Applicative f) => Monad (WhenMatched f k x y) where -#if !MIN_VERSION_base(4,8,0) - return = pure -#endif - m >>= f = zipWithMaybeAMatched $ \k x y -> do - res <- runWhenMatched m k x y - case res of - Nothing -> pure Nothing - Just r -> runWhenMatched (f r) k x y - {-# INLINE (>>=) #-} - --- | Map covariantly over a @'WhenMatched' f k x y@. -mapWhenMatched :: Functor f - => (a -> b) - -> WhenMatched f k x y a - -> WhenMatched f k x y b -mapWhenMatched f (WhenMatched g) = WhenMatched $ \k x y -> fmap (fmap f) (g k x y) -{-# INLINE mapWhenMatched #-} - --- | A tactic for dealing with keys present in both maps in 'merge'. --- --- A tactic of type @ SimpleWhenMatched k x y z @ is an abstract representation --- of a function of type @ k -> x -> y -> Maybe z @. -type SimpleWhenMatched = WhenMatched Identity - --- | When a key is found in both maps, apply a function to the --- key and values and use the result in the merged map. --- --- @ --- zipWithMatched :: (k -> x -> y -> z) --- -> SimpleWhenMatched k x y z --- @ -zipWithMatched :: Applicative f - => (k -> x -> y -> z) - -> WhenMatched f k x y z -zipWithMatched f = WhenMatched $ \ k x y -> pure . Just $ f k x y -{-# INLINE zipWithMatched #-} - --- | When a key is found in both maps, apply a function to the --- key and values to produce an action and use its result in the merged map. -zipWithAMatched :: Applicative f - => (k -> x -> y -> f z) - -> WhenMatched f k x y z -zipWithAMatched f = WhenMatched $ \ k x y -> Just <$> f k x y -{-# INLINE zipWithAMatched #-} - --- | When a key is found in both maps, apply a function to the --- key and values and maybe use the result in the merged map. --- --- @ --- zipWithMaybeMatched :: (k -> x -> y -> Maybe z) --- -> SimpleWhenMatched k x y z --- @ -zipWithMaybeMatched :: Applicative f - => (k -> x -> y -> Maybe z) - -> WhenMatched f k x y z -zipWithMaybeMatched f = WhenMatched $ \ k x y -> pure $ f k x y -{-# INLINE zipWithMaybeMatched #-} - --- | When a key is found in both maps, apply a function to the --- key and values, perform the resulting action, and maybe use --- the result in the merged map. --- --- This is the fundamental 'WhenMatched' tactic. -zipWithMaybeAMatched :: (k -> x -> y -> f (Maybe z)) - -> WhenMatched f k x y z -zipWithMaybeAMatched f = WhenMatched $ \ k x y -> f k x y -{-# INLINE zipWithMaybeAMatched #-} - --- | Drop all the entries whose keys are missing from the other --- map. --- --- @ --- dropMissing :: SimpleWhenMissing k x y --- @ --- --- prop> dropMissing = mapMaybeMissing (\_ _ -> Nothing) --- --- but @dropMissing@ is much faster. -dropMissing :: Applicative f => WhenMissing f k x y -dropMissing = WhenMissing - { missingSubtree = const (pure Tip) - , missingKey = \_ _ -> pure Nothing } -{-# INLINE dropMissing #-} - --- | Preserve, unchanged, the entries whose keys are missing from --- the other map. --- --- @ --- preserveMissing :: SimpleWhenMissing k x x --- @ --- --- prop> preserveMissing = Lazy.Merge.mapMaybeMissing (\_ x -> Just x) --- --- but @preserveMissing@ is much faster. -preserveMissing :: Applicative f => WhenMissing f k x x -preserveMissing = WhenMissing - { missingSubtree = pure - , missingKey = \_ v -> pure (Just v) } -{-# INLINE preserveMissing #-} - --- | Map over the entries whose keys are missing from the other map. --- --- @ --- mapMissing :: (k -> x -> y) -> SimpleWhenMissing k x y --- @ --- --- prop> mapMissing f = mapMaybeMissing (\k x -> Just $ f k x) --- --- but @mapMissing@ is somewhat faster. -mapMissing :: Applicative f => (k -> x -> y) -> WhenMissing f k x y -mapMissing f = WhenMissing - { missingSubtree = \m -> pure $! mapWithKey f m - , missingKey = \ k x -> pure $ Just (f k x) } -{-# INLINE mapMissing #-} - --- | Map over the entries whose keys are missing from the other map, --- optionally removing some. This is the most powerful 'SimpleWhenMissing' --- tactic, but others are usually more efficient. --- --- @ --- mapMaybeMissing :: (k -> x -> Maybe y) -> SimpleWhenMissing k x y --- @ --- --- prop> mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x)) --- --- but @mapMaybeMissing@ uses fewer unnecessary 'Applicative' operations. -mapMaybeMissing :: Applicative f => (k -> x -> Maybe y) -> WhenMissing f k x y -mapMaybeMissing f = WhenMissing - { missingSubtree = \m -> pure $! mapMaybeWithKey f m - , missingKey = \k x -> pure $! f k x } -{-# INLINE mapMaybeMissing #-} - --- | Filter the entries whose keys are missing from the other map. --- --- @ --- filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing k x x --- @ --- --- prop> filterMissing f = Lazy.Merge.mapMaybeMissing $ \k x -> guard (f k x) *> Just x --- --- but this should be a little faster. -filterMissing :: Applicative f - => (k -> x -> Bool) -> WhenMissing f k x x -filterMissing f = WhenMissing - { missingSubtree = \m -> pure $! filterWithKey f m - , missingKey = \k x -> pure $! if f k x then Just x else Nothing } -{-# INLINE filterMissing #-} - --- | Filter the entries whose keys are missing from the other map --- using some 'Applicative' action. --- --- @ --- filterAMissing f = Lazy.Merge.traverseMaybeMissing $ --- \k x -> (\b -> guard b *> Just x) <$> f k x --- @ --- --- but this should be a little faster. -filterAMissing :: Applicative f - => (k -> x -> f Bool) -> WhenMissing f k x x -filterAMissing f = WhenMissing - { missingSubtree = \m -> filterWithKeyA f m - , missingKey = \k x -> bool Nothing (Just x) <$> f k x } -{-# INLINE filterAMissing #-} - --- | This wasn't in Data.Bool until 4.7.0, so we define it here -bool :: a -> a -> Bool -> a -bool f _ False = f -bool _ t True = t - --- | Traverse over the entries whose keys are missing from the other map. -traverseMissing :: Applicative f - => (k -> x -> f y) -> WhenMissing f k x y -traverseMissing f = WhenMissing - { missingSubtree = traverseWithKey f - , missingKey = \k x -> Just <$> f k x } -{-# INLINE traverseMissing #-} - --- | Traverse over the entries whose keys are missing from the other map, --- optionally producing values to put in the result. --- This is the most powerful 'WhenMissing' tactic, but others are usually --- more efficient. -traverseMaybeMissing :: Applicative f - => (k -> x -> f (Maybe y)) -> WhenMissing f k x y -traverseMaybeMissing f = WhenMissing - { missingSubtree = traverseMaybeWithKey f - , missingKey = f } -{-# INLINE traverseMaybeMissing #-} - --- | Merge two maps. --- --- @merge@ takes two 'WhenMissing' tactics, a 'WhenMatched' --- tactic and two maps. It uses the tactics to merge the maps. --- Its behavior is best understood via its fundamental tactics, --- 'mapMaybeMissing' and 'zipWithMaybeMatched'. --- --- Consider --- --- @ --- merge (mapMaybeMissing g1) --- (mapMaybeMissing g2) --- (zipWithMaybeMatched f) --- m1 m2 --- @ --- --- Take, for example, --- --- @ --- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] --- m2 = [(1, "one"), (2, "two"), (4, "three")] --- @ --- --- @merge@ will first ''align'' these maps by key: --- --- @ --- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] --- m2 = [(1, "one"), (2, "two"), (4, "three")] --- @ --- --- It will then pass the individual entries and pairs of entries --- to @g1@, @g2@, or @f@ as appropriate: --- --- @ --- maybes = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"] --- @ --- --- This produces a 'Maybe' for each key: --- --- @ --- keys = 0 1 2 3 4 --- results = [Nothing, Just True, Just False, Nothing, Just True] --- @ --- --- Finally, the @Just@ results are collected into a map: --- --- @ --- return value = [(1, True), (2, False), (4, True)] --- @ --- --- The other tactics below are optimizations or simplifications of --- 'mapMaybeMissing' for special cases. Most importantly, --- --- * 'dropMissing' drops all the keys. --- * 'preserveMissing' leaves all the entries alone. --- --- When 'merge' is given three arguments, it is inlined at the call --- site. To prevent excessive inlining, you should typically use 'merge' --- to define your custom combining functions. --- --- --- Examples: --- --- prop> unionWithKey f = merge preserveMissing preserveMissing (zipWithMatched f) --- prop> intersectionWithKey f = merge dropMissing dropMissing (zipWithMatched f) --- prop> differenceWith f = merge diffPreserve diffDrop f --- prop> symmetricDifference = merge diffPreserve diffPreserve (\ _ _ _ -> Nothing) --- prop> mapEachPiece f g h = merge (diffMapWithKey f) (diffMapWithKey g) --- --- @since 0.5.8 -merge :: Ord k - => SimpleWhenMissing k a c -- ^ What to do with keys in @m1@ but not @m2@ - -> SimpleWhenMissing k b c -- ^ What to do with keys in @m2@ but not @m1@ - -> SimpleWhenMatched k a b c -- ^ What to do with keys in both @m1@ and @m2@ - -> Map k a -- ^ Map @m1@ - -> Map k b -- ^ Map @m2@ - -> Map k c -merge g1 g2 f m1 m2 = runIdentity $ - mergeA g1 g2 f m1 m2 -{-# INLINE merge #-} - --- | An applicative version of 'merge'. --- --- @mergeA@ takes two 'WhenMissing' tactics, a 'WhenMatched' --- tactic and two maps. It uses the tactics to merge the maps. --- Its behavior is best understood via its fundamental tactics, --- 'traverseMaybeMissing' and 'zipWithMaybeAMatched'. --- --- Consider --- --- @ --- mergeA (traverseMaybeMissing g1) --- (traverseMaybeMissing g2) --- (zipWithMaybeAMatched f) --- m1 m2 --- @ --- --- Take, for example, --- --- @ --- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] --- m2 = [(1, "one"), (2, "two"), (4, "three")] --- @ --- --- @mergeA@ will first ''align'' these maps by key: --- --- @ --- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] --- m2 = [(1, "one"), (2, "two"), (4, "three")] --- @ --- --- It will then pass the individual entries and pairs of entries --- to @g1@, @g2@, or @f@ as appropriate: --- --- @ --- actions = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"] --- @ --- --- Next, it will perform the actions in the @actions@ list in order from --- left to right. --- --- @ --- keys = 0 1 2 3 4 --- results = [Nothing, Just True, Just False, Nothing, Just True] --- @ --- --- Finally, the @Just@ results are collected into a map: --- --- @ --- return value = [(1, True), (2, False), (4, True)] --- @ --- --- The other tactics below are optimizations or simplifications of --- 'traverseMaybeMissing' for special cases. Most importantly, --- --- * 'dropMissing' drops all the keys. --- * 'preserveMissing' leaves all the entries alone. --- * 'mapMaybeMissing' does not use the 'Applicative' context. --- --- When 'mergeA' is given three arguments, it is inlined at the call --- site. To prevent excessive inlining, you should generally only use --- 'mergeA' to define custom combining functions. --- --- @since 0.5.8 -mergeA :: (Applicative f, Ord k) - => WhenMissing f k a c -- ^ What to do with keys in @m1@ but not @m2@ - -> WhenMissing f k b c -- ^ What to do with keys in @m2@ but not @m1@ - -> WhenMatched f k a b c -- ^ What to do with keys in both @m1@ and @m2@ - -> Map k a -- ^ Map @m1@ - -> Map k b -- ^ Map @m2@ - -> f (Map k c) -mergeA g1 WhenMissing{missingSubtree = g2} (WhenMatched f) = go - where - go t1 Tip = missingSubtree g1 t1 - go Tip t2 = g2 t2 - go (Bin _ kx x1 l1 r1) t2 = case splitLookup kx t2 of - (l2, mx2, r2) -> case mx2 of - Nothing -> (\l' mx' r' -> maybe link2 (link kx) mx' l' r') - <$> l1l2 <*> missingKey g1 kx x1 <*> r1r2 - Just x2 -> (\l' mx' r' -> maybe link2 (link kx) mx' l' r') - <$> l1l2 <*> f kx x1 x2 <*> r1r2 - where - !l1l2 = go l1 l2 - !r1r2 = go r1 r2 -{-# INLINE mergeA #-} - - -{-------------------------------------------------------------------- - MergeWithKey ---------------------------------------------------------------------} - --- | /O(n+m)/. An unsafe general combining function. --- --- WARNING: This function can produce corrupt maps and its results --- may depend on the internal structures of its inputs. Users should --- prefer 'merge' or 'mergeA'. --- --- When 'mergeWithKey' is given three arguments, it is inlined to the call --- site. You should therefore use 'mergeWithKey' only to define custom --- combining functions. For example, you could define 'unionWithKey', --- 'differenceWithKey' and 'intersectionWithKey' as --- --- > myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2 --- > myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2 --- > myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2 --- --- When calling @'mergeWithKey' combine only1 only2@, a function combining two --- 'Map's is created, such that --- --- * if a key is present in both maps, it is passed with both corresponding --- values to the @combine@ function. Depending on the result, the key is either --- present in the result with specified value, or is left out; --- --- * a nonempty subtree present only in the first map is passed to @only1@ and --- the output is added to the result; --- --- * a nonempty subtree present only in the second map is passed to @only2@ and --- the output is added to the result. --- --- The @only1@ and @only2@ methods /must return a map with a subset (possibly empty) of the keys of the given map/. --- The values can be modified arbitrarily. Most common variants of @only1@ and --- @only2@ are 'id' and @'const' 'empty'@, but for example @'map' f@, --- @'filterWithKey' f@, or @'mapMaybeWithKey' f@ could be used for any @f@. - -mergeWithKey :: Ord k - => (k -> a -> b -> Maybe c) - -> (Map k a -> Map k c) - -> (Map k b -> Map k c) - -> Map k a -> Map k b -> Map k c -mergeWithKey f g1 g2 = go - where - go Tip t2 = g2 t2 - go t1 Tip = g1 t1 - go (Bin _ kx x l1 r1) t2 = - case found of - Nothing -> case g1 (singleton kx x) of - Tip -> link2 l' r' - (Bin _ _ x' Tip Tip) -> link kx x' l' r' - _ -> error "mergeWithKey: Given function only1 does not fulfill required conditions (see documentation)" - Just x2 -> case f kx x x2 of - Nothing -> link2 l' r' - Just x' -> link kx x' l' r' - where - (l2, found, r2) = splitLookup kx t2 - l' = go l1 l2 - r' = go r1 r2 -{-# INLINE mergeWithKey #-} - -{-------------------------------------------------------------------- - Submap ---------------------------------------------------------------------} --- | /O(m*log(n/m + 1)), m <= n/. --- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@). --- -isSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool -isSubmapOf m1 m2 = isSubmapOfBy (==) m1 m2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE isSubmapOf #-} -#endif - -{- | /O(m*log(n/m + 1)), m <= n/. - The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if - all keys in @t1@ are in tree @t2@, and when @f@ returns 'True' when - applied to their respective values. For example, the following - expressions are all 'True': - - > isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) - > isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) - > isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)]) - - But the following are all 'False': - - > isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)]) - > isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) - > isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)]) - - --} -isSubmapOfBy :: Ord k => (a->b->Bool) -> Map k a -> Map k b -> Bool -isSubmapOfBy f t1 t2 - = (size t1 <= size t2) && (submap' f t1 t2) -#if __GLASGOW_HASKELL__ -{-# INLINABLE isSubmapOfBy #-} -#endif - -submap' :: Ord a => (b -> c -> Bool) -> Map a b -> Map a c -> Bool -submap' _ Tip _ = True -submap' _ _ Tip = False -submap' f (Bin _ kx x l r) t - = case found of - Nothing -> False - Just y -> f x y && submap' f l lt && submap' f r gt - where - (lt,found,gt) = splitLookup kx t -#if __GLASGOW_HASKELL__ -{-# INLINABLE submap' #-} -#endif - --- | /O(m*log(n/m + 1)), m <= n/. Is this a proper submap? (ie. a submap but not equal). --- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@). -isProperSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool -isProperSubmapOf m1 m2 - = isProperSubmapOfBy (==) m1 m2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE isProperSubmapOf #-} -#endif - -{- | /O(m*log(n/m + 1)), m <= n/. Is this a proper submap? (ie. a submap but not equal). - The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when - @m1@ and @m2@ are not equal, - all keys in @m1@ are in @m2@, and when @f@ returns 'True' when - applied to their respective values. For example, the following - expressions are all 'True': - - > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - - But the following are all 'False': - - > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) - > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) - > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) - - --} -isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool -isProperSubmapOfBy f t1 t2 - = (size t1 < size t2) && (submap' f t1 t2) -#if __GLASGOW_HASKELL__ -{-# INLINABLE isProperSubmapOfBy #-} -#endif - -{-------------------------------------------------------------------- - Filter and partition ---------------------------------------------------------------------} --- | /O(n)/. Filter all values that satisfy the predicate. --- --- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" --- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty --- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty - -filter :: (a -> Bool) -> Map k a -> Map k a -filter p m - = filterWithKey (\_ x -> p x) m - --- | /O(n)/. Filter all keys\/values that satisfy the predicate. --- --- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" - -filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a -filterWithKey _ Tip = Tip -filterWithKey p t@(Bin _ kx x l r) - | p kx x = if pl `ptrEq` l && pr `ptrEq` r - then t - else link kx x pl pr - | otherwise = link2 pl pr - where !pl = filterWithKey p l - !pr = filterWithKey p r - --- | /O(n)/. Filter keys and values using an 'Applicative' --- predicate. -filterWithKeyA :: Applicative f => (k -> a -> f Bool) -> Map k a -> f (Map k a) -filterWithKeyA _ Tip = pure Tip -filterWithKeyA p t@(Bin _ kx x l r) = - combine <$> p kx x <*> filterWithKeyA p l <*> filterWithKeyA p r - where - combine True pl pr - | pl `ptrEq` l && pr `ptrEq` r = t - | otherwise = link kx x pl pr - combine False pl pr = link2 pl pr - --- | /O(log n)/. Take while a predicate on the keys holds. --- The user is responsible for ensuring that for all keys @j@ and @k@ in the map, --- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. --- --- @ --- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' (p . fst) . 'toList' --- takeWhileAntitone p = 'filterWithKey' (\k _ -> p k) --- @ - -takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a -takeWhileAntitone _ Tip = Tip -takeWhileAntitone p (Bin _ kx x l r) - | p kx = link kx x l (takeWhileAntitone p r) - | otherwise = takeWhileAntitone p l - --- | /O(log n)/. Drop while a predicate on the keys holds. --- The user is responsible for ensuring that for all keys @j@ and @k@ in the map, --- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. --- --- @ --- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' (p . fst) . 'toList' --- dropWhileAntitone p = 'filterWithKey' (\k -> not (p k)) --- @ - -dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a -dropWhileAntitone _ Tip = Tip -dropWhileAntitone p (Bin _ kx x l r) - | p kx = dropWhileAntitone p r - | otherwise = link kx x (dropWhileAntitone p l) r - --- | /O(log n)/. Divide a map at the point where a predicate on the keys stops holding. --- The user is responsible for ensuring that for all keys @j@ and @k@ in the map, --- @j \< k ==\> p j \>= p k@. --- --- @ --- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs) --- spanAntitone p xs = partition p xs --- @ --- --- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the map --- at some /unspecified/ point where the predicate switches from holding to not --- holding (where the predicate is seen to hold before the first key and to fail --- after the last key). - -spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a) -spanAntitone p0 m = toPair (go p0 m) - where - go _ Tip = Tip :*: Tip - go p (Bin _ kx x l r) - | p kx = let u :*: v = go p r in link kx x l u :*: v - | otherwise = let u :*: v = go p l in u :*: link kx x v r - --- | /O(n)/. Partition the map according to a predicate. The first --- map contains all elements that satisfy the predicate, the second all --- elements that fail the predicate. See also 'split'. --- --- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") --- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) --- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) - -partition :: (a -> Bool) -> Map k a -> (Map k a,Map k a) -partition p m - = partitionWithKey (\_ x -> p x) m - --- | /O(n)/. Partition the map according to a predicate. The first --- map contains all elements that satisfy the predicate, the second all --- elements that fail the predicate. See also 'split'. --- --- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b") --- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) --- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) - -partitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a,Map k a) -partitionWithKey p0 t0 = toPair $ go p0 t0 - where - go _ Tip = (Tip :*: Tip) - go p t@(Bin _ kx x l r) - | p kx x = (if l1 `ptrEq` l && r1 `ptrEq` r - then t - else link kx x l1 r1) :*: link2 l2 r2 - | otherwise = link2 l1 r1 :*: - (if l2 `ptrEq` l && r2 `ptrEq` r - then t - else link kx x l2 r2) - where - (l1 :*: l2) = go p l - (r1 :*: r2) = go p r - --- | /O(n)/. Map values and collect the 'Just' results. --- --- > let f x = if x == "a" then Just "new a" else Nothing --- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a" - -mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b -mapMaybe f = mapMaybeWithKey (\_ x -> f x) - --- | /O(n)/. Map keys\/values and collect the 'Just' results. --- --- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing --- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3" - -mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b -mapMaybeWithKey _ Tip = Tip -mapMaybeWithKey f (Bin _ kx x l r) = case f kx x of - Just y -> link kx y (mapMaybeWithKey f l) (mapMaybeWithKey f r) - Nothing -> link2 (mapMaybeWithKey f l) (mapMaybeWithKey f r) - --- | /O(n)/. Traverse keys\/values and collect the 'Just' results. - -traverseMaybeWithKey :: Applicative f - => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b) -traverseMaybeWithKey = go - where - go _ Tip = pure Tip - go f (Bin _ kx x Tip Tip) = maybe Tip (\x' -> Bin 1 kx x' Tip Tip) <$> f kx x - go f (Bin _ kx x l r) = combine <$> go f l <*> f kx x <*> go f r - where - combine !l' mx !r' = case mx of - Nothing -> link2 l' r' - Just x' -> link kx x' l' r' - --- | /O(n)/. Map values and separate the 'Left' and 'Right' results. --- --- > let f a = if a < "c" then Left a else Right a --- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")]) --- > --- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) - -mapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c) -mapEither f m - = mapEitherWithKey (\_ x -> f x) m - --- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results. --- --- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a) --- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")]) --- > --- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) --- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")]) - -mapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c) -mapEitherWithKey f0 t0 = toPair $ go f0 t0 - where - go _ Tip = (Tip :*: Tip) - go f (Bin _ kx x l r) = case f kx x of - Left y -> link kx y l1 r1 :*: link2 l2 r2 - Right z -> link2 l1 r1 :*: link kx z l2 r2 - where - (l1 :*: l2) = go f l - (r1 :*: r2) = go f r - -{-------------------------------------------------------------------- - Mapping ---------------------------------------------------------------------} --- | /O(n)/. Map a function over all values in the map. --- --- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")] - -map :: (a -> b) -> Map k a -> Map k b -map f = go where - go Tip = Tip - go (Bin sx kx x l r) = Bin sx kx (f x) (go l) (go r) --- We use a `go` function to allow `map` to inline. This makes --- a big difference if someone uses `map (const x) m` instead --- of `x <$ m`; it doesn't seem to do any harm. - -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] map #-} -{-# RULES -"map/map" forall f g xs . map f (map g xs) = map (f . g) xs - #-} -#endif -#if __GLASGOW_HASKELL__ >= 709 --- Safe coercions were introduced in 7.8, but did not work well with RULES yet. -{-# RULES -"map/coerce" map coerce = coerce - #-} -#endif - --- | /O(n)/. Map a function over all values in the map. --- --- > let f key x = (show key) ++ ":" ++ x --- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")] - -mapWithKey :: (k -> a -> b) -> Map k a -> Map k b -mapWithKey _ Tip = Tip -mapWithKey f (Bin sx kx x l r) = Bin sx kx (f kx x) (mapWithKey f l) (mapWithKey f r) - -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] mapWithKey #-} -{-# RULES -"mapWithKey/mapWithKey" forall f g xs . mapWithKey f (mapWithKey g xs) = - mapWithKey (\k a -> f k (g k a)) xs -"mapWithKey/map" forall f g xs . mapWithKey f (map g xs) = - mapWithKey (\k a -> f k (g a)) xs -"map/mapWithKey" forall f g xs . map f (mapWithKey g xs) = - mapWithKey (\k a -> f (g k a)) xs - #-} -#endif - --- | /O(n)/. --- @'traverseWithKey' f m == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@ --- That is, behaves exactly like a regular 'traverse' except that the traversing --- function also has access to the key associated with a value. --- --- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')]) --- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing -traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b) -traverseWithKey f = go - where - go Tip = pure Tip - go (Bin 1 k v _ _) = (\v' -> Bin 1 k v' Tip Tip) <$> f k v - go (Bin s k v l r) = flip (Bin s k) <$> go l <*> f k v <*> go r -{-# INLINE traverseWithKey #-} - --- | /O(n)/. The function 'mapAccum' threads an accumulating --- argument through the map in ascending order of keys. --- --- > let f a b = (a ++ b, b ++ "X") --- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")]) - -mapAccum :: (a -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) -mapAccum f a m - = mapAccumWithKey (\a' _ x' -> f a' x') a m - --- | /O(n)/. The function 'mapAccumWithKey' threads an accumulating --- argument through the map in ascending order of keys. --- --- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X") --- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")]) - -mapAccumWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) -mapAccumWithKey f a t - = mapAccumL f a t - --- | /O(n)/. The function 'mapAccumL' threads an accumulating --- argument through the map in ascending order of keys. -mapAccumL :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) -mapAccumL _ a Tip = (a,Tip) -mapAccumL f a (Bin sx kx x l r) = - let (a1,l') = mapAccumL f a l - (a2,x') = f a1 kx x - (a3,r') = mapAccumL f a2 r - in (a3,Bin sx kx x' l' r') - --- | /O(n)/. The function 'mapAccumR' threads an accumulating --- argument through the map in descending order of keys. -mapAccumRWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) -mapAccumRWithKey _ a Tip = (a,Tip) -mapAccumRWithKey f a (Bin sx kx x l r) = - let (a1,r') = mapAccumRWithKey f a r - (a2,x') = f a1 kx x - (a3,l') = mapAccumRWithKey f a2 l - in (a3,Bin sx kx x' l' r') - --- | /O(n*log n)/. --- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@. --- --- The size of the result may be smaller if @f@ maps two or more distinct --- keys to the same new key. In this case the value at the greatest of the --- original keys is retained. --- --- > mapKeys (+ 1) (fromList [(5,"a"), (3,"b")]) == fromList [(4, "b"), (6, "a")] --- > mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c" --- > mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c" - -mapKeys :: Ord k2 => (k1->k2) -> Map k1 a -> Map k2 a -mapKeys f = fromList . foldrWithKey (\k x xs -> (f k, x) : xs) [] -#if __GLASGOW_HASKELL__ -{-# INLINABLE mapKeys #-} -#endif - --- | /O(n*log n)/. --- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@. --- --- The size of the result may be smaller if @f@ maps two or more distinct --- keys to the same new key. In this case the associated values will be --- combined using @c@. --- --- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab" --- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab" - -mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1->k2) -> Map k1 a -> Map k2 a -mapKeysWith c f = fromListWith c . foldrWithKey (\k x xs -> (f k, x) : xs) [] -#if __GLASGOW_HASKELL__ -{-# INLINABLE mapKeysWith #-} -#endif - - --- | /O(n)/. --- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@ --- is strictly monotonic. --- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@. --- /The precondition is not checked./ --- Semi-formally, we have: --- --- > and [x < y ==> f x < f y | x <- ls, y <- ls] --- > ==> mapKeysMonotonic f s == mapKeys f s --- > where ls = keys s --- --- This means that @f@ maps distinct original keys to distinct resulting keys. --- This function has better performance than 'mapKeys'. --- --- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")] --- > valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True --- > valid (mapKeysMonotonic (\ _ -> 1) (fromList [(5,"a"), (3,"b")])) == False - -mapKeysMonotonic :: (k1->k2) -> Map k1 a -> Map k2 a -mapKeysMonotonic _ Tip = Tip -mapKeysMonotonic f (Bin sz k x l r) = - Bin sz (f k) x (mapKeysMonotonic f l) (mapKeysMonotonic f r) - -{-------------------------------------------------------------------- - Folds ---------------------------------------------------------------------} - --- | /O(n)/. Fold the values in the map using the given right-associative --- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@. --- --- For example, --- --- > elems map = foldr (:) [] map --- --- > let f a len = len + (length a) --- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 -foldr :: (a -> b -> b) -> b -> Map k a -> b -foldr f z = go z - where - go z' Tip = z' - go z' (Bin _ _ x l r) = go (f x (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' :: (a -> b -> b) -> b -> Map k a -> b -foldr' f z = go z - where - go !z' Tip = z' - go z' (Bin _ _ x l r) = go (f x (go z' r)) l -{-# INLINE foldr' #-} - --- | /O(n)/. Fold the values in the map using the given left-associative --- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@. --- --- For example, --- --- > elems = reverse . foldl (flip (:)) [] --- --- > let f len a = len + (length a) --- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 -foldl :: (a -> b -> a) -> a -> Map k b -> a -foldl f z = go z - where - go z' Tip = z' - go z' (Bin _ _ x l r) = go (f (go z' l) x) 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 -> b -> a) -> a -> Map k b -> a -foldl' f z = go z - where - go !z' Tip = z' - go z' (Bin _ _ x l r) = go (f (go z' l) x) r -{-# INLINE foldl' #-} - --- | /O(n)/. Fold the keys and values in the map using the given right-associative --- binary operator, such that --- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@. --- --- For example, --- --- > keys map = foldrWithKey (\k x ks -> k:ks) [] map --- --- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" --- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)" -foldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b -foldrWithKey f z = go z - where - go z' Tip = z' - go z' (Bin _ kx x l r) = go (f kx x (go z' r)) l -{-# INLINE foldrWithKey #-} - --- | /O(n)/. A strict version of 'foldrWithKey'. Each application of the operator is --- evaluated before using the result in the next application. This --- function is strict in the starting value. -foldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b -foldrWithKey' f z = go z - where - go !z' Tip = z' - go z' (Bin _ kx x l r) = go (f kx x (go z' r)) l -{-# INLINE foldrWithKey' #-} - --- | /O(n)/. Fold the keys and values in the map using the given left-associative --- binary operator, such that --- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@. --- --- For example, --- --- > keys = reverse . foldlWithKey (\ks k x -> k:ks) [] --- --- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" --- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)" -foldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a -foldlWithKey f z = go z - where - go z' Tip = z' - go z' (Bin _ kx x l r) = go (f (go z' l) kx x) r -{-# INLINE foldlWithKey #-} - --- | /O(n)/. A strict version of 'foldlWithKey'. Each application of the operator is --- evaluated before using the result in the next application. This --- function is strict in the starting value. -foldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a -foldlWithKey' f z = go z - where - go !z' Tip = z' - go z' (Bin _ kx x l r) = go (f (go z' l) kx x) r -{-# INLINE foldlWithKey' #-} - --- | /O(n)/. Fold the keys and values in the map using the given monoid, such that --- --- @'foldMapWithKey' f = 'Prelude.fold' . 'mapWithKey' f@ --- --- This can be an asymptotically faster than 'foldrWithKey' or 'foldlWithKey' for some monoids. -foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m -foldMapWithKey f = go - where - go Tip = mempty - go (Bin 1 k v _ _) = f k v - go (Bin _ k v l r) = go l `mappend` (f k v `mappend` go r) -{-# INLINE foldMapWithKey #-} - -{-------------------------------------------------------------------- - List variations ---------------------------------------------------------------------} --- | /O(n)/. --- Return all elements of the map in the ascending order of their keys. --- Subject to list fusion. --- --- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"] --- > elems empty == [] - -elems :: Map k a -> [a] -elems = foldr (:) [] - --- | /O(n)/. Return all keys of the map in ascending order. Subject to list --- fusion. --- --- > keys (fromList [(5,"a"), (3,"b")]) == [3,5] --- > keys empty == [] - -keys :: Map k a -> [k] -keys = foldrWithKey (\k _ ks -> k : ks) [] - --- | /O(n)/. An alias for 'toAscList'. Return all key\/value pairs in the map --- in ascending key order. Subject to list fusion. --- --- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] --- > assocs empty == [] - -assocs :: Map k a -> [(k,a)] -assocs m - = toAscList m - --- | /O(n)/. The set of all keys of the map. --- --- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [3,5] --- > keysSet empty == Data.Set.empty - -keysSet :: Map k a -> Set.Set k -keysSet Tip = Set.Tip -keysSet (Bin sz kx _ l r) = Set.Bin sz kx (keysSet l) (keysSet r) - --- | /O(n)/. Build a map from a set of keys and a function which for each key --- computes its value. --- --- > fromSet (\k -> replicate k 'a') (Data.Set.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")] --- > fromSet undefined Data.Set.empty == empty - -fromSet :: (k -> a) -> Set.Set k -> Map k a -fromSet _ Set.Tip = Tip -fromSet f (Set.Bin sz x l r) = Bin sz x (f x) (fromSet f l) (fromSet f r) - -{-------------------------------------------------------------------- - Lists - use [foldlStrict] to reduce demand on the control-stack ---------------------------------------------------------------------} -#if __GLASGOW_HASKELL__ >= 708 -instance (Ord k) => GHCExts.IsList (Map k v) where - type Item (Map k v) = (k,v) - fromList = fromList - toList = toList -#endif - --- | /O(n*log n)/. Build a map from a list of key\/value pairs. See also 'fromAscList'. --- If the list contains more than one value for the same key, the last value --- for the key is retained. --- --- If the keys of the list are ordered, linear-time implementation is used, --- with the performance equal to 'fromDistinctAscList'. --- --- > fromList [] == empty --- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] --- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")] - --- For some reason, when 'singleton' is used in fromList or in --- create, it is not inlined, so we inline it manually. -fromList :: Ord k => [(k,a)] -> Map k a -fromList [] = Tip -fromList [(kx, x)] = Bin 1 kx x Tip Tip -fromList ((kx0, x0) : xs0) | not_ordered kx0 xs0 = fromList' (Bin 1 kx0 x0 Tip Tip) xs0 - | otherwise = go (1::Int) (Bin 1 kx0 x0 Tip Tip) xs0 - where - not_ordered _ [] = False - not_ordered kx ((ky,_) : _) = kx >= ky - {-# INLINE not_ordered #-} - - fromList' t0 xs = foldlStrict ins t0 xs - where ins t (k,x) = insert k x t - - go !_ t [] = t - go _ t [(kx, x)] = insertMax kx x t - go s l xs@((kx, x) : xss) | not_ordered kx xss = fromList' l xs - | otherwise = case create s xss of - (r, ys, []) -> go (s `shiftL` 1) (link kx x l r) ys - (r, _, ys) -> fromList' (link kx x l r) ys - - -- The create is returning a triple (tree, xs, ys). Both xs and ys - -- represent not yet processed elements and only one of them can be nonempty. - -- If ys is nonempty, the keys in ys are not ordered with respect to tree - -- and must be inserted using fromList'. Otherwise the keys have been - -- ordered so far. - create !_ [] = (Tip, [], []) - create s xs@(xp : xss) - | s == 1 = case xp of (kx, x) | not_ordered kx xss -> (Bin 1 kx x Tip Tip, [], xss) - | otherwise -> (Bin 1 kx x Tip Tip, xss, []) - | otherwise = case create (s `shiftR` 1) xs of - res@(_, [], _) -> res - (l, [(ky, y)], zs) -> (insertMax ky y l, [], zs) - (l, ys@((ky, y):yss), _) | not_ordered ky yss -> (l, [], ys) - | otherwise -> case create (s `shiftR` 1) yss of - (r, zs, ws) -> (link ky y l r, zs, ws) -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromList #-} -#endif - --- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'. --- --- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")] --- > fromListWith (++) [] == empty - -fromListWith :: Ord k => (a -> a -> a) -> [(k,a)] -> Map k a -fromListWith f xs - = fromListWithKey (\_ x y -> f x y) xs -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromListWith #-} -#endif - --- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWithKey'. --- --- > let f k a1 a2 = (show k) ++ a1 ++ a2 --- > fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "3ab"), (5, "5a5ba")] --- > fromListWithKey f [] == empty - -fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k,a)] -> Map k a -fromListWithKey f xs - = foldlStrict ins empty xs - where - ins t (k,x) = insertWithKey f k x t -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromListWithKey #-} -#endif - --- | /O(n)/. Convert the map to a list of key\/value pairs. Subject to list fusion. --- --- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] --- > toList empty == [] - -toList :: Map k a -> [(k,a)] -toList = toAscList - --- | /O(n)/. Convert the map to a list of key\/value pairs where the keys are --- in ascending order. Subject to list fusion. --- --- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] - -toAscList :: Map k a -> [(k,a)] -toAscList = foldrWithKey (\k x xs -> (k,x):xs) [] - --- | /O(n)/. Convert the map to a list of key\/value pairs where the keys --- are in descending order. Subject to list fusion. --- --- > toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")] - -toDescList :: Map k a -> [(k,a)] -toDescList = foldlWithKey (\xs k x -> (k,x):xs) [] - --- List fusion for the list generating functions. -#if __GLASGOW_HASKELL__ --- The foldrFB and foldlFB are fold{r,l}WithKey equivalents, used for list fusion. --- They are important to convert unfused methods back, see mapFB in prelude. -foldrFB :: (k -> a -> b -> b) -> b -> Map k a -> b -foldrFB = foldrWithKey -{-# INLINE[0] foldrFB #-} -foldlFB :: (a -> k -> b -> a) -> a -> Map k b -> a -foldlFB = foldlWithKey -{-# INLINE[0] foldlFB #-} - --- Inline assocs and toList, so that we need to fuse only toAscList. -{-# INLINE assocs #-} -{-# INLINE toList #-} - --- The fusion is enabled up to phase 2 included. If it does not succeed, --- convert in phase 1 the expanded elems,keys,to{Asc,Desc}List calls back to --- elems,keys,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 elems,keys,to{Asc,Desc}List -- it was forbidden to --- inline it before phase 0, otherwise the fusion rules would not fire at all. -{-# NOINLINE[0] elems #-} -{-# NOINLINE[0] keys #-} -{-# NOINLINE[0] toAscList #-} -{-# NOINLINE[0] toDescList #-} -{-# RULES "Map.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-} -{-# RULES "Map.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-} -{-# RULES "Map.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-} -{-# RULES "Map.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-} -{-# RULES "Map.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-} -{-# RULES "Map.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-} -{-# RULES "Map.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-} -{-# RULES "Map.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-} -#endif - -{-------------------------------------------------------------------- - Building trees from ascending/descending lists can be done in linear time. - - Note that if [xs] is ascending that: - fromAscList xs == fromList xs - fromAscListWith f xs == fromListWith f xs ---------------------------------------------------------------------} --- | /O(n)/. Build a map from an ascending list in linear time. --- /The precondition (input list is ascending) is not checked./ --- --- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] --- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")] --- > valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) == True --- > valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) == False - -fromAscList :: Eq k => [(k,a)] -> Map k a -fromAscList xs - = fromAscListWithKey (\_ x _ -> x) xs -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromAscList #-} -#endif - --- | /O(n)/. Build a map from a descending list in linear time. --- /The precondition (input list is descending) is not checked./ --- --- > fromDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")] --- > fromDescList [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "b")] --- > valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True --- > valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False - -fromDescList :: Eq k => [(k,a)] -> Map k a -fromDescList xs - = fromDescListWithKey (\_ x _ -> x) xs -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromDescList #-} -#endif - --- | /O(n)/. Build a map from an ascending list in linear time with a combining function for equal keys. --- /The precondition (input list is ascending) is not checked./ --- --- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] --- > valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) == True --- > valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False - -fromAscListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a -fromAscListWith f xs - = fromAscListWithKey (\_ x y -> f x y) xs -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromAscListWith #-} -#endif - --- | /O(n)/. Build a map from a descending list in linear time with a combining function for equal keys. --- /The precondition (input list is descending) is not checked./ --- --- > fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "ba")] --- > valid (fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")]) == True --- > valid (fromDescListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False - -fromDescListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a -fromDescListWith f xs - = fromDescListWithKey (\_ x y -> f x y) xs -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromDescListWith #-} -#endif - --- | /O(n)/. Build a map from an ascending list in linear time with a --- combining function for equal keys. --- /The precondition (input list is ascending) is not checked./ --- --- > let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2 --- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] == fromList [(3, "b"), (5, "5:b5:ba")] --- > valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) == True --- > valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False - -fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a -fromAscListWithKey f xs - = fromDistinctAscList (combineEq f xs) - where - -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] - combineEq _ xs' - = case xs' of - [] -> [] - [x] -> [x] - (x:xx) -> combineEq' x xx - - combineEq' z [] = [z] - combineEq' z@(kz,zz) (x@(kx,xx):xs') - | kx==kz = let yy = f kx xx zz in combineEq' (kx,yy) xs' - | otherwise = z:combineEq' x xs' -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromAscListWithKey #-} -#endif - --- | /O(n)/. Build a map from a descending list in linear time with a --- combining function for equal keys. --- /The precondition (input list is descending) is not checked./ --- --- > let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2 --- > fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "5:b5:ba")] --- > valid (fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")]) == True --- > valid (fromDescListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False -fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a -fromDescListWithKey f xs - = fromDistinctDescList (combineEq f xs) - where - -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] - combineEq _ xs' - = case xs' of - [] -> [] - [x] -> [x] - (x:xx) -> combineEq' x xx - - combineEq' z [] = [z] - combineEq' z@(kz,zz) (x@(kx,xx):xs') - | kx==kz = let yy = f kx xx zz in combineEq' (kx,yy) xs' - | otherwise = z:combineEq' x xs' -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromDescListWithKey #-} -#endif - - --- | /O(n)/. Build a map from an ascending list of distinct elements in linear time. --- /The precondition is not checked./ --- --- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] --- > valid (fromDistinctAscList [(3,"b"), (5,"a")]) == True --- > valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) == False - --- For some reason, when 'singleton' is used in fromDistinctAscList or in --- create, it is not inlined, so we inline it manually. -fromDistinctAscList :: [(k,a)] -> Map k a -fromDistinctAscList [] = Tip -fromDistinctAscList ((kx0, x0) : xs0) = go (1::Int) (Bin 1 kx0 x0 Tip Tip) xs0 - where - go !_ t [] = t - go s l ((kx, x) : xs) = case create s xs of - (r, ys) -> go (s `shiftL` 1) (link kx x l r) ys - - create !_ [] = (Tip, []) - create s xs@(x' : xs') - | s == 1 = case x' of (kx, x) -> (Bin 1 kx x Tip Tip, xs') - | otherwise = case create (s `shiftR` 1) xs of - res@(_, []) -> res - (l, (ky, y):ys) -> case create (s `shiftR` 1) ys of - (r, zs) -> (link ky y l r, zs) - --- | /O(n)/. Build a map from a descending list of distinct elements in linear time. --- /The precondition is not checked./ --- --- > fromDistinctDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")] --- > valid (fromDistinctDescList [(5,"a"), (3,"b")]) == True --- > valid (fromDistinctDescList [(5,"a"), (5,"b"), (3,"b")]) == False - --- For some reason, when 'singleton' is used in fromDistinctDescList or in --- create, it is not inlined, so we inline it manually. -fromDistinctDescList :: [(k,a)] -> Map k a -fromDistinctDescList [] = Tip -fromDistinctDescList ((kx0, x0) : xs0) = go (1 :: Int) (Bin 1 kx0 x0 Tip Tip) xs0 - where - go !_ t [] = t - go s r ((kx, x) : xs) = case create s xs of - (l, ys) -> go (s `shiftL` 1) (link kx x l r) ys - - create !_ [] = (Tip, []) - create s xs@(x' : xs') - | s == 1 = case x' of (kx, x) -> (Bin 1 kx x Tip Tip, xs') - | otherwise = case create (s `shiftR` 1) xs of - res@(_, []) -> res - (r, (ky, y):ys) -> case create (s `shiftR` 1) ys of - (l, zs) -> (link ky y l r, zs) - -{- --- Functions very similar to these were used to implement --- hedge union, intersection, and difference algorithms that we no --- longer use. These functions, however, seem likely to be useful --- in their own right, so I'm leaving them here in case we end up --- exporting them. - -{-------------------------------------------------------------------- - [filterGt b t] filter all keys >[b] from tree [t] - [filterLt b t] filter all keys <[b] from tree [t] ---------------------------------------------------------------------} -filterGt :: Ord k => k -> Map k v -> Map k v -filterGt !_ Tip = Tip -filterGt !b (Bin _ kx x l r) = - case compare b kx of LT -> link kx x (filterGt b l) r - EQ -> r - GT -> filterGt b r -#if __GLASGOW_HASKELL__ -{-# INLINABLE filterGt #-} -#endif - -filterLt :: Ord k => k -> Map k v -> Map k v -filterLt !_ Tip = Tip -filterLt !b (Bin _ kx x l r) = - case compare kx b of LT -> link kx x l (filterLt b r) - EQ -> l - GT -> filterLt b l -#if __GLASGOW_HASKELL__ -{-# INLINABLE filterLt #-} -#endif --} - -{-------------------------------------------------------------------- - Split ---------------------------------------------------------------------} --- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@ where --- the keys in @map1@ are smaller than @k@ and the keys in @map2@ larger than @k@. --- Any key equal to @k@ is found in neither @map1@ nor @map2@. --- --- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")]) --- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a") --- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") --- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty) --- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty) - -split :: Ord k => k -> Map k a -> (Map k a,Map k a) -split !k0 t0 = toPair $ go k0 t0 - where - go k t = - case t of - Tip -> Tip :*: Tip - Bin _ kx x l r -> case compare k kx of - LT -> let (lt :*: gt) = go k l in lt :*: link kx x gt r - GT -> let (lt :*: gt) = go k r in link kx x l lt :*: gt - EQ -> (l :*: r) -#if __GLASGOW_HASKELL__ -{-# INLINABLE split #-} -#endif - --- | /O(log n)/. The expression (@'splitLookup' k map@) splits a map just --- like 'split' but also returns @'lookup' k map@. --- --- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")]) --- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a") --- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a") --- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty) --- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty) -splitLookup :: Ord k => k -> Map k a -> (Map k a,Maybe a,Map k a) -splitLookup k0 m = case go k0 m of - StrictTriple l mv r -> (l, mv, r) - where - go :: Ord k => k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a) - go !k t = - case t of - Tip -> StrictTriple Tip Nothing Tip - Bin _ kx x l r -> case compare k kx of - LT -> let StrictTriple lt z gt = go k l - !gt' = link kx x gt r - in StrictTriple lt z gt' - GT -> let StrictTriple lt z gt = go k r - !lt' = link kx x l lt - in StrictTriple lt' z gt - EQ -> StrictTriple l (Just x) r -#if __GLASGOW_HASKELL__ -{-# INLINABLE splitLookup #-} -#endif - --- | A variant of 'splitLookup' that indicates only whether the --- key was present, rather than producing its value. This is used to --- implement 'intersection' to avoid allocating unnecessary 'Just' --- constructors. -splitMember :: Ord k => k -> Map k a -> (Map k a,Bool,Map k a) -splitMember k0 m = case go k0 m of - StrictTriple l mv r -> (l, mv, r) - where - go :: Ord k => k -> Map k a -> StrictTriple (Map k a) Bool (Map k a) - go !k t = - case t of - Tip -> StrictTriple Tip False Tip - Bin _ kx x l r -> case compare k kx of - LT -> let StrictTriple lt z gt = go k l - !gt' = link kx x gt r - in StrictTriple lt z gt' - GT -> let StrictTriple lt z gt = go k r - !lt' = link kx x l lt - in StrictTriple lt' z gt - EQ -> StrictTriple l True r -#if __GLASGOW_HASKELL__ -{-# INLINABLE splitMember #-} -#endif - -data StrictTriple a b c = StrictTriple !a !b !c - -{-------------------------------------------------------------------- - Utility functions that maintain the balance properties of the tree. - All constructors assume that all values in [l] < [k] and all values - in [r] > [k], and that [l] and [r] are valid trees. - - In order of sophistication: - [Bin sz k x l r] The type constructor. - [bin k x l r] Maintains the correct size, assumes that both [l] - and [r] are balanced with respect to each other. - [balance k x l r] Restores the balance and size. - Assumes that the original tree was balanced and - that [l] or [r] has changed by at most one element. - [link k x l r] Restores balance and size. - - Furthermore, we can construct a new tree from two trees. Both operations - assume that all values in [l] < all values in [r] and that [l] and [r] - are valid: - [glue l r] Glues [l] and [r] together. Assumes that [l] and - [r] are already balanced with respect to each other. - [link2 l r] Merges two trees and restores balance. ---------------------------------------------------------------------} - -{-------------------------------------------------------------------- - Link ---------------------------------------------------------------------} -link :: k -> a -> Map k a -> Map k a -> Map k a -link kx x Tip r = insertMin kx x r -link kx x l Tip = insertMax kx x l -link kx x l@(Bin sizeL ky y ly ry) r@(Bin sizeR kz z lz rz) - | delta*sizeL < sizeR = balanceL kz z (link kx x l lz) rz - | delta*sizeR < sizeL = balanceR ky y ly (link kx x ry r) - | otherwise = bin kx x l r - - --- insertMin and insertMax don't perform potentially expensive comparisons. -insertMax,insertMin :: k -> a -> Map k a -> Map k a -insertMax kx x t - = case t of - Tip -> singleton kx x - Bin _ ky y l r - -> balanceR ky y l (insertMax kx x r) - -insertMin kx x t - = case t of - Tip -> singleton kx x - Bin _ ky y l r - -> balanceL ky y (insertMin kx x l) r - -{-------------------------------------------------------------------- - [link2 l r]: merges two trees. ---------------------------------------------------------------------} -link2 :: Map k a -> Map k a -> Map k a -link2 Tip r = r -link2 l Tip = l -link2 l@(Bin sizeL kx x lx rx) r@(Bin sizeR ky y ly ry) - | delta*sizeL < sizeR = balanceL ky y (link2 l ly) ry - | delta*sizeR < sizeL = balanceR kx x lx (link2 rx r) - | otherwise = glue l r - -{-------------------------------------------------------------------- - [glue l r]: glues two trees together. - Assumes that [l] and [r] are already balanced with respect to each other. ---------------------------------------------------------------------} -glue :: Map k a -> Map k a -> Map k a -glue Tip r = r -glue l Tip = l -glue l r - | size l > size r = let ((km,m),l') = deleteFindMax l in balanceR km m l' r - | otherwise = let ((km,m),r') = deleteFindMin r in balanceL km m l r' - - --- | /O(log n)/. Delete and find the minimal element. --- --- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")]) --- > deleteFindMin Error: can not return the minimal element of an empty map - -deleteFindMin :: Map k a -> ((k,a),Map k a) -deleteFindMin t - = case t of - Bin _ k x Tip r -> ((k,x),r) - Bin _ k x l r -> let !(km,l') = deleteFindMin l - !t' = balanceR k x l' r - in (km, t') - Tip -> (error "Map.deleteFindMin: can not return the minimal element of an empty map", Tip) - --- | /O(log n)/. Delete and find the maximal element. --- --- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")]) --- > deleteFindMax empty Error: can not return the maximal element of an empty map - -deleteFindMax :: Map k a -> ((k,a),Map k a) -deleteFindMax t - = case t of - Bin _ k x l Tip -> ((k,x),l) - Bin _ k x l r -> let !(km,r') = deleteFindMax r - !t' = balanceL k x l r' - in (km, t') - Tip -> (error "Map.deleteFindMax: can not return the maximal element of an empty map", Tip) - - -{-------------------------------------------------------------------- - [balance l x r] balances two trees with value x. - The sizes of the trees should balance after decreasing the - size of one of them. (a rotation). - - [delta] is the maximal relative difference between the sizes of - two trees, it corresponds with the [w] in Adams' paper. - [ratio] is the ratio between an outer and inner sibling of the - heavier subtree in an unbalanced setting. It determines - whether a double or single rotation should be performed - to restore balance. It is corresponds with the inverse - of $\alpha$ in Adam's article. - - Note that according to the Adam's paper: - - [delta] should be larger than 4.646 with a [ratio] of 2. - - [delta] should be larger than 3.745 with a [ratio] of 1.534. - - But the Adam's paper is erroneous: - - It can be proved that for delta=2 and delta>=5 there does - not exist any ratio that would work. - - Delta=4.5 and ratio=2 does not work. - - That leaves two reasonable variants, delta=3 and delta=4, - both with ratio=2. - - - A lower [delta] leads to a more 'perfectly' balanced tree. - - A higher [delta] performs less rebalancing. - - In the benchmarks, delta=3 is faster on insert operations, - and delta=4 has slightly better deletes. As the insert speedup - is larger, we currently use delta=3. - ---------------------------------------------------------------------} -delta,ratio :: Int -delta = 3 -ratio = 2 - --- The balance function is equivalent to the following: --- --- balance :: k -> a -> Map k a -> Map k a -> Map k a --- balance k x l r --- | sizeL + sizeR <= 1 = Bin sizeX k x l r --- | sizeR > delta*sizeL = rotateL k x l r --- | sizeL > delta*sizeR = rotateR k x l r --- | otherwise = Bin sizeX k x l r --- where --- sizeL = size l --- sizeR = size r --- sizeX = sizeL + sizeR + 1 --- --- rotateL :: a -> b -> Map a b -> Map a b -> Map a b --- rotateL k x l r@(Bin _ _ _ ly ry) | size ly < ratio*size ry = singleL k x l r --- | otherwise = doubleL k x l r --- --- rotateR :: a -> b -> Map a b -> Map a b -> Map a b --- rotateR k x l@(Bin _ _ _ ly ry) r | size ry < ratio*size ly = singleR k x l r --- | otherwise = doubleR k x l r --- --- singleL, singleR :: a -> b -> Map a b -> Map a b -> Map a b --- singleL k1 x1 t1 (Bin _ k2 x2 t2 t3) = bin k2 x2 (bin k1 x1 t1 t2) t3 --- singleR k1 x1 (Bin _ k2 x2 t1 t2) t3 = bin k2 x2 t1 (bin k1 x1 t2 t3) --- --- doubleL, doubleR :: a -> b -> Map a b -> Map a b -> Map a b --- doubleL k1 x1 t1 (Bin _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = bin k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4) --- doubleR k1 x1 (Bin _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = bin k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4) --- --- It is only written in such a way that every node is pattern-matched only once. - -balance :: k -> a -> Map k a -> Map k a -> Map k a -balance k x l r = case l of - Tip -> case r of - Tip -> Bin 1 k x Tip Tip - (Bin _ _ _ Tip Tip) -> Bin 2 k x Tip r - (Bin _ rk rx Tip rr@(Bin _ _ _ _ _)) -> Bin 3 rk rx (Bin 1 k x Tip Tip) rr - (Bin _ rk rx (Bin _ rlk rlx _ _) Tip) -> Bin 3 rlk rlx (Bin 1 k x Tip Tip) (Bin 1 rk rx Tip Tip) - (Bin rs rk rx rl@(Bin rls rlk rlx rll rlr) rr@(Bin rrs _ _ _ _)) - | rls < ratio*rrs -> Bin (1+rs) rk rx (Bin (1+rls) k x Tip rl) rr - | otherwise -> Bin (1+rs) rlk rlx (Bin (1+size rll) k x Tip rll) (Bin (1+rrs+size rlr) rk rx rlr rr) - - (Bin ls lk lx ll lr) -> case r of - Tip -> case (ll, lr) of - (Tip, Tip) -> Bin 2 k x l Tip - (Tip, (Bin _ lrk lrx _ _)) -> Bin 3 lrk lrx (Bin 1 lk lx Tip Tip) (Bin 1 k x Tip Tip) - ((Bin _ _ _ _ _), Tip) -> Bin 3 lk lx ll (Bin 1 k x Tip Tip) - ((Bin lls _ _ _ _), (Bin lrs lrk lrx lrl lrr)) - | lrs < ratio*lls -> Bin (1+ls) lk lx ll (Bin (1+lrs) k x lr Tip) - | otherwise -> Bin (1+ls) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+size lrr) k x lrr Tip) - (Bin rs rk rx rl rr) - | rs > delta*ls -> case (rl, rr) of - (Bin rls rlk rlx rll rlr, Bin rrs _ _ _ _) - | rls < ratio*rrs -> Bin (1+ls+rs) rk rx (Bin (1+ls+rls) k x l rl) rr - | otherwise -> Bin (1+ls+rs) rlk rlx (Bin (1+ls+size rll) k x l rll) (Bin (1+rrs+size rlr) rk rx rlr rr) - (_, _) -> error "Failure in Data.Map.balance" - | ls > delta*rs -> case (ll, lr) of - (Bin lls _ _ _ _, Bin lrs lrk lrx lrl lrr) - | lrs < ratio*lls -> Bin (1+ls+rs) lk lx ll (Bin (1+rs+lrs) k x lr r) - | otherwise -> Bin (1+ls+rs) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+rs+size lrr) k x lrr r) - (_, _) -> error "Failure in Data.Map.balance" - | otherwise -> Bin (1+ls+rs) k x l r -{-# NOINLINE balance #-} - --- Functions balanceL and balanceR are specialised versions of balance. --- balanceL only checks whether the left subtree is too big, --- balanceR only checks whether the right subtree is too big. - --- balanceL is called when left subtree might have been inserted to or when --- right subtree might have been deleted from. -balanceL :: k -> a -> Map k a -> Map k a -> Map k a -balanceL k x l r = case r of - Tip -> case l of - Tip -> Bin 1 k x Tip Tip - (Bin _ _ _ Tip Tip) -> Bin 2 k x l Tip - (Bin _ lk lx Tip (Bin _ lrk lrx _ _)) -> Bin 3 lrk lrx (Bin 1 lk lx Tip Tip) (Bin 1 k x Tip Tip) - (Bin _ lk lx ll@(Bin _ _ _ _ _) Tip) -> Bin 3 lk lx ll (Bin 1 k x Tip Tip) - (Bin ls lk lx ll@(Bin lls _ _ _ _) lr@(Bin lrs lrk lrx lrl lrr)) - | lrs < ratio*lls -> Bin (1+ls) lk lx ll (Bin (1+lrs) k x lr Tip) - | otherwise -> Bin (1+ls) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+size lrr) k x lrr Tip) - - (Bin rs _ _ _ _) -> case l of - Tip -> Bin (1+rs) k x Tip r - - (Bin ls lk lx ll lr) - | ls > delta*rs -> case (ll, lr) of - (Bin lls _ _ _ _, Bin lrs lrk lrx lrl lrr) - | lrs < ratio*lls -> Bin (1+ls+rs) lk lx ll (Bin (1+rs+lrs) k x lr r) - | otherwise -> Bin (1+ls+rs) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+rs+size lrr) k x lrr r) - (_, _) -> error "Failure in Data.Map.balanceL" - | otherwise -> Bin (1+ls+rs) k x l r -{-# NOINLINE balanceL #-} - --- balanceR is called when right subtree might have been inserted to or when --- left subtree might have been deleted from. -balanceR :: k -> a -> Map k a -> Map k a -> Map k a -balanceR k x l r = case l of - Tip -> case r of - Tip -> Bin 1 k x Tip Tip - (Bin _ _ _ Tip Tip) -> Bin 2 k x Tip r - (Bin _ rk rx Tip rr@(Bin _ _ _ _ _)) -> Bin 3 rk rx (Bin 1 k x Tip Tip) rr - (Bin _ rk rx (Bin _ rlk rlx _ _) Tip) -> Bin 3 rlk rlx (Bin 1 k x Tip Tip) (Bin 1 rk rx Tip Tip) - (Bin rs rk rx rl@(Bin rls rlk rlx rll rlr) rr@(Bin rrs _ _ _ _)) - | rls < ratio*rrs -> Bin (1+rs) rk rx (Bin (1+rls) k x Tip rl) rr - | otherwise -> Bin (1+rs) rlk rlx (Bin (1+size rll) k x Tip rll) (Bin (1+rrs+size rlr) rk rx rlr rr) - - (Bin ls _ _ _ _) -> case r of - Tip -> Bin (1+ls) k x l Tip - - (Bin rs rk rx rl rr) - | rs > delta*ls -> case (rl, rr) of - (Bin rls rlk rlx rll rlr, Bin rrs _ _ _ _) - | rls < ratio*rrs -> Bin (1+ls+rs) rk rx (Bin (1+ls+rls) k x l rl) rr - | otherwise -> Bin (1+ls+rs) rlk rlx (Bin (1+ls+size rll) k x l rll) (Bin (1+rrs+size rlr) rk rx rlr rr) - (_, _) -> error "Failure in Data.Map.balanceR" - | otherwise -> Bin (1+ls+rs) k x l r -{-# NOINLINE balanceR #-} - - -{-------------------------------------------------------------------- - The bin constructor maintains the size of the tree ---------------------------------------------------------------------} -bin :: k -> a -> Map k a -> Map k a -> Map k a -bin k x l r - = Bin (size l + size r + 1) k x l r -{-# INLINE bin #-} - - -{-------------------------------------------------------------------- - Eq converts the tree to a list. In a lazy setting, this - actually seems one of the faster methods to compare two trees - and it is certainly the simplest :-) ---------------------------------------------------------------------} -instance (Eq k,Eq a) => Eq (Map k a) where - t1 == t2 = (size t1 == size t2) && (toAscList t1 == toAscList t2) - -{-------------------------------------------------------------------- - Ord ---------------------------------------------------------------------} - -instance (Ord k, Ord v) => Ord (Map k v) where - compare m1 m2 = compare (toAscList m1) (toAscList m2) - -{-------------------------------------------------------------------- - Functor ---------------------------------------------------------------------} -instance Functor (Map k) where - fmap f m = map f m -#ifdef __GLASGOW_HASKELL__ - _ <$ Tip = Tip - a <$ (Bin sx kx _ l r) = Bin sx kx a (a <$ l) (a <$ r) -#endif - -instance Traversable (Map k) where - traverse f = traverseWithKey (\_ -> f) - {-# INLINE traverse #-} - -instance Foldable.Foldable (Map k) where - fold = go - where go Tip = mempty - go (Bin 1 _ v _ _) = v - go (Bin _ _ v l r) = go l `mappend` (v `mappend` go r) - {-# INLINABLE fold #-} - foldr = foldr - {-# INLINE foldr #-} - foldl = foldl - {-# INLINE foldl #-} - foldMap f t = go t - where go Tip = mempty - go (Bin 1 _ v _ _) = f v - go (Bin _ _ v l r) = go l `mappend` (f v `mappend` go r) - {-# INLINE foldMap #-} - -#if MIN_VERSION_base(4,6,0) - foldl' = foldl' - {-# INLINE foldl' #-} - foldr' = foldr' - {-# INLINE foldr' #-} -#endif -#if MIN_VERSION_base(4,8,0) - length = size - {-# INLINE length #-} - null = null - {-# INLINE null #-} - toList = elems -- NB: Foldable.toList /= Map.toList - {-# INLINE toList #-} - elem = go - where go !_ Tip = False - go x (Bin _ _ v l r) = x == v || go x l || go x r - {-# INLINABLE elem #-} - maximum = start - where start Tip = error "Map.Foldable.maximum: called with empty map" - start (Bin _ _ v l r) = go (go v l) r - - go !m Tip = m - go m (Bin _ _ v l r) = go (go (max m v) l) r - {-# INLINABLE maximum #-} - minimum = start - where start Tip = error "Map.Foldable.minumum: called with empty map" - start (Bin _ _ v l r) = go (go v l) r - - go !m Tip = m - go m (Bin _ _ v l r) = go (go (min m v) l) r - {-# INLINABLE minimum #-} - sum = foldl' (+) 0 - {-# INLINABLE sum #-} - product = foldl' (*) 1 - {-# INLINABLE product #-} -#endif - -instance (NFData k, NFData a) => NFData (Map k a) where - rnf Tip = () - rnf (Bin _ kx x l r) = rnf kx `seq` rnf x `seq` rnf l `seq` rnf r - -{-------------------------------------------------------------------- - Read ---------------------------------------------------------------------} -instance (Ord k, Read k, Read e) => Read (Map k e) 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 - -{-------------------------------------------------------------------- - Show ---------------------------------------------------------------------} -instance (Show k, Show a) => Show (Map k a) where - showsPrec d m = showParen (d > 10) $ - showString "fromList " . shows (toList m) - --- | /O(n)/. Show the tree that implements the map. The tree is shown --- in a compressed, hanging format. See 'showTreeWith'. -{-# DEPRECATED showTree "This function is being removed from the public API." #-} -showTree :: (Show k,Show a) => Map k a -> String -showTree m - = showTreeWith showElem True False m - where - showElem k x = show k ++ ":=" ++ show x - - -{- | /O(n)/. The expression (@'showTreeWith' showelem hang wide map@) shows - the tree that implements the map. Elements are shown using the @showElem@ function. 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. - -> Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]] -> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t -> (4,()) -> +--(2,()) -> | +--(1,()) -> | +--(3,()) -> +--(5,()) -> -> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t -> (4,()) -> | -> +--(2,()) -> | | -> | +--(1,()) -> | | -> | +--(3,()) -> | -> +--(5,()) -> -> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t -> +--(5,()) -> | -> (4,()) -> | -> | +--(3,()) -> | | -> +--(2,()) -> | -> +--(1,()) - --} -{-# DEPRECATED showTreeWith "This function is being removed from the public API." #-} -showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String -showTreeWith showelem hang wide t - | hang = (showsTreeHang showelem wide [] t) "" - | otherwise = (showsTree showelem wide [] [] t) "" - -showsTree :: (k -> a -> String) -> Bool -> [String] -> [String] -> Map k a -> ShowS -showsTree showelem wide lbars rbars t - = case t of - Tip -> showsBars lbars . showString "|\n" - Bin _ kx x Tip Tip - -> showsBars lbars . showString (showelem kx x) . showString "\n" - Bin _ kx x l r - -> showsTree showelem wide (withBar rbars) (withEmpty rbars) r . - showWide wide rbars . - showsBars lbars . showString (showelem kx x) . showString "\n" . - showWide wide lbars . - showsTree showelem wide (withEmpty lbars) (withBar lbars) l - -showsTreeHang :: (k -> a -> String) -> Bool -> [String] -> Map k a -> ShowS -showsTreeHang showelem wide bars t - = case t of - Tip -> showsBars bars . showString "|\n" - Bin _ kx x Tip Tip - -> showsBars bars . showString (showelem kx x) . showString "\n" - Bin _ kx x l r - -> showsBars bars . showString (showelem kx x) . showString "\n" . - showWide wide bars . - showsTreeHang showelem wide (withBar bars) l . - showWide wide bars . - showsTreeHang showelem wide (withEmpty bars) r - -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 - -node :: String -node = "+--" - -withBar, withEmpty :: [String] -> [String] -withBar bars = "| ":bars -withEmpty bars = " ":bars - -{-------------------------------------------------------------------- - Typeable ---------------------------------------------------------------------} - -INSTANCE_TYPEABLE2(Map) - -{-------------------------------------------------------------------- - Assertions ---------------------------------------------------------------------} --- | /O(n)/. Test if the internal map structure is valid. --- --- > valid (fromAscList [(3,"b"), (5,"a")]) == True --- > valid (fromAscList [(5,"a"), (3,"b")]) == False - -valid :: Ord k => Map k a -> Bool -valid t - = balanced t && ordered t && validsize t - -ordered :: Ord a => Map a b -> Bool -ordered t - = bounded (const True) (const True) t - where - bounded lo hi t' - = case t' of - Tip -> True - Bin _ kx _ l r -> (lo kx) && (hi kx) && bounded lo (kx) hi r - --- | Exported only for "Debug.QuickCheck" -balanced :: Map k a -> Bool -balanced t - = case t of - Tip -> True - Bin _ _ _ l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) && - balanced l && balanced r - -validsize :: Map a b -> Bool -validsize t - = (realsize t == Just (size t)) - where - realsize t' - = case t' of - Tip -> Just 0 - Bin sz _ _ l r -> case (realsize l,realsize r) of - (Just n,Just m) | n+m+1 == sz -> Just sz - _ -> Nothing - -{-------------------------------------------------------------------- - Utilities ---------------------------------------------------------------------} - --- | /O(1)/. Decompose a map into pieces based on the structure of the underlying --- tree. This function is useful for consuming a map in parallel. --- --- No guarantee is made as to the sizes of the pieces; an internal, but --- deterministic process determines this. However, it is guaranteed that the pieces --- returned will be in ascending order (all elements in the first submap less than all --- elements in the second, and so on). --- --- Examples: --- --- > splitRoot (fromList (zip [1..6] ['a'..])) == --- > [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]] --- --- > splitRoot empty == [] --- --- Note that the current implementation does not return more than three submaps, --- but you should not depend on this behaviour because it can change in the --- future without notice. -splitRoot :: Map k b -> [Map k b] -splitRoot orig = - case orig of - Tip -> [] - Bin _ k v l r -> [l, singleton k v, r] -{-# INLINE splitRoot #-} diff --git a/Data/Map/Internal.hs b/Data/Map/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/Map/Internal.hs @@ -0,0 +1,4114 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE PatternGuards #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Trustworthy #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE TypeFamilies #-} +#define USE_MAGIC_PROXY 1 +#endif + +#ifdef USE_MAGIC_PROXY +{-# LANGUAGE MagicHash #-} +#endif + +#include "containers.h" + +#if !(WORD_SIZE_IN_BITS >= 61) +#define DEFINE_ALTERF_FALLBACK 1 +#endif + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Map.Internal +-- Copyright : (c) Daan Leijen 2002 +-- (c) Andriy Palamarchuk 2008 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. +-- +-- = Description +-- +-- An efficient implementation of maps from keys to values (dictionaries). +-- +-- Since many function names (but not the type name) clash with +-- "Prelude" names, this module is usually imported @qualified@, e.g. +-- +-- > import Data.Map (Map) +-- > import qualified Data.Map as Map +-- +-- The implementation of 'Map' is based on /size balanced/ binary trees (or +-- trees of /bounded balance/) as described by: +-- +-- * Stephen Adams, \"/Efficient sets: a balancing act/\", +-- Journal of Functional Programming 3(4):553-562, October 1993, +-- . +-- * J. Nievergelt and E.M. Reingold, +-- \"/Binary search trees of bounded balance/\", +-- SIAM journal of computing 2(1), March 1973. +-- +-- Bounds for 'union', 'intersection', and 'difference' are as given +-- by +-- +-- * Guy Blelloch, Daniel Ferizovic, and Yihan Sun, +-- \"/Just Join for Parallel Ordered Sets/\", +-- . +-- +-- Note that the implementation is /left-biased/ -- the elements of a +-- first argument are always preferred to the second, for example in +-- 'union' or 'insert'. +-- +-- Operation comments contain the operation time complexity in +-- the Big-O notation . +----------------------------------------------------------------------------- + +-- [Note: Using INLINABLE] +-- ~~~~~~~~~~~~~~~~~~~~~~~ +-- It is crucial to the performance that the functions specialize on the Ord +-- type when possible. GHC 7.0 and higher does this by itself when it sees th +-- unfolding of a function -- that is why all public functions are marked +-- INLINABLE (that exposes the unfolding). + + +-- [Note: Using INLINE] +-- ~~~~~~~~~~~~~~~~~~~~ +-- For other compilers and GHC pre 7.0, we mark some of the functions INLINE. +-- We mark the functions that just navigate down the tree (lookup, insert, +-- delete and similar). That navigation code gets inlined and thus specialized +-- when possible. There is a price to pay -- code growth. The code INLINED is +-- therefore only the tree navigation, all the real work (rebalancing) is not +-- INLINED by using a NOINLINE. +-- +-- All methods marked INLINE have to be nonrecursive -- a 'go' function doing +-- the real work is provided. + + +-- [Note: Type of local 'go' function] +-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +-- If the local 'go' function uses an Ord class, it sometimes heap-allocates +-- the Ord dictionary when the 'go' function does not have explicit type. +-- In that case we give 'go' explicit type. But this slightly decrease +-- performance, as the resulting 'go' function can float out to top level. + + +-- [Note: Local 'go' functions and capturing] +-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +-- As opposed to Map, when 'go' function captures an argument, increased +-- heap-allocation can occur: sometimes in a polymorphic function, the 'go' +-- floats out of its enclosing function and then it heap-allocates the +-- dictionary and the argument. Maybe it floats out too late and strictness +-- analyzer cannot see that these could be passed on stack. +-- + +-- [Note: Order of constructors] +-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +-- The order of constructors of Map matters when considering performance. +-- Currently in GHC 7.0, when type has 2 constructors, a forward conditional +-- jump is made when successfully matching second constructor. Successful match +-- of first constructor results in the forward jump not taken. +-- On GHC 7.0, reordering constructors from Tip | Bin to Bin | Tip +-- improves the benchmark by up to 10% on x86. + +module Data.Map.Internal ( + -- * Map type + Map(..) -- instance Eq,Show,Read + + -- * Operators + , (!), (!?), (\\) + + -- * Query + , null + , size + , member + , notMember + , lookup + , findWithDefault + , lookupLT + , lookupGT + , lookupLE + , lookupGE + + -- * Construction + , empty + , singleton + + -- ** Insertion + , insert + , insertWith + , insertWithKey + , insertLookupWithKey + + -- ** Delete\/Update + , delete + , adjust + , adjustWithKey + , update + , updateWithKey + , updateLookupWithKey + , alter + , alterF + + -- * Combine + + -- ** Union + , union + , unionWith + , unionWithKey + , unions + , unionsWith + + -- ** Difference + , difference + , differenceWith + , differenceWithKey + + -- ** Intersection + , intersection + , intersectionWith + , intersectionWithKey + + -- ** General combining function + , SimpleWhenMissing + , SimpleWhenMatched + , runWhenMatched + , runWhenMissing + , merge + -- *** @WhenMatched@ tactics + , zipWithMaybeMatched + , zipWithMatched + -- *** @WhenMissing@ tactics + , mapMaybeMissing + , dropMissing + , preserveMissing + , mapMissing + , filterMissing + + -- ** Applicative general combining function + , WhenMissing (..) + , WhenMatched (..) + , mergeA + + -- *** @WhenMatched@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , zipWithMaybeAMatched + , zipWithAMatched + + -- *** @WhenMissing@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , traverseMaybeMissing + , traverseMissing + , filterAMissing + + -- ** Deprecated general combining function + + , mergeWithKey + + -- * Traversal + -- ** Map + , map + , mapWithKey + , traverseWithKey + , traverseMaybeWithKey + , mapAccum + , mapAccumWithKey + , mapAccumRWithKey + , mapKeys + , mapKeysWith + , mapKeysMonotonic + + -- * Folds + , foldr + , foldl + , foldrWithKey + , foldlWithKey + , foldMapWithKey + + -- ** Strict folds + , foldr' + , foldl' + , foldrWithKey' + , foldlWithKey' + + -- * Conversion + , elems + , keys + , assocs + , keysSet + , fromSet + + -- ** Lists + , toList + , fromList + , fromListWith + , fromListWithKey + + -- ** Ordered lists + , toAscList + , toDescList + , fromAscList + , fromAscListWith + , fromAscListWithKey + , fromDistinctAscList + , fromDescList + , fromDescListWith + , fromDescListWithKey + , fromDistinctDescList + + -- * Filter + , filter + , filterWithKey + + , takeWhileAntitone + , dropWhileAntitone + , spanAntitone + + , restrictKeys + , withoutKeys + , partition + , partitionWithKey + + , mapMaybe + , mapMaybeWithKey + , mapEither + , mapEitherWithKey + + , split + , splitLookup + , splitRoot + + -- * Submap + , isSubmapOf, isSubmapOfBy + , isProperSubmapOf, isProperSubmapOfBy + + -- * Indexed + , lookupIndex + , findIndex + , elemAt + , updateAt + , deleteAt + , take + , drop + , splitAt + + -- * Min\/Max + , lookupMin + , lookupMax + , findMin + , findMax + , deleteMin + , deleteMax + , deleteFindMin + , deleteFindMax + , updateMin + , updateMax + , updateMinWithKey + , updateMaxWithKey + , minView + , maxView + , minViewWithKey + , maxViewWithKey + + -- Used by the strict version + , AreWeStrict (..) + , atKeyImpl +#if __GLASGOW_HASKELL__ && MIN_VERSION_base(4,8,0) + , atKeyPlain +#endif + , bin + , balance + , balanceL + , balanceR + , delta + , insertMax + , link + , link2 + , glue + , MaybeS(..) + , Identity(..) + + -- Used by Map.Lazy.Merge + , mapWhenMissing + , mapWhenMatched + , lmapWhenMissing + , contramapFirstWhenMatched + , contramapSecondWhenMatched + , mapGentlyWhenMissing + , mapGentlyWhenMatched + ) where + +#if MIN_VERSION_base(4,8,0) +import Data.Functor.Identity (Identity (..)) +#else +import Control.Applicative (Applicative(..), (<$>)) +import Data.Monoid (Monoid(..)) +import Data.Traversable (Traversable(traverse)) +#endif +#if MIN_VERSION_base(4,9,0) +import Data.Functor.Classes +import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) +#endif +import Control.Applicative (Const (..)) +import Control.DeepSeq (NFData(rnf)) +import Data.Bits (shiftL, shiftR) +import qualified Data.Foldable as Foldable +import Data.Typeable +import Prelude hiding (lookup, map, filter, foldr, foldl, null, splitAt, take, drop) + +import qualified Data.Set.Internal as Set +import Data.Set.Internal (Set) +import Utils.Containers.Internal.PtrEquality (ptrEq) +import Utils.Containers.Internal.StrictFold +import Utils.Containers.Internal.StrictPair +import Utils.Containers.Internal.StrictMaybe +import Utils.Containers.Internal.BitQueue +#ifdef DEFINE_ALTERF_FALLBACK +import Utils.Containers.Internal.BitUtil (wordSize) +#endif + +#if __GLASGOW_HASKELL__ +import GHC.Exts (build) +#if !MIN_VERSION_base(4,8,0) +import Data.Functor ((<$)) +#endif +#ifdef USE_MAGIC_PROXY +import GHC.Exts (Proxy#, proxy# ) +#endif +#if __GLASGOW_HASKELL__ >= 708 +import qualified GHC.Exts as GHCExts +#endif +import Text.Read hiding (lift) +import Data.Data +import qualified Control.Category as Category +#endif +#if __GLASGOW_HASKELL__ >= 708 +import Data.Coerce +#endif + + +{-------------------------------------------------------------------- + Operators +--------------------------------------------------------------------} +infixl 9 !,!?,\\ -- + +-- | /O(log n)/. Find the value at a key. +-- Calls 'error' when the element can not be found. +-- +-- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map +-- > fromList [(5,'a'), (3,'b')] ! 5 == 'a' + +(!) :: Ord k => Map k a -> k -> a +(!) m k = find k m +#if __GLASGOW_HASKELL__ +{-# INLINE (!) #-} +#endif + +-- | /O(log n)/. Find the value at a key. +-- Returns 'Nothing' when the element can not be found. +-- +-- prop> fromList [(5, 'a'), (3, 'b')] !? 1 == Nothing +-- prop> fromList [(5, 'a'), (3, 'b')] !? 5 == Just 'a' + +(!?) :: Ord k => Map k a -> k -> Maybe a +(!?) m k = lookup k m +#if __GLASGOW_HASKELL__ +{-# INLINE (!?) #-} +#endif + +-- | Same as 'difference'. +(\\) :: Ord k => Map k a -> Map k b -> Map k a +m1 \\ m2 = difference m1 m2 +#if __GLASGOW_HASKELL__ +{-# INLINE (\\) #-} +#endif + +{-------------------------------------------------------------------- + Size balanced trees. +--------------------------------------------------------------------} +-- | A Map from keys @k@ to values @a@. + +-- See Note: Order of constructors +data Map k a = Bin {-# UNPACK #-} !Size !k a !(Map k a) !(Map k a) + | Tip + +type Size = Int + +#if __GLASGOW_HASKELL__ >= 708 +type role Map nominal representational +#endif + +instance (Ord k) => Monoid (Map k v) where + mempty = empty + mconcat = unions +#if !(MIN_VERSION_base(4,9,0)) + mappend = union +#else + mappend = (<>) + +instance (Ord k) => Semigroup (Map k v) where + (<>) = union + stimes = stimesIdempotentMonoid +#endif + +#if __GLASGOW_HASKELL__ + +{-------------------------------------------------------------------- + A Data instance +--------------------------------------------------------------------} + +-- This instance preserves data abstraction at the cost of inefficiency. +-- We provide limited reflection services for the sake of data abstraction. + +instance (Data k, Data a, Ord k) => Data (Map k a) where + gfoldl f z m = z fromList `f` toList m + toConstr _ = fromListConstr + gunfold k z c = case constrIndex c of + 1 -> k (z fromList) + _ -> error "gunfold" + dataTypeOf _ = mapDataType + dataCast2 f = gcast2 f + +fromListConstr :: Constr +fromListConstr = mkConstr mapDataType "fromList" [] Prefix + +mapDataType :: DataType +mapDataType = mkDataType "Data.Map.Internal.Map" [fromListConstr] + +#endif + +{-------------------------------------------------------------------- + Query +--------------------------------------------------------------------} +-- | /O(1)/. Is the map empty? +-- +-- > Data.Map.null (empty) == True +-- > Data.Map.null (singleton 1 'a') == False + +null :: Map k a -> Bool +null Tip = True +null (Bin {}) = False +{-# INLINE null #-} + +-- | /O(1)/. The number of elements in the map. +-- +-- > size empty == 0 +-- > size (singleton 1 'a') == 1 +-- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3 + +size :: Map k a -> Int +size Tip = 0 +size (Bin sz _ _ _ _) = sz +{-# INLINE size #-} + + +-- | /O(log n)/. Lookup the value at a key in the map. +-- +-- The function will return the corresponding value as @('Just' value)@, +-- or 'Nothing' if the key isn't in the map. +-- +-- An example of using @lookup@: +-- +-- > import Prelude hiding (lookup) +-- > import Data.Map +-- > +-- > employeeDept = fromList([("John","Sales"), ("Bob","IT")]) +-- > deptCountry = fromList([("IT","USA"), ("Sales","France")]) +-- > countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")]) +-- > +-- > employeeCurrency :: String -> Maybe String +-- > employeeCurrency name = do +-- > dept <- lookup name employeeDept +-- > country <- lookup dept deptCountry +-- > lookup country countryCurrency +-- > +-- > main = do +-- > putStrLn $ "John's currency: " ++ (show (employeeCurrency "John")) +-- > putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete")) +-- +-- The output of this program: +-- +-- > John's currency: Just "Euro" +-- > Pete's currency: Nothing +lookup :: Ord k => k -> Map k a -> Maybe a +lookup = go + where + go !_ Tip = Nothing + go k (Bin _ kx x l r) = case compare k kx of + LT -> go k l + GT -> go k r + EQ -> Just x +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookup #-} +#else +{-# INLINE lookup #-} +#endif + +-- | /O(log n)/. Is the key a member of the map? See also 'notMember'. +-- +-- > member 5 (fromList [(5,'a'), (3,'b')]) == True +-- > member 1 (fromList [(5,'a'), (3,'b')]) == False +member :: Ord k => k -> Map k a -> Bool +member = go + where + go !_ Tip = False + go k (Bin _ kx _ l r) = case compare k kx of + LT -> go k l + GT -> go k r + EQ -> True +#if __GLASGOW_HASKELL__ +{-# INLINABLE member #-} +#else +{-# INLINE member #-} +#endif + +-- | /O(log n)/. Is the key not a member of the map? See also 'member'. +-- +-- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False +-- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True + +notMember :: Ord k => k -> Map k a -> Bool +notMember k m = not $ member k m +#if __GLASGOW_HASKELL__ +{-# INLINABLE notMember #-} +#else +{-# INLINE notMember #-} +#endif + +-- | /O(log n)/. Find the value at a key. +-- Calls 'error' when the element can not be found. +find :: Ord k => k -> Map k a -> a +find = go + where + go !_ Tip = error "Map.!: given key is not an element in the map" + go k (Bin _ kx x l r) = case compare k kx of + LT -> go k l + GT -> go k r + EQ -> x +#if __GLASGOW_HASKELL__ +{-# INLINABLE find #-} +#else +{-# INLINE find #-} +#endif + +-- | /O(log n)/. The expression @('findWithDefault' def k map)@ returns +-- the value at key @k@ or returns default value @def@ +-- when the key is not in the map. +-- +-- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' +-- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' +findWithDefault :: Ord k => a -> k -> Map k a -> a +findWithDefault = go + where + go def !_ Tip = def + go def k (Bin _ kx x l r) = case compare k kx of + LT -> go def k l + GT -> go def k r + EQ -> x +#if __GLASGOW_HASKELL__ +{-# INLINABLE findWithDefault #-} +#else +{-# INLINE findWithDefault #-} +#endif + +-- | /O(log n)/. Find largest key smaller than the given one and return the +-- corresponding (key, value) pair. +-- +-- > lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing +-- > lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') +lookupLT :: Ord k => k -> Map k v -> Maybe (k, v) +lookupLT = goNothing + where + goNothing !_ Tip = Nothing + goNothing k (Bin _ kx x l r) | k <= kx = goNothing k l + | otherwise = goJust k kx x r + + goJust !_ kx' x' Tip = Just (kx', x') + goJust k kx' x' (Bin _ kx x l r) | k <= kx = goJust k kx' x' l + | otherwise = goJust k kx x r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupLT #-} +#else +{-# INLINE lookupLT #-} +#endif + +-- | /O(log n)/. Find smallest key greater than the given one and return the +-- corresponding (key, value) pair. +-- +-- > lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') +-- > lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing +lookupGT :: Ord k => k -> Map k v -> Maybe (k, v) +lookupGT = goNothing + where + goNothing !_ Tip = Nothing + goNothing k (Bin _ kx x l r) | k < kx = goJust k kx x l + | otherwise = goNothing k r + + goJust !_ kx' x' Tip = Just (kx', x') + goJust k kx' x' (Bin _ kx x l r) | k < kx = goJust k kx x l + | otherwise = goJust k kx' x' r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupGT #-} +#else +{-# INLINE lookupGT #-} +#endif + +-- | /O(log n)/. Find largest key smaller or equal to the given one and return +-- the corresponding (key, value) pair. +-- +-- > lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing +-- > lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') +-- > lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') +lookupLE :: Ord k => k -> Map k v -> Maybe (k, v) +lookupLE = goNothing + where + goNothing !_ Tip = Nothing + goNothing k (Bin _ kx x l r) = case compare k kx of LT -> goNothing k l + EQ -> Just (kx, x) + GT -> goJust k kx x r + + goJust !_ kx' x' Tip = Just (kx', x') + goJust k kx' x' (Bin _ kx x l r) = case compare k kx of LT -> goJust k kx' x' l + EQ -> Just (kx, x) + GT -> goJust k kx x r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupLE #-} +#else +{-# INLINE lookupLE #-} +#endif + +-- | /O(log n)/. Find smallest key greater or equal to the given one and return +-- the corresponding (key, value) pair. +-- +-- > lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a') +-- > lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b') +-- > lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing +lookupGE :: Ord k => k -> Map k v -> Maybe (k, v) +lookupGE = goNothing + where + goNothing !_ Tip = Nothing + goNothing k (Bin _ kx x l r) = case compare k kx of LT -> goJust k kx x l + EQ -> Just (kx, x) + GT -> goNothing k r + + goJust !_ kx' x' Tip = Just (kx', x') + goJust k kx' x' (Bin _ kx x l r) = case compare k kx of LT -> goJust k kx x l + EQ -> Just (kx, x) + GT -> goJust k kx' x' r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupGE #-} +#else +{-# INLINE lookupGE #-} +#endif + +{-------------------------------------------------------------------- + Construction +--------------------------------------------------------------------} +-- | /O(1)/. The empty map. +-- +-- > empty == fromList [] +-- > size empty == 0 + +empty :: Map k a +empty = Tip +{-# INLINE empty #-} + +-- | /O(1)/. A map with a single element. +-- +-- > singleton 1 'a' == fromList [(1, 'a')] +-- > size (singleton 1 'a') == 1 + +singleton :: k -> a -> Map k a +singleton k x = Bin 1 k x Tip Tip +{-# INLINE singleton #-} + +{-------------------------------------------------------------------- + Insertion +--------------------------------------------------------------------} +-- | /O(log n)/. Insert a new key and value in the map. +-- If the key is already present in the map, the associated value is +-- replaced with the supplied value. 'insert' is equivalent to +-- @'insertWith' 'const'@. +-- +-- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')] +-- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] +-- > insert 5 'x' empty == singleton 5 'x' + +-- See Note: Type of local 'go' function +insert :: Ord k => k -> a -> Map k a -> Map k a +insert = go + where + -- Unlike insertR, we only get sharing here + -- when the inserted value is at the same address + -- as the present value. We try anyway. If we decide + -- not to, then Data.Map.Strict should probably + -- get its own union implementation. + go :: Ord k => k -> a -> Map k a -> Map k a + go !kx x Tip = singleton kx x + go !kx x t@(Bin sz ky y l r) = + case compare kx ky of + LT | l' `ptrEq` l -> t + | otherwise -> balanceL ky y l' r + where !l' = go kx x l + GT | r' `ptrEq` r -> t + | otherwise -> balanceR ky y l r' + where !r' = go kx x r + EQ | kx `ptrEq` ky && x `ptrEq` y -> t + | otherwise -> Bin sz kx x l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE insert #-} +#else +{-# INLINE insert #-} +#endif + +-- Insert a new key and value in the map if it is not already present. +-- Used by `union`. + +-- See Note: Type of local 'go' function +insertR :: Ord k => k -> a -> Map k a -> Map k a +insertR = go + where + go :: Ord k => k -> a -> Map k a -> Map k a + go !kx x Tip = singleton kx x + go kx x t@(Bin _ ky y l r) = + case compare kx ky of + LT | l' `ptrEq` l -> t + | otherwise -> balanceL ky y l' r + where !l' = go kx x l + GT | r' `ptrEq` r -> t + | otherwise -> balanceR ky y l r' + where !r' = go kx x r + EQ -> t +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertR #-} +#else +{-# INLINE insertR #-} +#endif + +-- | /O(log n)/. Insert with a function, combining new value and old value. +-- @'insertWith' f key value mp@ +-- will insert the pair (key, value) into @mp@ if key does +-- not exist in the map. If the key does exist, the function will +-- insert the pair @(key, f new_value old_value)@. +-- +-- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")] +-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] +-- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx" + +insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a +insertWith = go + where + -- We have no hope of making pointer equality tricks work + -- here, because lazy insertWith *always* changes the tree, + -- either adding a new entry or replacing an element with a + -- thunk. + go :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a + go _ !kx x Tip = singleton kx x + go f !kx x (Bin sy ky y l r) = + case compare kx ky of + LT -> balanceL ky y (go f kx x l) r + GT -> balanceR ky y l (go f kx x r) + EQ -> Bin sy kx (f x y) l r + +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertWith #-} +#else +{-# INLINE insertWith #-} +#endif + +-- | A helper function for 'unionWith'. When the key is already in +-- the map, the key is left alone, not replaced. The combining +-- function is flipped--it is applied to the old value and then the +-- new value. + +insertWithR :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a +insertWithR = go + where + go :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a + go _ !kx x Tip = singleton kx x + go f !kx x (Bin sy ky y l r) = + case compare kx ky of + LT -> balanceL ky y (go f kx x l) r + GT -> balanceR ky y l (go f kx x r) + EQ -> Bin sy ky (f y x) l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertWithR #-} +#else +{-# INLINE insertWithR #-} +#endif + +-- | /O(log n)/. Insert with a function, combining key, new value and old value. +-- @'insertWithKey' f key value mp@ +-- will insert the pair (key, value) into @mp@ if key does +-- not exist in the map. If the key does exist, the function will +-- insert the pair @(key,f key new_value old_value)@. +-- Note that the key passed to f is the same key passed to 'insertWithKey'. +-- +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value +-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")] +-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] +-- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx" + +-- See Note: Type of local 'go' function +insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a +insertWithKey = go + where + go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a + go _ !kx x Tip = singleton kx x + go f kx x (Bin sy ky y l r) = + case compare kx ky of + LT -> balanceL ky y (go f kx x l) r + GT -> balanceR ky y l (go f kx x r) + EQ -> Bin sy kx (f kx x y) l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertWithKey #-} +#else +{-# INLINE insertWithKey #-} +#endif + +-- | A helper function for 'unionWithKey'. When the key is already in +-- the map, the key is left alone, not replaced. The combining +-- function is flipped--it is applied to the old value and then the +-- new value. +insertWithKeyR :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a +insertWithKeyR = go + where + go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a + go _ !kx x Tip = singleton kx x + go f kx x (Bin sy ky y l r) = + case compare kx ky of + LT -> balanceL ky y (go f kx x l) r + GT -> balanceR ky y l (go f kx x r) + EQ -> Bin sy ky (f ky y x) l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertWithKeyR #-} +#else +{-# INLINE insertWithKeyR #-} +#endif + +-- | /O(log n)/. Combines insert operation with old value retrieval. +-- The expression (@'insertLookupWithKey' f k x map@) +-- is a pair where the first element is equal to (@'lookup' k map@) +-- and the second element equal to (@'insertWithKey' f k x map@). +-- +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value +-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")]) +-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")]) +-- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx") +-- +-- This is how to define @insertLookup@ using @insertLookupWithKey@: +-- +-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t +-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) +-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) + +-- See Note: Type of local 'go' function +insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a + -> (Maybe a, Map k a) +insertLookupWithKey f0 k0 x0 = toPair . go f0 k0 x0 + where + go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a) + go _ !kx x Tip = (Nothing :*: singleton kx x) + go f kx x (Bin sy ky y l r) = + case compare kx ky of + LT -> let !(found :*: l') = go f kx x l + !t' = balanceL ky y l' r + in (found :*: t') + GT -> let !(found :*: r') = go f kx x r + !t' = balanceR ky y l r' + in (found :*: t') + EQ -> (Just y :*: Bin sy kx (f kx x y) l r) +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertLookupWithKey #-} +#else +{-# INLINE insertLookupWithKey #-} +#endif + +{-------------------------------------------------------------------- + Deletion +--------------------------------------------------------------------} +-- | /O(log n)/. Delete a key and its value from the map. When the key is not +-- a member of the map, the original map is returned. +-- +-- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > delete 5 empty == empty + +-- See Note: Type of local 'go' function +delete :: Ord k => k -> Map k a -> Map k a +delete = go + where + go :: Ord k => k -> Map k a -> Map k a + go !_ Tip = Tip + go k t@(Bin _ kx x l r) = + case compare k kx of + LT | l' `ptrEq` l -> t + | otherwise -> balanceR kx x l' r + where !l' = go k l + GT | r' `ptrEq` r -> t + | otherwise -> balanceL kx x l r' + where !r' = go k r + EQ -> glue l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE delete #-} +#else +{-# INLINE delete #-} +#endif + +-- | /O(log n)/. Update a value at a specific key with the result of the provided function. +-- When the key is not +-- a member of the map, the original map is returned. +-- +-- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] +-- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > adjust ("new " ++) 7 empty == empty + +adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a +adjust f = adjustWithKey (\_ x -> f x) +#if __GLASGOW_HASKELL__ +{-# INLINABLE adjust #-} +#else +{-# INLINE adjust #-} +#endif + +-- | /O(log n)/. Adjust a value at a specific key. When the key is not +-- a member of the map, the original map is returned. +-- +-- > let f key x = (show key) ++ ":new " ++ x +-- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] +-- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > adjustWithKey f 7 empty == empty + +adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a +adjustWithKey = go + where + go :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a + go _ !_ Tip = Tip + go f k (Bin sx kx x l r) = + case compare k kx of + LT -> Bin sx kx x (go f k l) r + GT -> Bin sx kx x l (go f k r) + EQ -> Bin sx kx (f kx x) l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE adjustWithKey #-} +#else +{-# INLINE adjustWithKey #-} +#endif + +-- | /O(log n)/. The expression (@'update' f k map@) updates the value @x@ +-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@. +-- +-- > let f x = if x == "a" then Just "new a" else Nothing +-- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")] +-- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a +update f = updateWithKey (\_ x -> f x) +#if __GLASGOW_HASKELL__ +{-# INLINABLE update #-} +#else +{-# INLINE update #-} +#endif + +-- | /O(log n)/. The expression (@'updateWithKey' f k map@) updates the +-- value @x@ at @k@ (if it is in the map). If (@f k x@) is 'Nothing', +-- the element is deleted. If it is (@'Just' y@), the key @k@ is bound +-- to the new value @y@. +-- +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing +-- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")] +-- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +-- See Note: Type of local 'go' function +updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a +updateWithKey = go + where + go :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a + go _ !_ Tip = Tip + go f k(Bin sx kx x l r) = + case compare k kx of + LT -> balanceR kx x (go f k l) r + GT -> balanceL kx x l (go f k r) + EQ -> case f kx x of + Just x' -> Bin sx kx x' l r + Nothing -> glue l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE updateWithKey #-} +#else +{-# INLINE updateWithKey #-} +#endif + +-- | /O(log n)/. Lookup and update. See also 'updateWithKey'. +-- The function returns changed value, if it is updated. +-- Returns the original key value if the map entry is deleted. +-- +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing +-- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "5:new a", fromList [(3, "b"), (5, "5:new a")]) +-- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) +-- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a") + +-- See Note: Type of local 'go' function +updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a,Map k a) +updateLookupWithKey f0 k0 = toPair . go f0 k0 + where + go :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> StrictPair (Maybe a) (Map k a) + go _ !_ Tip = (Nothing :*: Tip) + go f k (Bin sx kx x l r) = + case compare k kx of + LT -> let !(found :*: l') = go f k l + !t' = balanceR kx x l' r + in (found :*: t') + GT -> let !(found :*: r') = go f k r + !t' = balanceL kx x l r' + in (found :*: t') + EQ -> case f kx x of + Just x' -> (Just x' :*: Bin sx kx x' l r) + Nothing -> let !glued = glue l r + in (Just x :*: glued) +#if __GLASGOW_HASKELL__ +{-# INLINABLE updateLookupWithKey #-} +#else +{-# INLINE updateLookupWithKey #-} +#endif + +-- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof. +-- 'alter' can be used to insert, delete, or update a value in a 'Map'. +-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@. +-- +-- > let f _ = Nothing +-- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] +-- > alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > +-- > let f _ = Just "c" +-- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")] +-- > alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")] + +-- See Note: Type of local 'go' function +alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a +alter = go + where + go :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a + go f !k Tip = case f Nothing of + Nothing -> Tip + Just x -> singleton k x + + go f k (Bin sx kx x l r) = case compare k kx of + LT -> balance kx x (go f k l) r + GT -> balance kx x l (go f k r) + EQ -> case f (Just x) of + Just x' -> Bin sx kx x' l r + Nothing -> glue l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE alter #-} +#else +{-# INLINE alter #-} +#endif + +-- Used to choose the appropriate alterF implementation. +data AreWeStrict = Strict | Lazy + +-- | /O(log n)/. The expression (@'alterF' f k map@) alters the value @x@ at +-- @k@, or absence thereof. 'alterF' can be used to inspect, insert, delete, +-- or update a value in a 'Map'. In short: @'lookup' k \<$\> 'alterF' f k m = f +-- ('lookup' k m)@. +-- +-- Example: +-- +-- @ +-- interactiveAlter :: Int -> Map Int String -> IO (Map Int String) +-- interactiveAlter k m = alterF f k m where +-- f Nothing -> do +-- putStrLn $ show k ++ +-- " was not found in the map. Would you like to add it?" +-- getUserResponse1 :: IO (Maybe String) +-- f (Just old) -> do +-- putStrLn "The key is currently bound to " ++ show old ++ +-- ". Would you like to change or delete it?" +-- getUserresponse2 :: IO (Maybe String) +-- @ +-- +-- 'alterF' is the most general operation for working with an individual +-- key that may or may not be in a given map. When used with trivial +-- functors like 'Identity' and 'Const', it is often slightly slower than +-- more specialized combinators like 'lookup' and 'insert'. However, when +-- the functor is non-trivial and key comparison is not particularly cheap, +-- it is the fastest way. +-- +-- Note on rewrite rules: +-- +-- This module includes GHC rewrite rules to optimize 'alterF' for +-- the 'Const' and 'Identity' functors. In general, these rules +-- improve performance. The sole exception is that when using +-- 'Identity', deleting a key that is already absent takes longer +-- than it would without the rules. If you expect this to occur +-- a very large fraction of the time, you might consider using a +-- private copy of the 'Identity' type. +-- +-- Note: 'alterF' is a flipped version of the 'at' combinator from +-- 'Control.Lens.At'. +-- +-- @since 0.5.8 +alterF :: (Functor f, Ord k) + => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) +alterF f k m = atKeyImpl Lazy k f m + +#ifndef __GLASGOW_HASKELL__ +{-# INLINE alterF #-} +#else +{-# INLINABLE [2] alterF #-} + +-- We can save a little time by recognizing the special case of +-- `Control.Applicative.Const` and just doing a lookup. +{-# RULES +"alterF/Const" forall k (f :: Maybe a -> Const b (Maybe a)) . alterF f k = \m -> Const . getConst . f $ lookup k m + #-} + +#if MIN_VERSION_base(4,8,0) +-- base 4.8 and above include Data.Functor.Identity, so we can +-- save a pretty decent amount of time by handling it specially. +{-# RULES +"alterF/Identity" forall k f . alterF f k = atKeyIdentity k f + #-} +#endif +#endif + +atKeyImpl :: (Functor f, Ord k) => + AreWeStrict -> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a) +#ifdef DEFINE_ALTERF_FALLBACK +atKeyImpl strict !k f m +-- It doesn't seem sensible to worry about overflowing the queue +-- if the word size is 61 or more. If I calculate it correctly, +-- that would take a map with nearly a quadrillion entries. + | wordSize < 61 && size m >= alterFCutoff = alterFFallback strict k f m +#endif +atKeyImpl strict !k f m = case lookupTrace k m of + TraceResult mv q -> (<$> f mv) $ \ fres -> + case fres of + Nothing -> case mv of + Nothing -> m + Just old -> deleteAlong old q m + Just new -> case strict of + Strict -> new `seq` case mv of + Nothing -> insertAlong q k new m + Just _ -> replaceAlong q new m + Lazy -> case mv of + Nothing -> insertAlong q k new m + Just _ -> replaceAlong q new m + +{-# INLINE atKeyImpl #-} + +#ifdef DEFINE_ALTERF_FALLBACK +alterFCutoff :: Int +#if WORD_SIZE_IN_BITS == 32 +alterFCutoff = 55744454 +#else +alterFCutoff = case wordSize of + 30 -> 17637893 + 31 -> 31356255 + 32 -> 55744454 + x -> (4^(x*2-2)) `quot` (3^(x*2-2)) -- Unlikely +#endif +#endif + +data TraceResult a = TraceResult (Maybe a) {-# UNPACK #-} !BitQueue + +-- Look up a key and return a result indicating whether it was found +-- and what path was taken. +lookupTrace :: Ord k => k -> Map k a -> TraceResult a +lookupTrace = go emptyQB + where + go :: Ord k => BitQueueB -> k -> Map k a -> TraceResult a + go !q !_ Tip = TraceResult Nothing (buildQ q) + go q k (Bin _ kx x l r) = case compare k kx of + LT -> (go $! q `snocQB` False) k l + GT -> (go $! q `snocQB` True) k r + EQ -> TraceResult (Just x) (buildQ q) + +-- GHC 7.8 doesn't manage to unbox the queue properly +-- unless we explicitly inline this function. This stuff +-- is a bit touchy, unfortunately. +#if __GLASGOW_HASKELL__ >= 710 +{-# INLINABLE lookupTrace #-} +#else +{-# INLINE lookupTrace #-} +#endif + +-- Insert at a location (which will always be a leaf) +-- described by the path passed in. +insertAlong :: BitQueue -> k -> a -> Map k a -> Map k a +insertAlong !_ kx x Tip = singleton kx x +insertAlong q kx x (Bin sz ky y l r) = + case unconsQ q of + Just (False, tl) -> balanceL ky y (insertAlong tl kx x l) r + Just (True,tl) -> balanceR ky y l (insertAlong tl kx x r) + Nothing -> Bin sz kx x l r -- Shouldn't happen + +-- Delete from a location (which will always be a node) +-- described by the path passed in. +-- +-- This is fairly horrifying! We don't actually have any +-- use for the old value we're deleting. But if GHC sees +-- that, then it will allocate a thunk representing the +-- Map with the key deleted before we have any reason to +-- believe we'll actually want that. This transformation +-- enhances sharing, but we don't care enough about that. +-- So deleteAlong needs to take the old value, and we need +-- to convince GHC somehow that it actually uses it. We +-- can't NOINLINE deleteAlong, because that would prevent +-- the BitQueue from being unboxed. So instead we pass the +-- old value to a NOINLINE constant function and then +-- convince GHC that we use the result throughout the +-- computation. Doing the obvious thing and just passing +-- the value itself through the recursion costs 3-4% time, +-- so instead we convert the value to a magical zero-width +-- proxy that's ultimately erased. +deleteAlong :: any -> BitQueue -> Map k a -> Map k a +deleteAlong old !q0 !m = go (bogus old) q0 m where +#ifdef USE_MAGIC_PROXY + go :: Proxy# () -> BitQueue -> Map k a -> Map k a +#else + go :: any -> BitQueue -> Map k a -> Map k a +#endif + go !_ !_ Tip = Tip + go foom q (Bin _ ky y l r) = + case unconsQ q of + Just (False, tl) -> balanceR ky y (go foom tl l) r + Just (True, tl) -> balanceL ky y l (go foom tl r) + Nothing -> glue l r + +#ifdef USE_MAGIC_PROXY +{-# NOINLINE bogus #-} +bogus :: a -> Proxy# () +bogus _ = proxy# +#else +-- No point hiding in this case. +{-# INLINE bogus #-} +bogus :: a -> a +bogus a = a +#endif + +-- Replace the value found in the node described +-- by the given path with a new one. +replaceAlong :: BitQueue -> a -> Map k a -> Map k a +replaceAlong !_ _ Tip = Tip -- Should not happen +replaceAlong q x (Bin sz ky y l r) = + case unconsQ q of + Just (False, tl) -> Bin sz ky y (replaceAlong tl x l) r + Just (True,tl) -> Bin sz ky y l (replaceAlong tl x r) + Nothing -> Bin sz ky x l r + +#if __GLASGOW_HASKELL__ && MIN_VERSION_base(4,8,0) +atKeyIdentity :: Ord k => k -> (Maybe a -> Identity (Maybe a)) -> Map k a -> Identity (Map k a) +atKeyIdentity k f t = Identity $ atKeyPlain Lazy k (coerce f) t +{-# INLINABLE atKeyIdentity #-} + +atKeyPlain :: Ord k => AreWeStrict -> k -> (Maybe a -> Maybe a) -> Map k a -> Map k a +atKeyPlain strict k0 f0 t = case go k0 f0 t of + AltSmaller t' -> t' + AltBigger t' -> t' + AltAdj t' -> t' + AltSame -> t + where + go :: Ord k => k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a + go !k f Tip = case f Nothing of + Nothing -> AltSame + Just x -> case strict of + Lazy -> AltBigger $ singleton k x + Strict -> x `seq` (AltBigger $ singleton k x) + + go k f (Bin sx kx x l r) = case compare k kx of + LT -> case go k f l of + AltSmaller l' -> AltSmaller $ balanceR kx x l' r + AltBigger l' -> AltBigger $ balanceL kx x l' r + AltAdj l' -> AltAdj $ Bin sx kx x l' r + AltSame -> AltSame + GT -> case go k f r of + AltSmaller r' -> AltSmaller $ balanceL kx x l r' + AltBigger r' -> AltBigger $ balanceR kx x l r' + AltAdj r' -> AltAdj $ Bin sx kx x l r' + AltSame -> AltSame + EQ -> case f (Just x) of + Just x' -> case strict of + Lazy -> AltAdj $ Bin sx kx x' l r + Strict -> x' `seq` (AltAdj $ Bin sx kx x' l r) + Nothing -> AltSmaller $ glue l r +{-# INLINE atKeyPlain #-} + +data Altered k a = AltSmaller !(Map k a) | AltBigger !(Map k a) | AltAdj !(Map k a) | AltSame +#endif + +#ifdef DEFINE_ALTERF_FALLBACK +-- When the map is too large to use a bit queue, we fall back to +-- this much slower version which uses a more "natural" implementation +-- improved with Yoneda to avoid repeated fmaps. This works okayish for +-- some operations, but it's pretty lousy for lookups. +alterFFallback :: (Functor f, Ord k) + => AreWeStrict -> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a) +alterFFallback Lazy k f t = alterFYoneda k (\m q -> q <$> f m) t id +alterFFallback Strict k f t = alterFYoneda k (\m q -> q . forceMaybe <$> f m) t id + where + forceMaybe Nothing = Nothing + forceMaybe may@(Just !_) = may +{-# NOINLINE alterFFallback #-} + +alterFYoneda :: Ord k => + k -> (Maybe a -> (Maybe a -> b) -> f b) -> Map k a -> (Map k a -> b) -> f b +alterFYoneda = go + where + go :: Ord k => + k -> (Maybe a -> (Maybe a -> b) -> f b) -> Map k a -> (Map k a -> b) -> f b + go !k f Tip g = f Nothing $ \ mx -> case mx of + Nothing -> g Tip + Just x -> g (singleton k x) + go k f (Bin sx kx x l r) g = case compare k kx of + LT -> go k f l (\m -> g (balance kx x m r)) + GT -> go k f r (\m -> g (balance kx x l m)) + EQ -> f (Just x) $ \ mx' -> case mx' of + Just x' -> g (Bin sx kx x' l r) + Nothing -> g (glue l r) +{-# INLINE alterFYoneda #-} +#endif + +{-------------------------------------------------------------------- + Indexing +--------------------------------------------------------------------} +-- | /O(log n)/. Return the /index/ of a key, which is its zero-based index in +-- the sequence sorted by keys. The index is a number from /0/ up to, but not +-- including, the 'size' of the map. Calls 'error' when the key is not +-- a 'member' of the map. +-- +-- > findIndex 2 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map +-- > findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0 +-- > findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1 +-- > findIndex 6 (fromList [(5,"a"), (3,"b")]) Error: element is not in the map + +-- See Note: Type of local 'go' function +findIndex :: Ord k => k -> Map k a -> Int +findIndex = go 0 + where + go :: Ord k => Int -> k -> Map k a -> Int + go !_ !_ Tip = error "Map.findIndex: element is not in the map" + go idx k (Bin _ kx _ l r) = case compare k kx of + LT -> go idx k l + GT -> go (idx + size l + 1) k r + EQ -> idx + size l +#if __GLASGOW_HASKELL__ +{-# INLINABLE findIndex #-} +#endif + +-- | /O(log n)/. Lookup the /index/ of a key, which is its zero-based index in +-- the sequence sorted by keys. The index is a number from /0/ up to, but not +-- including, the 'size' of the map. +-- +-- > isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")])) == False +-- > fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0 +-- > fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1 +-- > isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")])) == False + +-- See Note: Type of local 'go' function +lookupIndex :: Ord k => k -> Map k a -> Maybe Int +lookupIndex = go 0 + where + go :: Ord k => Int -> k -> Map k a -> Maybe Int + go !_ !_ Tip = Nothing + go idx k (Bin _ kx _ l r) = case compare k kx of + LT -> go idx k l + GT -> go (idx + size l + 1) k r + EQ -> Just $! idx + size l +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupIndex #-} +#endif + +-- | /O(log n)/. Retrieve an element by its /index/, i.e. by its zero-based +-- index in the sequence sorted by keys. If the /index/ is out of range (less +-- than zero, greater or equal to 'size' of the map), 'error' is called. +-- +-- > elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b") +-- > elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a") +-- > elemAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range + +elemAt :: Int -> Map k a -> (k,a) +elemAt !_ Tip = error "Map.elemAt: index out of range" +elemAt i (Bin _ kx x l r) + = case compare i sizeL of + LT -> elemAt i l + GT -> elemAt (i-sizeL-1) r + EQ -> (kx,x) + where + sizeL = size l + +-- | Take a given number of entries in key order, beginning +-- with the smallest keys. +-- +-- @ +-- take n = 'fromDistinctAscList' . 'Prelude.take' n . 'toAscList' +-- @ + +take :: Int -> Map k a -> Map k a +take i m | i >= size m = m +take i0 m0 = go i0 m0 + where + go i !_ | i <= 0 = Tip + go !_ Tip = Tip + go i (Bin _ kx x l r) = + case compare i sizeL of + LT -> go i l + GT -> link kx x l (go (i - sizeL - 1) r) + EQ -> l + where sizeL = size l + +-- | Drop a given number of entries in key order, beginning +-- with the smallest keys. +-- +-- @ +-- drop n = 'fromDistinctAscList' . 'Prelude.drop' n . 'toAscList' +-- @ +drop :: Int -> Map k a -> Map k a +drop i m | i >= size m = Tip +drop i0 m0 = go i0 m0 + where + go i m | i <= 0 = m + go !_ Tip = Tip + go i (Bin _ kx x l r) = + case compare i sizeL of + LT -> link kx x (go i l) r + GT -> go (i - sizeL - 1) r + EQ -> insertMin kx x r + where sizeL = size l + +-- | /O(log n)/. Split a map at a particular index. +-- +-- @ +-- splitAt !n !xs = ('take' n xs, 'drop' n xs) +-- @ +splitAt :: Int -> Map k a -> (Map k a, Map k a) +splitAt i0 m0 + | i0 >= size m0 = (m0, Tip) + | otherwise = toPair $ go i0 m0 + where + go i m | i <= 0 = Tip :*: m + go !_ Tip = Tip :*: Tip + go i (Bin _ kx x l r) + = case compare i sizeL of + LT -> case go i l of + ll :*: lr -> ll :*: link kx x lr r + GT -> case go (i - sizeL - 1) r of + rl :*: rr -> link kx x l rl :*: rr + EQ -> l :*: insertMin kx x r + where sizeL = size l + +-- | /O(log n)/. Update the element at /index/, i.e. by its zero-based index in +-- the sequence sorted by keys. If the /index/ is out of range (less than zero, +-- greater or equal to 'size' of the map), 'error' is called. +-- +-- > updateAt (\ _ _ -> Just "x") 0 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")] +-- > updateAt (\ _ _ -> Just "x") 1 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")] +-- > updateAt (\ _ _ -> Just "x") 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range +-- > updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range +-- > updateAt (\_ _ -> Nothing) 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" +-- > updateAt (\_ _ -> Nothing) 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > updateAt (\_ _ -> Nothing) 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range +-- > updateAt (\_ _ -> Nothing) (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range + +updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a +updateAt f !i t = + case t of + Tip -> error "Map.updateAt: index out of range" + Bin sx kx x l r -> case compare i sizeL of + LT -> balanceR kx x (updateAt f i l) r + GT -> balanceL kx x l (updateAt f (i-sizeL-1) r) + EQ -> case f kx x of + Just x' -> Bin sx kx x' l r + Nothing -> glue l r + where + sizeL = size l + +-- | /O(log n)/. Delete the element at /index/, i.e. by its zero-based index in +-- the sequence sorted by keys. If the /index/ is out of range (less than zero, +-- greater or equal to 'size' of the map), 'error' is called. +-- +-- > deleteAt 0 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" +-- > deleteAt 1 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > deleteAt 2 (fromList [(5,"a"), (3,"b")]) Error: index out of range +-- > deleteAt (-1) (fromList [(5,"a"), (3,"b")]) Error: index out of range + +deleteAt :: Int -> Map k a -> Map k a +deleteAt !i t = + case t of + Tip -> error "Map.deleteAt: index out of range" + Bin _ kx x l r -> case compare i sizeL of + LT -> balanceR kx x (deleteAt i l) r + GT -> balanceL kx x l (deleteAt (i-sizeL-1) r) + EQ -> glue l r + where + sizeL = size l + + +{-------------------------------------------------------------------- + Minimal, Maximal +--------------------------------------------------------------------} + +lookupMinSure :: k -> a -> Map k a -> (k, a) +lookupMinSure k a Tip = (k, a) +lookupMinSure _ _ (Bin _ k a l _) = lookupMinSure k a l + +-- | /O(log n)/. The minimal key of the map. Returns 'Nothing' if the map is empty. +-- +-- > lookupMin (fromList [(5,"a"), (3,"b")]) == Just (3,"b") +-- > findMin empty = Nothing +-- +-- @since 0.5.9 + +lookupMin :: Map k a -> Maybe (k,a) +lookupMin Tip = Nothing +lookupMin (Bin _ k x l _) = Just $! lookupMinSure k x l + +-- | /O(log n)/. The minimal key of the map. Calls 'error' if the map is empty. +-- +-- > findMin (fromList [(5,"a"), (3,"b")]) == (3,"b") +-- > findMin empty Error: empty map has no minimal element + +findMin :: Map k a -> (k,a) +findMin t + | Just r <- lookupMin t = r + | otherwise = error "Map.findMin: empty map has no minimal element" + +-- | /O(log n)/. The maximal key of the map. Calls 'error' if the map is empty. +-- +-- > findMax (fromList [(5,"a"), (3,"b")]) == (5,"a") +-- > findMax empty Error: empty map has no maximal element + +lookupMaxSure :: k -> a -> Map k a -> (k, a) +lookupMaxSure k a Tip = (k, a) +lookupMaxSure _ _ (Bin _ k a _ r) = lookupMaxSure k a r + +-- | /O(log n)/. The maximal key of the map. Returns 'Nothing' if the map is empty. +-- +-- > lookupMax (fromList [(5,"a"), (3,"b")]) == Just (5,"a") +-- > lookupMax empty = Nothing +-- +-- @since 0.5.9 + +lookupMax :: Map k a -> Maybe (k, a) +lookupMax Tip = Nothing +lookupMax (Bin _ k x _ r) = Just $! lookupMaxSure k x r + +findMax :: Map k a -> (k,a) +findMax t + | Just r <- lookupMax t = r + | otherwise = error "Map.findMax: empty map has no maximal element" + +-- | /O(log n)/. Delete the minimal key. Returns an empty map if the map is empty. +-- +-- > deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(5,"a"), (7,"c")] +-- > deleteMin empty == empty + +deleteMin :: Map k a -> Map k a +deleteMin (Bin _ _ _ Tip r) = r +deleteMin (Bin _ kx x l r) = balanceR kx x (deleteMin l) r +deleteMin Tip = Tip + +-- | /O(log n)/. Delete the maximal key. Returns an empty map if the map is empty. +-- +-- > deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(3,"b"), (5,"a")] +-- > deleteMax empty == empty + +deleteMax :: Map k a -> Map k a +deleteMax (Bin _ _ _ l Tip) = l +deleteMax (Bin _ kx x l r) = balanceL kx x l (deleteMax r) +deleteMax Tip = Tip + +-- | /O(log n)/. Update the value at the minimal key. +-- +-- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")] +-- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +updateMin :: (a -> Maybe a) -> Map k a -> Map k a +updateMin f m + = updateMinWithKey (\_ x -> f x) m + +-- | /O(log n)/. Update the value at the maximal key. +-- +-- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")] +-- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" + +updateMax :: (a -> Maybe a) -> Map k a -> Map k a +updateMax f m + = updateMaxWithKey (\_ x -> f x) m + + +-- | /O(log n)/. Update the value at the minimal key. +-- +-- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")] +-- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a +updateMinWithKey _ Tip = Tip +updateMinWithKey f (Bin sx kx x Tip r) = case f kx x of + Nothing -> r + Just x' -> Bin sx kx x' Tip r +updateMinWithKey f (Bin _ kx x l r) = balanceR kx x (updateMinWithKey f l) r + +-- | /O(log n)/. Update the value at the maximal key. +-- +-- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")] +-- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" + +updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a +updateMaxWithKey _ Tip = Tip +updateMaxWithKey f (Bin sx kx x l Tip) = case f kx x of + Nothing -> l + Just x' -> Bin sx kx x' l Tip +updateMaxWithKey f (Bin _ kx x l r) = balanceL kx x l (updateMaxWithKey f r) + +-- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and +-- the map stripped of that element, or 'Nothing' if passed an empty map. +-- +-- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a") +-- > minViewWithKey empty == Nothing + +minViewWithKey :: Map k a -> Maybe ((k,a), Map k a) +minViewWithKey Tip = Nothing +minViewWithKey (Bin _ k x l r) = + case minViewSure k x l r of + MinView km xm t -> Just ((km, xm), t) + +-- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and +-- the map stripped of that element, or 'Nothing' if passed an empty map. +-- +-- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b") +-- > maxViewWithKey empty == Nothing + +maxViewWithKey :: Map k a -> Maybe ((k,a), Map k a) +maxViewWithKey Tip = Nothing +maxViewWithKey (Bin _ k x l r) = + case maxViewSure k x l r of + MaxView km xm t -> Just ((km, xm), t) + +-- | /O(log n)/. Retrieves the value associated with minimal key of the +-- map, and the map stripped of that element, or 'Nothing' if passed an +-- empty map. +-- +-- > minView (fromList [(5,"a"), (3,"b")]) == Just ("b", singleton 5 "a") +-- > minView empty == Nothing + +minView :: Map k a -> Maybe (a, Map k a) +minView t = case minViewWithKey t of + Nothing -> Nothing + Just ((_, x), t') -> Just (x, t') + +-- | /O(log n)/. Retrieves the value associated with maximal key of the +-- map, and the map stripped of that element, or 'Nothing' if passed an +-- empty map. +-- +-- > maxView (fromList [(5,"a"), (3,"b")]) == Just ("a", singleton 3 "b") +-- > maxView empty == Nothing + +maxView :: Map k a -> Maybe (a, Map k a) +maxView t = case maxViewWithKey t of + Nothing -> Nothing + Just ((_, x), t') -> Just (x, t') + +{-------------------------------------------------------------------- + Union. +--------------------------------------------------------------------} +-- | The union of a list of maps: +-- (@'unions' == 'Prelude.foldl' 'union' 'empty'@). +-- +-- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] +-- > == fromList [(3, "b"), (5, "a"), (7, "C")] +-- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])] +-- > == fromList [(3, "B3"), (5, "A3"), (7, "C")] + +unions :: Ord k => [Map k a] -> Map k a +unions ts + = foldlStrict union empty ts +#if __GLASGOW_HASKELL__ +{-# INLINABLE unions #-} +#endif + +-- | The union of a list of maps, with a combining operation: +-- (@'unionsWith' f == 'Prelude.foldl' ('unionWith' f) 'empty'@). +-- +-- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])] +-- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")] + +unionsWith :: Ord k => (a->a->a) -> [Map k a] -> Map k a +unionsWith f ts + = foldlStrict (unionWith f) empty ts +#if __GLASGOW_HASKELL__ +{-# INLINABLE unionsWith #-} +#endif + +-- | /O(m*log(n\/m + 1)), m <= n/. +-- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@. +-- It prefers @t1@ when duplicate keys are encountered, +-- i.e. (@'union' == 'unionWith' 'const'@). +-- +-- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")] + +union :: Ord k => Map k a -> Map k a -> Map k a +union t1 Tip = t1 +union t1 (Bin _ k x Tip Tip) = insertR k x t1 +union (Bin _ k x Tip Tip) t2 = insert k x t2 +union Tip t2 = t2 +union t1@(Bin _ k1 x1 l1 r1) t2 = case split k1 t2 of + (l2, r2) | l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 -> t1 + | otherwise -> link k1 x1 l1l2 r1r2 + where !l1l2 = union l1 l2 + !r1r2 = union r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE union #-} +#endif + +{-------------------------------------------------------------------- + Union with a combining function +--------------------------------------------------------------------} +-- | /O(m*log(n\/m + 1)), m <= n/. Union with a combining function. +-- +-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")] + +unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a +-- QuickCheck says pointer equality never happens here. +unionWith _f t1 Tip = t1 +unionWith f t1 (Bin _ k x Tip Tip) = insertWithR f k x t1 +unionWith f (Bin _ k x Tip Tip) t2 = insertWith f k x t2 +unionWith _f Tip t2 = t2 +unionWith f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of + (l2, mb, r2) -> case mb of + Nothing -> link k1 x1 l1l2 r1r2 + Just x2 -> link k1 (f x1 x2) l1l2 r1r2 + where !l1l2 = unionWith f l1 l2 + !r1r2 = unionWith f r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE unionWith #-} +#endif + +-- | /O(m*log(n\/m + 1)), m <= n/. +-- Union with a combining function. +-- +-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value +-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")] + +unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a +unionWithKey _f t1 Tip = t1 +unionWithKey f t1 (Bin _ k x Tip Tip) = insertWithKeyR f k x t1 +unionWithKey f (Bin _ k x Tip Tip) t2 = insertWithKey f k x t2 +unionWithKey _f Tip t2 = t2 +unionWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of + (l2, mb, r2) -> case mb of + Nothing -> link k1 x1 l1l2 r1r2 + Just x2 -> link k1 (f k1 x1 x2) l1l2 r1r2 + where !l1l2 = unionWithKey f l1 l2 + !r1r2 = unionWithKey f r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE unionWithKey #-} +#endif + +{-------------------------------------------------------------------- + Difference +--------------------------------------------------------------------} + +-- | /O(m*log(n\/m + 1)), m <= n/. Difference of two maps. +-- Return elements of the first map not existing in the second map. +-- +-- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b" + +difference :: Ord k => Map k a -> Map k b -> Map k a +difference Tip _ = Tip +difference t1 Tip = t1 +difference t1 (Bin _ k _ l2 r2) = case split k t1 of + (l1, r1) + | size l1l2 + size r1r2 == size t1 -> t1 + | otherwise -> link2 l1l2 r1r2 + where + !l1l2 = difference l1 l2 + !r1r2 = difference r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE difference #-} +#endif + +-- | /O(m*log(n/m + 1)), m <= n/. Remove all keys in a 'Set' from a 'Map'. +-- +-- @ +-- m `withoutKeys` s = 'filterWithKey' (\k _ -> k `'Set.notMember'` s) m +-- @ +-- +-- @since 0.5.8 + +withoutKeys :: Ord k => Map k a -> Set k -> Map k a +withoutKeys Tip _ = Tip +withoutKeys m Set.Tip = m +withoutKeys m (Set.Bin _ k ls rs) = case splitMember k m of + (lm, b, rm) + | not b && lm' `ptrEq` lm && rm' `ptrEq` rm -> m + | otherwise -> link2 lm' rm' + where + !lm' = withoutKeys lm ls + !rm' = withoutKeys rm rs +#if __GLASGOW_HASKELL__ +{-# INLINABLE withoutKeys #-} +#endif + +-- | /O(n+m)/. Difference with a combining function. +-- When two equal keys are +-- encountered, the combining function is applied to the values of these keys. +-- If it returns 'Nothing', the element is discarded (proper set difference). If +-- it returns (@'Just' y@), the element is updated with a new value @y@. +-- +-- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing +-- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")]) +-- > == singleton 3 "b:B" +differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a +differenceWith f = merge preserveMissing dropMissing $ + zipWithMaybeMatched (\_ x y -> f x y) +#if __GLASGOW_HASKELL__ +{-# INLINABLE differenceWith #-} +#endif + +-- | /O(n+m)/. Difference with a combining function. When two equal keys are +-- encountered, the combining function is applied to the key and both values. +-- If it returns 'Nothing', the element is discarded (proper set difference). If +-- it returns (@'Just' y@), the element is updated with a new value @y@. +-- +-- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing +-- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")]) +-- > == singleton 3 "3:b|B" + +differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a +differenceWithKey f = + merge preserveMissing dropMissing (zipWithMaybeMatched f) +#if __GLASGOW_HASKELL__ +{-# INLINABLE differenceWithKey #-} +#endif + + +{-------------------------------------------------------------------- + Intersection +--------------------------------------------------------------------} +-- | /O(m*log(n\/m + 1)), m <= n/. Intersection of two maps. +-- Return data in the first map for the keys existing in both maps. +-- (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@). +-- +-- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a" + +intersection :: Ord k => Map k a -> Map k b -> Map k a +intersection Tip _ = Tip +intersection _ Tip = Tip +intersection t1@(Bin _ k x l1 r1) t2 + | mb = if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 + then t1 + else link k x l1l2 r1r2 + | otherwise = link2 l1l2 r1r2 + where + !(l2, mb, r2) = splitMember k t2 + !l1l2 = intersection l1 l2 + !r1r2 = intersection r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE intersection #-} +#endif + +-- | /O(m*log(n/m + 1)), m <= n/. Restrict a 'Map' to only those keys +-- found in a 'Set'. +-- +-- @ +-- m `restrictKeys` s = 'filterWithKey' (\k _ -> k `'Set.member'` s) m +-- @ +-- +-- @since 0.5.8 +restrictKeys :: Ord k => Map k a -> Set k -> Map k a +restrictKeys Tip _ = Tip +restrictKeys _ Set.Tip = Tip +restrictKeys m@(Bin _ k x l1 r1) s + | b = if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 + then m + else link k x l1l2 r1r2 + | otherwise = link2 l1l2 r1r2 + where + !(l2, b, r2) = Set.splitMember k s + !l1l2 = restrictKeys l1 l2 + !r1r2 = restrictKeys r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE restrictKeys #-} +#endif + +-- | /O(m*log(n\/m + 1)), m <= n/. Intersection with a combining function. +-- +-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA" + +intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c +-- We have no hope of pointer equality tricks here because every single +-- element in the result will be a thunk. +intersectionWith _f Tip _ = Tip +intersectionWith _f _ Tip = Tip +intersectionWith f (Bin _ k x1 l1 r1) t2 = case mb of + Just x2 -> link k (f x1 x2) l1l2 r1r2 + Nothing -> link2 l1l2 r1r2 + where + !(l2, mb, r2) = splitLookup k t2 + !l1l2 = intersectionWith f l1 l2 + !r1r2 = intersectionWith f r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE intersectionWith #-} +#endif + +-- | /O(m*log(n\/m + 1)), m <= n/. Intersection with a combining function. +-- +-- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar +-- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A" + +intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c +intersectionWithKey _f Tip _ = Tip +intersectionWithKey _f _ Tip = Tip +intersectionWithKey f (Bin _ k x1 l1 r1) t2 = case mb of + Just x2 -> link k (f k x1 x2) l1l2 r1r2 + Nothing -> link2 l1l2 r1r2 + where + !(l2, mb, r2) = splitLookup k t2 + !l1l2 = intersectionWithKey f l1 l2 + !r1r2 = intersectionWithKey f r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE intersectionWithKey #-} +#endif + +#if !MIN_VERSION_base (4,8,0) +-- | The identity type. +newtype Identity a = Identity { runIdentity :: a } +#if __GLASGOW_HASKELL__ == 708 +instance Functor Identity where + fmap = coerce +instance Applicative Identity where + (<*>) = coerce + pure = Identity +#else +instance Functor Identity where + fmap f (Identity a) = Identity (f a) +instance Applicative Identity where + Identity f <*> Identity x = Identity (f x) + pure = Identity +#endif +#endif + +-- | A tactic for dealing with keys present in one map but not the other in +-- 'merge' or 'mergeA'. +-- +-- A tactic of type @ WhenMissing f k x z @ is an abstract representation +-- of a function of type @ k -> x -> f (Maybe z) @. + +data WhenMissing f k x y = WhenMissing + { missingSubtree :: Map k x -> f (Map k y) + , missingKey :: k -> x -> f (Maybe y)} + +instance (Applicative f, Monad f) => Functor (WhenMissing f k x) where + fmap = mapWhenMissing + {-# INLINE fmap #-} + +instance (Applicative f, Monad f) + => Category.Category (WhenMissing f k) where + id = preserveMissing + f . g = traverseMaybeMissing $ + \ k x -> missingKey g k x >>= \y -> + case y of + Nothing -> pure Nothing + Just q -> missingKey f k q + {-# INLINE id #-} + {-# INLINE (.) #-} + +-- | Equivalent to @ ReaderT k (ReaderT x (MaybeT f)) @. +instance (Applicative f, Monad f) => Applicative (WhenMissing f k x) where + pure x = mapMissing (\ _ _ -> x) + f <*> g = traverseMaybeMissing $ \k x -> do + res1 <- missingKey f k x + case res1 of + Nothing -> pure Nothing + Just r -> (pure $!) . fmap r =<< missingKey g k x + {-# INLINE pure #-} + {-# INLINE (<*>) #-} + +-- | Equivalent to @ ReaderT k (ReaderT x (MaybeT f)) @. +instance (Applicative f, Monad f) => Monad (WhenMissing f k x) where +#if !MIN_VERSION_base(4,8,0) + return = pure +#endif + m >>= f = traverseMaybeMissing $ \k x -> do + res1 <- missingKey m k x + case res1 of + Nothing -> pure Nothing + Just r -> missingKey (f r) k x + {-# INLINE (>>=) #-} + +-- | Map covariantly over a @'WhenMissing' f k x@. +mapWhenMissing :: (Applicative f, Monad f) + => (a -> b) + -> WhenMissing f k x a -> WhenMissing f k x b +mapWhenMissing f t = WhenMissing + { missingSubtree = \m -> missingSubtree t m >>= \m' -> pure $! fmap f m' + , missingKey = \k x -> missingKey t k x >>= \q -> (pure $! fmap f q) } +{-# INLINE mapWhenMissing #-} + +-- | Map covariantly over a @'WhenMissing' f k x@, using only a 'Functor f' +-- constraint. +mapGentlyWhenMissing :: Functor f + => (a -> b) + -> WhenMissing f k x a -> WhenMissing f k x b +mapGentlyWhenMissing f t = WhenMissing + { missingSubtree = \m -> fmap f <$> missingSubtree t m + , missingKey = \k x -> fmap f <$> missingKey t k x } +{-# INLINE mapGentlyWhenMissing #-} + +-- | Map covariantly over a @'WhenMatched' f k x@, using only a 'Functor f' +-- constraint. +mapGentlyWhenMatched :: Functor f + => (a -> b) + -> WhenMatched f k x y a -> WhenMatched f k x y b +mapGentlyWhenMatched f t = zipWithMaybeAMatched $ + \k x y -> fmap f <$> runWhenMatched t k x y +{-# INLINE mapGentlyWhenMatched #-} + +-- | Map contravariantly over a @'WhenMissing' f k _ x@. +lmapWhenMissing :: (b -> a) -> WhenMissing f k a x -> WhenMissing f k b x +lmapWhenMissing f t = WhenMissing + { missingSubtree = \m -> missingSubtree t (fmap f m) + , missingKey = \k x -> missingKey t k (f x) } +{-# INLINE lmapWhenMissing #-} + +-- | Map contravariantly over a @'WhenMatched' f k _ y z@. +contramapFirstWhenMatched :: (b -> a) + -> WhenMatched f k a y z + -> WhenMatched f k b y z +contramapFirstWhenMatched f t = WhenMatched $ + \k x y -> runWhenMatched t k (f x) y +{-# INLINE contramapFirstWhenMatched #-} + +-- | Map contravariantly over a @'WhenMatched' f k x _ z@. +contramapSecondWhenMatched :: (b -> a) + -> WhenMatched f k x a z + -> WhenMatched f k x b z +contramapSecondWhenMatched f t = WhenMatched $ + \k x y -> runWhenMatched t k x (f y) +{-# INLINE contramapSecondWhenMatched #-} + +-- | A tactic for dealing with keys present in one map but not the other in +-- 'merge'. +-- +-- A tactic of type @ SimpleWhenMissing k x z @ is an abstract representation +-- of a function of type @ k -> x -> Maybe z @. +type SimpleWhenMissing = WhenMissing Identity + +-- | A tactic for dealing with keys present in both +-- maps in 'merge' or 'mergeA'. +-- +-- A tactic of type @ WhenMatched f k x y z @ is an abstract representation +-- of a function of type @ k -> x -> y -> f (Maybe z) @. +newtype WhenMatched f k x y z = WhenMatched + { matchedKey :: k -> x -> y -> f (Maybe z) } + +-- | Along with zipWithMaybeAMatched, witnesses the isomorphism between +-- @WhenMatched f k x y z@ and @k -> x -> y -> f (Maybe z)@. +runWhenMatched :: WhenMatched f k x y z -> k -> x -> y -> f (Maybe z) +runWhenMatched = matchedKey +{-# INLINE runWhenMatched #-} + +-- | Along with traverseMaybeMissing, witnesses the isomorphism between +-- @WhenMissing f k x y@ and @k -> x -> f (Maybe y)@. +runWhenMissing :: WhenMissing f k x y -> k -> x -> f (Maybe y) +runWhenMissing = missingKey +{-# INLINE runWhenMissing #-} + +instance Functor f => Functor (WhenMatched f k x y) where + fmap = mapWhenMatched + {-# INLINE fmap #-} + +instance (Monad f, Applicative f) => Category.Category (WhenMatched f k x) where + id = zipWithMatched (\_ _ y -> y) + f . g = zipWithMaybeAMatched $ + \k x y -> do + res <- runWhenMatched g k x y + case res of + Nothing -> pure Nothing + Just r -> runWhenMatched f k x r + {-# INLINE id #-} + {-# INLINE (.) #-} + +-- | Equivalent to @ ReaderT k (ReaderT x (ReaderT y (MaybeT f))) @ +instance (Monad f, Applicative f) => Applicative (WhenMatched f k x y) where + pure x = zipWithMatched (\_ _ _ -> x) + fs <*> xs = zipWithMaybeAMatched $ \k x y -> do + res <- runWhenMatched fs k x y + case res of + Nothing -> pure Nothing + Just r -> (pure $!) . fmap r =<< runWhenMatched xs k x y + {-# INLINE pure #-} + {-# INLINE (<*>) #-} + +-- | Equivalent to @ ReaderT k (ReaderT x (ReaderT y (MaybeT f))) @ +instance (Monad f, Applicative f) => Monad (WhenMatched f k x y) where +#if !MIN_VERSION_base(4,8,0) + return = pure +#endif + m >>= f = zipWithMaybeAMatched $ \k x y -> do + res <- runWhenMatched m k x y + case res of + Nothing -> pure Nothing + Just r -> runWhenMatched (f r) k x y + {-# INLINE (>>=) #-} + +-- | Map covariantly over a @'WhenMatched' f k x y@. +mapWhenMatched :: Functor f + => (a -> b) + -> WhenMatched f k x y a + -> WhenMatched f k x y b +mapWhenMatched f (WhenMatched g) = WhenMatched $ \k x y -> fmap (fmap f) (g k x y) +{-# INLINE mapWhenMatched #-} + +-- | A tactic for dealing with keys present in both maps in 'merge'. +-- +-- A tactic of type @ SimpleWhenMatched k x y z @ is an abstract representation +-- of a function of type @ k -> x -> y -> Maybe z @. +type SimpleWhenMatched = WhenMatched Identity + +-- | When a key is found in both maps, apply a function to the +-- key and values and use the result in the merged map. +-- +-- @ +-- zipWithMatched :: (k -> x -> y -> z) +-- -> SimpleWhenMatched k x y z +-- @ +zipWithMatched :: Applicative f + => (k -> x -> y -> z) + -> WhenMatched f k x y z +zipWithMatched f = WhenMatched $ \ k x y -> pure . Just $ f k x y +{-# INLINE zipWithMatched #-} + +-- | When a key is found in both maps, apply a function to the +-- key and values to produce an action and use its result in the merged map. +zipWithAMatched :: Applicative f + => (k -> x -> y -> f z) + -> WhenMatched f k x y z +zipWithAMatched f = WhenMatched $ \ k x y -> Just <$> f k x y +{-# INLINE zipWithAMatched #-} + +-- | When a key is found in both maps, apply a function to the +-- key and values and maybe use the result in the merged map. +-- +-- @ +-- zipWithMaybeMatched :: (k -> x -> y -> Maybe z) +-- -> SimpleWhenMatched k x y z +-- @ +zipWithMaybeMatched :: Applicative f + => (k -> x -> y -> Maybe z) + -> WhenMatched f k x y z +zipWithMaybeMatched f = WhenMatched $ \ k x y -> pure $ f k x y +{-# INLINE zipWithMaybeMatched #-} + +-- | When a key is found in both maps, apply a function to the +-- key and values, perform the resulting action, and maybe use +-- the result in the merged map. +-- +-- This is the fundamental 'WhenMatched' tactic. +zipWithMaybeAMatched :: (k -> x -> y -> f (Maybe z)) + -> WhenMatched f k x y z +zipWithMaybeAMatched f = WhenMatched $ \ k x y -> f k x y +{-# INLINE zipWithMaybeAMatched #-} + +-- | Drop all the entries whose keys are missing from the other +-- map. +-- +-- @ +-- dropMissing :: SimpleWhenMissing k x y +-- @ +-- +-- prop> dropMissing = mapMaybeMissing (\_ _ -> Nothing) +-- +-- but @dropMissing@ is much faster. +dropMissing :: Applicative f => WhenMissing f k x y +dropMissing = WhenMissing + { missingSubtree = const (pure Tip) + , missingKey = \_ _ -> pure Nothing } +{-# INLINE dropMissing #-} + +-- | Preserve, unchanged, the entries whose keys are missing from +-- the other map. +-- +-- @ +-- preserveMissing :: SimpleWhenMissing k x x +-- @ +-- +-- prop> preserveMissing = Lazy.Merge.mapMaybeMissing (\_ x -> Just x) +-- +-- but @preserveMissing@ is much faster. +preserveMissing :: Applicative f => WhenMissing f k x x +preserveMissing = WhenMissing + { missingSubtree = pure + , missingKey = \_ v -> pure (Just v) } +{-# INLINE preserveMissing #-} + +-- | Map over the entries whose keys are missing from the other map. +-- +-- @ +-- mapMissing :: (k -> x -> y) -> SimpleWhenMissing k x y +-- @ +-- +-- prop> mapMissing f = mapMaybeMissing (\k x -> Just $ f k x) +-- +-- but @mapMissing@ is somewhat faster. +mapMissing :: Applicative f => (k -> x -> y) -> WhenMissing f k x y +mapMissing f = WhenMissing + { missingSubtree = \m -> pure $! mapWithKey f m + , missingKey = \ k x -> pure $ Just (f k x) } +{-# INLINE mapMissing #-} + +-- | Map over the entries whose keys are missing from the other map, +-- optionally removing some. This is the most powerful 'SimpleWhenMissing' +-- tactic, but others are usually more efficient. +-- +-- @ +-- mapMaybeMissing :: (k -> x -> Maybe y) -> SimpleWhenMissing k x y +-- @ +-- +-- prop> mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x)) +-- +-- but @mapMaybeMissing@ uses fewer unnecessary 'Applicative' operations. +mapMaybeMissing :: Applicative f => (k -> x -> Maybe y) -> WhenMissing f k x y +mapMaybeMissing f = WhenMissing + { missingSubtree = \m -> pure $! mapMaybeWithKey f m + , missingKey = \k x -> pure $! f k x } +{-# INLINE mapMaybeMissing #-} + +-- | Filter the entries whose keys are missing from the other map. +-- +-- @ +-- filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing k x x +-- @ +-- +-- prop> filterMissing f = Lazy.Merge.mapMaybeMissing $ \k x -> guard (f k x) *> Just x +-- +-- but this should be a little faster. +filterMissing :: Applicative f + => (k -> x -> Bool) -> WhenMissing f k x x +filterMissing f = WhenMissing + { missingSubtree = \m -> pure $! filterWithKey f m + , missingKey = \k x -> pure $! if f k x then Just x else Nothing } +{-# INLINE filterMissing #-} + +-- | Filter the entries whose keys are missing from the other map +-- using some 'Applicative' action. +-- +-- @ +-- filterAMissing f = Lazy.Merge.traverseMaybeMissing $ +-- \k x -> (\b -> guard b *> Just x) <$> f k x +-- @ +-- +-- but this should be a little faster. +filterAMissing :: Applicative f + => (k -> x -> f Bool) -> WhenMissing f k x x +filterAMissing f = WhenMissing + { missingSubtree = \m -> filterWithKeyA f m + , missingKey = \k x -> bool Nothing (Just x) <$> f k x } +{-# INLINE filterAMissing #-} + +-- | This wasn't in Data.Bool until 4.7.0, so we define it here +bool :: a -> a -> Bool -> a +bool f _ False = f +bool _ t True = t + +-- | Traverse over the entries whose keys are missing from the other map. +traverseMissing :: Applicative f + => (k -> x -> f y) -> WhenMissing f k x y +traverseMissing f = WhenMissing + { missingSubtree = traverseWithKey f + , missingKey = \k x -> Just <$> f k x } +{-# INLINE traverseMissing #-} + +-- | Traverse over the entries whose keys are missing from the other map, +-- optionally producing values to put in the result. +-- This is the most powerful 'WhenMissing' tactic, but others are usually +-- more efficient. +traverseMaybeMissing :: Applicative f + => (k -> x -> f (Maybe y)) -> WhenMissing f k x y +traverseMaybeMissing f = WhenMissing + { missingSubtree = traverseMaybeWithKey f + , missingKey = f } +{-# INLINE traverseMaybeMissing #-} + +-- | Merge two maps. +-- +-- @merge@ takes two 'WhenMissing' tactics, a 'WhenMatched' +-- tactic and two maps. It uses the tactics to merge the maps. +-- Its behavior is best understood via its fundamental tactics, +-- 'mapMaybeMissing' and 'zipWithMaybeMatched'. +-- +-- Consider +-- +-- @ +-- merge (mapMaybeMissing g1) +-- (mapMaybeMissing g2) +-- (zipWithMaybeMatched f) +-- m1 m2 +-- @ +-- +-- Take, for example, +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- @merge@ will first ''align'' these maps by key: +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- It will then pass the individual entries and pairs of entries +-- to @g1@, @g2@, or @f@ as appropriate: +-- +-- @ +-- maybes = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"] +-- @ +-- +-- This produces a 'Maybe' for each key: +-- +-- @ +-- keys = 0 1 2 3 4 +-- results = [Nothing, Just True, Just False, Nothing, Just True] +-- @ +-- +-- Finally, the @Just@ results are collected into a map: +-- +-- @ +-- return value = [(1, True), (2, False), (4, True)] +-- @ +-- +-- The other tactics below are optimizations or simplifications of +-- 'mapMaybeMissing' for special cases. Most importantly, +-- +-- * 'dropMissing' drops all the keys. +-- * 'preserveMissing' leaves all the entries alone. +-- +-- When 'merge' is given three arguments, it is inlined at the call +-- site. To prevent excessive inlining, you should typically use 'merge' +-- to define your custom combining functions. +-- +-- +-- Examples: +-- +-- prop> unionWithKey f = merge preserveMissing preserveMissing (zipWithMatched f) +-- prop> intersectionWithKey f = merge dropMissing dropMissing (zipWithMatched f) +-- prop> differenceWith f = merge diffPreserve diffDrop f +-- prop> symmetricDifference = merge diffPreserve diffPreserve (\ _ _ _ -> Nothing) +-- prop> mapEachPiece f g h = merge (diffMapWithKey f) (diffMapWithKey g) +-- +-- @since 0.5.8 +merge :: Ord k + => SimpleWhenMissing k a c -- ^ What to do with keys in @m1@ but not @m2@ + -> SimpleWhenMissing k b c -- ^ What to do with keys in @m2@ but not @m1@ + -> SimpleWhenMatched k a b c -- ^ What to do with keys in both @m1@ and @m2@ + -> Map k a -- ^ Map @m1@ + -> Map k b -- ^ Map @m2@ + -> Map k c +merge g1 g2 f m1 m2 = runIdentity $ + mergeA g1 g2 f m1 m2 +{-# INLINE merge #-} + +-- | An applicative version of 'merge'. +-- +-- @mergeA@ takes two 'WhenMissing' tactics, a 'WhenMatched' +-- tactic and two maps. It uses the tactics to merge the maps. +-- Its behavior is best understood via its fundamental tactics, +-- 'traverseMaybeMissing' and 'zipWithMaybeAMatched'. +-- +-- Consider +-- +-- @ +-- mergeA (traverseMaybeMissing g1) +-- (traverseMaybeMissing g2) +-- (zipWithMaybeAMatched f) +-- m1 m2 +-- @ +-- +-- Take, for example, +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- @mergeA@ will first ''align'' these maps by key: +-- +-- @ +-- m1 = [(0, 'a'), (1, 'b'), (3,'c'), (4, 'd')] +-- m2 = [(1, "one"), (2, "two"), (4, "three")] +-- @ +-- +-- It will then pass the individual entries and pairs of entries +-- to @g1@, @g2@, or @f@ as appropriate: +-- +-- @ +-- actions = [g1 0 'a', f 1 'b' "one", g2 2 "two", g1 3 'c', f 4 'd' "three"] +-- @ +-- +-- Next, it will perform the actions in the @actions@ list in order from +-- left to right. +-- +-- @ +-- keys = 0 1 2 3 4 +-- results = [Nothing, Just True, Just False, Nothing, Just True] +-- @ +-- +-- Finally, the @Just@ results are collected into a map: +-- +-- @ +-- return value = [(1, True), (2, False), (4, True)] +-- @ +-- +-- The other tactics below are optimizations or simplifications of +-- 'traverseMaybeMissing' for special cases. Most importantly, +-- +-- * 'dropMissing' drops all the keys. +-- * 'preserveMissing' leaves all the entries alone. +-- * 'mapMaybeMissing' does not use the 'Applicative' context. +-- +-- When 'mergeA' is given three arguments, it is inlined at the call +-- site. To prevent excessive inlining, you should generally only use +-- 'mergeA' to define custom combining functions. +-- +-- @since 0.5.8 +mergeA + :: (Applicative f, Ord k) + => WhenMissing f k a c -- ^ What to do with keys in @m1@ but not @m2@ + -> WhenMissing f k b c -- ^ What to do with keys in @m2@ but not @m1@ + -> WhenMatched f k a b c -- ^ What to do with keys in both @m1@ and @m2@ + -> Map k a -- ^ Map @m1@ + -> Map k b -- ^ Map @m2@ + -> f (Map k c) +mergeA + WhenMissing{missingSubtree = g1t, missingKey = g1k} + WhenMissing{missingSubtree = g2t} + (WhenMatched f) = go + where + go t1 Tip = g1t t1 + go Tip t2 = g2t t2 + go (Bin _ kx x1 l1 r1) t2 = case splitLookup kx t2 of + (l2, mx2, r2) -> case mx2 of + Nothing -> (\l' mx' r' -> maybe link2 (link kx) mx' l' r') + <$> l1l2 <*> g1k kx x1 <*> r1r2 + Just x2 -> (\l' mx' r' -> maybe link2 (link kx) mx' l' r') + <$> l1l2 <*> f kx x1 x2 <*> r1r2 + where + !l1l2 = go l1 l2 + !r1r2 = go r1 r2 +{-# INLINE mergeA #-} + + +{-------------------------------------------------------------------- + MergeWithKey +--------------------------------------------------------------------} + +-- | /O(n+m)/. An unsafe general combining function. +-- +-- WARNING: This function can produce corrupt maps and its results +-- may depend on the internal structures of its inputs. Users should +-- prefer 'merge' or 'mergeA'. +-- +-- When 'mergeWithKey' is given three arguments, it is inlined to the call +-- site. You should therefore use 'mergeWithKey' only to define custom +-- combining functions. For example, you could define 'unionWithKey', +-- 'differenceWithKey' and 'intersectionWithKey' as +-- +-- > myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2 +-- > myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2 +-- > myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2 +-- +-- When calling @'mergeWithKey' combine only1 only2@, a function combining two +-- 'Map's is created, such that +-- +-- * if a key is present in both maps, it is passed with both corresponding +-- values to the @combine@ function. Depending on the result, the key is either +-- present in the result with specified value, or is left out; +-- +-- * a nonempty subtree present only in the first map is passed to @only1@ and +-- the output is added to the result; +-- +-- * a nonempty subtree present only in the second map is passed to @only2@ and +-- the output is added to the result. +-- +-- The @only1@ and @only2@ methods /must return a map with a subset (possibly empty) of the keys of the given map/. +-- The values can be modified arbitrarily. Most common variants of @only1@ and +-- @only2@ are 'id' and @'const' 'empty'@, but for example @'map' f@, +-- @'filterWithKey' f@, or @'mapMaybeWithKey' f@ could be used for any @f@. + +mergeWithKey :: Ord k + => (k -> a -> b -> Maybe c) + -> (Map k a -> Map k c) + -> (Map k b -> Map k c) + -> Map k a -> Map k b -> Map k c +mergeWithKey f g1 g2 = go + where + go Tip t2 = g2 t2 + go t1 Tip = g1 t1 + go (Bin _ kx x l1 r1) t2 = + case found of + Nothing -> case g1 (singleton kx x) of + Tip -> link2 l' r' + (Bin _ _ x' Tip Tip) -> link kx x' l' r' + _ -> error "mergeWithKey: Given function only1 does not fulfill required conditions (see documentation)" + Just x2 -> case f kx x x2 of + Nothing -> link2 l' r' + Just x' -> link kx x' l' r' + where + (l2, found, r2) = splitLookup kx t2 + l' = go l1 l2 + r' = go r1 r2 +{-# INLINE mergeWithKey #-} + +{-------------------------------------------------------------------- + Submap +--------------------------------------------------------------------} +-- | /O(m*log(n/m + 1)), m <= n/. +-- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@). +-- +isSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool +isSubmapOf m1 m2 = isSubmapOfBy (==) m1 m2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE isSubmapOf #-} +#endif + +{- | /O(m*log(n/m + 1)), m <= n/. + The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if + all keys in @t1@ are in tree @t2@, and when @f@ returns 'True' when + applied to their respective values. For example, the following + expressions are all 'True': + + > isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) + > isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) + > isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)]) + + But the following are all 'False': + + > isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)]) + > isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) + > isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)]) + + +-} +isSubmapOfBy :: Ord k => (a->b->Bool) -> Map k a -> Map k b -> Bool +isSubmapOfBy f t1 t2 + = (size t1 <= size t2) && (submap' f t1 t2) +#if __GLASGOW_HASKELL__ +{-# INLINABLE isSubmapOfBy #-} +#endif + +submap' :: Ord a => (b -> c -> Bool) -> Map a b -> Map a c -> Bool +submap' _ Tip _ = True +submap' _ _ Tip = False +submap' f (Bin _ kx x l r) t + = case found of + Nothing -> False + Just y -> f x y && submap' f l lt && submap' f r gt + where + (lt,found,gt) = splitLookup kx t +#if __GLASGOW_HASKELL__ +{-# INLINABLE submap' #-} +#endif + +-- | /O(m*log(n/m + 1)), m <= n/. Is this a proper submap? (ie. a submap but not equal). +-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@). +isProperSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool +isProperSubmapOf m1 m2 + = isProperSubmapOfBy (==) m1 m2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE isProperSubmapOf #-} +#endif + +{- | /O(m*log(n/m + 1)), m <= n/. Is this a proper submap? (ie. a submap but not equal). + The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when + @m1@ and @m2@ are not equal, + all keys in @m1@ are in @m2@, and when @f@ returns 'True' when + applied to their respective values. For example, the following + expressions are all 'True': + + > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + + But the following are all 'False': + + > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) + > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) + > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) + + +-} +isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool +isProperSubmapOfBy f t1 t2 + = (size t1 < size t2) && (submap' f t1 t2) +#if __GLASGOW_HASKELL__ +{-# INLINABLE isProperSubmapOfBy #-} +#endif + +{-------------------------------------------------------------------- + Filter and partition +--------------------------------------------------------------------} +-- | /O(n)/. Filter all values that satisfy the predicate. +-- +-- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b" +-- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty +-- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty + +filter :: (a -> Bool) -> Map k a -> Map k a +filter p m + = filterWithKey (\_ x -> p x) m + +-- | /O(n)/. Filter all keys\/values that satisfy the predicate. +-- +-- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" + +filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a +filterWithKey _ Tip = Tip +filterWithKey p t@(Bin _ kx x l r) + | p kx x = if pl `ptrEq` l && pr `ptrEq` r + then t + else link kx x pl pr + | otherwise = link2 pl pr + where !pl = filterWithKey p l + !pr = filterWithKey p r + +-- | /O(n)/. Filter keys and values using an 'Applicative' +-- predicate. +filterWithKeyA :: Applicative f => (k -> a -> f Bool) -> Map k a -> f (Map k a) +filterWithKeyA _ Tip = pure Tip +filterWithKeyA p t@(Bin _ kx x l r) = + combine <$> p kx x <*> filterWithKeyA p l <*> filterWithKeyA p r + where + combine True pl pr + | pl `ptrEq` l && pr `ptrEq` r = t + | otherwise = link kx x pl pr + combine False pl pr = link2 pl pr + +-- | /O(log n)/. Take while a predicate on the keys holds. +-- The user is responsible for ensuring that for all keys @j@ and @k@ in the map, +-- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. +-- +-- @ +-- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' (p . fst) . 'toList' +-- takeWhileAntitone p = 'filterWithKey' (\k _ -> p k) +-- @ + +takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a +takeWhileAntitone _ Tip = Tip +takeWhileAntitone p (Bin _ kx x l r) + | p kx = link kx x l (takeWhileAntitone p r) + | otherwise = takeWhileAntitone p l + +-- | /O(log n)/. Drop while a predicate on the keys holds. +-- The user is responsible for ensuring that for all keys @j@ and @k@ in the map, +-- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. +-- +-- @ +-- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' (p . fst) . 'toList' +-- dropWhileAntitone p = 'filterWithKey' (\k -> not (p k)) +-- @ + +dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a +dropWhileAntitone _ Tip = Tip +dropWhileAntitone p (Bin _ kx x l r) + | p kx = dropWhileAntitone p r + | otherwise = link kx x (dropWhileAntitone p l) r + +-- | /O(log n)/. Divide a map at the point where a predicate on the keys stops holding. +-- The user is responsible for ensuring that for all keys @j@ and @k@ in the map, +-- @j \< k ==\> p j \>= p k@. +-- +-- @ +-- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs) +-- spanAntitone p xs = partition p xs +-- @ +-- +-- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the map +-- at some /unspecified/ point where the predicate switches from holding to not +-- holding (where the predicate is seen to hold before the first key and to fail +-- after the last key). + +spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a) +spanAntitone p0 m = toPair (go p0 m) + where + go _ Tip = Tip :*: Tip + go p (Bin _ kx x l r) + | p kx = let u :*: v = go p r in link kx x l u :*: v + | otherwise = let u :*: v = go p l in u :*: link kx x v r + +-- | /O(n)/. Partition the map according to a predicate. The first +-- map contains all elements that satisfy the predicate, the second all +-- elements that fail the predicate. See also 'split'. +-- +-- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") +-- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) +-- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) + +partition :: (a -> Bool) -> Map k a -> (Map k a,Map k a) +partition p m + = partitionWithKey (\_ x -> p x) m + +-- | /O(n)/. Partition the map according to a predicate. The first +-- map contains all elements that satisfy the predicate, the second all +-- elements that fail the predicate. See also 'split'. +-- +-- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b") +-- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty) +-- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")]) + +partitionWithKey :: (k -> a -> Bool) -> Map k a -> (Map k a,Map k a) +partitionWithKey p0 t0 = toPair $ go p0 t0 + where + go _ Tip = (Tip :*: Tip) + go p t@(Bin _ kx x l r) + | p kx x = (if l1 `ptrEq` l && r1 `ptrEq` r + then t + else link kx x l1 r1) :*: link2 l2 r2 + | otherwise = link2 l1 r1 :*: + (if l2 `ptrEq` l && r2 `ptrEq` r + then t + else link kx x l2 r2) + where + (l1 :*: l2) = go p l + (r1 :*: r2) = go p r + +-- | /O(n)/. Map values and collect the 'Just' results. +-- +-- > let f x = if x == "a" then Just "new a" else Nothing +-- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a" + +mapMaybe :: (a -> Maybe b) -> Map k a -> Map k b +mapMaybe f = mapMaybeWithKey (\_ x -> f x) + +-- | /O(n)/. Map keys\/values and collect the 'Just' results. +-- +-- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing +-- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3" + +mapMaybeWithKey :: (k -> a -> Maybe b) -> Map k a -> Map k b +mapMaybeWithKey _ Tip = Tip +mapMaybeWithKey f (Bin _ kx x l r) = case f kx x of + Just y -> link kx y (mapMaybeWithKey f l) (mapMaybeWithKey f r) + Nothing -> link2 (mapMaybeWithKey f l) (mapMaybeWithKey f r) + +-- | /O(n)/. Traverse keys\/values and collect the 'Just' results. + +traverseMaybeWithKey :: Applicative f + => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b) +traverseMaybeWithKey = go + where + go _ Tip = pure Tip + go f (Bin _ kx x Tip Tip) = maybe Tip (\x' -> Bin 1 kx x' Tip Tip) <$> f kx x + go f (Bin _ kx x l r) = combine <$> go f l <*> f kx x <*> go f r + where + combine !l' mx !r' = case mx of + Nothing -> link2 l' r' + Just x' -> link kx x' l' r' + +-- | /O(n)/. Map values and separate the 'Left' and 'Right' results. +-- +-- > let f a = if a < "c" then Left a else Right a +-- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")]) +-- > +-- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) + +mapEither :: (a -> Either b c) -> Map k a -> (Map k b, Map k c) +mapEither f m + = mapEitherWithKey (\_ x -> f x) m + +-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results. +-- +-- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a) +-- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")]) +-- > +-- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")]) +-- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")]) + +mapEitherWithKey :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c) +mapEitherWithKey f0 t0 = toPair $ go f0 t0 + where + go _ Tip = (Tip :*: Tip) + go f (Bin _ kx x l r) = case f kx x of + Left y -> link kx y l1 r1 :*: link2 l2 r2 + Right z -> link2 l1 r1 :*: link kx z l2 r2 + where + (l1 :*: l2) = go f l + (r1 :*: r2) = go f r + +{-------------------------------------------------------------------- + Mapping +--------------------------------------------------------------------} +-- | /O(n)/. Map a function over all values in the map. +-- +-- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")] + +map :: (a -> b) -> Map k a -> Map k b +map f = go where + go Tip = Tip + go (Bin sx kx x l r) = Bin sx kx (f x) (go l) (go r) +-- We use a `go` function to allow `map` to inline. This makes +-- a big difference if someone uses `map (const x) m` instead +-- of `x <$ m`; it doesn't seem to do any harm. + +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] map #-} +{-# RULES +"map/map" forall f g xs . map f (map g xs) = map (f . g) xs + #-} +#endif +#if __GLASGOW_HASKELL__ >= 709 +-- Safe coercions were introduced in 7.8, but did not work well with RULES yet. +{-# RULES +"map/coerce" map coerce = coerce + #-} +#endif + +-- | /O(n)/. Map a function over all values in the map. +-- +-- > let f key x = (show key) ++ ":" ++ x +-- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")] + +mapWithKey :: (k -> a -> b) -> Map k a -> Map k b +mapWithKey _ Tip = Tip +mapWithKey f (Bin sx kx x l r) = Bin sx kx (f kx x) (mapWithKey f l) (mapWithKey f r) + +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] mapWithKey #-} +{-# RULES +"mapWithKey/mapWithKey" forall f g xs . mapWithKey f (mapWithKey g xs) = + mapWithKey (\k a -> f k (g k a)) xs +"mapWithKey/map" forall f g xs . mapWithKey f (map g xs) = + mapWithKey (\k a -> f k (g a)) xs +"map/mapWithKey" forall f g xs . map f (mapWithKey g xs) = + mapWithKey (\k a -> f (g k a)) xs + #-} +#endif + +-- | /O(n)/. +-- @'traverseWithKey' f m == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@ +-- That is, behaves exactly like a regular 'traverse' except that the traversing +-- function also has access to the key associated with a value. +-- +-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')]) +-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')]) == Nothing +traverseWithKey :: Applicative t => (k -> a -> t b) -> Map k a -> t (Map k b) +traverseWithKey f = go + where + go Tip = pure Tip + go (Bin 1 k v _ _) = (\v' -> Bin 1 k v' Tip Tip) <$> f k v + go (Bin s k v l r) = flip (Bin s k) <$> go l <*> f k v <*> go r +{-# INLINE traverseWithKey #-} + +-- | /O(n)/. The function 'mapAccum' threads an accumulating +-- argument through the map in ascending order of keys. +-- +-- > let f a b = (a ++ b, b ++ "X") +-- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")]) + +mapAccum :: (a -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) +mapAccum f a m + = mapAccumWithKey (\a' _ x' -> f a' x') a m + +-- | /O(n)/. The function 'mapAccumWithKey' threads an accumulating +-- argument through the map in ascending order of keys. +-- +-- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X") +-- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")]) + +mapAccumWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) +mapAccumWithKey f a t + = mapAccumL f a t + +-- | /O(n)/. The function 'mapAccumL' threads an accumulating +-- argument through the map in ascending order of keys. +mapAccumL :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) +mapAccumL _ a Tip = (a,Tip) +mapAccumL f a (Bin sx kx x l r) = + let (a1,l') = mapAccumL f a l + (a2,x') = f a1 kx x + (a3,r') = mapAccumL f a2 r + in (a3,Bin sx kx x' l' r') + +-- | /O(n)/. The function 'mapAccumR' threads an accumulating +-- argument through the map in descending order of keys. +mapAccumRWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c) +mapAccumRWithKey _ a Tip = (a,Tip) +mapAccumRWithKey f a (Bin sx kx x l r) = + let (a1,r') = mapAccumRWithKey f a r + (a2,x') = f a1 kx x + (a3,l') = mapAccumRWithKey f a2 l + in (a3,Bin sx kx x' l' r') + +-- | /O(n*log n)/. +-- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@. +-- +-- The size of the result may be smaller if @f@ maps two or more distinct +-- keys to the same new key. In this case the value at the greatest of the +-- original keys is retained. +-- +-- > mapKeys (+ 1) (fromList [(5,"a"), (3,"b")]) == fromList [(4, "b"), (6, "a")] +-- > mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c" +-- > mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c" + +mapKeys :: Ord k2 => (k1->k2) -> Map k1 a -> Map k2 a +mapKeys f = fromList . foldrWithKey (\k x xs -> (f k, x) : xs) [] +#if __GLASGOW_HASKELL__ +{-# INLINABLE mapKeys #-} +#endif + +-- | /O(n*log n)/. +-- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@. +-- +-- The size of the result may be smaller if @f@ maps two or more distinct +-- keys to the same new key. In this case the associated values will be +-- combined using @c@. +-- +-- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab" +-- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab" + +mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1->k2) -> Map k1 a -> Map k2 a +mapKeysWith c f = fromListWith c . foldrWithKey (\k x xs -> (f k, x) : xs) [] +#if __GLASGOW_HASKELL__ +{-# INLINABLE mapKeysWith #-} +#endif + + +-- | /O(n)/. +-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@ +-- is strictly monotonic. +-- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@. +-- /The precondition is not checked./ +-- Semi-formally, we have: +-- +-- > and [x < y ==> f x < f y | x <- ls, y <- ls] +-- > ==> mapKeysMonotonic f s == mapKeys f s +-- > where ls = keys s +-- +-- This means that @f@ maps distinct original keys to distinct resulting keys. +-- This function has better performance than 'mapKeys'. +-- +-- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")] +-- > valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True +-- > valid (mapKeysMonotonic (\ _ -> 1) (fromList [(5,"a"), (3,"b")])) == False + +mapKeysMonotonic :: (k1->k2) -> Map k1 a -> Map k2 a +mapKeysMonotonic _ Tip = Tip +mapKeysMonotonic f (Bin sz k x l r) = + Bin sz (f k) x (mapKeysMonotonic f l) (mapKeysMonotonic f r) + +{-------------------------------------------------------------------- + Folds +--------------------------------------------------------------------} + +-- | /O(n)/. Fold the values in the map using the given right-associative +-- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@. +-- +-- For example, +-- +-- > elems map = foldr (:) [] map +-- +-- > let f a len = len + (length a) +-- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 +foldr :: (a -> b -> b) -> b -> Map k a -> b +foldr f z = go z + where + go z' Tip = z' + go z' (Bin _ _ x l r) = go (f x (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' :: (a -> b -> b) -> b -> Map k a -> b +foldr' f z = go z + where + go !z' Tip = z' + go z' (Bin _ _ x l r) = go (f x (go z' r)) l +{-# INLINE foldr' #-} + +-- | /O(n)/. Fold the values in the map using the given left-associative +-- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@. +-- +-- For example, +-- +-- > elems = reverse . foldl (flip (:)) [] +-- +-- > let f len a = len + (length a) +-- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4 +foldl :: (a -> b -> a) -> a -> Map k b -> a +foldl f z = go z + where + go z' Tip = z' + go z' (Bin _ _ x l r) = go (f (go z' l) x) 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 -> b -> a) -> a -> Map k b -> a +foldl' f z = go z + where + go !z' Tip = z' + go z' (Bin _ _ x l r) = go (f (go z' l) x) r +{-# INLINE foldl' #-} + +-- | /O(n)/. Fold the keys and values in the map using the given right-associative +-- binary operator, such that +-- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@. +-- +-- For example, +-- +-- > keys map = foldrWithKey (\k x ks -> k:ks) [] map +-- +-- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" +-- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)" +foldrWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b +foldrWithKey f z = go z + where + go z' Tip = z' + go z' (Bin _ kx x l r) = go (f kx x (go z' r)) l +{-# INLINE foldrWithKey #-} + +-- | /O(n)/. A strict version of 'foldrWithKey'. Each application of the operator is +-- evaluated before using the result in the next application. This +-- function is strict in the starting value. +foldrWithKey' :: (k -> a -> b -> b) -> b -> Map k a -> b +foldrWithKey' f z = go z + where + go !z' Tip = z' + go z' (Bin _ kx x l r) = go (f kx x (go z' r)) l +{-# INLINE foldrWithKey' #-} + +-- | /O(n)/. Fold the keys and values in the map using the given left-associative +-- binary operator, such that +-- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@. +-- +-- For example, +-- +-- > keys = reverse . foldlWithKey (\ks k x -> k:ks) [] +-- +-- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")" +-- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)" +foldlWithKey :: (a -> k -> b -> a) -> a -> Map k b -> a +foldlWithKey f z = go z + where + go z' Tip = z' + go z' (Bin _ kx x l r) = go (f (go z' l) kx x) r +{-# INLINE foldlWithKey #-} + +-- | /O(n)/. A strict version of 'foldlWithKey'. Each application of the operator is +-- evaluated before using the result in the next application. This +-- function is strict in the starting value. +foldlWithKey' :: (a -> k -> b -> a) -> a -> Map k b -> a +foldlWithKey' f z = go z + where + go !z' Tip = z' + go z' (Bin _ kx x l r) = go (f (go z' l) kx x) r +{-# INLINE foldlWithKey' #-} + +-- | /O(n)/. Fold the keys and values in the map using the given monoid, such that +-- +-- @'foldMapWithKey' f = 'Prelude.fold' . 'mapWithKey' f@ +-- +-- This can be an asymptotically faster than 'foldrWithKey' or 'foldlWithKey' for some monoids. +foldMapWithKey :: Monoid m => (k -> a -> m) -> Map k a -> m +foldMapWithKey f = go + where + go Tip = mempty + go (Bin 1 k v _ _) = f k v + go (Bin _ k v l r) = go l `mappend` (f k v `mappend` go r) +{-# INLINE foldMapWithKey #-} + +{-------------------------------------------------------------------- + List variations +--------------------------------------------------------------------} +-- | /O(n)/. +-- Return all elements of the map in the ascending order of their keys. +-- Subject to list fusion. +-- +-- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"] +-- > elems empty == [] + +elems :: Map k a -> [a] +elems = foldr (:) [] + +-- | /O(n)/. Return all keys of the map in ascending order. Subject to list +-- fusion. +-- +-- > keys (fromList [(5,"a"), (3,"b")]) == [3,5] +-- > keys empty == [] + +keys :: Map k a -> [k] +keys = foldrWithKey (\k _ ks -> k : ks) [] + +-- | /O(n)/. An alias for 'toAscList'. Return all key\/value pairs in the map +-- in ascending key order. Subject to list fusion. +-- +-- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] +-- > assocs empty == [] + +assocs :: Map k a -> [(k,a)] +assocs m + = toAscList m + +-- | /O(n)/. The set of all keys of the map. +-- +-- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [3,5] +-- > keysSet empty == Data.Set.empty + +keysSet :: Map k a -> Set.Set k +keysSet Tip = Set.Tip +keysSet (Bin sz kx _ l r) = Set.Bin sz kx (keysSet l) (keysSet r) + +-- | /O(n)/. Build a map from a set of keys and a function which for each key +-- computes its value. +-- +-- > fromSet (\k -> replicate k 'a') (Data.Set.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")] +-- > fromSet undefined Data.Set.empty == empty + +fromSet :: (k -> a) -> Set.Set k -> Map k a +fromSet _ Set.Tip = Tip +fromSet f (Set.Bin sz x l r) = Bin sz x (f x) (fromSet f l) (fromSet f r) + +{-------------------------------------------------------------------- + Lists + use [foldlStrict] to reduce demand on the control-stack +--------------------------------------------------------------------} +#if __GLASGOW_HASKELL__ >= 708 +instance (Ord k) => GHCExts.IsList (Map k v) where + type Item (Map k v) = (k,v) + fromList = fromList + toList = toList +#endif + +-- | /O(n*log n)/. Build a map from a list of key\/value pairs. See also 'fromAscList'. +-- If the list contains more than one value for the same key, the last value +-- for the key is retained. +-- +-- If the keys of the list are ordered, linear-time implementation is used, +-- with the performance equal to 'fromDistinctAscList'. +-- +-- > fromList [] == empty +-- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")] +-- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")] + +-- For some reason, when 'singleton' is used in fromList or in +-- create, it is not inlined, so we inline it manually. +fromList :: Ord k => [(k,a)] -> Map k a +fromList [] = Tip +fromList [(kx, x)] = Bin 1 kx x Tip Tip +fromList ((kx0, x0) : xs0) | not_ordered kx0 xs0 = fromList' (Bin 1 kx0 x0 Tip Tip) xs0 + | otherwise = go (1::Int) (Bin 1 kx0 x0 Tip Tip) xs0 + where + not_ordered _ [] = False + not_ordered kx ((ky,_) : _) = kx >= ky + {-# INLINE not_ordered #-} + + fromList' t0 xs = foldlStrict ins t0 xs + where ins t (k,x) = insert k x t + + go !_ t [] = t + go _ t [(kx, x)] = insertMax kx x t + go s l xs@((kx, x) : xss) | not_ordered kx xss = fromList' l xs + | otherwise = case create s xss of + (r, ys, []) -> go (s `shiftL` 1) (link kx x l r) ys + (r, _, ys) -> fromList' (link kx x l r) ys + + -- The create is returning a triple (tree, xs, ys). Both xs and ys + -- represent not yet processed elements and only one of them can be nonempty. + -- If ys is nonempty, the keys in ys are not ordered with respect to tree + -- and must be inserted using fromList'. Otherwise the keys have been + -- ordered so far. + create !_ [] = (Tip, [], []) + create s xs@(xp : xss) + | s == 1 = case xp of (kx, x) | not_ordered kx xss -> (Bin 1 kx x Tip Tip, [], xss) + | otherwise -> (Bin 1 kx x Tip Tip, xss, []) + | otherwise = case create (s `shiftR` 1) xs of + res@(_, [], _) -> res + (l, [(ky, y)], zs) -> (insertMax ky y l, [], zs) + (l, ys@((ky, y):yss), _) | not_ordered ky yss -> (l, [], ys) + | otherwise -> case create (s `shiftR` 1) yss of + (r, zs, ws) -> (link ky y l r, zs, ws) +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromList #-} +#endif + +-- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'. +-- +-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")] +-- > fromListWith (++) [] == empty + +fromListWith :: Ord k => (a -> a -> a) -> [(k,a)] -> Map k a +fromListWith f xs + = fromListWithKey (\_ x y -> f x y) xs +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromListWith #-} +#endif + +-- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWithKey'. +-- +-- > let f k a1 a2 = (show k) ++ a1 ++ a2 +-- > fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "3ab"), (5, "5a5ba")] +-- > fromListWithKey f [] == empty + +fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k,a)] -> Map k a +fromListWithKey f xs + = foldlStrict ins empty xs + where + ins t (k,x) = insertWithKey f k x t +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromListWithKey #-} +#endif + +-- | /O(n)/. Convert the map to a list of key\/value pairs. Subject to list fusion. +-- +-- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] +-- > toList empty == [] + +toList :: Map k a -> [(k,a)] +toList = toAscList + +-- | /O(n)/. Convert the map to a list of key\/value pairs where the keys are +-- in ascending order. Subject to list fusion. +-- +-- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")] + +toAscList :: Map k a -> [(k,a)] +toAscList = foldrWithKey (\k x xs -> (k,x):xs) [] + +-- | /O(n)/. Convert the map to a list of key\/value pairs where the keys +-- are in descending order. Subject to list fusion. +-- +-- > toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")] + +toDescList :: Map k a -> [(k,a)] +toDescList = foldlWithKey (\xs k x -> (k,x):xs) [] + +-- List fusion for the list generating functions. +#if __GLASGOW_HASKELL__ +-- The foldrFB and foldlFB are fold{r,l}WithKey equivalents, used for list fusion. +-- They are important to convert unfused methods back, see mapFB in prelude. +foldrFB :: (k -> a -> b -> b) -> b -> Map k a -> b +foldrFB = foldrWithKey +{-# INLINE[0] foldrFB #-} +foldlFB :: (a -> k -> b -> a) -> a -> Map k b -> a +foldlFB = foldlWithKey +{-# INLINE[0] foldlFB #-} + +-- Inline assocs and toList, so that we need to fuse only toAscList. +{-# INLINE assocs #-} +{-# INLINE toList #-} + +-- The fusion is enabled up to phase 2 included. If it does not succeed, +-- convert in phase 1 the expanded elems,keys,to{Asc,Desc}List calls back to +-- elems,keys,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 elems,keys,to{Asc,Desc}List -- it was forbidden to +-- inline it before phase 0, otherwise the fusion rules would not fire at all. +{-# NOINLINE[0] elems #-} +{-# NOINLINE[0] keys #-} +{-# NOINLINE[0] toAscList #-} +{-# NOINLINE[0] toDescList #-} +{-# RULES "Map.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-} +{-# RULES "Map.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-} +{-# RULES "Map.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-} +{-# RULES "Map.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-} +{-# RULES "Map.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-} +{-# RULES "Map.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-} +{-# RULES "Map.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-} +{-# RULES "Map.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-} +#endif + +{-------------------------------------------------------------------- + Building trees from ascending/descending lists can be done in linear time. + + Note that if [xs] is ascending that: + fromAscList xs == fromList xs + fromAscListWith f xs == fromListWith f xs +--------------------------------------------------------------------} +-- | /O(n)/. Build a map from an ascending list in linear time. +-- /The precondition (input list is ascending) is not checked./ +-- +-- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] +-- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")] +-- > valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) == True +-- > valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) == False + +fromAscList :: Eq k => [(k,a)] -> Map k a +fromAscList xs + = fromDistinctAscList (combineEq xs) + where + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] + combineEq xs' + = case xs' of + [] -> [] + [x] -> [x] + (x:xx) -> combineEq' x xx + + combineEq' z [] = [z] + combineEq' z@(kz,_) (x@(kx,xx):xs') + | kx==kz = combineEq' (kx,xx) xs' + | otherwise = z:combineEq' x xs' +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromAscList #-} +#endif + +-- | /O(n)/. Build a map from a descending list in linear time. +-- /The precondition (input list is descending) is not checked./ +-- +-- > fromDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")] +-- > fromDescList [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "b")] +-- > valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True +-- > valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False + +fromDescList :: Eq k => [(k,a)] -> Map k a +fromDescList xs = fromDistinctDescList (combineEq xs) + where + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] + combineEq xs' + = case xs' of + [] -> [] + [x] -> [x] + (x:xx) -> combineEq' x xx + + combineEq' z [] = [z] + combineEq' z@(kz,_) (x@(kx,xx):xs') + | kx==kz = combineEq' (kx,xx) xs' + | otherwise = z:combineEq' x xs' +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromDescList #-} +#endif + +-- | /O(n)/. Build a map from an ascending list in linear time with a combining function for equal keys. +-- /The precondition (input list is ascending) is not checked./ +-- +-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")] +-- > valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) == True +-- > valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False + +fromAscListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a +fromAscListWith f xs + = fromAscListWithKey (\_ x y -> f x y) xs +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromAscListWith #-} +#endif + +-- | /O(n)/. Build a map from a descending list in linear time with a combining function for equal keys. +-- /The precondition (input list is descending) is not checked./ +-- +-- > fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "ba")] +-- > valid (fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")]) == True +-- > valid (fromDescListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False + +fromDescListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a +fromDescListWith f xs + = fromDescListWithKey (\_ x y -> f x y) xs +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromDescListWith #-} +#endif + +-- | /O(n)/. Build a map from an ascending list in linear time with a +-- combining function for equal keys. +-- /The precondition (input list is ascending) is not checked./ +-- +-- > let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2 +-- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] == fromList [(3, "b"), (5, "5:b5:ba")] +-- > valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) == True +-- > valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False + +fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a +fromAscListWithKey f xs + = fromDistinctAscList (combineEq f xs) + where + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] + combineEq _ xs' + = case xs' of + [] -> [] + [x] -> [x] + (x:xx) -> combineEq' x xx + + combineEq' z [] = [z] + combineEq' z@(kz,zz) (x@(kx,xx):xs') + | kx==kz = let yy = f kx xx zz in combineEq' (kx,yy) xs' + | otherwise = z:combineEq' x xs' +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromAscListWithKey #-} +#endif + +-- | /O(n)/. Build a map from a descending list in linear time with a +-- combining function for equal keys. +-- /The precondition (input list is descending) is not checked./ +-- +-- > let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2 +-- > fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "5:b5:ba")] +-- > valid (fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")]) == True +-- > valid (fromDescListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False +fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a +fromDescListWithKey f xs + = fromDistinctDescList (combineEq f xs) + where + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs] + combineEq _ xs' + = case xs' of + [] -> [] + [x] -> [x] + (x:xx) -> combineEq' x xx + + combineEq' z [] = [z] + combineEq' z@(kz,zz) (x@(kx,xx):xs') + | kx==kz = let yy = f kx xx zz in combineEq' (kx,yy) xs' + | otherwise = z:combineEq' x xs' +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromDescListWithKey #-} +#endif + + +-- | /O(n)/. Build a map from an ascending list of distinct elements in linear time. +-- /The precondition is not checked./ +-- +-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")] +-- > valid (fromDistinctAscList [(3,"b"), (5,"a")]) == True +-- > valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) == False + +-- For some reason, when 'singleton' is used in fromDistinctAscList or in +-- create, it is not inlined, so we inline it manually. +fromDistinctAscList :: [(k,a)] -> Map k a +fromDistinctAscList [] = Tip +fromDistinctAscList ((kx0, x0) : xs0) = go (1::Int) (Bin 1 kx0 x0 Tip Tip) xs0 + where + go !_ t [] = t + go s l ((kx, x) : xs) = case create s xs of + (r :*: ys) -> let !t' = link kx x l r + in go (s `shiftL` 1) t' ys + + create !_ [] = (Tip :*: []) + create s xs@(x' : xs') + | s == 1 = case x' of (kx, x) -> (Bin 1 kx x Tip Tip :*: xs') + | otherwise = case create (s `shiftR` 1) xs of + res@(_ :*: []) -> res + (l :*: (ky, y):ys) -> case create (s `shiftR` 1) ys of + (r :*: zs) -> (link ky y l r :*: zs) + +-- | /O(n)/. Build a map from a descending list of distinct elements in linear time. +-- /The precondition is not checked./ +-- +-- > fromDistinctDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")] +-- > valid (fromDistinctDescList [(5,"a"), (3,"b")]) == True +-- > valid (fromDistinctDescList [(5,"a"), (5,"b"), (3,"b")]) == False + +-- For some reason, when 'singleton' is used in fromDistinctDescList or in +-- create, it is not inlined, so we inline it manually. +fromDistinctDescList :: [(k,a)] -> Map k a +fromDistinctDescList [] = Tip +fromDistinctDescList ((kx0, x0) : xs0) = go (1 :: Int) (Bin 1 kx0 x0 Tip Tip) xs0 + where + go !_ t [] = t + go s r ((kx, x) : xs) = case create s xs of + (l :*: ys) -> let !t' = link kx x l r + in go (s `shiftL` 1) t' ys + + create !_ [] = (Tip :*: []) + create s xs@(x' : xs') + | s == 1 = case x' of (kx, x) -> (Bin 1 kx x Tip Tip :*: xs') + | otherwise = case create (s `shiftR` 1) xs of + res@(_ :*: []) -> res + (r :*: (ky, y):ys) -> case create (s `shiftR` 1) ys of + (l :*: zs) -> (link ky y l r :*: zs) + +{- +-- Functions very similar to these were used to implement +-- hedge union, intersection, and difference algorithms that we no +-- longer use. These functions, however, seem likely to be useful +-- in their own right, so I'm leaving them here in case we end up +-- exporting them. + +{-------------------------------------------------------------------- + [filterGt b t] filter all keys >[b] from tree [t] + [filterLt b t] filter all keys <[b] from tree [t] +--------------------------------------------------------------------} +filterGt :: Ord k => k -> Map k v -> Map k v +filterGt !_ Tip = Tip +filterGt !b (Bin _ kx x l r) = + case compare b kx of LT -> link kx x (filterGt b l) r + EQ -> r + GT -> filterGt b r +#if __GLASGOW_HASKELL__ +{-# INLINABLE filterGt #-} +#endif + +filterLt :: Ord k => k -> Map k v -> Map k v +filterLt !_ Tip = Tip +filterLt !b (Bin _ kx x l r) = + case compare kx b of LT -> link kx x l (filterLt b r) + EQ -> l + GT -> filterLt b l +#if __GLASGOW_HASKELL__ +{-# INLINABLE filterLt #-} +#endif +-} + +{-------------------------------------------------------------------- + Split +--------------------------------------------------------------------} +-- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@ where +-- the keys in @map1@ are smaller than @k@ and the keys in @map2@ larger than @k@. +-- Any key equal to @k@ is found in neither @map1@ nor @map2@. +-- +-- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")]) +-- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a") +-- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a") +-- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty) +-- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty) + +split :: Ord k => k -> Map k a -> (Map k a,Map k a) +split !k0 t0 = toPair $ go k0 t0 + where + go k t = + case t of + Tip -> Tip :*: Tip + Bin _ kx x l r -> case compare k kx of + LT -> let (lt :*: gt) = go k l in lt :*: link kx x gt r + GT -> let (lt :*: gt) = go k r in link kx x l lt :*: gt + EQ -> (l :*: r) +#if __GLASGOW_HASKELL__ +{-# INLINABLE split #-} +#endif + +-- | /O(log n)/. The expression (@'splitLookup' k map@) splits a map just +-- like 'split' but also returns @'lookup' k map@. +-- +-- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")]) +-- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a") +-- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a") +-- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty) +-- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty) +splitLookup :: Ord k => k -> Map k a -> (Map k a,Maybe a,Map k a) +splitLookup k0 m = case go k0 m of + StrictTriple l mv r -> (l, mv, r) + where + go :: Ord k => k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a) + go !k t = + case t of + Tip -> StrictTriple Tip Nothing Tip + Bin _ kx x l r -> case compare k kx of + LT -> let StrictTriple lt z gt = go k l + !gt' = link kx x gt r + in StrictTriple lt z gt' + GT -> let StrictTriple lt z gt = go k r + !lt' = link kx x l lt + in StrictTriple lt' z gt + EQ -> StrictTriple l (Just x) r +#if __GLASGOW_HASKELL__ +{-# INLINABLE splitLookup #-} +#endif + +-- | A variant of 'splitLookup' that indicates only whether the +-- key was present, rather than producing its value. This is used to +-- implement 'intersection' to avoid allocating unnecessary 'Just' +-- constructors. +splitMember :: Ord k => k -> Map k a -> (Map k a,Bool,Map k a) +splitMember k0 m = case go k0 m of + StrictTriple l mv r -> (l, mv, r) + where + go :: Ord k => k -> Map k a -> StrictTriple (Map k a) Bool (Map k a) + go !k t = + case t of + Tip -> StrictTriple Tip False Tip + Bin _ kx x l r -> case compare k kx of + LT -> let StrictTriple lt z gt = go k l + !gt' = link kx x gt r + in StrictTriple lt z gt' + GT -> let StrictTriple lt z gt = go k r + !lt' = link kx x l lt + in StrictTriple lt' z gt + EQ -> StrictTriple l True r +#if __GLASGOW_HASKELL__ +{-# INLINABLE splitMember #-} +#endif + +data StrictTriple a b c = StrictTriple !a !b !c + +{-------------------------------------------------------------------- + Utility functions that maintain the balance properties of the tree. + All constructors assume that all values in [l] < [k] and all values + in [r] > [k], and that [l] and [r] are valid trees. + + In order of sophistication: + [Bin sz k x l r] The type constructor. + [bin k x l r] Maintains the correct size, assumes that both [l] + and [r] are balanced with respect to each other. + [balance k x l r] Restores the balance and size. + Assumes that the original tree was balanced and + that [l] or [r] has changed by at most one element. + [link k x l r] Restores balance and size. + + Furthermore, we can construct a new tree from two trees. Both operations + assume that all values in [l] < all values in [r] and that [l] and [r] + are valid: + [glue l r] Glues [l] and [r] together. Assumes that [l] and + [r] are already balanced with respect to each other. + [link2 l r] Merges two trees and restores balance. +--------------------------------------------------------------------} + +{-------------------------------------------------------------------- + Link +--------------------------------------------------------------------} +link :: k -> a -> Map k a -> Map k a -> Map k a +link kx x Tip r = insertMin kx x r +link kx x l Tip = insertMax kx x l +link kx x l@(Bin sizeL ky y ly ry) r@(Bin sizeR kz z lz rz) + | delta*sizeL < sizeR = balanceL kz z (link kx x l lz) rz + | delta*sizeR < sizeL = balanceR ky y ly (link kx x ry r) + | otherwise = bin kx x l r + + +-- insertMin and insertMax don't perform potentially expensive comparisons. +insertMax,insertMin :: k -> a -> Map k a -> Map k a +insertMax kx x t + = case t of + Tip -> singleton kx x + Bin _ ky y l r + -> balanceR ky y l (insertMax kx x r) + +insertMin kx x t + = case t of + Tip -> singleton kx x + Bin _ ky y l r + -> balanceL ky y (insertMin kx x l) r + +{-------------------------------------------------------------------- + [link2 l r]: merges two trees. +--------------------------------------------------------------------} +link2 :: Map k a -> Map k a -> Map k a +link2 Tip r = r +link2 l Tip = l +link2 l@(Bin sizeL kx x lx rx) r@(Bin sizeR ky y ly ry) + | delta*sizeL < sizeR = balanceL ky y (link2 l ly) ry + | delta*sizeR < sizeL = balanceR kx x lx (link2 rx r) + | otherwise = glue l r + +{-------------------------------------------------------------------- + [glue l r]: glues two trees together. + Assumes that [l] and [r] are already balanced with respect to each other. +--------------------------------------------------------------------} +glue :: Map k a -> Map k a -> Map k a +glue Tip r = r +glue l Tip = l +glue l@(Bin sl kl xl ll lr) r@(Bin sr kr xr rl rr) + | sl > sr = let !(MaxView km m l') = maxViewSure kl xl ll lr in balanceR km m l' r + | otherwise = let !(MinView km m r') = minViewSure kr xr rl rr in balanceL km m l r' + +data MinView k a = MinView !k a !(Map k a) +data MaxView k a = MaxView !k a !(Map k a) + +minViewSure :: k -> a -> Map k a -> Map k a -> MinView k a +minViewSure = go + where + go k x Tip r = MinView k x r + go k x (Bin _ kl xl ll lr) r = + case go kl xl ll lr of + MinView km xm l' -> MinView km xm (balanceR k x l' r) + +maxViewSure :: k -> a -> Map k a -> Map k a -> MaxView k a +maxViewSure = go + where + go k x l Tip = MaxView k x l + go k x l (Bin _ kr xr rl rr) = + case go kr xr rl rr of + MaxView km xm r' -> MaxView km xm (balanceL k x l r') + +-- | /O(log n)/. Delete and find the minimal element. +-- +-- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")]) +-- > deleteFindMin Error: can not return the minimal element of an empty map + +deleteFindMin :: Map k a -> ((k,a),Map k a) +deleteFindMin t = case minViewWithKey t of + Nothing -> (error "Map.deleteFindMin: can not return the minimal element of an empty map", Tip) + Just res -> res + +-- | /O(log n)/. Delete and find the maximal element. +-- +-- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")]) +-- > deleteFindMax empty Error: can not return the maximal element of an empty map + +deleteFindMax :: Map k a -> ((k,a),Map k a) +deleteFindMax t = case maxViewWithKey t of + Nothing -> (error "Map.deleteFindMax: can not return the maximal element of an empty map", Tip) + Just res -> res + +{-------------------------------------------------------------------- + [balance l x r] balances two trees with value x. + The sizes of the trees should balance after decreasing the + size of one of them. (a rotation). + + [delta] is the maximal relative difference between the sizes of + two trees, it corresponds with the [w] in Adams' paper. + [ratio] is the ratio between an outer and inner sibling of the + heavier subtree in an unbalanced setting. It determines + whether a double or single rotation should be performed + to restore balance. It is corresponds with the inverse + of $\alpha$ in Adam's article. + + Note that according to the Adam's paper: + - [delta] should be larger than 4.646 with a [ratio] of 2. + - [delta] should be larger than 3.745 with a [ratio] of 1.534. + + But the Adam's paper is erroneous: + - It can be proved that for delta=2 and delta>=5 there does + not exist any ratio that would work. + - Delta=4.5 and ratio=2 does not work. + + That leaves two reasonable variants, delta=3 and delta=4, + both with ratio=2. + + - A lower [delta] leads to a more 'perfectly' balanced tree. + - A higher [delta] performs less rebalancing. + + In the benchmarks, delta=3 is faster on insert operations, + and delta=4 has slightly better deletes. As the insert speedup + is larger, we currently use delta=3. + +--------------------------------------------------------------------} +delta,ratio :: Int +delta = 3 +ratio = 2 + +-- The balance function is equivalent to the following: +-- +-- balance :: k -> a -> Map k a -> Map k a -> Map k a +-- balance k x l r +-- | sizeL + sizeR <= 1 = Bin sizeX k x l r +-- | sizeR > delta*sizeL = rotateL k x l r +-- | sizeL > delta*sizeR = rotateR k x l r +-- | otherwise = Bin sizeX k x l r +-- where +-- sizeL = size l +-- sizeR = size r +-- sizeX = sizeL + sizeR + 1 +-- +-- rotateL :: a -> b -> Map a b -> Map a b -> Map a b +-- rotateL k x l r@(Bin _ _ _ ly ry) | size ly < ratio*size ry = singleL k x l r +-- | otherwise = doubleL k x l r +-- +-- rotateR :: a -> b -> Map a b -> Map a b -> Map a b +-- rotateR k x l@(Bin _ _ _ ly ry) r | size ry < ratio*size ly = singleR k x l r +-- | otherwise = doubleR k x l r +-- +-- singleL, singleR :: a -> b -> Map a b -> Map a b -> Map a b +-- singleL k1 x1 t1 (Bin _ k2 x2 t2 t3) = bin k2 x2 (bin k1 x1 t1 t2) t3 +-- singleR k1 x1 (Bin _ k2 x2 t1 t2) t3 = bin k2 x2 t1 (bin k1 x1 t2 t3) +-- +-- doubleL, doubleR :: a -> b -> Map a b -> Map a b -> Map a b +-- doubleL k1 x1 t1 (Bin _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = bin k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4) +-- doubleR k1 x1 (Bin _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = bin k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4) +-- +-- It is only written in such a way that every node is pattern-matched only once. + +balance :: k -> a -> Map k a -> Map k a -> Map k a +balance k x l r = case l of + Tip -> case r of + Tip -> Bin 1 k x Tip Tip + (Bin _ _ _ Tip Tip) -> Bin 2 k x Tip r + (Bin _ rk rx Tip rr@(Bin _ _ _ _ _)) -> Bin 3 rk rx (Bin 1 k x Tip Tip) rr + (Bin _ rk rx (Bin _ rlk rlx _ _) Tip) -> Bin 3 rlk rlx (Bin 1 k x Tip Tip) (Bin 1 rk rx Tip Tip) + (Bin rs rk rx rl@(Bin rls rlk rlx rll rlr) rr@(Bin rrs _ _ _ _)) + | rls < ratio*rrs -> Bin (1+rs) rk rx (Bin (1+rls) k x Tip rl) rr + | otherwise -> Bin (1+rs) rlk rlx (Bin (1+size rll) k x Tip rll) (Bin (1+rrs+size rlr) rk rx rlr rr) + + (Bin ls lk lx ll lr) -> case r of + Tip -> case (ll, lr) of + (Tip, Tip) -> Bin 2 k x l Tip + (Tip, (Bin _ lrk lrx _ _)) -> Bin 3 lrk lrx (Bin 1 lk lx Tip Tip) (Bin 1 k x Tip Tip) + ((Bin _ _ _ _ _), Tip) -> Bin 3 lk lx ll (Bin 1 k x Tip Tip) + ((Bin lls _ _ _ _), (Bin lrs lrk lrx lrl lrr)) + | lrs < ratio*lls -> Bin (1+ls) lk lx ll (Bin (1+lrs) k x lr Tip) + | otherwise -> Bin (1+ls) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+size lrr) k x lrr Tip) + (Bin rs rk rx rl rr) + | rs > delta*ls -> case (rl, rr) of + (Bin rls rlk rlx rll rlr, Bin rrs _ _ _ _) + | rls < ratio*rrs -> Bin (1+ls+rs) rk rx (Bin (1+ls+rls) k x l rl) rr + | otherwise -> Bin (1+ls+rs) rlk rlx (Bin (1+ls+size rll) k x l rll) (Bin (1+rrs+size rlr) rk rx rlr rr) + (_, _) -> error "Failure in Data.Map.balance" + | ls > delta*rs -> case (ll, lr) of + (Bin lls _ _ _ _, Bin lrs lrk lrx lrl lrr) + | lrs < ratio*lls -> Bin (1+ls+rs) lk lx ll (Bin (1+rs+lrs) k x lr r) + | otherwise -> Bin (1+ls+rs) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+rs+size lrr) k x lrr r) + (_, _) -> error "Failure in Data.Map.balance" + | otherwise -> Bin (1+ls+rs) k x l r +{-# NOINLINE balance #-} + +-- Functions balanceL and balanceR are specialised versions of balance. +-- balanceL only checks whether the left subtree is too big, +-- balanceR only checks whether the right subtree is too big. + +-- balanceL is called when left subtree might have been inserted to or when +-- right subtree might have been deleted from. +balanceL :: k -> a -> Map k a -> Map k a -> Map k a +balanceL k x l r = case r of + Tip -> case l of + Tip -> Bin 1 k x Tip Tip + (Bin _ _ _ Tip Tip) -> Bin 2 k x l Tip + (Bin _ lk lx Tip (Bin _ lrk lrx _ _)) -> Bin 3 lrk lrx (Bin 1 lk lx Tip Tip) (Bin 1 k x Tip Tip) + (Bin _ lk lx ll@(Bin _ _ _ _ _) Tip) -> Bin 3 lk lx ll (Bin 1 k x Tip Tip) + (Bin ls lk lx ll@(Bin lls _ _ _ _) lr@(Bin lrs lrk lrx lrl lrr)) + | lrs < ratio*lls -> Bin (1+ls) lk lx ll (Bin (1+lrs) k x lr Tip) + | otherwise -> Bin (1+ls) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+size lrr) k x lrr Tip) + + (Bin rs _ _ _ _) -> case l of + Tip -> Bin (1+rs) k x Tip r + + (Bin ls lk lx ll lr) + | ls > delta*rs -> case (ll, lr) of + (Bin lls _ _ _ _, Bin lrs lrk lrx lrl lrr) + | lrs < ratio*lls -> Bin (1+ls+rs) lk lx ll (Bin (1+rs+lrs) k x lr r) + | otherwise -> Bin (1+ls+rs) lrk lrx (Bin (1+lls+size lrl) lk lx ll lrl) (Bin (1+rs+size lrr) k x lrr r) + (_, _) -> error "Failure in Data.Map.balanceL" + | otherwise -> Bin (1+ls+rs) k x l r +{-# NOINLINE balanceL #-} + +-- balanceR is called when right subtree might have been inserted to or when +-- left subtree might have been deleted from. +balanceR :: k -> a -> Map k a -> Map k a -> Map k a +balanceR k x l r = case l of + Tip -> case r of + Tip -> Bin 1 k x Tip Tip + (Bin _ _ _ Tip Tip) -> Bin 2 k x Tip r + (Bin _ rk rx Tip rr@(Bin _ _ _ _ _)) -> Bin 3 rk rx (Bin 1 k x Tip Tip) rr + (Bin _ rk rx (Bin _ rlk rlx _ _) Tip) -> Bin 3 rlk rlx (Bin 1 k x Tip Tip) (Bin 1 rk rx Tip Tip) + (Bin rs rk rx rl@(Bin rls rlk rlx rll rlr) rr@(Bin rrs _ _ _ _)) + | rls < ratio*rrs -> Bin (1+rs) rk rx (Bin (1+rls) k x Tip rl) rr + | otherwise -> Bin (1+rs) rlk rlx (Bin (1+size rll) k x Tip rll) (Bin (1+rrs+size rlr) rk rx rlr rr) + + (Bin ls _ _ _ _) -> case r of + Tip -> Bin (1+ls) k x l Tip + + (Bin rs rk rx rl rr) + | rs > delta*ls -> case (rl, rr) of + (Bin rls rlk rlx rll rlr, Bin rrs _ _ _ _) + | rls < ratio*rrs -> Bin (1+ls+rs) rk rx (Bin (1+ls+rls) k x l rl) rr + | otherwise -> Bin (1+ls+rs) rlk rlx (Bin (1+ls+size rll) k x l rll) (Bin (1+rrs+size rlr) rk rx rlr rr) + (_, _) -> error "Failure in Data.Map.balanceR" + | otherwise -> Bin (1+ls+rs) k x l r +{-# NOINLINE balanceR #-} + + +{-------------------------------------------------------------------- + The bin constructor maintains the size of the tree +--------------------------------------------------------------------} +bin :: k -> a -> Map k a -> Map k a -> Map k a +bin k x l r + = Bin (size l + size r + 1) k x l r +{-# INLINE bin #-} + + +{-------------------------------------------------------------------- + Eq converts the tree to a list. In a lazy setting, this + actually seems one of the faster methods to compare two trees + and it is certainly the simplest :-) +--------------------------------------------------------------------} +instance (Eq k,Eq a) => Eq (Map k a) where + t1 == t2 = (size t1 == size t2) && (toAscList t1 == toAscList t2) + +{-------------------------------------------------------------------- + Ord +--------------------------------------------------------------------} + +instance (Ord k, Ord v) => Ord (Map k v) where + compare m1 m2 = compare (toAscList m1) (toAscList m2) + +#if MIN_VERSION_base(4,9,0) +{-------------------------------------------------------------------- + Lifted instances +--------------------------------------------------------------------} + +instance Eq2 Map where + liftEq2 eqk eqv m n = + size m == size n && liftEq (liftEq2 eqk eqv) (toList m) (toList n) + +instance Eq k => Eq1 (Map k) where + liftEq = liftEq2 (==) + +instance Ord2 Map where + liftCompare2 cmpk cmpv m n = + liftCompare (liftCompare2 cmpk cmpv) (toList m) (toList n) + +instance Ord k => Ord1 (Map k) where + liftCompare = liftCompare2 compare + +instance Show2 Map where + liftShowsPrec2 spk slk spv slv d m = + showsUnaryWith (liftShowsPrec sp sl) "fromList" d (toList m) + where + sp = liftShowsPrec2 spk slk spv slv + sl = liftShowList2 spk slk spv slv + +instance Show k => Show1 (Map k) where + liftShowsPrec = liftShowsPrec2 showsPrec showList + +instance (Ord k, Read k) => Read1 (Map k) where + liftReadsPrec rp rl = readsData $ + readsUnaryWith (liftReadsPrec rp' rl') "fromList" fromList + where + rp' = liftReadsPrec rp rl + rl' = liftReadList rp rl +#endif + +{-------------------------------------------------------------------- + Functor +--------------------------------------------------------------------} +instance Functor (Map k) where + fmap f m = map f m +#ifdef __GLASGOW_HASKELL__ + _ <$ Tip = Tip + a <$ (Bin sx kx _ l r) = Bin sx kx a (a <$ l) (a <$ r) +#endif + +instance Traversable (Map k) where + traverse f = traverseWithKey (\_ -> f) + {-# INLINE traverse #-} + +instance Foldable.Foldable (Map k) where + fold = go + where go Tip = mempty + go (Bin 1 _ v _ _) = v + go (Bin _ _ v l r) = go l `mappend` (v `mappend` go r) + {-# INLINABLE fold #-} + foldr = foldr + {-# INLINE foldr #-} + foldl = foldl + {-# INLINE foldl #-} + foldMap f t = go t + where go Tip = mempty + go (Bin 1 _ v _ _) = f v + go (Bin _ _ v l r) = go l `mappend` (f v `mappend` go r) + {-# INLINE foldMap #-} + +#if MIN_VERSION_base(4,6,0) + foldl' = foldl' + {-# INLINE foldl' #-} + foldr' = foldr' + {-# INLINE foldr' #-} +#endif +#if MIN_VERSION_base(4,8,0) + length = size + {-# INLINE length #-} + null = null + {-# INLINE null #-} + toList = elems -- NB: Foldable.toList /= Map.toList + {-# INLINE toList #-} + elem = go + where go !_ Tip = False + go x (Bin _ _ v l r) = x == v || go x l || go x r + {-# INLINABLE elem #-} + maximum = start + where start Tip = error "Map.Foldable.maximum: called with empty map" + start (Bin _ _ v l r) = go (go v l) r + + go !m Tip = m + go m (Bin _ _ v l r) = go (go (max m v) l) r + {-# INLINABLE maximum #-} + minimum = start + where start Tip = error "Map.Foldable.minumum: called with empty map" + start (Bin _ _ v l r) = go (go v l) r + + go !m Tip = m + go m (Bin _ _ v l r) = go (go (min m v) l) r + {-# INLINABLE minimum #-} + sum = foldl' (+) 0 + {-# INLINABLE sum #-} + product = foldl' (*) 1 + {-# INLINABLE product #-} +#endif + +instance (NFData k, NFData a) => NFData (Map k a) where + rnf Tip = () + rnf (Bin _ kx x l r) = rnf kx `seq` rnf x `seq` rnf l `seq` rnf r + +{-------------------------------------------------------------------- + Read +--------------------------------------------------------------------} +instance (Ord k, Read k, Read e) => Read (Map k e) 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 + +{-------------------------------------------------------------------- + Show +--------------------------------------------------------------------} +instance (Show k, Show a) => Show (Map k a) where + showsPrec d m = showParen (d > 10) $ + showString "fromList " . shows (toList m) + +{-------------------------------------------------------------------- + Typeable +--------------------------------------------------------------------} + +INSTANCE_TYPEABLE2(Map) + +{-------------------------------------------------------------------- + Utilities +--------------------------------------------------------------------} + +-- | /O(1)/. Decompose a map into pieces based on the structure of the underlying +-- tree. This function is useful for consuming a map in parallel. +-- +-- No guarantee is made as to the sizes of the pieces; an internal, but +-- deterministic process determines this. However, it is guaranteed that the pieces +-- returned will be in ascending order (all elements in the first submap less than all +-- elements in the second, and so on). +-- +-- Examples: +-- +-- > splitRoot (fromList (zip [1..6] ['a'..])) == +-- > [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]] +-- +-- > splitRoot empty == [] +-- +-- Note that the current implementation does not return more than three submaps, +-- but you should not depend on this behaviour because it can change in the +-- future without notice. +splitRoot :: Map k b -> [Map k b] +splitRoot orig = + case orig of + Tip -> [] + Bin _ k v l r -> [l, singleton k v, r] +{-# INLINE splitRoot #-} diff --git a/Data/Map/Internal/Debug.hs b/Data/Map/Internal/Debug.hs new file mode 100644 --- /dev/null +++ b/Data/Map/Internal/Debug.hs @@ -0,0 +1,144 @@ +{-# LANGUAGE CPP #-} +#include "containers.h" + +module Data.Map.Internal.Debug where + +import Data.Map.Internal (Map (..), size, delta) +import Control.Monad (guard) + +-- | /O(n)/. Show the tree that implements the map. The tree is shown +-- in a compressed, hanging format. See 'showTreeWith'. +showTree :: (Show k,Show a) => Map k a -> String +showTree m + = showTreeWith showElem True False m + where + showElem k x = show k ++ ":=" ++ show x + + +{- | /O(n)/. The expression (@'showTreeWith' showelem hang wide map@) shows + the tree that implements the map. Elements are shown using the @showElem@ function. 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. + +> Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]] +> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t +> (4,()) +> +--(2,()) +> | +--(1,()) +> | +--(3,()) +> +--(5,()) +> +> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t +> (4,()) +> | +> +--(2,()) +> | | +> | +--(1,()) +> | | +> | +--(3,()) +> | +> +--(5,()) +> +> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t +> +--(5,()) +> | +> (4,()) +> | +> | +--(3,()) +> | | +> +--(2,()) +> | +> +--(1,()) + +-} +showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String +showTreeWith showelem hang wide t + | hang = (showsTreeHang showelem wide [] t) "" + | otherwise = (showsTree showelem wide [] [] t) "" + +showsTree :: (k -> a -> String) -> Bool -> [String] -> [String] -> Map k a -> ShowS +showsTree showelem wide lbars rbars t + = case t of + Tip -> showsBars lbars . showString "|\n" + Bin _ kx x Tip Tip + -> showsBars lbars . showString (showelem kx x) . showString "\n" + Bin _ kx x l r + -> showsTree showelem wide (withBar rbars) (withEmpty rbars) r . + showWide wide rbars . + showsBars lbars . showString (showelem kx x) . showString "\n" . + showWide wide lbars . + showsTree showelem wide (withEmpty lbars) (withBar lbars) l + +showsTreeHang :: (k -> a -> String) -> Bool -> [String] -> Map k a -> ShowS +showsTreeHang showelem wide bars t + = case t of + Tip -> showsBars bars . showString "|\n" + Bin _ kx x Tip Tip + -> showsBars bars . showString (showelem kx x) . showString "\n" + Bin _ kx x l r + -> showsBars bars . showString (showelem kx x) . showString "\n" . + showWide wide bars . + showsTreeHang showelem wide (withBar bars) l . + showWide wide bars . + showsTreeHang showelem wide (withEmpty bars) r + +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 + +node :: String +node = "+--" + +withBar, withEmpty :: [String] -> [String] +withBar bars = "| ":bars +withEmpty bars = " ":bars + +{-------------------------------------------------------------------- + Assertions +--------------------------------------------------------------------} +-- | /O(n)/. Test if the internal map structure is valid. +-- +-- > valid (fromAscList [(3,"b"), (5,"a")]) == True +-- > valid (fromAscList [(5,"a"), (3,"b")]) == False + +valid :: Ord k => Map k a -> Bool +valid t + = balanced t && ordered t && validsize t + +-- | Test if the keys are ordered correctly. +ordered :: Ord a => Map a b -> Bool +ordered t + = bounded (const True) (const True) t + where + bounded lo hi t' + = case t' of + Tip -> True + Bin _ kx _ l r -> (lo kx) && (hi kx) && bounded lo (kx) hi r + +-- | Test if a map obeys the balance invariants. +balanced :: Map k a -> Bool +balanced t + = case t of + Tip -> True + Bin _ _ _ l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) && + balanced l && balanced r + +-- | Test if each node of a map reports its size correctly. +validsize :: Map a b -> Bool +validsize t = case slowSize t of + Nothing -> False + Just _ -> True + where + slowSize Tip = Just 0 + slowSize (Bin sz _ _ l r) = do + ls <- slowSize l + rs <- slowSize r + guard (sz == ls + rs + 1) + return sz diff --git a/Data/Map/Internal/DeprecatedShowTree.hs b/Data/Map/Internal/DeprecatedShowTree.hs new file mode 100644 --- /dev/null +++ b/Data/Map/Internal/DeprecatedShowTree.hs @@ -0,0 +1,56 @@ +{-# LANGUAGE CPP #-} + +#include "containers.h" + +-- | This module simply holds deprecated copies of functions from +-- Data.Map.Internal.Debug. +module Data.Map.Internal.DeprecatedShowTree where + +import qualified Data.Map.Internal.Debug as Debug +import Data.Map.Internal (Map) + +-- | /O(n)/. Show the tree that implements the map. The tree is shown +-- in a compressed, hanging format. See 'showTreeWith'. +{-# DEPRECATED showTree "'showTree' is now in \"Data.Map.Internal.Debug\"" #-} +showTree :: (Show k,Show a) => Map k a -> String +showTree = Debug.showTree + +{- | /O(n)/. The expression (@'showTreeWith' showelem hang wide map@) shows + the tree that implements the map. Elements are shown using the @showElem@ function. 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. + +> Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]] +> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t +> (4,()) +> +--(2,()) +> | +--(1,()) +> | +--(3,()) +> +--(5,()) +> +> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t +> (4,()) +> | +> +--(2,()) +> | | +> | +--(1,()) +> | | +> | +--(3,()) +> | +> +--(5,()) +> +> Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t +> +--(5,()) +> | +> (4,()) +> | +> | +--(3,()) +> | | +> +--(2,()) +> | +> +--(1,()) + +-} +{-# DEPRECATED showTreeWith "'showTreeWith' is now in \"Data.Map.Internal.Debug\"" #-} +showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String +showTreeWith = Debug.showTreeWith diff --git a/Data/Map/Lazy.hs b/Data/Map/Lazy.hs --- a/Data/Map/Lazy.hs +++ b/Data/Map/Lazy.hs @@ -66,14 +66,14 @@ Map -- instance Eq,Show,Read -- * Operators - , (!), (\\) + , (!), (!?), (\\) -- * Query - , M.null + , null , size , member , notMember - , M.lookup + , lookup , findWithDefault , lookupLT , lookupGT @@ -128,7 +128,7 @@ -- * Traversal -- ** Map - , M.map + , map , mapWithKey , traverseWithKey , traverseMaybeWithKey @@ -140,8 +140,8 @@ , mapKeysMonotonic -- * Folds - , M.foldr - , M.foldl + , foldr + , foldl , foldrWithKey , foldlWithKey , foldMapWithKey @@ -178,7 +178,7 @@ , fromDistinctDescList -- * Filter - , M.filter + , filter , filterWithKey , restrictKeys , withoutKeys @@ -212,6 +212,8 @@ , splitAt -- * Min\/Max + , lookupMin + , lookupMax , findMin , findMax , deleteMin @@ -233,7 +235,9 @@ , valid ) where -import Data.Map.Base as M +import Data.Map.Internal +import Data.Map.Internal.DeprecatedShowTree (showTree, showTreeWith) +import Data.Map.Internal.Debug (valid) import Prelude () -- $strictness diff --git a/Data/Map/Lazy/Merge.hs b/Data/Map/Lazy/Merge.hs --- a/Data/Map/Lazy/Merge.hs +++ b/Data/Map/Lazy/Merge.hs @@ -1,23 +1,12 @@ {-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} -#endif #if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 {-# LANGUAGE Safe #-} #endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE RoleAnnotations #-} -{-# LANGUAGE TypeFamilies #-} -#define USE_MAGIC_PROXY 1 -#endif -#if USE_MAGIC_PROXY -{-# LANGUAGE MagicHash #-} -#endif - #include "containers.h" +{-# OPTIONS_HADDOCK hide #-} + ----------------------------------------------------------------------------- -- | -- Module : Data.Map.Lazy.Merge @@ -45,59 +34,7 @@ -- inefficient in many cases and should usually be avoided. The instances -- for 'WhenMatched' tactics should not pose any major efficiency problems. -module Data.Map.Lazy.Merge ( - -- ** Simple merge tactic types - SimpleWhenMissing - , SimpleWhenMatched - - -- ** General combining function - , merge - - -- *** @WhenMatched@ tactics - , zipWithMaybeMatched - , zipWithMatched - - -- *** @WhenMissing@ tactics - , mapMaybeMissing - , dropMissing - , preserveMissing - , mapMissing - , filterMissing - - -- ** Applicative merge tactic types - , WhenMissing - , WhenMatched - - -- ** Applicative general combining function - , mergeA - - -- *** @WhenMatched@ tactics - -- | The tactics described for 'merge' work for - -- 'mergeA' as well. Furthermore, the following - -- are available. - , zipWithMaybeAMatched - , zipWithAMatched - - -- *** @WhenMissing@ tactics - -- | The tactics described for 'merge' work for - -- 'mergeA' as well. Furthermore, the following - -- are available. - , traverseMaybeMissing - , traverseMissing - , filterAMissing - - -- *** Covariant maps for tactics - , mapWhenMissing - , mapWhenMatched - - -- *** Contravariant maps for tactics - , lmapWhenMissing - , contramapFirstWhenMatched - , contramapSecondWhenMatched - - -- *** Miscellaneous tactic functions - , runWhenMatched - , runWhenMissing - ) where +module Data.Map.Lazy.Merge {-# DEPRECATED "Use \"Data.Map.Merge.Lazy\"." #-} + ( module Data.Map.Merge.Lazy ) where -import Data.Map.Base +import Data.Map.Merge.Lazy diff --git a/Data/Map/Merge/Lazy.hs b/Data/Map/Merge/Lazy.hs new file mode 100644 --- /dev/null +++ b/Data/Map/Merge/Lazy.hs @@ -0,0 +1,103 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Safe #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE TypeFamilies #-} +#define USE_MAGIC_PROXY 1 +#endif + +#if USE_MAGIC_PROXY +{-# LANGUAGE MagicHash #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Map.Merge.Lazy +-- Copyright : (c) David Feuer 2016 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- This module defines an API for writing functions that merge two +-- maps. The key functions are 'merge' and 'mergeA'. +-- Each of these can be used with several different \"merge tactics\". +-- +-- The 'merge' and 'mergeA' functions are shared by +-- the lazy and strict modules. Only the choice of merge tactics +-- determines strictness. If you use 'Data.Map.Strict.Merge.mapMissing' +-- from "Data.Map.Strict.Merge" then the results will be forced before +-- they are inserted. If you use 'Data.Map.Lazy.Merge.mapMissing' from +-- this module then they will not. +-- +-- == Efficiency note +-- +-- The 'Category', 'Applicative', and 'Monad' instances for 'WhenMissing' +-- tactics are included because they are valid. However, they are +-- inefficient in many cases and should usually be avoided. The instances +-- for 'WhenMatched' tactics should not pose any major efficiency problems. + +module Data.Map.Merge.Lazy ( + -- ** Simple merge tactic types + SimpleWhenMissing + , SimpleWhenMatched + + -- ** General combining function + , merge + + -- *** @WhenMatched@ tactics + , zipWithMaybeMatched + , zipWithMatched + + -- *** @WhenMissing@ tactics + , mapMaybeMissing + , dropMissing + , preserveMissing + , mapMissing + , filterMissing + + -- ** Applicative merge tactic types + , WhenMissing + , WhenMatched + + -- ** Applicative general combining function + , mergeA + + -- *** @WhenMatched@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , zipWithMaybeAMatched + , zipWithAMatched + + -- *** @WhenMissing@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , traverseMaybeMissing + , traverseMissing + , filterAMissing + + -- *** Covariant maps for tactics + , mapWhenMissing + , mapWhenMatched + + -- *** Contravariant maps for tactics + , lmapWhenMissing + , contramapFirstWhenMatched + , contramapSecondWhenMatched + + -- *** Miscellaneous tactic functions + , runWhenMatched + , runWhenMissing + ) where + +import Data.Map.Internal diff --git a/Data/Map/Merge/Strict.hs b/Data/Map/Merge/Strict.hs new file mode 100644 --- /dev/null +++ b/Data/Map/Merge/Strict.hs @@ -0,0 +1,99 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Safe #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE TypeFamilies #-} +#define USE_MAGIC_PROXY 1 +#endif + +#if USE_MAGIC_PROXY +{-# LANGUAGE MagicHash #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Map.Merge.Strict +-- Copyright : (c) David Feuer 2016 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- This module defines an API for writing functions that merge two +-- maps. The key functions are 'merge' and 'mergeA'. +-- Each of these can be used with several different \"merge tactics\". +-- +-- The 'merge' and 'mergeA' functions are shared by +-- the lazy and strict modules. Only the choice of merge tactics +-- determines strictness. If you use 'Data.Map.Strict.Merge.mapMissing' +-- from this module then the results will be forced before they are +-- inserted. If you use 'Data.Map.Lazy.Merge.mapMissing' from +-- "Data.Map.Lazy.Merge" then they will not. +-- +-- == Efficiency note +-- +-- The 'Category', 'Applicative', and 'Monad' instances for 'WhenMissing' +-- tactics are included because they are valid. However, they are +-- inefficient in many cases and should usually be avoided. The instances +-- for 'WhenMatched' tactics should not pose any major efficiency problems. + +module Data.Map.Merge.Strict ( + -- ** Simple merge tactic types + SimpleWhenMissing + , SimpleWhenMatched + + -- ** General combining function + , merge + + -- *** @WhenMatched@ tactics + , zipWithMaybeMatched + , zipWithMatched + + -- *** @WhenMissing@ tactics + , mapMaybeMissing + , dropMissing + , preserveMissing + , mapMissing + , filterMissing + + -- ** Applicative merge tactic types + , WhenMissing + , WhenMatched + + -- ** Applicative general combining function + , mergeA + + -- *** @WhenMatched@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , zipWithMaybeAMatched + , zipWithAMatched + + -- *** @WhenMissing@ tactics + -- | The tactics described for 'merge' work for + -- 'mergeA' as well. Furthermore, the following + -- are available. + , traverseMaybeMissing + , traverseMissing + , filterAMissing + + -- ** Covariant maps for tactics + , mapWhenMissing + , mapWhenMatched + + -- ** Miscellaneous functions on tactics + + , runWhenMatched + , runWhenMissing + ) where + +import Data.Map.Strict.Internal diff --git a/Data/Map/Strict.hs b/Data/Map/Strict.hs --- a/Data/Map/Strict.hs +++ b/Data/Map/Strict.hs @@ -63,7 +63,7 @@ -- on strict maps, the resulting maps will be lazy. ----------------------------------------------------------------------------- --- See the notes at the beginning of Data.Map.Base. +-- See the notes at the beginning of Data.Map.Internal. module Data.Map.Strict ( @@ -74,7 +74,7 @@ Map -- instance Eq,Show,Read -- * Operators - , (!), (\\) + , (!), (!?), (\\) -- * Query , null @@ -221,6 +221,8 @@ , splitAt -- * Min\/Max + , lookupMin + , lookupMax , findMin , findMax , deleteMin diff --git a/Data/Map/Strict/Internal.hs b/Data/Map/Strict/Internal.hs --- a/Data/Map/Strict/Internal.hs +++ b/Data/Map/Strict/Internal.hs @@ -4,8 +4,6 @@ {-# LANGUAGE Trustworthy #-} #endif -{-# OPTIONS_HADDOCK hide #-} - #include "containers.h" ----------------------------------------------------------------------------- @@ -79,7 +77,7 @@ -- on strict maps, the resulting maps will be lazy. ----------------------------------------------------------------------------- --- See the notes at the beginning of Data.Map.Base. +-- See the notes at the beginning of Data.Map.Internal. module Data.Map.Strict.Internal ( @@ -90,7 +88,7 @@ Map(..) -- instance Eq,Show,Read -- * Operators - , (!), (\\) + , (!), (!?), (\\) -- * Query , null @@ -275,6 +273,8 @@ , splitAt -- * Min\/Max + , lookupMin + , lookupMax , findMin , findMax , deleteMin @@ -294,16 +294,11 @@ , showTree , showTreeWith , valid - - , bin - , balanced - , link - , link2 ) where import Prelude hiding (lookup,map,filter,foldr,foldl,null,take,drop,splitAt) -import Data.Map.Base +import Data.Map.Internal ( Map (..) , AreWeStrict (..) , WhenMissing (..) @@ -319,6 +314,7 @@ , merge , mergeA , (!) + , (!?) , (\\) , assocs , atKeyImpl @@ -370,6 +366,8 @@ , lookupIndex , lookupLE , lookupLT + , lookupMin + , lookupMax , mapKeys , mapKeysMonotonic , maxView @@ -383,8 +381,6 @@ , partition , partitionWithKey , restrictKeys - , showTree - , showTreeWith , size , spanAntitone , split @@ -398,18 +394,18 @@ , toDescList , union , unions - , valid , withoutKeys ) -import Data.Map.Base (bin, balanced) +import Data.Map.Internal.DeprecatedShowTree (showTree, showTreeWith) +import Data.Map.Internal.Debug (valid) import Control.Applicative (Const (..)) #if !MIN_VERSION_base(4,8,0) import Control.Applicative (Applicative (..), (<$>)) #endif -import qualified Data.Set.Base as Set -import Data.Utils.StrictFold -import Data.Utils.StrictPair +import qualified Data.Set.Internal as Set +import Utils.Containers.Internal.StrictFold +import Utils.Containers.Internal.StrictPair import Data.Bits (shiftL, shiftR) #if __GLASGOW_HASKELL__ >= 709 @@ -461,7 +457,7 @@ -- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x' -- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a' --- See Map.Base.Note: Local 'go' functions and capturing +-- See Map.Internal.Note: Local 'go' functions and capturing findWithDefault :: Ord k => a -> k -> Map k a -> a findWithDefault def k = k `seq` go where @@ -501,7 +497,7 @@ -- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')] -- > insert 5 'x' empty == singleton 5 'x' --- See Map.Base.Note: Type of local 'go' function +-- See Map.Internal.Note: Type of local 'go' function insert :: Ord k => k -> a -> Map k a -> Map k a insert = go where @@ -572,7 +568,7 @@ -- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")] -- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx" --- See Map.Base.Note: Type of local 'go' function +-- See Map.Internal.Note: Type of local 'go' function insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a insertWithKey = go where @@ -627,7 +623,7 @@ -- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")]) -- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")]) --- See Map.Base.Note: Type of local 'go' function +-- See Map.Internal.Note: Type of local 'go' function insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a) insertLookupWithKey f0 kx0 x0 t0 = toPair $ go f0 kx0 x0 t0 @@ -720,7 +716,7 @@ -- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")] -- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a" --- See Map.Base.Note: Type of local 'go' function +-- See Map.Internal.Note: Type of local 'go' function updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a updateWithKey = go where @@ -748,7 +744,7 @@ -- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")]) -- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a") --- See Map.Base.Note: Type of local 'go' function +-- See Map.Internal.Note: Type of local 'go' function updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a,Map k a) updateLookupWithKey f0 k0 t0 = toPair $ go f0 k0 t0 where @@ -781,7 +777,7 @@ -- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")] -- > alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")] --- See Map.Base.Note: Type of local 'go' function +-- See Map.Internal.Note: Type of local 'go' function alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a alter = go where @@ -1679,16 +1675,18 @@ fromDistinctAscList ((kx0, x0) : xs0) = x0 `seq` go (1::Int) (Bin 1 kx0 x0 Tip Tip) xs0 where go !_ t [] = t - go s l ((kx, x) : xs) = case create s xs of - (r, ys) -> x `seq` go (s `shiftL` 1) (link kx x l r) ys + go s l ((kx, x) : xs) = + case create s xs of + (r :*: ys) -> x `seq` let !t' = link kx x l r + in go (s `shiftL` 1) t' ys - create !_ [] = (Tip, []) + create !_ [] = (Tip :*: []) create s xs@(x' : xs') - | s == 1 = case x' of (kx, x) -> x `seq` (Bin 1 kx x Tip Tip, xs') + | s == 1 = case x' of (kx, x) -> x `seq` (Bin 1 kx x Tip Tip :*: xs') | otherwise = case create (s `shiftR` 1) xs of - res@(_, []) -> res - (l, (ky, y):ys) -> case create (s `shiftR` 1) ys of - (r, zs) -> y `seq` (link ky y l r, zs) + res@(_ :*: []) -> res + (l :*: (ky, y):ys) -> case create (s `shiftR` 1) ys of + (r :*: zs) -> y `seq` (link ky y l r :*: zs) -- | /O(n)/. Build a map from a descending list of distinct elements in linear time. -- /The precondition is not checked./ @@ -1704,13 +1702,15 @@ fromDistinctDescList ((kx0, x0) : xs0) = x0 `seq` go (1::Int) (Bin 1 kx0 x0 Tip Tip) xs0 where go !_ t [] = t - go s r ((kx, x) : xs) = case create s xs of - (l, ys) -> x `seq` go (s `shiftL` 1) (link kx x l r) ys + go s r ((kx, x) : xs) = + case create s xs of + (l :*: ys) -> x `seq` let !t' = link kx x l r + in go (s `shiftL` 1) t' ys - create !_ [] = (Tip, []) + create !_ [] = (Tip :*: []) create s xs@(x' : xs') - | s == 1 = case x' of (kx, x) -> x `seq` (Bin 1 kx x Tip Tip, xs') + | s == 1 = case x' of (kx, x) -> x `seq` (Bin 1 kx x Tip Tip :*: xs') | otherwise = case create (s `shiftR` 1) xs of - res@(_, []) -> res - (r, (ky, y):ys) -> case create (s `shiftR` 1) ys of - (l, zs) -> y `seq` (link ky y l r, zs) + res@(_ :*: []) -> res + (r :*: (ky, y):ys) -> case create (s `shiftR` 1) ys of + (l :*: zs) -> y `seq` (link ky y l r :*: zs) diff --git a/Data/Map/Strict/Merge.hs b/Data/Map/Strict/Merge.hs --- a/Data/Map/Strict/Merge.hs +++ b/Data/Map/Strict/Merge.hs @@ -1,23 +1,12 @@ {-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} -#endif #if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 {-# LANGUAGE Safe #-} #endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE RoleAnnotations #-} -{-# LANGUAGE TypeFamilies #-} -#define USE_MAGIC_PROXY 1 -#endif -#if USE_MAGIC_PROXY -{-# LANGUAGE MagicHash #-} -#endif - #include "containers.h" +{-# OPTIONS_HADDOCK hide #-} + ----------------------------------------------------------------------------- -- | -- Module : Data.Map.Strict.Merge @@ -45,55 +34,7 @@ -- inefficient in many cases and should usually be avoided. The instances -- for 'WhenMatched' tactics should not pose any major efficiency problems. -module Data.Map.Strict.Merge ( - -- ** Simple merge tactic types - SimpleWhenMissing - , SimpleWhenMatched - - -- ** General combining function - , merge - - -- *** @WhenMatched@ tactics - , zipWithMaybeMatched - , zipWithMatched - - -- *** @WhenMissing@ tactics - , mapMaybeMissing - , dropMissing - , preserveMissing - , mapMissing - , filterMissing - - -- ** Applicative merge tactic types - , WhenMissing - , WhenMatched - - -- ** Applicative general combining function - , mergeA - - -- *** @WhenMatched@ tactics - -- | The tactics described for 'merge' work for - -- 'mergeA' as well. Furthermore, the following - -- are available. - , zipWithMaybeAMatched - , zipWithAMatched - - -- *** @WhenMissing@ tactics - -- | The tactics described for 'merge' work for - -- 'mergeA' as well. Furthermore, the following - -- are available. - , traverseMaybeMissing - , traverseMissing - , filterAMissing - - -- ** Covariant maps for tactics - , mapWhenMissing - , mapWhenMatched - - -- ** Miscellaneous functions on tactics - - , runWhenMatched - , runWhenMissing - ) where +module Data.Map.Strict.Merge {-# DEPRECATED "Use \"Data.Map.Merge.Strict\"." #-} + ( module Data.Map.Merge.Strict ) where -import Data.Map.Strict.Internal +import Data.Map.Merge.Strict diff --git a/Data/Sequence.hs b/Data/Sequence.hs --- a/Data/Sequence.hs +++ b/Data/Sequence.hs @@ -149,5 +149,5 @@ zipWith4, -- :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e ) where -import Data.Sequence.Base +import Data.Sequence.Internal import Prelude () diff --git a/Data/Sequence/Base.hs b/Data/Sequence/Base.hs deleted file mode 100644 --- a/Data/Sequence/Base.hs +++ /dev/null @@ -1,4280 +0,0 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ >= 800 -#define DEFINE_PATTERN_SYNONYMS 1 -#endif -#if __GLASGOW_HASKELL__ -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE StandaloneDeriving #-} -{-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE ScopedTypeVariables #-} -#endif -#if __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Trustworthy #-} -#endif -#if __GLASGOW_HASKELL__ >= 702 -{-# LANGUAGE DeriveGeneric #-} -#endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE TypeFamilies #-} -#endif -#ifdef DEFINE_PATTERN_SYNONYMS -{-# LANGUAGE PatternSynonyms #-} -{-# LANGUAGE ViewPatterns #-} -#endif - -#include "containers.h" - -{-# OPTIONS_HADDOCK hide #-} - ------------------------------------------------------------------------------ --- | --- Module : Data.Sequence.Base --- Copyright : (c) Ross Paterson 2005 --- (c) Louis Wasserman 2009 --- (c) Bertram Felgenhauer, David Feuer, Ross Paterson, and --- Milan Straka 2014 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : experimental --- Portability : portable --- --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. --- --- = Description --- --- General purpose finite sequences. --- Apart from being finite and having strict operations, sequences --- also differ from lists in supporting a wider variety of operations --- efficiently. --- --- An amortized running time is given for each operation, with /n/ referring --- to the length of the sequence and /i/ being the integral index used by --- some operations. These bounds hold even in a persistent (shared) setting. --- --- The implementation uses 2-3 finger trees annotated with sizes, --- as described in section 4.2 of --- --- * Ralf Hinze and Ross Paterson, --- \"Finger trees: a simple general-purpose data structure\", --- /Journal of Functional Programming/ 16:2 (2006) pp 197-217. --- --- --- /Note/: Many of these operations have the same names as similar --- operations on lists in the "Prelude". The ambiguity may be resolved --- using either qualification or the @hiding@ clause. --- --- /Warning/: The size of a 'Seq' must not exceed @maxBound::Int@. Violation --- of this condition is not detected and if the size limit is exceeded, the --- behaviour of the sequence is undefined. This is unlikely to occur in most --- applications, but some care may be required when using '><', '<*>', '*>', or --- '>>', particularly repeatedly and particularly in combination with --- 'replicate' or 'fromFunction'. --- ------------------------------------------------------------------------------ - -module Data.Sequence.Base ( - Elem(..), FingerTree(..), Node(..), Digit(..), Sized(..), MaybeForce, -#if defined(DEFINE_PATTERN_SYNONYMS) - Seq (.., Empty, (:<|), (:|>)), -#else - Seq (..), -#endif - - -- * Construction - empty, -- :: Seq a - singleton, -- :: a -> Seq a - (<|), -- :: a -> Seq a -> Seq a - (|>), -- :: Seq a -> a -> Seq a - (><), -- :: Seq a -> Seq a -> Seq a - fromList, -- :: [a] -> Seq a - fromFunction, -- :: Int -> (Int -> a) -> Seq a - fromArray, -- :: Ix i => Array i a -> Seq a - -- ** Repetition - replicate, -- :: Int -> a -> Seq a - replicateA, -- :: Applicative f => Int -> f a -> f (Seq a) - replicateM, -- :: Monad m => Int -> m a -> m (Seq a) - cycleTaking, -- :: Int -> Seq a -> Seq a - -- ** Iterative construction - iterateN, -- :: Int -> (a -> a) -> a -> Seq a - unfoldr, -- :: (b -> Maybe (a, b)) -> b -> Seq a - unfoldl, -- :: (b -> Maybe (b, a)) -> b -> Seq a - -- * Deconstruction - -- | Additional functions for deconstructing sequences are available - -- via the 'Foldable' instance of 'Seq'. - - -- ** Queries - null, -- :: Seq a -> Bool - length, -- :: Seq a -> Int - -- ** Views - ViewL(..), - viewl, -- :: Seq a -> ViewL a - ViewR(..), - viewr, -- :: Seq a -> ViewR a - -- * Scans - scanl, -- :: (a -> b -> a) -> a -> Seq b -> Seq a - scanl1, -- :: (a -> a -> a) -> Seq a -> Seq a - scanr, -- :: (a -> b -> b) -> b -> Seq a -> Seq b - scanr1, -- :: (a -> a -> a) -> Seq a -> Seq a - -- * Sublists - tails, -- :: Seq a -> Seq (Seq a) - inits, -- :: Seq a -> Seq (Seq a) - chunksOf, -- :: Int -> Seq a -> Seq (Seq a) - -- ** Sequential searches - takeWhileL, -- :: (a -> Bool) -> Seq a -> Seq a - takeWhileR, -- :: (a -> Bool) -> Seq a -> Seq a - dropWhileL, -- :: (a -> Bool) -> Seq a -> Seq a - dropWhileR, -- :: (a -> Bool) -> Seq a -> Seq a - spanl, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) - spanr, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) - breakl, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) - breakr, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) - partition, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) - filter, -- :: (a -> Bool) -> Seq a -> Seq a - -- * Sorting - sort, -- :: Ord a => Seq a -> Seq a - sortBy, -- :: (a -> a -> Ordering) -> Seq a -> Seq a - unstableSort, -- :: Ord a => Seq a -> Seq a - unstableSortBy, -- :: (a -> a -> Ordering) -> Seq a -> Seq a - -- * Indexing - lookup, -- :: Int -> Seq a -> Maybe a - (!?), -- :: Seq a -> Int -> Maybe a - index, -- :: Seq a -> Int -> a - adjust, -- :: (a -> a) -> Int -> Seq a -> Seq a - adjust', -- :: (a -> a) -> Int -> Seq a -> Seq a - update, -- :: Int -> a -> Seq a -> Seq a - take, -- :: Int -> Seq a -> Seq a - drop, -- :: Int -> Seq a -> Seq a - insertAt, -- :: Int -> a -> Seq a -> Seq a - deleteAt, -- :: Int -> Seq a -> Seq a - splitAt, -- :: Int -> Seq a -> (Seq a, Seq a) - -- ** Indexing with predicates - -- | These functions perform sequential searches from the left - -- or right ends of the sequence, returning indices of matching - -- elements. - elemIndexL, -- :: Eq a => a -> Seq a -> Maybe Int - elemIndicesL, -- :: Eq a => a -> Seq a -> [Int] - elemIndexR, -- :: Eq a => a -> Seq a -> Maybe Int - elemIndicesR, -- :: Eq a => a -> Seq a -> [Int] - findIndexL, -- :: (a -> Bool) -> Seq a -> Maybe Int - findIndicesL, -- :: (a -> Bool) -> Seq a -> [Int] - findIndexR, -- :: (a -> Bool) -> Seq a -> Maybe Int - findIndicesR, -- :: (a -> Bool) -> Seq a -> [Int] - -- * Folds - -- | General folds are available via the 'Foldable' instance of 'Seq'. - foldMapWithIndex, -- :: Monoid m => (Int -> a -> m) -> Seq a -> m - foldlWithIndex, -- :: (b -> Int -> a -> b) -> b -> Seq a -> b - foldrWithIndex, -- :: (Int -> a -> b -> b) -> b -> Seq a -> b - -- * Transformations - mapWithIndex, -- :: (Int -> a -> b) -> Seq a -> Seq b - traverseWithIndex, -- :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) - reverse, -- :: Seq a -> Seq a - intersperse, -- :: a -> Seq a -> Seq a - -- ** Zips - zip, -- :: Seq a -> Seq b -> Seq (a, b) - zipWith, -- :: (a -> b -> c) -> Seq a -> Seq b -> Seq c - zip3, -- :: Seq a -> Seq b -> Seq c -> Seq (a, b, c) - zipWith3, -- :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d - zip4, -- :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a, b, c, d) - zipWith4, -- :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e -#if TESTING - deep, - node2, - node3, -#endif - ) where - -import Prelude hiding ( - Functor(..), -#if MIN_VERSION_base(4,8,0) - Applicative, (<$>), foldMap, Monoid, -#endif - null, length, lookup, take, drop, splitAt, foldl, foldl1, foldr, foldr1, - scanl, scanl1, scanr, scanr1, replicate, zip, zipWith, zip3, zipWith3, - takeWhile, dropWhile, iterate, reverse, filter, mapM, sum, all) -import qualified Data.List -import Control.Applicative (Applicative(..), (<$>), (<**>), Alternative, - WrappedMonad(..), liftA, liftA2, liftA3) -import qualified Control.Applicative as Applicative (Alternative(..)) -import Control.DeepSeq (NFData(rnf)) -import Control.Monad (MonadPlus(..), ap) -import Data.Monoid (Monoid(..)) -import Data.Functor (Functor(..)) -#if MIN_VERSION_base(4,6,0) -import Data.Foldable (Foldable(foldl, foldl1, foldr, foldr1, foldMap, foldl', foldr'), toList) -#else -import Data.Foldable (Foldable(foldl, foldl1, foldr, foldr1, foldMap), foldl', toList) -#endif - -#if MIN_VERSION_base(4,9,0) -import qualified Data.Semigroup as Semigroup -#endif -import Data.Traversable -import Data.Typeable - --- GHC specific stuff -#ifdef __GLASGOW_HASKELL__ -import GHC.Exts (build) -import Text.Read (Lexeme(Ident), lexP, parens, prec, - readPrec, readListPrec, readListPrecDefault) -import Data.Data -import Data.String (IsString(..)) -#endif -#if __GLASGOW_HASKELL__ >= 706 -import GHC.Generics (Generic, Generic1) -#elif __GLASGOW_HASKELL__ >= 702 -import GHC.Generics (Generic) -#endif - --- Array stuff, with GHC.Arr on GHC -import Data.Array (Ix, Array) -import qualified Data.Array -#ifdef __GLASGOW_HASKELL__ -import qualified GHC.Arr -#endif - --- Coercion on GHC 7.8+ -#if __GLASGOW_HASKELL__ >= 708 -import Data.Coerce -import qualified GHC.Exts -#else -#endif - --- Identity functor on base 4.8 (GHC 7.10+) -#if MIN_VERSION_base(4,8,0) -import Data.Functor.Identity (Identity(..)) -#endif - -#if !MIN_VERSION_base(4,8,0) -import Data.Word (Word) -#endif - -import Data.Utils.StrictPair (StrictPair (..), toPair) - -default () - --- We define our own copy here, for Monoid only, even though this --- is now a Semigroup operator in base. The essential reason is that --- we have absolutely no use for semigroups in this module. Everything --- that needs to sum things up requires a Monoid constraint to deal --- with empty sequences. I'm not sure if there's a risk of walking --- through dictionaries to reach <> from Monoid, but I see no reason --- to risk it. -infixr 6 <> -(<>) :: Monoid m => m -> m -> m -(<>) = mappend -{-# INLINE (<>) #-} - -infixr 5 `consTree` -infixl 5 `snocTree` -infixr 5 `appendTree0` - -infixr 5 >< -infixr 5 <|, :< -infixl 5 |>, :> - -#ifdef DEFINE_PATTERN_SYNONYMS -infixr 5 :<| -infixl 5 :|> - --- TODO: Once GHC implements some way to prevent non-exhaustive --- pattern match warnings for pattern synonyms, we should be --- sure to take advantage of that. - --- | A pattern synonym matching an empty sequence. -pattern Empty :: Seq a -pattern Empty = Seq EmptyT - --- | A pattern synonym viewing the front of a non-empty --- sequence. -pattern (:<|) :: a -> Seq a -> Seq a -pattern x :<| xs <- (viewl -> x :< xs) - where - x :<| xs = x <| xs - --- | A pattern synonym viewing the rear of a non-empty --- sequence. -pattern (:|>) :: Seq a -> a -> Seq a -pattern xs :|> x <- (viewr -> xs :> x) - where - xs :|> x = xs |> x -#endif - -class Sized a where - size :: a -> Int - --- In much the same way that Sized lets us handle the --- sizes of elements and nodes uniformly, MaybeForce lets --- us handle their strictness (or lack thereof) uniformly. --- We can `mseq` something and not have to worry about --- whether it's an element or a node. -class MaybeForce a where - maybeRwhnf :: a -> () - -mseq :: MaybeForce a => a -> b -> b -mseq a b = case maybeRwhnf a of () -> b -{-# INLINE mseq #-} - -infixr 0 $!? -($!?) :: MaybeForce a => (a -> b) -> a -> b -f $!? a = case maybeRwhnf a of () -> f a -{-# INLINE ($!?) #-} - -instance MaybeForce (Elem a) where - maybeRwhnf _ = () - {-# INLINE maybeRwhnf #-} - -instance MaybeForce (Node a) where - maybeRwhnf !_ = () - {-# INLINE maybeRwhnf #-} - --- A wrapper making mseq = seq -newtype ForceBox a = ForceBox a -instance MaybeForce (ForceBox a) where - maybeRwhnf !_ = () -instance Sized (ForceBox a) where - size _ = 1 - --- | General-purpose finite sequences. -newtype Seq a = Seq (FingerTree (Elem a)) - -instance Functor Seq where - fmap = fmapSeq -#ifdef __GLASGOW_HASKELL__ - x <$ s = replicate (length s) x -#endif - -fmapSeq :: (a -> b) -> Seq a -> Seq b -fmapSeq f (Seq xs) = Seq (fmap (fmap f) xs) -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] fmapSeq #-} -{-# RULES -"fmapSeq/fmapSeq" forall f g xs . fmapSeq f (fmapSeq g xs) = fmapSeq (f . g) xs - #-} -#endif -#if __GLASGOW_HASKELL__ >= 709 --- Safe coercions were introduced in 7.8, but did not work well with RULES yet. -{-# RULES -"fmapSeq/coerce" fmapSeq coerce = coerce - #-} -#endif - -instance Foldable Seq where - foldMap f (Seq xs) = foldMap (foldMap f) xs -#if __GLASGOW_HASKELL__ >= 708 - foldr f z (Seq xs) = foldr (coerce f) z xs - foldr' f z (Seq xs) = foldr' (coerce f) z xs -#else - foldr f z (Seq xs) = foldr (flip (foldr f)) z xs -#if MIN_VERSION_base(4,6,0) - foldr' f z (Seq xs) = foldr' (flip (foldr' f)) z xs -#endif -#endif - foldl f z (Seq xs) = foldl (foldl f) z xs -#if MIN_VERSION_base(4,6,0) - foldl' f z (Seq xs) = foldl' (foldl' f) z xs -#endif - - foldr1 f (Seq xs) = getElem (foldr1 f' xs) - where f' (Elem x) (Elem y) = Elem (f x y) - - foldl1 f (Seq xs) = getElem (foldl1 f' xs) - where f' (Elem x) (Elem y) = Elem (f x y) - -#if MIN_VERSION_base(4,8,0) - length = length - {-# INLINE length #-} - null = null - {-# INLINE null #-} -#endif - -#if __GLASGOW_HASKELL__ >= 708 --- The natural definition of traverse, used for implementations that don't --- support coercions, `fmap`s into each `Elem`, then `fmap`s again over the --- result to turn it from a `FingerTree` to a `Seq`. None of this mapping is --- necessary! We could avoid it without coercions, I believe, by writing a --- bunch of traversal functions to deal with the `Elem` stuff specially (for --- FingerTrees, Digits, and Nodes), but using coercions we only need to --- duplicate code at the FingerTree level. We coerce the `Seq a` to a --- `FingerTree a`, stripping off all the Elem junk, then use a weird FingerTree --- traversing function that coerces back to Seq within the functor. -instance Traversable Seq where - traverse f xs = traverseFTE f (coerce xs) - -traverseFTE :: Applicative f => (a -> f b) -> FingerTree a -> f (Seq b) -traverseFTE _f EmptyT = pure empty -traverseFTE f (Single x) = Seq . Single . Elem <$> f x -traverseFTE f (Deep s pr m sf) = - (\pr' m' sf' -> coerce $ Deep s pr' m' sf') <$> - traverse f pr <*> traverse (traverse f) m <*> traverse f sf -#else -instance Traversable Seq where - traverse f (Seq xs) = Seq <$> traverse (traverse f) xs -#endif - -instance NFData a => NFData (Seq a) where - rnf (Seq xs) = rnf xs - -instance Monad Seq where - return = pure - xs >>= f = foldl' add empty xs - where add ys x = ys >< f x - (>>) = (*>) - -instance Applicative Seq where - pure = singleton - xs *> ys = cycleNTimes (length xs) ys - - fs <*> xs@(Seq xsFT) = case viewl fs of - EmptyL -> empty - firstf :< fs' -> case viewr fs' of - EmptyR -> fmap firstf xs - Seq fs''FT :> lastf -> case rigidify xsFT of - RigidEmpty -> empty - RigidOne (Elem x) -> fmap ($x) fs - RigidTwo (Elem x1) (Elem x2) -> - Seq $ ap2FT firstf fs''FT lastf (x1, x2) - RigidThree (Elem x1) (Elem x2) (Elem x3) -> - Seq $ ap3FT firstf fs''FT lastf (x1, x2, x3) - RigidFull r@(Rigid s pr _m sf) -> Seq $ - Deep (s * length fs) - (fmap (fmap firstf) (nodeToDigit pr)) - (aptyMiddle (fmap firstf) (fmap lastf) fmap fs''FT r) - (fmap (fmap lastf) (nodeToDigit sf)) - - -ap2FT :: (a -> b) -> FingerTree (Elem (a->b)) -> (a -> b) -> (a,a) -> FingerTree (Elem b) -ap2FT firstf fs lastf (x,y) = - Deep (size fs * 2 + 4) - (Two (Elem $ firstf x) (Elem $ firstf y)) - (mapMulFT 2 (\(Elem f) -> Node2 2 (Elem (f x)) (Elem (f y))) fs) - (Two (Elem $ lastf x) (Elem $ lastf y)) - -ap3FT :: (a -> b) -> FingerTree (Elem (a->b)) -> (a -> b) -> (a,a,a) -> FingerTree (Elem b) -ap3FT firstf fs lastf (x,y,z) = Deep (size fs * 3 + 6) - (Three (Elem $ firstf x) (Elem $ firstf y) (Elem $ firstf z)) - (mapMulFT 3 (\(Elem f) -> Node3 3 (Elem (f x)) (Elem (f y)) (Elem (f z))) fs) - (Three (Elem $ lastf x) (Elem $ lastf y) (Elem $ lastf z)) - - -data Rigidified a = RigidEmpty - | RigidOne a - | RigidTwo a a - | RigidThree a a a - | RigidFull (Rigid a) -#ifdef TESTING - deriving Show -#endif - --- | A finger tree whose top level has only Two and/or Three digits, and whose --- other levels have only One and Two digits. A Rigid tree is precisely what one --- gets by unzipping/inverting a 2-3 tree, so it is precisely what we need to --- turn a finger tree into in order to transform it into a 2-3 tree. -data Rigid a = Rigid {-# UNPACK #-} !Int !(Digit23 a) (Thin (Node a)) !(Digit23 a) -#ifdef TESTING - deriving Show -#endif - --- | A finger tree whose digits are all ones and twos -data Thin a = EmptyTh - | SingleTh a - | DeepTh {-# UNPACK #-} !Int !(Digit12 a) (Thin (Node a)) !(Digit12 a) -#ifdef TESTING - deriving Show -#endif - -data Digit12 a = One12 a | Two12 a a -#ifdef TESTING - deriving Show -#endif - --- | Sometimes, we want to emphasize that we are viewing a node as a top-level --- digit of a 'Rigid' tree. -type Digit23 a = Node a - --- | 'aptyMiddle' does most of the hard work of computing @fs<*>xs@. It --- produces the center part of a finger tree, with a prefix corresponding to --- the prefix of @xs@ and a suffix corresponding to the suffix of @xs@ omitted; --- the missing suffix and prefix are added by the caller. For the recursive --- call, it squashes the prefix and the suffix into the center tree. Once it --- gets to the bottom, it turns the tree into a 2-3 tree, applies 'mapMulFT' to --- produce the main body, and glues all the pieces together. --- --- 'map23' itself is a bit horrifying because of the nested types involved. Its --- job is to map over the *elements* of a 2-3 tree, rather than the subtrees. --- If we used a higher-order nested type with MPTC, we could probably use a --- class, but as it is we have to build up 'map23' explicitly through the --- recursion. -aptyMiddle - :: (c -> d) - -> (c -> d) - -> ((a -> b) -> c -> d) - -> FingerTree (Elem (a -> b)) - -> Rigid c - -> FingerTree (Node d) - --- Not at the bottom yet - -aptyMiddle firstf - lastf - map23 - fs - (Rigid s pr (DeepTh sm prm mm sfm) sf) - = Deep (sm + s * (size fs + 1)) -- note: sm = s - size pr - size sf - (fmap (fmap firstf) (digit12ToDigit prm)) - (aptyMiddle (fmap firstf) - (fmap lastf) - (fmap . map23) - fs - (Rigid s (squashL pr prm) mm (squashR sfm sf))) - (fmap (fmap lastf) (digit12ToDigit sfm)) - --- At the bottom - -aptyMiddle firstf - lastf - map23 - fs - (Rigid s pr EmptyTh sf) - = deep - (One (fmap firstf sf)) - (mapMulFT s (\(Elem f) -> fmap (fmap (map23 f)) converted) fs) - (One (fmap lastf pr)) - where converted = node2 pr sf - -aptyMiddle firstf - lastf - map23 - fs - (Rigid s pr (SingleTh q) sf) - = deep - (Two (fmap firstf q) (fmap firstf sf)) - (mapMulFT s (\(Elem f) -> fmap (fmap (map23 f)) converted) fs) - (Two (fmap lastf pr) (fmap lastf q)) - where converted = node3 pr q sf - -digit12ToDigit :: Digit12 a -> Digit a -digit12ToDigit (One12 a) = One a -digit12ToDigit (Two12 a b) = Two a b - --- Squash the first argument down onto the left side of the second. -squashL :: Digit23 a -> Digit12 (Node a) -> Digit23 (Node a) -squashL m (One12 n) = node2 m n -squashL m (Two12 n1 n2) = node3 m n1 n2 - --- Squash the second argument down onto the right side of the first -squashR :: Digit12 (Node a) -> Digit23 a -> Digit23 (Node a) -squashR (One12 n) m = node2 n m -squashR (Two12 n1 n2) m = node3 n1 n2 m - - --- | /O(m*n)/ (incremental) Takes an /O(m)/ function and a finger tree of size --- /n/ and maps the function over the tree leaves. Unlike the usual 'fmap', the --- function is applied to the "leaves" of the 'FingerTree' (i.e., given a --- @FingerTree (Elem a)@, it applies the function to elements of type @Elem --- a@), replacing the leaves with subtrees of at least the same height, e.g., --- @Node(Node(Elem y))@. The multiplier argument serves to make the annotations --- match up properly. -mapMulFT :: Int -> (a -> b) -> FingerTree a -> FingerTree b -mapMulFT _ _ EmptyT = EmptyT -mapMulFT _mul f (Single a) = Single (f a) -mapMulFT mul f (Deep s pr m sf) = Deep (mul * s) (fmap f pr) (mapMulFT mul (mapMulNode mul f) m) (fmap f sf) - -mapMulNode :: Int -> (a -> b) -> Node a -> Node b -mapMulNode mul f (Node2 s a b) = Node2 (mul * s) (f a) (f b) -mapMulNode mul f (Node3 s a b c) = Node3 (mul * s) (f a) (f b) (f c) - --- | /O(log n)/ (incremental) Takes the extra flexibility out of a 'FingerTree' --- to make it a genuine 2-3 finger tree. The result of 'rigidify' will have --- only two and three digits at the top level and only one and two --- digits elsewhere. If the tree has fewer than four elements, 'rigidify' --- will simply extract them, and will not build a tree. -rigidify :: FingerTree (Elem a) -> Rigidified (Elem a) --- The patterns below just fix up the top level of the tree; 'rigidify' --- delegates the hard work to 'thin'. - -rigidify EmptyT = RigidEmpty - -rigidify (Single q) = RigidOne q - --- The left digit is Two or Three -rigidify (Deep s (Two a b) m sf) = rigidifyRight s (node2 a b) m sf -rigidify (Deep s (Three a b c) m sf) = rigidifyRight s (node3 a b c) m sf - --- The left digit is Four -rigidify (Deep s (Four a b c d) m sf) = rigidifyRight s (node2 a b) (node2 c d `consTree` m) sf - --- The left digit is One -rigidify (Deep s (One a) m sf) = case viewLTree m of - ConsLTree (Node2 _ b c) m' -> rigidifyRight s (node3 a b c) m' sf - ConsLTree (Node3 _ b c d) m' -> rigidifyRight s (node2 a b) (node2 c d `consTree` m') sf - EmptyLTree -> case sf of - One b -> RigidTwo a b - Two b c -> RigidThree a b c - Three b c d -> RigidFull $ Rigid s (node2 a b) EmptyTh (node2 c d) - Four b c d e -> RigidFull $ Rigid s (node3 a b c) EmptyTh (node2 d e) - --- | /O(log n)/ (incremental) Takes a tree whose left side has been rigidified --- and finishes the job. -rigidifyRight :: Int -> Digit23 (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> Rigidified (Elem a) - --- The right digit is Two, Three, or Four -rigidifyRight s pr m (Two a b) = RigidFull $ Rigid s pr (thin m) (node2 a b) -rigidifyRight s pr m (Three a b c) = RigidFull $ Rigid s pr (thin m) (node3 a b c) -rigidifyRight s pr m (Four a b c d) = RigidFull $ Rigid s pr (thin $ m `snocTree` node2 a b) (node2 c d) - --- The right digit is One -rigidifyRight s pr m (One e) = case viewRTree m of - SnocRTree m' (Node2 _ a b) -> RigidFull $ Rigid s pr (thin m') (node3 a b e) - SnocRTree m' (Node3 _ a b c) -> RigidFull $ Rigid s pr (thin $ m' `snocTree` node2 a b) (node2 c e) - EmptyRTree -> case pr of - Node2 _ a b -> RigidThree a b e - Node3 _ a b c -> RigidFull $ Rigid s (node2 a b) EmptyTh (node2 c e) - --- | /O(log n)/ (incremental) Rejigger a finger tree so the digits are all ones --- and twos. -thin :: Sized a => FingerTree a -> Thin a --- Note that 'thin12' will produce a 'DeepTh' constructor immediately before --- recursively calling 'thin'. -thin EmptyT = EmptyTh -thin (Single a) = SingleTh a -thin (Deep s pr m sf) = - case pr of - One a -> thin12 s (One12 a) m sf - Two a b -> thin12 s (Two12 a b) m sf - Three a b c -> thin12 s (One12 a) (node2 b c `consTree` m) sf - Four a b c d -> thin12 s (Two12 a b) (node2 c d `consTree` m) sf - -thin12 :: Sized a => Int -> Digit12 a -> FingerTree (Node a) -> Digit a -> Thin a -thin12 s pr m (One a) = DeepTh s pr (thin m) (One12 a) -thin12 s pr m (Two a b) = DeepTh s pr (thin m) (Two12 a b) -thin12 s pr m (Three a b c) = DeepTh s pr (thin $ m `snocTree` node2 a b) (One12 c) -thin12 s pr m (Four a b c d) = DeepTh s pr (thin $ m `snocTree` node2 a b) (Two12 c d) - --- | Intersperse an element between the elements of a sequence. --- --- @ --- intersperse a empty = empty --- intersperse a (singleton x) = singleton x --- intersperse a (fromList [x,y]) = fromList [x,a,y] --- intersperse a (fromList [x,y,z]) = fromList [x,a,y,a,z] --- @ --- --- @since 0.5.8 -intersperse :: a -> Seq a -> Seq a -intersperse y xs = case viewl xs of - EmptyL -> empty - p :< ps -> p <| (ps <**> (const y <| singleton id)) --- We used to use --- --- intersperse y xs = drop 1 $ xs <**> (const y <| singleton id) --- --- but if length xs = ((maxBound :: Int) `quot` 2) + 1 then --- --- length (xs <**> (const y <| singleton id)) will wrap around to negative --- and the drop won't work. The new implementation can produce a result --- right up to maxBound :: Int - -instance MonadPlus Seq where - mzero = empty - mplus = (><) - -instance Alternative Seq where - empty = empty - (<|>) = (><) - -instance Eq a => Eq (Seq a) where - xs == ys = length xs == length ys && toList xs == toList ys - -instance Ord a => Ord (Seq a) where - compare xs ys = compare (toList xs) (toList ys) - -#if TESTING -instance Show a => Show (Seq a) where - showsPrec p (Seq x) = showsPrec p x -#else -instance Show a => Show (Seq a) where - showsPrec p xs = showParen (p > 10) $ - showString "fromList " . shows (toList xs) -#endif - -instance Read a => Read (Seq a) 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 - -instance Monoid (Seq a) where - mempty = empty - mappend = (><) - -#if MIN_VERSION_base(4,9,0) -instance Semigroup.Semigroup (Seq a) where - (<>) = (><) -#endif - -INSTANCE_TYPEABLE1(Seq) - -#if __GLASGOW_HASKELL__ -instance Data a => Data (Seq a) where - gfoldl f z s = case viewl s of - EmptyL -> z empty - x :< xs -> z (<|) `f` x `f` xs - - gunfold k z c = case constrIndex c of - 1 -> z empty - 2 -> k (k (z (<|))) - _ -> error "gunfold" - - toConstr xs - | null xs = emptyConstr - | otherwise = consConstr - - dataTypeOf _ = seqDataType - - dataCast1 f = gcast1 f - -emptyConstr, consConstr :: Constr -emptyConstr = mkConstr seqDataType "empty" [] Prefix -consConstr = mkConstr seqDataType "<|" [] Infix - -seqDataType :: DataType -seqDataType = mkDataType "Data.Sequence.Seq" [emptyConstr, consConstr] -#endif - --- Finger trees - -data FingerTree a - = EmptyT - | Single a - | Deep {-# UNPACK #-} !Int !(Digit a) (FingerTree (Node a)) !(Digit a) -#if TESTING - deriving Show -#endif - -instance Sized a => Sized (FingerTree a) where - {-# SPECIALIZE instance Sized (FingerTree (Elem a)) #-} - {-# SPECIALIZE instance Sized (FingerTree (Node a)) #-} - size EmptyT = 0 - size (Single x) = size x - size (Deep v _ _ _) = v - -instance Foldable FingerTree where - foldMap _ EmptyT = mempty - foldMap f (Single x) = f x - foldMap f (Deep _ pr m sf) = - foldMap f pr <> foldMap (foldMap f) m <> foldMap f sf - - foldr _ z EmptyT = z - foldr f z (Single x) = x `f` z - foldr f z (Deep _ pr m sf) = - foldr f (foldr (flip (foldr f)) (foldr f z sf) m) pr - - foldl _ z EmptyT = z - foldl f z (Single x) = z `f` x - foldl f z (Deep _ pr m sf) = - foldl f (foldl (foldl f) (foldl f z pr) m) sf - -#if MIN_VERSION_base(4,6,0) - foldr' _ z EmptyT = z - foldr' f z (Single x) = f x z - foldr' f z (Deep _ pr m sf) = foldr' f mres pr - where !sfRes = foldr' f z sf - !mres = foldr' (flip (foldr' f)) sfRes m - - foldl' _ z EmptyT = z - foldl' f z (Single x) = z `f` x - foldl' f z (Deep _ pr m sf) = foldl' f mres sf - where !prRes = foldl' f z pr - !mres = foldl' (foldl' f) prRes m -#endif - - foldr1 _ EmptyT = error "foldr1: empty sequence" - foldr1 _ (Single x) = x - foldr1 f (Deep _ pr m sf) = - foldr f (foldr (flip (foldr f)) (foldr1 f sf) m) pr - - foldl1 _ EmptyT = error "foldl1: empty sequence" - foldl1 _ (Single x) = x - foldl1 f (Deep _ pr m sf) = - foldl f (foldl (foldl f) (foldl1 f pr) m) sf - -instance Functor FingerTree where - fmap _ EmptyT = EmptyT - fmap f (Single x) = Single (f x) - fmap f (Deep v pr m sf) = - Deep v (fmap f pr) (fmap (fmap f) m) (fmap f sf) - -instance Traversable FingerTree where - traverse _ EmptyT = pure EmptyT - traverse f (Single x) = Single <$> f x - traverse f (Deep v pr m sf) = - deep' v <$> traverse f pr <*> traverse (traverse f) m <*> - traverse f sf - -instance NFData a => NFData (FingerTree a) where - rnf EmptyT = () - rnf (Single x) = rnf x - rnf (Deep _ pr m sf) = rnf pr `seq` rnf sf `seq` rnf m - -{-# INLINE deep #-} -deep :: Sized a => Digit a -> FingerTree (Node a) -> Digit a -> FingerTree a -deep pr m sf = Deep (size pr + size m + size sf) pr m sf - -{-# INLINE pullL #-} -pullL :: Int -> FingerTree (Node a) -> Digit a -> FingerTree a -pullL s m sf = case viewLTree m of - EmptyLTree -> digitToTree' s sf - ConsLTree pr m' -> Deep s (nodeToDigit pr) m' sf - -{-# INLINE pullR #-} -pullR :: Int -> Digit a -> FingerTree (Node a) -> FingerTree a -pullR s pr m = case viewRTree m of - EmptyRTree -> digitToTree' s pr - SnocRTree m' sf -> Deep s pr m' (nodeToDigit sf) - --- Digits - -data Digit a - = One a - | Two a a - | Three a a a - | Four a a a a -#if TESTING - deriving Show -#endif - -instance Foldable Digit where - foldMap f (One a) = f a - foldMap f (Two a b) = f a <> f b - foldMap f (Three a b c) = f a <> f b <> f c - foldMap f (Four a b c d) = f a <> f b <> f c <> f d - - foldr f z (One a) = a `f` z - foldr f z (Two a b) = a `f` (b `f` z) - foldr f z (Three a b c) = a `f` (b `f` (c `f` z)) - foldr f z (Four a b c d) = a `f` (b `f` (c `f` (d `f` z))) - - foldl f z (One a) = z `f` a - foldl f z (Two a b) = (z `f` a) `f` b - foldl f z (Three a b c) = ((z `f` a) `f` b) `f` c - foldl f z (Four a b c d) = (((z `f` a) `f` b) `f` c) `f` d - -#if MIN_VERSION_base(4,6,0) - foldr' f z (One a) = a `f` z - foldr' f z (Two a b) = f a $! f b z - foldr' f z (Three a b c) = f a $! f b $! f c z - foldr' f z (Four a b c d) = f a $! f b $! f c $! f d z - - foldl' f z (One a) = f z a - foldl' f z (Two a b) = (f $! f z a) b - foldl' f z (Three a b c) = (f $! (f $! f z a) b) c - foldl' f z (Four a b c d) = (f $! (f $! (f $! f z a) b) c) d -#endif - - foldr1 _ (One a) = a - foldr1 f (Two a b) = a `f` b - foldr1 f (Three a b c) = a `f` (b `f` c) - foldr1 f (Four a b c d) = a `f` (b `f` (c `f` d)) - - foldl1 _ (One a) = a - foldl1 f (Two a b) = a `f` b - foldl1 f (Three a b c) = (a `f` b) `f` c - foldl1 f (Four a b c d) = ((a `f` b) `f` c) `f` d - -instance Functor Digit where - {-# INLINE fmap #-} - fmap f (One a) = One (f a) - fmap f (Two a b) = Two (f a) (f b) - fmap f (Three a b c) = Three (f a) (f b) (f c) - fmap f (Four a b c d) = Four (f a) (f b) (f c) (f d) - -instance Traversable Digit where - {-# INLINE traverse #-} - traverse f (One a) = One <$> f a - traverse f (Two a b) = Two <$> f a <*> f b - traverse f (Three a b c) = Three <$> f a <*> f b <*> f c - traverse f (Four a b c d) = Four <$> f a <*> f b <*> f c <*> f d - -instance NFData a => NFData (Digit a) where - rnf (One a) = rnf a - rnf (Two a b) = rnf a `seq` rnf b - rnf (Three a b c) = rnf a `seq` rnf b `seq` rnf c - rnf (Four a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d - -instance Sized a => Sized (Digit a) where - {-# INLINE size #-} - size = foldl1 (+) . fmap size - -{-# SPECIALIZE digitToTree :: Digit (Elem a) -> FingerTree (Elem a) #-} -{-# SPECIALIZE digitToTree :: Digit (Node a) -> FingerTree (Node a) #-} -digitToTree :: Sized a => Digit a -> FingerTree a -digitToTree (One a) = Single a -digitToTree (Two a b) = deep (One a) EmptyT (One b) -digitToTree (Three a b c) = deep (Two a b) EmptyT (One c) -digitToTree (Four a b c d) = deep (Two a b) EmptyT (Two c d) - --- | Given the size of a digit and the digit itself, efficiently converts --- it to a FingerTree. -digitToTree' :: Int -> Digit a -> FingerTree a -digitToTree' n (Four a b c d) = Deep n (Two a b) EmptyT (Two c d) -digitToTree' n (Three a b c) = Deep n (Two a b) EmptyT (One c) -digitToTree' n (Two a b) = Deep n (One a) EmptyT (One b) -digitToTree' !_n (One a) = Single a - --- Nodes - -data Node a - = Node2 {-# UNPACK #-} !Int a a - | Node3 {-# UNPACK #-} !Int a a a -#if TESTING - deriving Show -#endif - --- Sometimes, we need to apply a Node2, Node3, or Deep constructor --- to a size and pass the result to a function. If we calculate, --- say, `Node2 n <$> x <*> y`, then according to -ddump-simpl, --- GHC boxes up `n`, passes it to the strict constructor for `Node2`, --- and passes the result to `fmap`. Using `node2'` instead prevents --- this, forming a closure with the unboxed size. -{-# INLINE node2' #-} -node2' :: Int -> a -> a -> Node a -node2' !s = \a b -> Node2 s a b - -{-# INLINE node3' #-} -node3' :: Int -> a -> a -> a -> Node a -node3' !s = \a b c -> Node3 s a b c - -{-# INLINE deep' #-} -deep' :: Int -> Digit a -> FingerTree (Node a) -> Digit a -> FingerTree a -deep' !s = \pr m sf -> Deep s pr m sf - -instance Foldable Node where - foldMap f (Node2 _ a b) = f a <> f b - foldMap f (Node3 _ a b c) = f a <> f b <> f c - - foldr f z (Node2 _ a b) = a `f` (b `f` z) - foldr f z (Node3 _ a b c) = a `f` (b `f` (c `f` z)) - - foldl f z (Node2 _ a b) = (z `f` a) `f` b - foldl f z (Node3 _ a b c) = ((z `f` a) `f` b) `f` c - -#if MIN_VERSION_base(4,6,0) - foldr' f z (Node2 _ a b) = f a $! f b z - foldr' f z (Node3 _ a b c) = f a $! f b $! f c z - - foldl' f z (Node2 _ a b) = (f $! f z a) b - foldl' f z (Node3 _ a b c) = (f $! (f $! f z a) b) c -#endif - -instance Functor Node where - {-# INLINE fmap #-} - fmap f (Node2 v a b) = Node2 v (f a) (f b) - fmap f (Node3 v a b c) = Node3 v (f a) (f b) (f c) - -instance Traversable Node where - {-# INLINE traverse #-} - traverse f (Node2 v a b) = node2' v <$> f a <*> f b - traverse f (Node3 v a b c) = node3' v <$> f a <*> f b <*> f c - -instance NFData a => NFData (Node a) where - rnf (Node2 _ a b) = rnf a `seq` rnf b - rnf (Node3 _ a b c) = rnf a `seq` rnf b `seq` rnf c - -instance Sized (Node a) where - size (Node2 v _ _) = v - size (Node3 v _ _ _) = v - -{-# INLINE node2 #-} -node2 :: Sized a => a -> a -> Node a -node2 a b = Node2 (size a + size b) a b - -{-# INLINE node3 #-} -node3 :: Sized a => a -> a -> a -> Node a -node3 a b c = Node3 (size a + size b + size c) a b c - -nodeToDigit :: Node a -> Digit a -nodeToDigit (Node2 _ a b) = Two a b -nodeToDigit (Node3 _ a b c) = Three a b c - --- Elements - -newtype Elem a = Elem { getElem :: a } -#if TESTING - deriving Show -#endif - -instance Sized (Elem a) where - size _ = 1 - -instance Functor Elem where -#if __GLASGOW_HASKELL__ >= 708 --- This cuts the time for <*> by around a fifth. - fmap = coerce -#else - fmap f (Elem x) = Elem (f x) -#endif - -instance Foldable Elem where - foldr f z (Elem x) = f x z -#if __GLASGOW_HASKELL__ >= 708 - foldMap = coerce - foldl = coerce - foldl' = coerce -#else - foldMap f (Elem x) = f x - foldl f z (Elem x) = f z x -#if MIN_VERSION_base(4,6,0) - foldl' f z (Elem x) = f z x -#endif -#endif - -instance Traversable Elem where - traverse f (Elem x) = Elem <$> f x - -instance NFData a => NFData (Elem a) where - rnf (Elem x) = rnf x - -------------------------------------------------------- --- Applicative construction -------------------------------------------------------- -#if !MIN_VERSION_base(4,8,0) -newtype Identity a = Identity {runIdentity :: a} - -instance Functor Identity where - fmap f (Identity x) = Identity (f x) - -instance Applicative Identity where - pure = Identity - Identity f <*> Identity x = Identity (f x) -#endif - --- | This is essentially a clone of Control.Monad.State.Strict. -newtype State s a = State {runState :: s -> (s, a)} - -instance Functor (State s) where - fmap = liftA - -instance Monad (State s) where - {-# INLINE return #-} - {-# INLINE (>>=) #-} - return = pure - m >>= k = State $ \ s -> case runState m s of - (s', x) -> runState (k x) s' - -instance Applicative (State s) where - {-# INLINE pure #-} - pure x = State $ \ s -> (s, x) - (<*>) = ap - -execState :: State s a -> s -> a -execState m x = snd (runState m x) - --- | 'applicativeTree' takes an Applicative-wrapped construction of a --- piece of a FingerTree, assumed to always have the same size (which --- is put in the second argument), and replicates it as many times as --- specified. This is a generalization of 'replicateA', which itself --- is a generalization of many Data.Sequence methods. -{-# SPECIALIZE applicativeTree :: Int -> Int -> State s a -> State s (FingerTree a) #-} -{-# SPECIALIZE applicativeTree :: Int -> Int -> Identity a -> Identity (FingerTree a) #-} --- Special note: the Identity specialization automatically does node sharing, --- reducing memory usage of the resulting tree to /O(log n)/. -applicativeTree :: Applicative f => Int -> Int -> f a -> f (FingerTree a) -applicativeTree n !mSize m = case n of - 0 -> pure EmptyT - 1 -> fmap Single m - 2 -> deepA one emptyTree one - 3 -> deepA two emptyTree one - 4 -> deepA two emptyTree two - 5 -> deepA three emptyTree two - 6 -> deepA three emptyTree three - _ -> case n `quotRem` 3 of - (q,0) -> deepA three (applicativeTree (q - 2) mSize' n3) three - (q,1) -> deepA two (applicativeTree (q - 1) mSize' n3) two - (q,_) -> deepA three (applicativeTree (q - 1) mSize' n3) two - where !mSize' = 3 * mSize - n3 = liftA3 (node3' mSize') m m m - where - one = fmap One m - two = liftA2 Two m m - three = liftA3 Three m m m - deepA = liftA3 (deep' (n * mSize)) - emptyTree = pure EmptyT - ------------------------------------------------------------------------- --- Construction ------------------------------------------------------------------------- - --- | /O(1)/. The empty sequence. -empty :: Seq a -empty = Seq EmptyT - --- | /O(1)/. A singleton sequence. -singleton :: a -> Seq a -singleton x = Seq (Single (Elem x)) - --- | /O(log n)/. @replicate n x@ is a sequence consisting of @n@ copies of @x@. -replicate :: Int -> a -> Seq a -replicate n x - | n >= 0 = runIdentity (replicateA n (Identity x)) - | otherwise = error "replicate takes a nonnegative integer argument" - --- | 'replicateA' is an 'Applicative' version of 'replicate', and makes --- /O(log n)/ calls to '<*>' and 'pure'. --- --- > replicateA n x = sequenceA (replicate n x) -replicateA :: Applicative f => Int -> f a -> f (Seq a) -replicateA n x - | n >= 0 = Seq <$> applicativeTree n 1 (Elem <$> x) - | otherwise = error "replicateA takes a nonnegative integer argument" - --- | 'replicateM' is a sequence counterpart of 'Control.Monad.replicateM'. --- --- > replicateM n x = sequence (replicate n x) -replicateM :: Monad m => Int -> m a -> m (Seq a) -replicateM n x - | n >= 0 = unwrapMonad (replicateA n (WrapMonad x)) - | otherwise = error "replicateM takes a nonnegative integer argument" - --- | /O(log(k))/. @'cycleTaking' k xs@ forms a sequence of length @k@ by --- repeatedly concatenating @xs@ with itself. @xs@ may only be empty if --- @k@ is 0. --- --- prop> cycleTaking k = fromList . take k . cycle . toList - --- If you wish to concatenate a non-empty sequence @xs@ with itself precisely --- @k@ times, you can use @cycleTaking (k * length xs)@ or just --- @replicate k () *> xs@. --- --- @since 0.5.8 -cycleTaking :: Int -> Seq a -> Seq a -cycleTaking n !_xs | n <= 0 = empty -cycleTaking _n xs | null xs = error "cycleTaking cannot take a positive number of elements from an empty cycle." -cycleTaking n xs = cycleNTimes reps xs >< take final xs - where - (reps, final) = n `quotRem` length xs - --- | /O(log(kn))/. @'cycleNTimes' k xs@ concatenates @k@ copies of @xs@. This --- operation uses time and additional space logarithmic in the size of its --- result. -cycleNTimes :: Int -> Seq a -> Seq a -cycleNTimes n !xs - | n <= 0 = empty - | n == 1 = xs -cycleNTimes n (Seq xsFT) = case rigidify xsFT of - RigidEmpty -> empty - RigidOne (Elem x) -> replicate n x - RigidTwo x1 x2 -> Seq $ - Deep (n*2) pair - (runIdentity $ applicativeTree (n-2) 2 (Identity (node2 x1 x2))) - pair - where pair = Two x1 x2 - RigidThree x1 x2 x3 -> Seq $ - Deep (n*3) triple - (runIdentity $ applicativeTree (n-2) 3 (Identity (node3 x1 x2 x3))) - triple - where triple = Three x1 x2 x3 - RigidFull r@(Rigid s pr _m sf) -> Seq $ - Deep (n*s) - (nodeToDigit pr) - (cycleNMiddle (n-2) r) - (nodeToDigit sf) - -cycleNMiddle - :: Int - -> Rigid c - -> FingerTree (Node c) - --- Not at the bottom yet - -cycleNMiddle !n - (Rigid s pr (DeepTh sm prm mm sfm) sf) - = Deep (sm + s * (n + 1)) -- note: sm = s - size pr - size sf - (digit12ToDigit prm) - (cycleNMiddle n - (Rigid s (squashL pr prm) mm (squashR sfm sf))) - (digit12ToDigit sfm) - --- At the bottom - -cycleNMiddle n - (Rigid s pr EmptyTh sf) - = deep - (One sf) - (runIdentity $ applicativeTree n s (Identity converted)) - (One pr) - where converted = node2 pr sf - -cycleNMiddle n - (Rigid s pr (SingleTh q) sf) - = deep - (Two q sf) - (runIdentity $ applicativeTree n s (Identity converted)) - (Two pr q) - where converted = node3 pr q sf - - --- | /O(1)/. Add an element to the left end of a sequence. --- Mnemonic: a triangle with the single element at the pointy end. -(<|) :: a -> Seq a -> Seq a -x <| Seq xs = Seq (Elem x `consTree` xs) - -{-# SPECIALIZE consTree :: Elem a -> FingerTree (Elem a) -> FingerTree (Elem a) #-} -{-# SPECIALIZE consTree :: Node a -> FingerTree (Node a) -> FingerTree (Node a) #-} -consTree :: Sized a => a -> FingerTree a -> FingerTree a -consTree a EmptyT = Single a -consTree a (Single b) = deep (One a) EmptyT (One b) --- As described in the paper, we force the middle of a tree --- *before* consing onto it; this preserves the amortized --- bounds but prevents repeated consing from building up --- gigantic suspensions. -consTree a (Deep s (Four b c d e) m sf) = m `seq` - Deep (size a + s) (Two a b) (node3 c d e `consTree` m) sf -consTree a (Deep s (Three b c d) m sf) = - Deep (size a + s) (Four a b c d) m sf -consTree a (Deep s (Two b c) m sf) = - Deep (size a + s) (Three a b c) m sf -consTree a (Deep s (One b) m sf) = - Deep (size a + s) (Two a b) m sf - -cons' :: a -> Seq a -> Seq a -cons' x (Seq xs) = Seq (Elem x `consTree'` xs) - -snoc' :: Seq a -> a -> Seq a -snoc' (Seq xs) x = Seq (xs `snocTree'` Elem x) - -{-# SPECIALIZE consTree' :: Elem a -> FingerTree (Elem a) -> FingerTree (Elem a) #-} -{-# SPECIALIZE consTree' :: Node a -> FingerTree (Node a) -> FingerTree (Node a) #-} -consTree' :: Sized a => a -> FingerTree a -> FingerTree a -consTree' a EmptyT = Single a -consTree' a (Single b) = deep (One a) EmptyT (One b) --- As described in the paper, we force the middle of a tree --- *before* consing onto it; this preserves the amortized --- bounds but prevents repeated consing from building up --- gigantic suspensions. -consTree' a (Deep s (Four b c d e) m sf) = - Deep (size a + s) (Two a b) m' sf - where !m' = abc `consTree'` m - !abc = node3 c d e -consTree' a (Deep s (Three b c d) m sf) = - Deep (size a + s) (Four a b c d) m sf -consTree' a (Deep s (Two b c) m sf) = - Deep (size a + s) (Three a b c) m sf -consTree' a (Deep s (One b) m sf) = - Deep (size a + s) (Two a b) m sf - --- | /O(1)/. Add an element to the right end of a sequence. --- Mnemonic: a triangle with the single element at the pointy end. -(|>) :: Seq a -> a -> Seq a -Seq xs |> x = Seq (xs `snocTree` Elem x) - -{-# SPECIALIZE snocTree :: FingerTree (Elem a) -> Elem a -> FingerTree (Elem a) #-} -{-# SPECIALIZE snocTree :: FingerTree (Node a) -> Node a -> FingerTree (Node a) #-} -snocTree :: Sized a => FingerTree a -> a -> FingerTree a -snocTree EmptyT a = Single a -snocTree (Single a) b = deep (One a) EmptyT (One b) --- See note on `seq` in `consTree`. -snocTree (Deep s pr m (Four a b c d)) e = m `seq` - Deep (s + size e) pr (m `snocTree` node3 a b c) (Two d e) -snocTree (Deep s pr m (Three a b c)) d = - Deep (s + size d) pr m (Four a b c d) -snocTree (Deep s pr m (Two a b)) c = - Deep (s + size c) pr m (Three a b c) -snocTree (Deep s pr m (One a)) b = - Deep (s + size b) pr m (Two a b) - -{-# SPECIALIZE snocTree' :: FingerTree (Elem a) -> Elem a -> FingerTree (Elem a) #-} -{-# SPECIALIZE snocTree' :: FingerTree (Node a) -> Node a -> FingerTree (Node a) #-} -snocTree' :: Sized a => FingerTree a -> a -> FingerTree a -snocTree' EmptyT a = Single a -snocTree' (Single a) b = deep (One a) EmptyT (One b) --- See note on `seq` in `consTree`. -snocTree' (Deep s pr m (Four a b c d)) e = - Deep (s + size e) pr m' (Two d e) - where !m' = m `snocTree'` abc - !abc = node3 a b c -snocTree' (Deep s pr m (Three a b c)) d = - Deep (s + size d) pr m (Four a b c d) -snocTree' (Deep s pr m (Two a b)) c = - Deep (s + size c) pr m (Three a b c) -snocTree' (Deep s pr m (One a)) b = - Deep (s + size b) pr m (Two a b) - --- | /O(log(min(n1,n2)))/. Concatenate two sequences. -(><) :: Seq a -> Seq a -> Seq a -Seq xs >< Seq ys = Seq (appendTree0 xs ys) - --- The appendTree/addDigits gunk below is machine generated - -appendTree0 :: FingerTree (Elem a) -> FingerTree (Elem a) -> FingerTree (Elem a) -appendTree0 EmptyT xs = - xs -appendTree0 xs EmptyT = - xs -appendTree0 (Single x) xs = - x `consTree` xs -appendTree0 xs (Single x) = - xs `snocTree` x -appendTree0 (Deep s1 pr1 m1 sf1) (Deep s2 pr2 m2 sf2) = - Deep (s1 + s2) pr1 m sf2 - where !m = addDigits0 m1 sf1 pr2 m2 - -addDigits0 :: FingerTree (Node (Elem a)) -> Digit (Elem a) -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> FingerTree (Node (Elem a)) -addDigits0 m1 (One a) (One b) m2 = - appendTree1 m1 (node2 a b) m2 -addDigits0 m1 (One a) (Two b c) m2 = - appendTree1 m1 (node3 a b c) m2 -addDigits0 m1 (One a) (Three b c d) m2 = - appendTree2 m1 (node2 a b) (node2 c d) m2 -addDigits0 m1 (One a) (Four b c d e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits0 m1 (Two a b) (One c) m2 = - appendTree1 m1 (node3 a b c) m2 -addDigits0 m1 (Two a b) (Two c d) m2 = - appendTree2 m1 (node2 a b) (node2 c d) m2 -addDigits0 m1 (Two a b) (Three c d e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits0 m1 (Two a b) (Four c d e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits0 m1 (Three a b c) (One d) m2 = - appendTree2 m1 (node2 a b) (node2 c d) m2 -addDigits0 m1 (Three a b c) (Two d e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits0 m1 (Three a b c) (Three d e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits0 m1 (Three a b c) (Four d e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits0 m1 (Four a b c d) (One e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits0 m1 (Four a b c d) (Two e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits0 m1 (Four a b c d) (Three e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits0 m1 (Four a b c d) (Four e f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 - -appendTree1 :: FingerTree (Node a) -> Node a -> FingerTree (Node a) -> FingerTree (Node a) -appendTree1 EmptyT !a xs = - a `consTree` xs -appendTree1 xs !a EmptyT = - xs `snocTree` a -appendTree1 (Single x) !a xs = - x `consTree` a `consTree` xs -appendTree1 xs !a (Single x) = - xs `snocTree` a `snocTree` x -appendTree1 (Deep s1 pr1 m1 sf1) a (Deep s2 pr2 m2 sf2) = - Deep (s1 + size a + s2) pr1 m sf2 - where !m = addDigits1 m1 sf1 a pr2 m2 - -addDigits1 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) -addDigits1 m1 (One a) b (One c) m2 = - appendTree1 m1 (node3 a b c) m2 -addDigits1 m1 (One a) b (Two c d) m2 = - appendTree2 m1 (node2 a b) (node2 c d) m2 -addDigits1 m1 (One a) b (Three c d e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits1 m1 (One a) b (Four c d e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits1 m1 (Two a b) c (One d) m2 = - appendTree2 m1 (node2 a b) (node2 c d) m2 -addDigits1 m1 (Two a b) c (Two d e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits1 m1 (Two a b) c (Three d e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits1 m1 (Two a b) c (Four d e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits1 m1 (Three a b c) d (One e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits1 m1 (Three a b c) d (Two e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits1 m1 (Three a b c) d (Three e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits1 m1 (Three a b c) d (Four e f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits1 m1 (Four a b c d) e (One f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits1 m1 (Four a b c d) e (Two f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits1 m1 (Four a b c d) e (Three f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits1 m1 (Four a b c d) e (Four f g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 - -appendTree2 :: FingerTree (Node a) -> Node a -> Node a -> FingerTree (Node a) -> FingerTree (Node a) -appendTree2 EmptyT !a !b xs = - a `consTree` b `consTree` xs -appendTree2 xs !a !b EmptyT = - xs `snocTree` a `snocTree` b -appendTree2 (Single x) a b xs = - x `consTree` a `consTree` b `consTree` xs -appendTree2 xs a b (Single x) = - xs `snocTree` a `snocTree` b `snocTree` x -appendTree2 (Deep s1 pr1 m1 sf1) a b (Deep s2 pr2 m2 sf2) = - Deep (s1 + size a + size b + s2) pr1 m sf2 - where !m = addDigits2 m1 sf1 a b pr2 m2 - -addDigits2 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) -addDigits2 m1 (One a) b c (One d) m2 = - appendTree2 m1 (node2 a b) (node2 c d) m2 -addDigits2 m1 (One a) b c (Two d e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits2 m1 (One a) b c (Three d e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits2 m1 (One a) b c (Four d e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits2 m1 (Two a b) c d (One e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits2 m1 (Two a b) c d (Two e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits2 m1 (Two a b) c d (Three e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits2 m1 (Two a b) c d (Four e f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits2 m1 (Three a b c) d e (One f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits2 m1 (Three a b c) d e (Two f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits2 m1 (Three a b c) d e (Three f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits2 m1 (Three a b c) d e (Four f g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits2 m1 (Four a b c d) e f (One g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits2 m1 (Four a b c d) e f (Two g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits2 m1 (Four a b c d) e f (Three g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits2 m1 (Four a b c d) e f (Four g h i j) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 - -appendTree3 :: FingerTree (Node a) -> Node a -> Node a -> Node a -> FingerTree (Node a) -> FingerTree (Node a) -appendTree3 EmptyT !a !b !c xs = - a `consTree` b `consTree` c `consTree` xs -appendTree3 xs !a !b !c EmptyT = - xs `snocTree` a `snocTree` b `snocTree` c -appendTree3 (Single x) a b c xs = - x `consTree` a `consTree` b `consTree` c `consTree` xs -appendTree3 xs a b c (Single x) = - xs `snocTree` a `snocTree` b `snocTree` c `snocTree` x -appendTree3 (Deep s1 pr1 m1 sf1) a b c (Deep s2 pr2 m2 sf2) = - Deep (s1 + size a + size b + size c + s2) pr1 m sf2 - where !m = addDigits3 m1 sf1 a b c pr2 m2 - -addDigits3 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Node a -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) -addDigits3 m1 (One a) !b !c !d (One e) m2 = - appendTree2 m1 (node3 a b c) (node2 d e) m2 -addDigits3 m1 (One a) b c d (Two e f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits3 m1 (One a) b c d (Three e f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits3 m1 (One a) b c d (Four e f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits3 m1 (Two a b) !c !d !e (One f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits3 m1 (Two a b) c d e (Two f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits3 m1 (Two a b) c d e (Three f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits3 m1 (Two a b) c d e (Four f g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits3 m1 (Three a b c) !d !e !f (One g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits3 m1 (Three a b c) d e f (Two g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits3 m1 (Three a b c) d e f (Three g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits3 m1 (Three a b c) d e f (Four g h i j) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 -addDigits3 m1 (Four a b c d) !e !f !g (One h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits3 m1 (Four a b c d) e f g (Two h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits3 m1 (Four a b c d) e f g (Three h i j) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 -addDigits3 m1 (Four a b c d) e f g (Four h i j k) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node2 j k) m2 - -appendTree4 :: FingerTree (Node a) -> Node a -> Node a -> Node a -> Node a -> FingerTree (Node a) -> FingerTree (Node a) -appendTree4 EmptyT !a !b !c !d xs = - a `consTree` b `consTree` c `consTree` d `consTree` xs -appendTree4 xs !a !b !c !d EmptyT = - xs `snocTree` a `snocTree` b `snocTree` c `snocTree` d -appendTree4 (Single x) a b c d xs = - x `consTree` a `consTree` b `consTree` c `consTree` d `consTree` xs -appendTree4 xs a b c d (Single x) = - xs `snocTree` a `snocTree` b `snocTree` c `snocTree` d `snocTree` x -appendTree4 (Deep s1 pr1 m1 sf1) a b c d (Deep s2 pr2 m2 sf2) = - Deep (s1 + size a + size b + size c + size d + s2) pr1 m sf2 - where !m = addDigits4 m1 sf1 a b c d pr2 m2 - -addDigits4 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Node a -> Node a -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) -addDigits4 m1 (One a) !b !c !d !e (One f) m2 = - appendTree2 m1 (node3 a b c) (node3 d e f) m2 -addDigits4 m1 (One a) b c d e (Two f g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits4 m1 (One a) b c d e (Three f g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits4 m1 (One a) b c d e (Four f g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits4 m1 (Two a b) !c !d !e !f (One g) m2 = - appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 -addDigits4 m1 (Two a b) c d e f (Two g h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits4 m1 (Two a b) c d e f (Three g h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits4 m1 (Two a b) c d e f (Four g h i j) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 -addDigits4 m1 (Three a b c) !d !e !f !g (One h) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 -addDigits4 m1 (Three a b c) d e f g (Two h i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits4 m1 (Three a b c) d e f g (Three h i j) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 -addDigits4 m1 (Three a b c) d e f g (Four h i j k) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node2 j k) m2 -addDigits4 m1 (Four a b c d) !e !f !g !h (One i) m2 = - appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 -addDigits4 m1 (Four a b c d) !e !f !g !h (Two i j) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 -addDigits4 m1 (Four a b c d) !e !f !g !h (Three i j k) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node2 j k) m2 -addDigits4 m1 (Four a b c d) !e !f !g !h (Four i j k l) m2 = - appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node3 j k l) m2 - --- | Builds a sequence from a seed value. Takes time linear in the --- number of generated elements. /WARNING:/ If the number of generated --- elements is infinite, this method will not terminate. -unfoldr :: (b -> Maybe (a, b)) -> b -> Seq a -unfoldr f = unfoldr' empty - -- uses tail recursion rather than, for instance, the List implementation. - where unfoldr' !as b = maybe as (\ (a, b') -> unfoldr' (as `snoc'` a) b') (f b) - --- | @'unfoldl' f x@ is equivalent to @'reverse' ('unfoldr' ('fmap' swap . f) x)@. -unfoldl :: (b -> Maybe (b, a)) -> b -> Seq a -unfoldl f = unfoldl' empty - where unfoldl' !as b = maybe as (\ (b', a) -> unfoldl' (a `cons'` as) b') (f b) - --- | /O(n)/. Constructs a sequence by repeated application of a function --- to a seed value. --- --- > iterateN n f x = fromList (Prelude.take n (Prelude.iterate f x)) -iterateN :: Int -> (a -> a) -> a -> Seq a -iterateN n f x - | n >= 0 = replicateA n (State (\ y -> (f y, y))) `execState` x - | otherwise = error "iterateN takes a nonnegative integer argument" - ------------------------------------------------------------------------- --- Deconstruction ------------------------------------------------------------------------- - --- | /O(1)/. Is this the empty sequence? -null :: Seq a -> Bool -null (Seq EmptyT) = True -null _ = False - --- | /O(1)/. The number of elements in the sequence. -length :: Seq a -> Int -length (Seq xs) = size xs - --- Views - -data ViewLTree a = ConsLTree a (FingerTree a) | EmptyLTree -data ViewRTree a = SnocRTree (FingerTree a) a | EmptyRTree - --- | View of the left end of a sequence. -data ViewL a - = EmptyL -- ^ empty sequence - | a :< Seq a -- ^ leftmost element and the rest of the sequence - deriving (Eq, Ord, Show, Read) - -#if __GLASGOW_HASKELL__ -deriving instance Data a => Data (ViewL a) -#endif -#if __GLASGOW_HASKELL__ >= 706 -deriving instance Generic1 ViewL -#endif -#if __GLASGOW_HASKELL__ >= 702 -deriving instance Generic (ViewL a) -#endif - -INSTANCE_TYPEABLE1(ViewL) - -instance Functor ViewL where - {-# INLINE fmap #-} - fmap _ EmptyL = EmptyL - fmap f (x :< xs) = f x :< fmap f xs - -instance Foldable ViewL where - foldr _ z EmptyL = z - foldr f z (x :< xs) = f x (foldr f z xs) - - foldl _ z EmptyL = z - foldl f z (x :< xs) = foldl f (f z x) xs - - foldl1 _ EmptyL = error "foldl1: empty view" - foldl1 f (x :< xs) = foldl f x xs - -#if MIN_VERSION_base(4,8,0) - null EmptyL = True - null (_ :< _) = False - - length EmptyL = 0 - length (_ :< xs) = 1 + length xs -#endif - -instance Traversable ViewL where - traverse _ EmptyL = pure EmptyL - traverse f (x :< xs) = (:<) <$> f x <*> traverse f xs - --- | /O(1)/. Analyse the left end of a sequence. -viewl :: Seq a -> ViewL a -viewl (Seq xs) = case viewLTree xs of - EmptyLTree -> EmptyL - ConsLTree (Elem x) xs' -> x :< Seq xs' - -{-# SPECIALIZE viewLTree :: FingerTree (Elem a) -> ViewLTree (Elem a) #-} -{-# SPECIALIZE viewLTree :: FingerTree (Node a) -> ViewLTree (Node a) #-} -viewLTree :: Sized a => FingerTree a -> ViewLTree a -viewLTree EmptyT = EmptyLTree -viewLTree (Single a) = ConsLTree a EmptyT -viewLTree (Deep s (One a) m sf) = ConsLTree a (pullL (s - size a) m sf) -viewLTree (Deep s (Two a b) m sf) = - ConsLTree a (Deep (s - size a) (One b) m sf) -viewLTree (Deep s (Three a b c) m sf) = - ConsLTree a (Deep (s - size a) (Two b c) m sf) -viewLTree (Deep s (Four a b c d) m sf) = - ConsLTree a (Deep (s - size a) (Three b c d) m sf) - --- | View of the right end of a sequence. -data ViewR a - = EmptyR -- ^ empty sequence - | Seq a :> a -- ^ the sequence minus the rightmost element, - -- and the rightmost element - deriving (Eq, Ord, Show, Read) - -#if __GLASGOW_HASKELL__ -deriving instance Data a => Data (ViewR a) -#endif -#if __GLASGOW_HASKELL__ >= 706 -deriving instance Generic1 ViewR -#endif -#if __GLASGOW_HASKELL__ >= 702 -deriving instance Generic (ViewR a) -#endif - -INSTANCE_TYPEABLE1(ViewR) - -instance Functor ViewR where - {-# INLINE fmap #-} - fmap _ EmptyR = EmptyR - fmap f (xs :> x) = fmap f xs :> f x - -instance Foldable ViewR where - foldMap _ EmptyR = mempty - foldMap f (xs :> x) = foldMap f xs <> f x - - foldr _ z EmptyR = z - foldr f z (xs :> x) = foldr f (f x z) xs - - foldl _ z EmptyR = z - foldl f z (xs :> x) = foldl f z xs `f` x - - foldr1 _ EmptyR = error "foldr1: empty view" - foldr1 f (xs :> x) = foldr f x xs -#if MIN_VERSION_base(4,8,0) - null EmptyR = True - null (_ :> _) = False - - length EmptyR = 0 - length (xs :> _) = length xs + 1 -#endif - -instance Traversable ViewR where - traverse _ EmptyR = pure EmptyR - traverse f (xs :> x) = (:>) <$> traverse f xs <*> f x - --- | /O(1)/. Analyse the right end of a sequence. -viewr :: Seq a -> ViewR a -viewr (Seq xs) = case viewRTree xs of - EmptyRTree -> EmptyR - SnocRTree xs' (Elem x) -> Seq xs' :> x - -{-# SPECIALIZE viewRTree :: FingerTree (Elem a) -> ViewRTree (Elem a) #-} -{-# SPECIALIZE viewRTree :: FingerTree (Node a) -> ViewRTree (Node a) #-} -viewRTree :: Sized a => FingerTree a -> ViewRTree a -viewRTree EmptyT = EmptyRTree -viewRTree (Single z) = SnocRTree EmptyT z -viewRTree (Deep s pr m (One z)) = SnocRTree (pullR (s - size z) pr m) z -viewRTree (Deep s pr m (Two y z)) = - SnocRTree (Deep (s - size z) pr m (One y)) z -viewRTree (Deep s pr m (Three x y z)) = - SnocRTree (Deep (s - size z) pr m (Two x y)) z -viewRTree (Deep s pr m (Four w x y z)) = - SnocRTree (Deep (s - size z) pr m (Three w x y)) z - ------------------------------------------------------------------------- --- Scans --- --- These are not particularly complex applications of the Traversable --- functor, though making the correspondence with Data.List exact --- requires the use of (<|) and (|>). --- --- Note that save for the single (<|) or (|>), we maintain the original --- structure of the Seq, not having to do any restructuring of our own. --- --- wasserman.louis@gmail.com, 5/23/09 ------------------------------------------------------------------------- - --- | 'scanl' is similar to 'foldl', but returns a sequence of reduced --- values from the left: --- --- > scanl f z (fromList [x1, x2, ...]) = fromList [z, z `f` x1, (z `f` x1) `f` x2, ...] -scanl :: (a -> b -> a) -> a -> Seq b -> Seq a -scanl f z0 xs = z0 <| snd (mapAccumL (\ x z -> let x' = f x z in (x', x')) z0 xs) - --- | 'scanl1' is a variant of 'scanl' that has no starting value argument: --- --- > scanl1 f (fromList [x1, x2, ...]) = fromList [x1, x1 `f` x2, ...] -scanl1 :: (a -> a -> a) -> Seq a -> Seq a -scanl1 f xs = case viewl xs of - EmptyL -> error "scanl1 takes a nonempty sequence as an argument" - x :< xs' -> scanl f x xs' - --- | 'scanr' is the right-to-left dual of 'scanl'. -scanr :: (a -> b -> b) -> b -> Seq a -> Seq b -scanr f z0 xs = snd (mapAccumR (\ z x -> let z' = f x z in (z', z')) z0 xs) |> z0 - --- | 'scanr1' is a variant of 'scanr' that has no starting value argument. -scanr1 :: (a -> a -> a) -> Seq a -> Seq a -scanr1 f xs = case viewr xs of - EmptyR -> error "scanr1 takes a nonempty sequence as an argument" - xs' :> x -> scanr f x xs' - --- Indexing - --- | /O(log(min(i,n-i)))/. The element at the specified position, --- counting from 0. The argument should thus be a non-negative --- integer less than the size of the sequence. --- If the position is out of range, 'index' fails with an error. --- --- prop> xs `index` i = toList xs !! i --- --- Caution: 'index' necessarily delays retrieving the requested --- element until the result is forced. It can therefore lead to a space --- leak if the result is stored, unforced, in another structure. To retrieve --- an element immediately without forcing it, use 'lookup' or '(!?)'. -index :: Seq a -> Int -> a -index (Seq xs) i - -- See note on unsigned arithmetic in splitAt - | fromIntegral i < (fromIntegral (size xs) :: Word) = case lookupTree i xs of - Place _ (Elem x) -> x - | otherwise = error "index out of bounds" - --- | /O(log(min(i,n-i)))/. The element at the specified position, --- counting from 0. If the specified position is negative or at --- least the length of the sequence, 'lookup' returns 'Nothing'. --- --- prop> 0 <= i < length xs ==> lookup i xs == Just (toList xs !! i) --- prop> i < 0 || i >= length xs ==> lookup i xs = Nothing --- --- Unlike 'index', this can be used to retrieve an element without --- forcing it. For example, to insert the fifth element of a sequence --- @xs@ into a 'Data.Map.Lazy.Map' @m@ at key @k@, you could use --- --- @ --- case lookup 5 xs of --- Nothing -> m --- Just x -> 'Data.Map.Lazy.insert' k x m --- @ --- --- @since 0.5.8 -lookup :: Int -> Seq a -> Maybe a -lookup i (Seq xs) - -- Note: we perform the lookup *before* applying the Just constructor - -- to ensure that we don't hold a reference to the whole sequence in - -- a thunk. If we applied the Just constructor around the case, the - -- actual lookup wouldn't be performed unless and until the value was - -- forced. - | fromIntegral i < (fromIntegral (size xs) :: Word) = case lookupTree i xs of - Place _ (Elem x) -> Just x - | otherwise = Nothing - --- | /O(log(min(i,n-i)))/. A flipped, infix version of `lookup`. --- --- @since 0.5.8 -(!?) :: Seq a -> Int -> Maybe a -(!?) = flip lookup - -data Place a = Place {-# UNPACK #-} !Int a -#if TESTING - deriving Show -#endif - -{-# SPECIALIZE lookupTree :: Int -> FingerTree (Elem a) -> Place (Elem a) #-} -{-# SPECIALIZE lookupTree :: Int -> FingerTree (Node a) -> Place (Node a) #-} -lookupTree :: Sized a => Int -> FingerTree a -> Place a -lookupTree !_ EmptyT = error "lookupTree of empty tree" -lookupTree i (Single x) = Place i x -lookupTree i (Deep _ pr m sf) - | i < spr = lookupDigit i pr - | i < spm = case lookupTree (i - spr) m of - Place i' xs -> lookupNode i' xs - | otherwise = lookupDigit (i - spm) sf - where - spr = size pr - spm = spr + size m - -{-# SPECIALIZE lookupNode :: Int -> Node (Elem a) -> Place (Elem a) #-} -{-# SPECIALIZE lookupNode :: Int -> Node (Node a) -> Place (Node a) #-} -lookupNode :: Sized a => Int -> Node a -> Place a -lookupNode i (Node2 _ a b) - | i < sa = Place i a - | otherwise = Place (i - sa) b - where - sa = size a -lookupNode i (Node3 _ a b c) - | i < sa = Place i a - | i < sab = Place (i - sa) b - | otherwise = Place (i - sab) c - where - sa = size a - sab = sa + size b - -{-# SPECIALIZE lookupDigit :: Int -> Digit (Elem a) -> Place (Elem a) #-} -{-# SPECIALIZE lookupDigit :: Int -> Digit (Node a) -> Place (Node a) #-} -lookupDigit :: Sized a => Int -> Digit a -> Place a -lookupDigit i (One a) = Place i a -lookupDigit i (Two a b) - | i < sa = Place i a - | otherwise = Place (i - sa) b - where - sa = size a -lookupDigit i (Three a b c) - | i < sa = Place i a - | i < sab = Place (i - sa) b - | otherwise = Place (i - sab) c - where - sa = size a - sab = sa + size b -lookupDigit i (Four a b c d) - | i < sa = Place i a - | i < sab = Place (i - sa) b - | i < sabc = Place (i - sab) c - | otherwise = Place (i - sabc) d - where - sa = size a - sab = sa + size b - sabc = sab + size c - --- | /O(log(min(i,n-i)))/. Replace the element at the specified position. --- If the position is out of range, the original sequence is returned. -update :: Int -> a -> Seq a -> Seq a -update i x (Seq xs) - -- See note on unsigned arithmetic in splitAt - | fromIntegral i < (fromIntegral (size xs) :: Word) = Seq (updateTree (Elem x) i xs) - | otherwise = Seq xs - --- It seems a shame to copy the implementation of the top layer of --- `adjust` instead of just using `update i x = adjust (const x) i`. --- With the latter implementation, updating the same position many --- times could lead to silly thunks building up around that position. --- The thunks will each look like @const v a@, where @v@ is the new --- value and @a@ the old. -updateTree :: Elem a -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) -updateTree _ !_ EmptyT = EmptyT -- Unreachable -updateTree v _i (Single _) = Single v -updateTree v i (Deep s pr m sf) - | i < spr = Deep s (updateDigit v i pr) m sf - | i < spm = let !m' = adjustTree (updateNode v) (i - spr) m - in Deep s pr m' sf - | otherwise = Deep s pr m (updateDigit v (i - spm) sf) - where - spr = size pr - spm = spr + size m - -updateNode :: Elem a -> Int -> Node (Elem a) -> Node (Elem a) -updateNode v i (Node2 s a b) - | i < sa = Node2 s v b - | otherwise = Node2 s a v - where - sa = size a -updateNode v i (Node3 s a b c) - | i < sa = Node3 s v b c - | i < sab = Node3 s a v c - | otherwise = Node3 s a b v - where - sa = size a - sab = sa + size b - -updateDigit :: Elem a -> Int -> Digit (Elem a) -> Digit (Elem a) -updateDigit v !_i (One _) = One v -updateDigit v i (Two a b) - | i < sa = Two v b - | otherwise = Two a v - where - sa = size a -updateDigit v i (Three a b c) - | i < sa = Three v b c - | i < sab = Three a v c - | otherwise = Three a b v - where - sa = size a - sab = sa + size b -updateDigit v i (Four a b c d) - | i < sa = Four v b c d - | i < sab = Four a v c d - | i < sabc = Four a b v d - | otherwise = Four a b c v - where - sa = size a - sab = sa + size b - sabc = sab + size c - --- | /O(log(min(i,n-i)))/. Update the element at the specified position. If --- the position is out of range, the original sequence is returned. 'adjust' --- can lead to poor performance and even memory leaks, because it does not --- force the new value before installing it in the sequence. 'adjust'' should --- usually be preferred. -adjust :: (a -> a) -> Int -> Seq a -> Seq a -adjust f i (Seq xs) - -- See note on unsigned arithmetic in splitAt - | fromIntegral i < (fromIntegral (size xs) :: Word) = Seq (adjustTree (`seq` fmap f) i xs) - | otherwise = Seq xs - --- | /O(log(min(i,n-i)))/. Update the element at the specified position. --- If the position is out of range, the original sequence is returned. --- The new value is forced before it is installed in the sequence. --- --- @ --- adjust' f i xs = --- case xs !? i of --- Nothing -> xs --- Just x -> let !x' = f x --- in update i x' xs --- @ --- --- @since 0.5.8 -adjust' :: forall a . (a -> a) -> Int -> Seq a -> Seq a -#if __GLASGOW_HASKELL__ >= 708 -adjust' f i xs - -- See note on unsigned arithmetic in splitAt - | fromIntegral i < (fromIntegral (length xs) :: Word) = - coerce $ adjustTree (\ !_k (ForceBox a) -> ForceBox (f a)) i (coerce xs) - | otherwise = xs -#else --- This is inefficient, but fixing it would take a lot of fuss and bother --- for little immediate gain. We can deal with that when we have another --- Haskell implementation to worry about. -adjust' f i xs = - case xs !? i of - Nothing -> xs - Just x -> let !x' = f x - in update i x' xs -#endif - -{-# SPECIALIZE adjustTree :: (Int -> ForceBox a -> ForceBox a) -> Int -> FingerTree (ForceBox a) -> FingerTree (ForceBox a) #-} -{-# SPECIALIZE adjustTree :: (Int -> Elem a -> Elem a) -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) #-} -{-# SPECIALIZE adjustTree :: (Int -> Node a -> Node a) -> Int -> FingerTree (Node a) -> FingerTree (Node a) #-} -adjustTree :: (Sized a, MaybeForce a) => (Int -> a -> a) -> - Int -> FingerTree a -> FingerTree a -adjustTree _ !_ EmptyT = EmptyT -- Unreachable -adjustTree f i (Single x) = Single $!? f i x -adjustTree f i (Deep s pr m sf) - | i < spr = Deep s (adjustDigit f i pr) m sf - | i < spm = let !m' = adjustTree (adjustNode f) (i - spr) m - in Deep s pr m' sf - | otherwise = Deep s pr m (adjustDigit f (i - spm) sf) - where - spr = size pr - spm = spr + size m - -{-# SPECIALIZE adjustNode :: (Int -> Elem a -> Elem a) -> Int -> Node (Elem a) -> Node (Elem a) #-} -{-# SPECIALIZE adjustNode :: (Int -> Node a -> Node a) -> Int -> Node (Node a) -> Node (Node a) #-} -adjustNode :: (Sized a, MaybeForce a) => (Int -> a -> a) -> Int -> Node a -> Node a -adjustNode f i (Node2 s a b) - | i < sa = let fia = f i a in fia `mseq` Node2 s fia b - | otherwise = let fisab = f (i - sa) b in fisab `mseq` Node2 s a fisab - where - sa = size a -adjustNode f i (Node3 s a b c) - | i < sa = let fia = f i a in fia `mseq` Node3 s fia b c - | i < sab = let fisab = f (i - sa) b in fisab `mseq` Node3 s a fisab c - | otherwise = let fisabc = f (i - sab) c in fisabc `mseq` Node3 s a b fisabc - where - sa = size a - sab = sa + size b - -{-# SPECIALIZE adjustDigit :: (Int -> Elem a -> Elem a) -> Int -> Digit (Elem a) -> Digit (Elem a) #-} -{-# SPECIALIZE adjustDigit :: (Int -> Node a -> Node a) -> Int -> Digit (Node a) -> Digit (Node a) #-} -adjustDigit :: (Sized a, MaybeForce a) => (Int -> a -> a) -> Int -> Digit a -> Digit a -adjustDigit f !i (One a) = One $!? f i a -adjustDigit f i (Two a b) - | i < sa = let fia = f i a in fia `mseq` Two fia b - | otherwise = let fisab = f (i - sa) b in fisab `mseq` Two a fisab - where - sa = size a -adjustDigit f i (Three a b c) - | i < sa = let fia = f i a in fia `mseq` Three fia b c - | i < sab = let fisab = f (i - sa) b in fisab `mseq` Three a fisab c - | otherwise = let fisabc = f (i - sab) c in fisabc `mseq` Three a b fisabc - where - sa = size a - sab = sa + size b -adjustDigit f i (Four a b c d) - | i < sa = let fia = f i a in fia `mseq` Four fia b c d - | i < sab = let fisab = f (i - sa) b in fisab `mseq` Four a fisab c d - | i < sabc = let fisabc = f (i - sab) c in fisabc `mseq` Four a b fisabc d - | otherwise = let fisabcd = f (i - sabc) d in fisabcd `mseq` Four a b c fisabcd - where - sa = size a - sab = sa + size b - sabc = sab + size c - --- | /O(log(min(i,n-i)))/. @'insertAt' i x xs@ inserts @x@ into @xs@ --- at the index @i@, shifting the rest of the sequence over. --- --- @ --- insertAt 2 x (fromList [a,b,c,d]) = fromList [a,b,x,c,d] --- insertAt 4 x (fromList [a,b,c,d]) = insertAt 10 x (fromList [a,b,c,d]) --- = fromList [a,b,c,d,x] --- @ --- --- prop> insertAt i x xs = take i xs >< singleton x >< drop i xs --- --- @since 0.5.8 -insertAt :: Int -> a -> Seq a -> Seq a -insertAt i a s@(Seq xs) - | fromIntegral i < (fromIntegral (size xs) :: Word) - = Seq (insTree (`seq` InsTwo (Elem a)) i xs) - | i <= 0 = a <| s - | otherwise = s |> a - -data Ins a = InsOne a | InsTwo a a - -{-# SPECIALIZE insTree :: (Int -> Elem a -> Ins (Elem a)) -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) #-} -{-# SPECIALIZE insTree :: (Int -> Node a -> Ins (Node a)) -> Int -> FingerTree (Node a) -> FingerTree (Node a) #-} -insTree :: Sized a => (Int -> a -> Ins a) -> - Int -> FingerTree a -> FingerTree a -insTree _ !_ EmptyT = EmptyT -- Unreachable -insTree f i (Single x) = case f i x of - InsOne x' -> Single x' - InsTwo m n -> deep (One m) EmptyT (One n) -insTree f i (Deep s pr m sf) - | i < spr = case insLeftDigit f i pr of - InsLeftDig pr' -> Deep (s + 1) pr' m sf - InsDigNode pr' n -> m `seq` Deep (s + 1) pr' (n `consTree` m) sf - | i < spm = let !m' = insTree (insNode f) (i - spr) m - in Deep (s + 1) pr m' sf - | otherwise = case insRightDigit f (i - spm) sf of - InsRightDig sf' -> Deep (s + 1) pr m sf' - InsNodeDig n sf' -> m `seq` Deep (s + 1) pr (m `snocTree` n) sf' - where - spr = size pr - spm = spr + size m - -{-# SPECIALIZE insNode :: (Int -> Elem a -> Ins (Elem a)) -> Int -> Node (Elem a) -> Ins (Node (Elem a)) #-} -{-# SPECIALIZE insNode :: (Int -> Node a -> Ins (Node a)) -> Int -> Node (Node a) -> Ins (Node (Node a)) #-} -insNode :: Sized a => (Int -> a -> Ins a) -> Int -> Node a -> Ins (Node a) -insNode f i (Node2 s a b) - | i < sa = case f i a of - InsOne n -> InsOne $ Node2 (s + 1) n b - InsTwo m n -> InsOne $ Node3 (s + 1) m n b - | otherwise = case f (i - sa) b of - InsOne n -> InsOne $ Node2 (s + 1) a n - InsTwo m n -> InsOne $ Node3 (s + 1) a m n - where sa = size a -insNode f i (Node3 s a b c) - | i < sa = case f i a of - InsOne n -> InsOne $ Node3 (s + 1) n b c - InsTwo m n -> InsTwo (Node2 (sa + 1) m n) (Node2 (s - sa) b c) - | i < sab = case f (i - sa) b of - InsOne n -> InsOne $ Node3 (s + 1) a n c - InsTwo m n -> InsTwo am nc - where !am = node2 a m - !nc = node2 n c - | otherwise = case f (i - sab) c of - InsOne n -> InsOne $ Node3 (s + 1) a b n - InsTwo m n -> InsTwo (Node2 sab a b) (Node2 (s - sab + 1) m n) - where sa = size a - sab = sa + size b - -data InsDigNode a = InsLeftDig !(Digit a) | InsDigNode !(Digit a) !(Node a) -{-# SPECIALIZE insLeftDigit :: (Int -> Elem a -> Ins (Elem a)) -> Int -> Digit (Elem a) -> InsDigNode (Elem a) #-} -{-# SPECIALIZE insLeftDigit :: (Int -> Node a -> Ins (Node a)) -> Int -> Digit (Node a) -> InsDigNode (Node a) #-} -insLeftDigit :: Sized a => (Int -> a -> Ins a) -> Int -> Digit a -> InsDigNode a -insLeftDigit f !i (One a) = case f i a of - InsOne a' -> InsLeftDig $ One a' - InsTwo a1 a2 -> InsLeftDig $ Two a1 a2 -insLeftDigit f i (Two a b) - | i < sa = case f i a of - InsOne a' -> InsLeftDig $ Two a' b - InsTwo a1 a2 -> InsLeftDig $ Three a1 a2 b - | otherwise = case f (i - sa) b of - InsOne b' -> InsLeftDig $ Two a b' - InsTwo b1 b2 -> InsLeftDig $ Three a b1 b2 - where sa = size a -insLeftDigit f i (Three a b c) - | i < sa = case f i a of - InsOne a' -> InsLeftDig $ Three a' b c - InsTwo a1 a2 -> InsLeftDig $ Four a1 a2 b c - | i < sab = case f (i - sa) b of - InsOne b' -> InsLeftDig $ Three a b' c - InsTwo b1 b2 -> InsLeftDig $ Four a b1 b2 c - | otherwise = case f (i - sab) c of - InsOne c' -> InsLeftDig $ Three a b c' - InsTwo c1 c2 -> InsLeftDig $ Four a b c1 c2 - where sa = size a - sab = sa + size b -insLeftDigit f i (Four a b c d) - | i < sa = case f i a of - InsOne a' -> InsLeftDig $ Four a' b c d - InsTwo a1 a2 -> InsDigNode (Two a1 a2) (node3 b c d) - | i < sab = case f (i - sa) b of - InsOne b' -> InsLeftDig $ Four a b' c d - InsTwo b1 b2 -> InsDigNode (Two a b1) (node3 b2 c d) - | i < sabc = case f (i - sab) c of - InsOne c' -> InsLeftDig $ Four a b c' d - InsTwo c1 c2 -> InsDigNode (Two a b) (node3 c1 c2 d) - | otherwise = case f (i - sabc) d of - InsOne d' -> InsLeftDig $ Four a b c d' - InsTwo d1 d2 -> InsDigNode (Two a b) (node3 c d1 d2) - where sa = size a - sab = sa + size b - sabc = sab + size c - -data InsNodeDig a = InsRightDig !(Digit a) | InsNodeDig !(Node a) !(Digit a) -{-# SPECIALIZE insRightDigit :: (Int -> Elem a -> Ins (Elem a)) -> Int -> Digit (Elem a) -> InsNodeDig (Elem a) #-} -{-# SPECIALIZE insRightDigit :: (Int -> Node a -> Ins (Node a)) -> Int -> Digit (Node a) -> InsNodeDig (Node a) #-} -insRightDigit :: Sized a => (Int -> a -> Ins a) -> Int -> Digit a -> InsNodeDig a -insRightDigit f !i (One a) = case f i a of - InsOne a' -> InsRightDig $ One a' - InsTwo a1 a2 -> InsRightDig $ Two a1 a2 -insRightDigit f i (Two a b) - | i < sa = case f i a of - InsOne a' -> InsRightDig $ Two a' b - InsTwo a1 a2 -> InsRightDig $ Three a1 a2 b - | otherwise = case f (i - sa) b of - InsOne b' -> InsRightDig $ Two a b' - InsTwo b1 b2 -> InsRightDig $ Three a b1 b2 - where sa = size a -insRightDigit f i (Three a b c) - | i < sa = case f i a of - InsOne a' -> InsRightDig $ Three a' b c - InsTwo a1 a2 -> InsRightDig $ Four a1 a2 b c - | i < sab = case f (i - sa) b of - InsOne b' -> InsRightDig $ Three a b' c - InsTwo b1 b2 -> InsRightDig $ Four a b1 b2 c - | otherwise = case f (i - sab) c of - InsOne c' -> InsRightDig $ Three a b c' - InsTwo c1 c2 -> InsRightDig $ Four a b c1 c2 - where sa = size a - sab = sa + size b -insRightDigit f i (Four a b c d) - | i < sa = case f i a of - InsOne a' -> InsRightDig $ Four a' b c d - InsTwo a1 a2 -> InsNodeDig (node3 a1 a2 b) (Two c d) - | i < sab = case f (i - sa) b of - InsOne b' -> InsRightDig $ Four a b' c d - InsTwo b1 b2 -> InsNodeDig (node3 a b1 b2) (Two c d) - | i < sabc = case f (i - sab) c of - InsOne c' -> InsRightDig $ Four a b c' d - InsTwo c1 c2 -> InsNodeDig (node3 a b c1) (Two c2 d) - | otherwise = case f (i - sabc) d of - InsOne d' -> InsRightDig $ Four a b c d' - InsTwo d1 d2 -> InsNodeDig (node3 a b c) (Two d1 d2) - where sa = size a - sab = sa + size b - sabc = sab + size c - --- | /O(log(min(i,n-i)))/. Delete the element of a sequence at a given --- index. Return the original sequence if the index is out of range. --- --- @ --- deleteAt 2 [a,b,c,d] = [a,b,d] --- deleteAt 4 [a,b,c,d] = deleteAt (-1) [a,b,c,d] = [a,b,c,d] --- @ --- --- @since 0.5.8 -deleteAt :: Int -> Seq a -> Seq a -deleteAt i (Seq xs) - | fromIntegral i < (fromIntegral (size xs) :: Word) = Seq $ delTreeE i xs - | otherwise = Seq xs - -delTreeE :: Int -> FingerTree (Elem a) -> FingerTree (Elem a) -delTreeE !_i EmptyT = EmptyT -- Unreachable -delTreeE _i Single{} = EmptyT -delTreeE i (Deep s pr m sf) - | i < spr = delLeftDigitE i s pr m sf - | i < spm = case delTree delNodeE (i - spr) m of - FullTree m' -> Deep (s - 1) pr m' sf - DefectTree e -> delRebuildMiddle (s - 1) pr e sf - | otherwise = delRightDigitE (i - spm) s pr m sf - where spr = size pr - spm = spr + size m - -delNodeE :: Int -> Node (Elem a) -> Del (Elem a) -delNodeE i (Node3 _ a b c) = case i of - 0 -> Full $ Node2 2 b c - 1 -> Full $ Node2 2 a c - _ -> Full $ Node2 2 a b -delNodeE i (Node2 _ a b) = case i of - 0 -> Defect b - _ -> Defect a - - -delLeftDigitE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) -delLeftDigitE !_i s One{} m sf = pullL (s - 1) m sf -delLeftDigitE i s (Two a b) m sf - | i == 0 = Deep (s - 1) (One b) m sf - | otherwise = Deep (s - 1) (One a) m sf -delLeftDigitE i s (Three a b c) m sf - | i == 0 = Deep (s - 1) (Two b c) m sf - | i == 1 = Deep (s - 1) (Two a c) m sf - | otherwise = Deep (s - 1) (Two a b) m sf -delLeftDigitE i s (Four a b c d) m sf - | i == 0 = Deep (s - 1) (Three b c d) m sf - | i == 1 = Deep (s - 1) (Three a c d) m sf - | i == 2 = Deep (s - 1) (Three a b d) m sf - | otherwise = Deep (s - 1) (Three a b c) m sf - -delRightDigitE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) -delRightDigitE !_i s pr m One{} = pullR (s - 1) pr m -delRightDigitE i s pr m (Two a b) - | i == 0 = Deep (s - 1) pr m (One b) - | otherwise = Deep (s - 1) pr m (One a) -delRightDigitE i s pr m (Three a b c) - | i == 0 = Deep (s - 1) pr m (Two b c) - | i == 1 = Deep (s - 1) pr m (Two a c) - | otherwise = deep pr m (Two a b) -delRightDigitE i s pr m (Four a b c d) - | i == 0 = Deep (s - 1) pr m (Three b c d) - | i == 1 = Deep (s - 1) pr m (Three a c d) - | i == 2 = Deep (s - 1) pr m (Three a b d) - | otherwise = Deep (s - 1) pr m (Three a b c) - -data DelTree a = FullTree !(FingerTree (Node a)) | DefectTree a - -{-# SPECIALIZE delTree :: (Int -> Node (Elem a) -> Del (Elem a)) -> Int -> FingerTree (Node (Elem a)) -> DelTree (Elem a) #-} -{-# SPECIALIZE delTree :: (Int -> Node (Node a) -> Del (Node a)) -> Int -> FingerTree (Node (Node a)) -> DelTree (Node a) #-} -delTree :: Sized a => (Int -> Node a -> Del a) -> Int -> FingerTree (Node a) -> DelTree a -delTree _f !_i EmptyT = FullTree EmptyT -- Unreachable -delTree f i (Single a) = case f i a of - Full a' -> FullTree (Single a') - Defect e -> DefectTree e -delTree f i (Deep s pr m sf) - | i < spr = case delDigit f i pr of - FullDig pr' -> FullTree $ Deep (s - 1) pr' m sf - DefectDig e -> case viewLTree m of - EmptyLTree -> FullTree $ delRebuildRightDigit (s - 1) e sf - ConsLTree n m' -> FullTree $ delRebuildLeftSide (s - 1) e n m' sf - | i < spm = case delTree (delNode f) (i - spr) m of - FullTree m' -> FullTree (Deep (s - 1) pr m' sf) - DefectTree e -> FullTree $ delRebuildMiddle (s - 1) pr e sf - | otherwise = case delDigit f (i - spm) sf of - FullDig sf' -> FullTree $ Deep (s - 1) pr m sf' - DefectDig e -> case viewRTree m of - EmptyRTree -> FullTree $ delRebuildLeftDigit (s - 1) pr e - SnocRTree m' n -> FullTree $ delRebuildRightSide (s - 1) pr m' n e - where spr = size pr - spm = spr + size m - -data Del a = Full !(Node a) | Defect a - -{-# SPECIALIZE delNode :: (Int -> Node (Elem a) -> Del (Elem a)) -> Int -> Node (Node (Elem a)) -> Del (Node (Elem a)) #-} -{-# SPECIALIZE delNode :: (Int -> Node (Node a) -> Del (Node a)) -> Int -> Node (Node (Node a)) -> Del (Node (Node a)) #-} -delNode :: Sized a => (Int -> Node a -> Del a) -> Int -> Node (Node a) -> Del (Node a) -delNode f i (Node3 s a b c) - | i < sa = case f i a of - Full a' -> Full $ Node3 (s - 1) a' b c - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> Full $ Node3 (s - 1) (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) c - where !sx = size x - Node2 sxy x y -> Full $ Node2 (s - 1) (Node3 (sxy + se) e x y) c - | i < sab = case f (i - sa) b of - Full b' -> Full $ Node3 (s - 1) a b' c - Defect e -> let !se = size e in case a of - Node3 sxyz x y z -> Full $ Node3 (s - 1) (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) c - where !sz = size z - Node2 sxy x y -> Full $ Node2 (s - 1) (Node3 (sxy + se) x y e) c - | otherwise = case f (i - sab) c of - Full c' -> Full $ Node3 (s - 1) a b c' - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> Full $ Node3 (s - 1) a (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) - where !sz = size z - Node2 sxy x y -> Full $ Node2 (s - 1) a (Node3 (sxy + se) x y e) - where sa = size a - sab = sa + size b -delNode f i (Node2 s a b) - | i < sa = case f i a of - Full a' -> Full $ Node2 (s - 1) a' b - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> Full $ Node2 (s - 1) (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) - where !sx = size x - Node2 _ x y -> Defect $ Node3 (s - 1) e x y - | otherwise = case f (i - sa) b of - Full b' -> Full $ Node2 (s - 1) a b' - Defect e -> let !se = size e in case a of - Node3 sxyz x y z -> Full $ Node2 (s - 1) (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) - where !sz = size z - Node2 _ x y -> Defect $ Node3 (s - 1) x y e - where sa = size a - -{-# SPECIALIZE delRebuildRightDigit :: Int -> Elem a -> Digit (Node (Elem a)) -> FingerTree (Node (Elem a)) #-} -{-# SPECIALIZE delRebuildRightDigit :: Int -> Node a -> Digit (Node (Node a)) -> FingerTree (Node (Node a)) #-} -delRebuildRightDigit :: Sized a => Int -> a -> Digit (Node a) -> FingerTree (Node a) -delRebuildRightDigit s p (One a) = let !sp = size p in case a of - Node3 sxyz x y z -> Deep s (One (Node2 (sp + sx) p x)) EmptyT (One (Node2 (sxyz - sx) y z)) - where !sx = size x - Node2 sxy x y -> Single (Node3 (sp + sxy) p x y) -delRebuildRightDigit s p (Two a b) = let !sp = size p in case a of - Node3 sxyz x y z -> Deep s (Two (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z)) EmptyT (One b) - where !sx = size x - Node2 sxy x y -> Deep s (One (Node3 (sp + sxy) p x y)) EmptyT (One b) -delRebuildRightDigit s p (Three a b c) = let !sp = size p in case a of - Node3 sxyz x y z -> Deep s (Two (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z)) EmptyT (Two b c) - where !sx = size x - Node2 sxy x y -> Deep s (Two (Node3 (sp + sxy) p x y) b) EmptyT (One c) -delRebuildRightDigit s p (Four a b c d) = let !sp = size p in case a of - Node3 sxyz x y z -> Deep s (Three (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z) b) EmptyT (Two c d) - where !sx = size x - Node2 sxy x y -> Deep s (Two (Node3 (sp + sxy) p x y) b) EmptyT (Two c d) - -{-# SPECIALIZE delRebuildLeftDigit :: Int -> Digit (Node (Elem a)) -> Elem a -> FingerTree (Node (Elem a)) #-} -{-# SPECIALIZE delRebuildLeftDigit :: Int -> Digit (Node (Node a)) -> Node a -> FingerTree (Node (Node a)) #-} -delRebuildLeftDigit :: Sized a => Int -> Digit (Node a) -> a -> FingerTree (Node a) -delRebuildLeftDigit s (One a) p = let !sp = size p in case a of - Node3 sxyz x y z -> Deep s (One (Node2 (sxyz - sz) x y)) EmptyT (One (Node2 (sz + sp) z p)) - where !sz = size z - Node2 sxy x y -> Single (Node3 (sxy + sp) x y p) -delRebuildLeftDigit s (Two a b) p = let !sp = size p in case b of - Node3 sxyz x y z -> Deep s (Two a (Node2 (sxyz - sz) x y)) EmptyT (One (Node2 (sz + sp) z p)) - where !sz = size z - Node2 sxy x y -> Deep s (One a) EmptyT (One (Node3 (sxy + sp) x y p)) -delRebuildLeftDigit s (Three a b c) p = let !sp = size p in case c of - Node3 sxyz x y z -> Deep s (Two a b) EmptyT (Two (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) - where !sz = size z - Node2 sxy x y -> Deep s (Two a b) EmptyT (One (Node3 (sxy + sp) x y p)) -delRebuildLeftDigit s (Four a b c d) p = let !sp = size p in case d of - Node3 sxyz x y z -> Deep s (Three a b c) EmptyT (Two (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) - where !sz = size z - Node2 sxy x y -> Deep s (Two a b) EmptyT (Two c (Node3 (sxy + sp) x y p)) - -delRebuildLeftSide :: Sized a - => Int -> a -> Node (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) - -> FingerTree (Node a) -delRebuildLeftSide s p (Node2 _ a b) m sf = let !sp = size p in case a of - Node2 sxy x y -> Deep s (Two (Node3 (sp + sxy) p x y) b) m sf - Node3 sxyz x y z -> Deep s (Three (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z) b) m sf - where !sx = size x -delRebuildLeftSide s p (Node3 _ a b c) m sf = let !sp = size p in case a of - Node2 sxy x y -> Deep s (Three (Node3 (sp + sxy) p x y) b c) m sf - Node3 sxyz x y z -> Deep s (Four (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z) b c) m sf - where !sx = size x - -delRebuildRightSide :: Sized a - => Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Node (Node a) -> a - -> FingerTree (Node a) -delRebuildRightSide s pr m (Node2 _ a b) p = let !sp = size p in case b of - Node2 sxy x y -> Deep s pr m (Two a (Node3 (sxy + sp) x y p)) - Node3 sxyz x y z -> Deep s pr m (Three a (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) - where !sz = size z -delRebuildRightSide s pr m (Node3 _ a b c) p = let !sp = size p in case c of - Node2 sxy x y -> Deep s pr m (Three a b (Node3 (sxy + sp) x y p)) - Node3 sxyz x y z -> Deep s pr m (Four a b (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) - where !sz = size z - -delRebuildMiddle :: Sized a - => Int -> Digit a -> a -> Digit a - -> FingerTree a -delRebuildMiddle s (One a) e sf = Deep s (Two a e) EmptyT sf -delRebuildMiddle s (Two a b) e sf = Deep s (Three a b e) EmptyT sf -delRebuildMiddle s (Three a b c) e sf = Deep s (Four a b c e) EmptyT sf -delRebuildMiddle s (Four a b c d) e sf = Deep s (Two a b) (Single (node3 c d e)) sf - -data DelDig a = FullDig !(Digit (Node a)) | DefectDig a - -{-# SPECIALIZE delDigit :: (Int -> Node (Elem a) -> Del (Elem a)) -> Int -> Digit (Node (Elem a)) -> DelDig (Elem a) #-} -{-# SPECIALIZE delDigit :: (Int -> Node (Node a) -> Del (Node a)) -> Int -> Digit (Node (Node a)) -> DelDig (Node a) #-} -delDigit :: Sized a => (Int -> Node a -> Del a) -> Int -> Digit (Node a) -> DelDig a -delDigit f !i (One a) = case f i a of - Full a' -> FullDig $ One a' - Defect e -> DefectDig e -delDigit f i (Two a b) - | i < sa = case f i a of - Full a' -> FullDig $ Two a' b - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> FullDig $ Two (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) - where !sx = size x - Node2 sxy x y -> FullDig $ One (Node3 (se + sxy) e x y) - | otherwise = case f (i - sa) b of - Full b' -> FullDig $ Two a b' - Defect e -> let !se = size e in case a of - Node3 sxyz x y z -> FullDig $ Two (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) - where !sz = size z - Node2 sxy x y -> FullDig $ One (Node3 (sxy + se) x y e) - where sa = size a -delDigit f i (Three a b c) - | i < sa = case f i a of - Full a' -> FullDig $ Three a' b c - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> FullDig $ Three (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) c - where !sx = size x - Node2 sxy x y -> FullDig $ Two (Node3 (se + sxy) e x y) c - | i < sab = case f (i - sa) b of - Full b' -> FullDig $ Three a b' c - Defect e -> let !se = size e in case a of - Node3 sxyz x y z -> FullDig $ Three (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) c - where !sz = size z - Node2 sxy x y -> FullDig $ Two (Node3 (sxy + se) x y e) c - | otherwise = case f (i - sab) c of - Full c' -> FullDig $ Three a b c' - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> FullDig $ Three a (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) - where !sz = size z - Node2 sxy x y -> FullDig $ Two a (Node3 (sxy + se) x y e) - where sa = size a - sab = sa + size b -delDigit f i (Four a b c d) - | i < sa = case f i a of - Full a' -> FullDig $ Four a' b c d - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> FullDig $ Four (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) c d - where !sx = size x - Node2 sxy x y -> FullDig $ Three (Node3 (se + sxy) e x y) c d - | i < sab = case f (i - sa) b of - Full b' -> FullDig $ Four a b' c d - Defect e -> let !se = size e in case a of - Node3 sxyz x y z -> FullDig $ Four (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) c d - where !sz = size z - Node2 sxy x y -> FullDig $ Three (Node3 (sxy + se) x y e) c d - | i < sabc = case f (i - sab) c of - Full c' -> FullDig $ Four a b c' d - Defect e -> let !se = size e in case b of - Node3 sxyz x y z -> FullDig $ Four a (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) d - where !sz = size z - Node2 sxy x y -> FullDig $ Three a (Node3 (sxy + se) x y e) d - | otherwise = case f (i - sabc) d of - Full d' -> FullDig $ Four a b c d' - Defect e -> let !se = size e in case c of - Node3 sxyz x y z -> FullDig $ Four a b (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) - where !sz = size z - Node2 sxy x y -> FullDig $ Three a b (Node3 (sxy + se) x y e) - where sa = size a - sab = sa + size b - sabc = sab + size c - - --- | /O(n)/. A generalization of 'fmap', 'mapWithIndex' takes a mapping --- function that also depends on the element's index, and applies it to every --- element in the sequence. -mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b -mapWithIndex f' (Seq xs') = Seq $ mapWithIndexTree (\s (Elem a) -> Elem (f' s a)) 0 xs' - where - {-# SPECIALIZE mapWithIndexTree :: (Int -> Elem y -> b) -> Int -> FingerTree (Elem y) -> FingerTree b #-} - {-# SPECIALIZE mapWithIndexTree :: (Int -> Node y -> b) -> Int -> FingerTree (Node y) -> FingerTree b #-} - mapWithIndexTree :: Sized a => (Int -> a -> b) -> Int -> FingerTree a -> FingerTree b - mapWithIndexTree _ !_s EmptyT = EmptyT - mapWithIndexTree f s (Single xs) = Single $ f s xs - mapWithIndexTree f s (Deep n pr m sf) = - Deep n - (mapWithIndexDigit f s pr) - (mapWithIndexTree (mapWithIndexNode f) sPspr m) - (mapWithIndexDigit f sPsprm sf) - where - !sPspr = s + size pr - !sPsprm = sPspr + size m - - {-# SPECIALIZE mapWithIndexDigit :: (Int -> Elem y -> b) -> Int -> Digit (Elem y) -> Digit b #-} - {-# SPECIALIZE mapWithIndexDigit :: (Int -> Node y -> b) -> Int -> Digit (Node y) -> Digit b #-} - mapWithIndexDigit :: Sized a => (Int -> a -> b) -> Int -> Digit a -> Digit b - mapWithIndexDigit f !s (One a) = One (f s a) - mapWithIndexDigit f s (Two a b) = Two (f s a) (f sPsa b) - where - !sPsa = s + size a - mapWithIndexDigit f s (Three a b c) = - Three (f s a) (f sPsa b) (f sPsab c) - where - !sPsa = s + size a - !sPsab = sPsa + size b - mapWithIndexDigit f s (Four a b c d) = - Four (f s a) (f sPsa b) (f sPsab c) (f sPsabc d) - where - !sPsa = s + size a - !sPsab = sPsa + size b - !sPsabc = sPsab + size c - - {-# SPECIALIZE mapWithIndexNode :: (Int -> Elem y -> b) -> Int -> Node (Elem y) -> Node b #-} - {-# SPECIALIZE mapWithIndexNode :: (Int -> Node y -> b) -> Int -> Node (Node y) -> Node b #-} - mapWithIndexNode :: Sized a => (Int -> a -> b) -> Int -> Node a -> Node b - mapWithIndexNode f s (Node2 ns a b) = Node2 ns (f s a) (f sPsa b) - where - !sPsa = s + size a - mapWithIndexNode f s (Node3 ns a b c) = - Node3 ns (f s a) (f sPsa b) (f sPsab c) - where - !sPsa = s + size a - !sPsab = sPsa + size b - -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] mapWithIndex #-} -{-# RULES -"mapWithIndex/mapWithIndex" forall f g xs . mapWithIndex f (mapWithIndex g xs) = - mapWithIndex (\k a -> f k (g k a)) xs -"mapWithIndex/fmapSeq" forall f g xs . mapWithIndex f (fmapSeq g xs) = - mapWithIndex (\k a -> f k (g a)) xs -"fmapSeq/mapWithIndex" forall f g xs . fmapSeq f (mapWithIndex g xs) = - mapWithIndex (\k a -> f (g k a)) xs - #-} -#endif - - --- | /O(n)/. A generalization of 'foldMap', 'foldMapWithIndex' takes a folding --- function that also depends on the element's index, and applies it to every --- element in the sequence. --- --- @since 0.5.8 -foldMapWithIndex :: Monoid m => (Int -> a -> m) -> Seq a -> m -foldMapWithIndex f' (Seq xs') = foldMapWithIndexTreeE (lift_elem f') 0 xs' - where - lift_elem :: (Int -> a -> m) -> (Int -> Elem a -> m) -#if __GLASGOW_HASKELL__ >= 708 - lift_elem g = coerce g -#else - lift_elem g = \s (Elem a) -> g s a -#endif - {-# INLINE lift_elem #-} --- We have to specialize these functions by hand, unfortunately, because --- GHC does not specialize until *all* instances are determined. --- Although the Sized instance is known at compile time, the Monoid --- instance generally is not. - foldMapWithIndexTreeE :: Monoid m => (Int -> Elem a -> m) -> Int -> FingerTree (Elem a) -> m - foldMapWithIndexTreeE _ !_s EmptyT = mempty - foldMapWithIndexTreeE f s (Single xs) = f s xs - foldMapWithIndexTreeE f s (Deep _ pr m sf) = - foldMapWithIndexDigitE f s pr <> - foldMapWithIndexTreeN (foldMapWithIndexNodeE f) sPspr m <> - foldMapWithIndexDigitE f sPsprm sf - where - !sPspr = s + size pr - !sPsprm = sPspr + size m - - foldMapWithIndexTreeN :: Monoid m => (Int -> Node a -> m) -> Int -> FingerTree (Node a) -> m - foldMapWithIndexTreeN _ !_s EmptyT = mempty - foldMapWithIndexTreeN f s (Single xs) = f s xs - foldMapWithIndexTreeN f s (Deep _ pr m sf) = - foldMapWithIndexDigitN f s pr <> - foldMapWithIndexTreeN (foldMapWithIndexNodeN f) sPspr m <> - foldMapWithIndexDigitN f sPsprm sf - where - !sPspr = s + size pr - !sPsprm = sPspr + size m - - foldMapWithIndexDigitE :: Monoid m => (Int -> Elem a -> m) -> Int -> Digit (Elem a) -> m - foldMapWithIndexDigitE f i t = foldMapWithIndexDigit f i t - - foldMapWithIndexDigitN :: Monoid m => (Int -> Node a -> m) -> Int -> Digit (Node a) -> m - foldMapWithIndexDigitN f i t = foldMapWithIndexDigit f i t - - {-# INLINE foldMapWithIndexDigit #-} - foldMapWithIndexDigit :: (Monoid m, Sized a) => (Int -> a -> m) -> Int -> Digit a -> m - foldMapWithIndexDigit f !s (One a) = f s a - foldMapWithIndexDigit f s (Two a b) = f s a <> f sPsa b - where - !sPsa = s + size a - foldMapWithIndexDigit f s (Three a b c) = - f s a <> f sPsa b <> f sPsab c - where - !sPsa = s + size a - !sPsab = sPsa + size b - foldMapWithIndexDigit f s (Four a b c d) = - f s a <> f sPsa b <> f sPsab c <> f sPsabc d - where - !sPsa = s + size a - !sPsab = sPsa + size b - !sPsabc = sPsab + size c - - foldMapWithIndexNodeE :: Monoid m => (Int -> Elem a -> m) -> Int -> Node (Elem a) -> m - foldMapWithIndexNodeE f i t = foldMapWithIndexNode f i t - - foldMapWithIndexNodeN :: Monoid m => (Int -> Node a -> m) -> Int -> Node (Node a) -> m - foldMapWithIndexNodeN f i t = foldMapWithIndexNode f i t - - {-# INLINE foldMapWithIndexNode #-} - foldMapWithIndexNode :: (Monoid m, Sized a) => (Int -> a -> m) -> Int -> Node a -> m - foldMapWithIndexNode f !s (Node2 _ a b) = f s a <> f sPsa b - where - !sPsa = s + size a - foldMapWithIndexNode f s (Node3 _ a b c) = - f s a <> f sPsa b <> f sPsab c - where - !sPsa = s + size a - !sPsab = sPsa + size b - -#if __GLASGOW_HASKELL__ -{-# INLINABLE foldMapWithIndex #-} -#endif - --- | 'traverseWithIndex' is a version of 'traverse' that also offers --- access to the index of each element. --- --- @since 0.5.8 -traverseWithIndex :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) -traverseWithIndex f' (Seq xs') = Seq <$> traverseWithIndexTreeE (\s (Elem a) -> Elem <$> f' s a) 0 xs' - where --- We have to specialize these functions by hand, unfortunately, because --- GHC does not specialize until *all* instances are determined. --- Although the Sized instance is known at compile time, the Applicative --- instance generally is not. - traverseWithIndexTreeE :: Applicative f => (Int -> Elem a -> f b) -> Int -> FingerTree (Elem a) -> f (FingerTree b) - traverseWithIndexTreeE _ !_s EmptyT = pure EmptyT - traverseWithIndexTreeE f s (Single xs) = Single <$> f s xs - traverseWithIndexTreeE f s (Deep n pr m sf) = - deep' n <$> - traverseWithIndexDigitE f s pr <*> - traverseWithIndexTreeN (traverseWithIndexNodeE f) sPspr m <*> - traverseWithIndexDigitE f sPsprm sf - where - !sPspr = s + size pr - !sPsprm = sPspr + size m - - traverseWithIndexTreeN :: Applicative f => (Int -> Node a -> f b) -> Int -> FingerTree (Node a) -> f (FingerTree b) - traverseWithIndexTreeN _ !_s EmptyT = pure EmptyT - traverseWithIndexTreeN f s (Single xs) = Single <$> f s xs - traverseWithIndexTreeN f s (Deep n pr m sf) = - deep' n <$> - traverseWithIndexDigitN f s pr <*> - traverseWithIndexTreeN (traverseWithIndexNodeN f) sPspr m <*> - traverseWithIndexDigitN f sPsprm sf - where - !sPspr = s + size pr - !sPsprm = sPspr + size m - - traverseWithIndexDigitE :: Applicative f => (Int -> Elem a -> f b) -> Int -> Digit (Elem a) -> f (Digit b) - traverseWithIndexDigitE f i t = traverseWithIndexDigit f i t - - traverseWithIndexDigitN :: Applicative f => (Int -> Node a -> f b) -> Int -> Digit (Node a) -> f (Digit b) - traverseWithIndexDigitN f i t = traverseWithIndexDigit f i t - - {-# INLINE traverseWithIndexDigit #-} - traverseWithIndexDigit :: (Applicative f, Sized a) => (Int -> a -> f b) -> Int -> Digit a -> f (Digit b) - traverseWithIndexDigit f !s (One a) = One <$> f s a - traverseWithIndexDigit f s (Two a b) = Two <$> f s a <*> f sPsa b - where - !sPsa = s + size a - traverseWithIndexDigit f s (Three a b c) = - Three <$> f s a <*> f sPsa b <*> f sPsab c - where - !sPsa = s + size a - !sPsab = sPsa + size b - traverseWithIndexDigit f s (Four a b c d) = - Four <$> f s a <*> f sPsa b <*> f sPsab c <*> f sPsabc d - where - !sPsa = s + size a - !sPsab = sPsa + size b - !sPsabc = sPsab + size c - - traverseWithIndexNodeE :: Applicative f => (Int -> Elem a -> f b) -> Int -> Node (Elem a) -> f (Node b) - traverseWithIndexNodeE f i t = traverseWithIndexNode f i t - - traverseWithIndexNodeN :: Applicative f => (Int -> Node a -> f b) -> Int -> Node (Node a) -> f (Node b) - traverseWithIndexNodeN f i t = traverseWithIndexNode f i t - - {-# INLINE traverseWithIndexNode #-} - traverseWithIndexNode :: (Applicative f, Sized a) => (Int -> a -> f b) -> Int -> Node a -> f (Node b) - traverseWithIndexNode f !s (Node2 ns a b) = node2' ns <$> f s a <*> f sPsa b - where - !sPsa = s + size a - traverseWithIndexNode f s (Node3 ns a b c) = - node3' ns <$> f s a <*> f sPsa b <*> f sPsab c - where - !sPsa = s + size a - !sPsab = sPsa + size b - - -{-# NOINLINE [1] traverseWithIndex #-} -#ifdef __GLASGOW_HASKELL__ -{-# RULES -"travWithIndex/mapWithIndex" forall f g xs . traverseWithIndex f (mapWithIndex g xs) = - traverseWithIndex (\k a -> f k (g k a)) xs -"travWithIndex/fmapSeq" forall f g xs . traverseWithIndex f (fmapSeq g xs) = - traverseWithIndex (\k a -> f k (g a)) xs - #-} -#endif -{- -It might be nice to be able to rewrite - -traverseWithIndex f (fromFunction i g) -to -replicateAWithIndex i (\k -> f k (g k)) -and -traverse f (fromFunction i g) -to -replicateAWithIndex i (f . g) - -but we don't have replicateAWithIndex as yet. - -We might wish for a rule like -"fmapSeq/travWithIndex" forall f g xs . fmapSeq f <$> traverseWithIndex g xs = - traverseWithIndex (\k a -> f <$> g k a) xs -Unfortunately, this rule could screw up the inliner's treatment of -fmap in general, and it also relies on the arbitrary Functor being -valid. --} - - --- | /O(n)/. Convert a given sequence length and a function representing that --- sequence into a sequence. -fromFunction :: Int -> (Int -> a) -> Seq a -fromFunction len f | len < 0 = error "Data.Sequence.fromFunction called with negative len" - | len == 0 = empty - | otherwise = Seq $ create (lift_elem f) 1 0 len - where - create :: (Int -> a) -> Int -> Int -> Int -> FingerTree a - create b{-tree_builder-} !s{-tree_size-} !i{-start_index-} trees = case trees of - 1 -> Single $ b i - 2 -> Deep (2*s) (One (b i)) EmptyT (One (b (i+s))) - 3 -> Deep (3*s) (createTwo i) EmptyT (One (b (i+2*s))) - 4 -> Deep (4*s) (createTwo i) EmptyT (createTwo (i+2*s)) - 5 -> Deep (5*s) (createThree i) EmptyT (createTwo (i+3*s)) - 6 -> Deep (6*s) (createThree i) EmptyT (createThree (i+3*s)) - _ -> case trees `quotRem` 3 of - (trees', 1) -> Deep (trees*s) (createTwo i) - (create mb (3*s) (i+2*s) (trees'-1)) - (createTwo (i+(2+3*(trees'-1))*s)) - (trees', 2) -> Deep (trees*s) (createThree i) - (create mb (3*s) (i+3*s) (trees'-1)) - (createTwo (i+(3+3*(trees'-1))*s)) - (trees', _) -> Deep (trees*s) (createThree i) - (create mb (3*s) (i+3*s) (trees'-2)) - (createThree (i+(3+3*(trees'-2))*s)) - where - createTwo j = Two (b j) (b (j + s)) - {-# INLINE createTwo #-} - createThree j = Three (b j) (b (j + s)) (b (j + 2*s)) - {-# INLINE createThree #-} - mb j = Node3 (3*s) (b j) (b (j + s)) (b (j + 2*s)) - {-# INLINE mb #-} - - lift_elem :: (Int -> a) -> (Int -> Elem a) -#if __GLASGOW_HASKELL__ >= 708 - lift_elem g = coerce g -#else - lift_elem g = Elem . g -#endif - {-# INLINE lift_elem #-} - --- | /O(n)/. Create a sequence consisting of the elements of an 'Array'. --- Note that the resulting sequence elements may be evaluated lazily (as on GHC), --- so you must force the entire structure to be sure that the original array --- can be garbage-collected. -fromArray :: Ix i => Array i a -> Seq a -#ifdef __GLASGOW_HASKELL__ -fromArray a = fromFunction (GHC.Arr.numElements a) (GHC.Arr.unsafeAt a) - where - -- The following definition uses (Ix i) constraing, which is needed for the - -- other fromArray definition. - _ = Data.Array.rangeSize (Data.Array.bounds a) -#else -fromArray a = fromList2 (Data.Array.rangeSize (Data.Array.bounds a)) (Data.Array.elems a) -#endif - --- Splitting - --- | /O(log(min(i,n-i)))/. The first @i@ elements of a sequence. --- If @i@ is negative, @'take' i s@ yields the empty sequence. --- If the sequence contains fewer than @i@ elements, the whole sequence --- is returned. -take :: Int -> Seq a -> Seq a -take i xs@(Seq t) - -- See note on unsigned arithmetic in splitAt - | fromIntegral i - 1 < (fromIntegral (length xs) - 1 :: Word) = - Seq (takeTreeE i t) - | i <= 0 = empty - | otherwise = xs - -takeTreeE :: Int -> FingerTree (Elem a) -> FingerTree (Elem a) -takeTreeE !_i EmptyT = EmptyT -takeTreeE i t@(Single _) - | i <= 0 = EmptyT - | otherwise = t -takeTreeE i (Deep s pr m sf) - | i < spr = takePrefixE i pr - | i < spm = case takeTreeN im m of - ml :*: xs -> takeMiddleE (im - size ml) spr pr ml xs - | otherwise = takeSuffixE (i - spm) s pr m sf - where - spr = size pr - spm = spr + size m - im = i - spr - -takeTreeN :: Int -> FingerTree (Node a) -> StrictPair (FingerTree (Node a)) (Node a) -takeTreeN !_i EmptyT = error "takeTreeN of empty tree" -takeTreeN _i (Single x) = EmptyT :*: x -takeTreeN i (Deep s pr m sf) - | i < spr = takePrefixN i pr - | i < spm = case takeTreeN im m of - ml :*: xs -> takeMiddleN (im - size ml) spr pr ml xs - | otherwise = takeSuffixN (i - spm) s pr m sf where - spr = size pr - spm = spr + size m - im = i - spr - -takeMiddleN :: Int -> Int - -> Digit (Node a) -> FingerTree (Node (Node a)) -> Node (Node a) - -> StrictPair (FingerTree (Node a)) (Node a) -takeMiddleN i spr pr ml (Node2 _ a b) - | i < sa = pullR sprml pr ml :*: a - | otherwise = Deep sprmla pr ml (One a) :*: b - where - sa = size a - sprml = spr + size ml - sprmla = sa + sprml -takeMiddleN i spr pr ml (Node3 _ a b c) - | i < sa = pullR sprml pr ml :*: a - | i < sab = Deep sprmla pr ml (One a) :*: b - | otherwise = Deep sprmlab pr ml (Two a b) :*: c - where - sa = size a - sab = sa + size b - sprml = spr + size ml - sprmla = sa + sprml - sprmlab = sprmla + size b - -takeMiddleE :: Int -> Int - -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Node (Elem a) - -> FingerTree (Elem a) -takeMiddleE i spr pr ml (Node2 _ a _) - | i < 1 = pullR sprml pr ml - | otherwise = Deep sprmla pr ml (One a) - where - sprml = spr + size ml - sprmla = 1 + sprml -takeMiddleE i spr pr ml (Node3 _ a b _) - | i < 1 = pullR sprml pr ml - | i < 2 = Deep sprmla pr ml (One a) - | otherwise = Deep sprmlab pr ml (Two a b) - where - sprml = spr + size ml - sprmla = 1 + sprml - sprmlab = sprmla + 1 - -takePrefixE :: Int -> Digit (Elem a) -> FingerTree (Elem a) -takePrefixE !_i (One _) = EmptyT -takePrefixE i (Two a _) - | i < 1 = EmptyT - | otherwise = Single a -takePrefixE i (Three a b _) - | i < 1 = EmptyT - | i < 2 = Single a - | otherwise = Deep 2 (One a) EmptyT (One b) -takePrefixE i (Four a b c _) - | i < 1 = EmptyT - | i < 2 = Single a - | i < 3 = Deep 2 (One a) EmptyT (One b) - | otherwise = Deep 3 (Two a b) EmptyT (One c) - -takePrefixN :: Int -> Digit (Node a) - -> StrictPair (FingerTree (Node a)) (Node a) -takePrefixN !_i (One a) = EmptyT :*: a -takePrefixN i (Two a b) - | i < sa = EmptyT :*: a - | otherwise = Single a :*: b - where - sa = size a -takePrefixN i (Three a b c) - | i < sa = EmptyT :*: a - | i < sab = Single a :*: b - | otherwise = Deep sab (One a) EmptyT (One b) :*: c - where - sa = size a - sab = sa + size b -takePrefixN i (Four a b c d) - | i < sa = EmptyT :*: a - | i < sab = Single a :*: b - | i < sabc = Deep sab (One a) EmptyT (One b) :*: c - | otherwise = Deep sabc (Two a b) EmptyT (One c) :*: d - where - sa = size a - sab = sa + size b - sabc = sab + size c - -takeSuffixE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> - FingerTree (Elem a) -takeSuffixE !_i !s pr m (One _) = pullR (s - 1) pr m -takeSuffixE i s pr m (Two a _) - | i < 1 = pullR (s - 2) pr m - | otherwise = Deep (s - 1) pr m (One a) -takeSuffixE i s pr m (Three a b _) - | i < 1 = pullR (s - 3) pr m - | i < 2 = Deep (s - 2) pr m (One a) - | otherwise = Deep (s - 1) pr m (Two a b) -takeSuffixE i s pr m (Four a b c _) - | i < 1 = pullR (s - 4) pr m - | i < 2 = Deep (s - 3) pr m (One a) - | i < 3 = Deep (s - 2) pr m (Two a b) - | otherwise = Deep (s - 1) pr m (Three a b c) - -takeSuffixN :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> - StrictPair (FingerTree (Node a)) (Node a) -takeSuffixN !_i !s pr m (One a) = pullR (s - size a) pr m :*: a -takeSuffixN i s pr m (Two a b) - | i < sa = pullR (s - sa - size b) pr m :*: a - | otherwise = Deep (s - size b) pr m (One a) :*: b - where - sa = size a -takeSuffixN i s pr m (Three a b c) - | i < sa = pullR (s - sab - size c) pr m :*: a - | i < sab = Deep (s - size b - size c) pr m (One a) :*: b - | otherwise = Deep (s - size c) pr m (Two a b) :*: c - where - sa = size a - sab = sa + size b -takeSuffixN i s pr m (Four a b c d) - | i < sa = pullR (s - sa - sbcd) pr m :*: a - | i < sab = Deep (s - sbcd) pr m (One a) :*: b - | i < sabc = Deep (s - scd) pr m (Two a b) :*: c - | otherwise = Deep (s - sd) pr m (Three a b c) :*: d - where - sa = size a - sab = sa + size b - sabc = sab + size c - sd = size d - scd = size c + sd - sbcd = size b + scd - --- | /O(log(min(i,n-i)))/. Elements of a sequence after the first @i@. --- If @i@ is negative, @'drop' i s@ yields the whole sequence. --- If the sequence contains fewer than @i@ elements, the empty sequence --- is returned. -drop :: Int -> Seq a -> Seq a -drop i xs@(Seq t) - -- See note on unsigned arithmetic in splitAt - | fromIntegral i - 1 < (fromIntegral (length xs) - 1 :: Word) = - Seq (takeTreeER (length xs - i) t) - | i <= 0 = xs - | otherwise = empty - --- We implement `drop` using a "take from the rear" strategy. There's no --- particular technical reason for this; it just lets us reuse the arithmetic --- from `take` (which itself reuses the arithmetic from `splitAt`) instead of --- figuring it out from scratch and ending up with lots of off-by-one errors. -takeTreeER :: Int -> FingerTree (Elem a) -> FingerTree (Elem a) -takeTreeER !_i EmptyT = EmptyT -takeTreeER i t@(Single _) - | i <= 0 = EmptyT - | otherwise = t -takeTreeER i (Deep s pr m sf) - | i < ssf = takeSuffixER i sf - | i < ssm = case takeTreeNR im m of - xs :*: mr -> takeMiddleER (im - size mr) ssf xs mr sf - | otherwise = takePrefixER (i - ssm) s pr m sf - where - ssf = size sf - ssm = ssf + size m - im = i - ssf - -takeTreeNR :: Int -> FingerTree (Node a) -> StrictPair (Node a) (FingerTree (Node a)) -takeTreeNR !_i EmptyT = error "takeTreeNR of empty tree" -takeTreeNR _i (Single x) = x :*: EmptyT -takeTreeNR i (Deep s pr m sf) - | i < ssf = takeSuffixNR i sf - | i < ssm = case takeTreeNR im m of - xs :*: mr -> takeMiddleNR (im - size mr) ssf xs mr sf - | otherwise = takePrefixNR (i - ssm) s pr m sf where - ssf = size sf - ssm = ssf + size m - im = i - ssf - -takeMiddleNR :: Int -> Int - -> Node (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) - -> StrictPair (Node a) (FingerTree (Node a)) -takeMiddleNR i ssf (Node2 _ a b) mr sf - | i < sb = b :*: pullL ssfmr mr sf - | otherwise = a :*: Deep ssfmrb (One b) mr sf - where - sb = size b - ssfmr = ssf + size mr - ssfmrb = sb + ssfmr -takeMiddleNR i ssf (Node3 _ a b c) mr sf - | i < sc = c :*: pullL ssfmr mr sf - | i < sbc = b :*: Deep ssfmrc (One c) mr sf - | otherwise = a :*: Deep ssfmrbc (Two b c) mr sf - where - sc = size c - sbc = sc + size b - ssfmr = ssf + size mr - ssfmrc = sc + ssfmr - ssfmrbc = ssfmrc + size b - -takeMiddleER :: Int -> Int - -> Node (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) - -> FingerTree (Elem a) -takeMiddleER i ssf (Node2 _ _ b) mr sf - | i < 1 = pullL ssfmr mr sf - | otherwise = Deep ssfmrb (One b) mr sf - where - ssfmr = ssf + size mr - ssfmrb = 1 + ssfmr -takeMiddleER i ssf (Node3 _ _ b c) mr sf - | i < 1 = pullL ssfmr mr sf - | i < 2 = Deep ssfmrc (One c) mr sf - | otherwise = Deep ssfmrbc (Two b c) mr sf - where - ssfmr = ssf + size mr - ssfmrc = 1 + ssfmr - ssfmrbc = ssfmr + 2 - -takeSuffixER :: Int -> Digit (Elem a) -> FingerTree (Elem a) -takeSuffixER !_i (One _) = EmptyT -takeSuffixER i (Two _ b) - | i < 1 = EmptyT - | otherwise = Single b -takeSuffixER i (Three _ b c) - | i < 1 = EmptyT - | i < 2 = Single c - | otherwise = Deep 2 (One b) EmptyT (One c) -takeSuffixER i (Four _ b c d) - | i < 1 = EmptyT - | i < 2 = Single d - | i < 3 = Deep 2 (One c) EmptyT (One d) - | otherwise = Deep 3 (Two b c) EmptyT (One d) - -takeSuffixNR :: Int -> Digit (Node a) - -> StrictPair (Node a) (FingerTree (Node a)) -takeSuffixNR !_i (One a) = a :*: EmptyT -takeSuffixNR i (Two a b) - | i < sb = b :*: EmptyT - | otherwise = a :*: Single b - where - sb = size b -takeSuffixNR i (Three a b c) - | i < sc = c :*: EmptyT - | i < sbc = b :*: Single c - | otherwise = a :*: Deep sbc (One b) EmptyT (One c) - where - sc = size c - sbc = sc + size b -takeSuffixNR i (Four a b c d) - | i < sd = d :*: EmptyT - | i < scd = c :*: Single d - | i < sbcd = b :*: Deep scd (One c) EmptyT (One d) - | otherwise = a :*: Deep sbcd (Two b c) EmptyT (One d) - where - sd = size d - scd = sd + size c - sbcd = scd + size b - -takePrefixER :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> - FingerTree (Elem a) -takePrefixER !_i !s (One _) m sf = pullL (s - 1) m sf -takePrefixER i s (Two _ b) m sf - | i < 1 = pullL (s - 2) m sf - | otherwise = Deep (s - 1) (One b) m sf -takePrefixER i s (Three _ b c) m sf - | i < 1 = pullL (s - 3) m sf - | i < 2 = Deep (s - 2) (One c) m sf - | otherwise = Deep (s - 1) (Two b c) m sf -takePrefixER i s (Four _ b c d) m sf - | i < 1 = pullL (s - 4) m sf - | i < 2 = Deep (s - 3) (One d) m sf - | i < 3 = Deep (s - 2) (Two c d) m sf - | otherwise = Deep (s - 1) (Three b c d) m sf - -takePrefixNR :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> - StrictPair (Node a) (FingerTree (Node a)) -takePrefixNR !_i !s (One a) m sf = a :*: pullL (s - size a) m sf -takePrefixNR i s (Two a b) m sf - | i < sb = b :*: pullL (s - sb - size a) m sf - | otherwise = a :*: Deep (s - size a) (One b) m sf - where - sb = size b -takePrefixNR i s (Three a b c) m sf - | i < sc = c :*: pullL (s - sbc - size a) m sf - | i < sbc = b :*: Deep (s - size b - size a) (One c) m sf - | otherwise = a :*: Deep (s - size a) (Two b c) m sf - where - sc = size c - sbc = sc + size b -takePrefixNR i s (Four a b c d) m sf - | i < sd = d :*: pullL (s - sd - sabc) m sf - | i < scd = c :*: Deep (s - sabc) (One d) m sf - | i < sbcd = b :*: Deep (s - sab) (Two c d) m sf - | otherwise = a :*: Deep (s - sa) (Three b c d) m sf - where - sa = size a - sab = sa + size b - sabc = sab + size c - sd = size d - scd = size c + sd - sbcd = size b + scd - --- | /O(log(min(i,n-i)))/. Split a sequence at a given position. --- @'splitAt' i s = ('take' i s, 'drop' i s)@. -splitAt :: Int -> Seq a -> (Seq a, Seq a) -splitAt i xs@(Seq t) - -- We use an unsigned comparison to make the common case - -- faster. This only works because our representation of - -- sizes as (signed) Ints gives us a free high bit to play - -- with. Note also that there's no sharing to lose in the - -- case that the length is 0. - | fromIntegral i - 1 < (fromIntegral (length xs) - 1 :: Word) = - case splitTreeE i t of - l :*: r -> (Seq l, Seq r) - | i <= 0 = (empty, xs) - | otherwise = (xs, empty) - --- | /O(log(min(i,n-i))) A version of 'splitAt' that does not attempt to --- enhance sharing when the split point is less than or equal to 0, and that --- gives completely wrong answers when the split point is at least the length --- of the sequence, unless the sequence is a singleton. This is used to --- implement zipWith and chunksOf, which are extremely sensitive to the cost of --- splitting very short sequences. There is just enough of a speed increase to --- make this worth the trouble. -uncheckedSplitAt :: Int -> Seq a -> (Seq a, Seq a) -uncheckedSplitAt i (Seq xs) = case splitTreeE i xs of - l :*: r -> (Seq l, Seq r) - -data Split a = Split !(FingerTree (Node a)) !(Node a) !(FingerTree (Node a)) -#if TESTING - deriving Show -#endif - -splitTreeE :: Int -> FingerTree (Elem a) -> StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) -splitTreeE !_i EmptyT = EmptyT :*: EmptyT -splitTreeE i t@(Single _) - | i <= 0 = EmptyT :*: t - | otherwise = t :*: EmptyT -splitTreeE i (Deep s pr m sf) - | i < spr = splitPrefixE i s pr m sf - | i < spm = case splitTreeN im m of - Split ml xs mr -> splitMiddleE (im - size ml) s spr pr ml xs mr sf - | otherwise = splitSuffixE (i - spm) s pr m sf - where - spr = size pr - spm = spr + size m - im = i - spr - -splitTreeN :: Int -> FingerTree (Node a) -> Split a -splitTreeN !_i EmptyT = error "splitTreeN of empty tree" -splitTreeN _i (Single x) = Split EmptyT x EmptyT -splitTreeN i (Deep s pr m sf) - | i < spr = splitPrefixN i s pr m sf - | i < spm = case splitTreeN im m of - Split ml xs mr -> splitMiddleN (im - size ml) s spr pr ml xs mr sf - | otherwise = splitSuffixN (i - spm) s pr m sf where - spr = size pr - spm = spr + size m - im = i - spr - -splitMiddleN :: Int -> Int -> Int - -> Digit (Node a) -> FingerTree (Node (Node a)) -> Node (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) - -> Split a -splitMiddleN i s spr pr ml (Node2 _ a b) mr sf - | i < sa = Split (pullR sprml pr ml) a (Deep (s - sprmla) (One b) mr sf) - | otherwise = Split (Deep sprmla pr ml (One a)) b (pullL (s - sprmla - size b) mr sf) - where - sa = size a - sprml = spr + size ml - sprmla = sa + sprml -splitMiddleN i s spr pr ml (Node3 _ a b c) mr sf - | i < sa = Split (pullR sprml pr ml) a (Deep (s - sprmla) (Two b c) mr sf) - | i < sab = Split (Deep sprmla pr ml (One a)) b (Deep (s - sprmlab) (One c) mr sf) - | otherwise = Split (Deep sprmlab pr ml (Two a b)) c (pullL (s - sprmlab - size c) mr sf) - where - sa = size a - sab = sa + size b - sprml = spr + size ml - sprmla = sa + sprml - sprmlab = sprmla + size b - -splitMiddleE :: Int -> Int -> Int - -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Node (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) - -> StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) -splitMiddleE i s spr pr ml (Node2 _ a b) mr sf - | i < 1 = pullR sprml pr ml :*: Deep (s - sprml) (Two a b) mr sf - | otherwise = Deep sprmla pr ml (One a) :*: Deep (s - sprmla) (One b) mr sf - where - sprml = spr + size ml - sprmla = 1 + sprml -splitMiddleE i s spr pr ml (Node3 _ a b c) mr sf = case i of - 0 -> pullR sprml pr ml :*: Deep (s - sprml) (Three a b c) mr sf - 1 -> Deep sprmla pr ml (One a) :*: Deep (s - sprmla) (Two b c) mr sf - _ -> Deep sprmlab pr ml (Two a b) :*: Deep (s - sprmlab) (One c) mr sf - where - sprml = spr + size ml - sprmla = 1 + sprml - sprmlab = sprmla + 1 - -splitPrefixE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> - StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) -splitPrefixE !_i !s (One a) m sf = EmptyT :*: Deep s (One a) m sf -splitPrefixE i s (Two a b) m sf = case i of - 0 -> EmptyT :*: Deep s (Two a b) m sf - _ -> Single a :*: Deep (s - 1) (One b) m sf -splitPrefixE i s (Three a b c) m sf = case i of - 0 -> EmptyT :*: Deep s (Three a b c) m sf - 1 -> Single a :*: Deep (s - 1) (Two b c) m sf - _ -> Deep 2 (One a) EmptyT (One b) :*: Deep (s - 2) (One c) m sf -splitPrefixE i s (Four a b c d) m sf = case i of - 0 -> EmptyT :*: Deep s (Four a b c d) m sf - 1 -> Single a :*: Deep (s - 1) (Three b c d) m sf - 2 -> Deep 2 (One a) EmptyT (One b) :*: Deep (s - 2) (Two c d) m sf - _ -> Deep 3 (Two a b) EmptyT (One c) :*: Deep (s - 3) (One d) m sf - -splitPrefixN :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> - Split a -splitPrefixN !_i !s (One a) m sf = Split EmptyT a (pullL (s - size a) m sf) -splitPrefixN i s (Two a b) m sf - | i < sa = Split EmptyT a (Deep (s - sa) (One b) m sf) - | otherwise = Split (Single a) b (pullL (s - sa - size b) m sf) - where - sa = size a -splitPrefixN i s (Three a b c) m sf - | i < sa = Split EmptyT a (Deep (s - sa) (Two b c) m sf) - | i < sab = Split (Single a) b (Deep (s - sab) (One c) m sf) - | otherwise = Split (Deep sab (One a) EmptyT (One b)) c (pullL (s - sab - size c) m sf) - where - sa = size a - sab = sa + size b -splitPrefixN i s (Four a b c d) m sf - | i < sa = Split EmptyT a $ Deep (s - sa) (Three b c d) m sf - | i < sab = Split (Single a) b $ Deep (s - sab) (Two c d) m sf - | i < sabc = Split (Deep sab (One a) EmptyT (One b)) c $ Deep (s - sabc) (One d) m sf - | otherwise = Split (Deep sabc (Two a b) EmptyT (One c)) d $ pullL (s - sabc - size d) m sf - where - sa = size a - sab = sa + size b - sabc = sab + size c - -splitSuffixE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> - StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) -splitSuffixE !_i !s pr m (One a) = pullR (s - 1) pr m :*: Single a -splitSuffixE i s pr m (Two a b) = case i of - 0 -> pullR (s - 2) pr m :*: Deep 2 (One a) EmptyT (One b) - _ -> Deep (s - 1) pr m (One a) :*: Single b -splitSuffixE i s pr m (Three a b c) = case i of - 0 -> pullR (s - 3) pr m :*: Deep 3 (Two a b) EmptyT (One c) - 1 -> Deep (s - 2) pr m (One a) :*: Deep 2 (One b) EmptyT (One c) - _ -> Deep (s - 1) pr m (Two a b) :*: Single c -splitSuffixE i s pr m (Four a b c d) = case i of - 0 -> pullR (s - 4) pr m :*: Deep 4 (Two a b) EmptyT (Two c d) - 1 -> Deep (s - 3) pr m (One a) :*: Deep 3 (Two b c) EmptyT (One d) - 2 -> Deep (s - 2) pr m (Two a b) :*: Deep 2 (One c) EmptyT (One d) - _ -> Deep (s - 1) pr m (Three a b c) :*: Single d - -splitSuffixN :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> - Split a -splitSuffixN !_i !s pr m (One a) = Split (pullR (s - size a) pr m) a EmptyT -splitSuffixN i s pr m (Two a b) - | i < sa = Split (pullR (s - sa - size b) pr m) a (Single b) - | otherwise = Split (Deep (s - size b) pr m (One a)) b EmptyT - where - sa = size a -splitSuffixN i s pr m (Three a b c) - | i < sa = Split (pullR (s - sab - size c) pr m) a (deep (One b) EmptyT (One c)) - | i < sab = Split (Deep (s - size b - size c) pr m (One a)) b (Single c) - | otherwise = Split (Deep (s - size c) pr m (Two a b)) c EmptyT - where - sa = size a - sab = sa + size b -splitSuffixN i s pr m (Four a b c d) - | i < sa = Split (pullR (s - sa - sbcd) pr m) a (Deep sbcd (Two b c) EmptyT (One d)) - | i < sab = Split (Deep (s - sbcd) pr m (One a)) b (Deep scd (One c) EmptyT (One d)) - | i < sabc = Split (Deep (s - scd) pr m (Two a b)) c (Single d) - | otherwise = Split (Deep (s - sd) pr m (Three a b c)) d EmptyT - where - sa = size a - sab = sa + size b - sabc = sab + size c - sd = size d - scd = size c + sd - sbcd = size b + scd - --- | /O(n)/. @chunksOf n xs@ splits @xs@ into chunks of size @n>0@. --- If @n@ does not divide the length of @xs@ evenly, then the last element --- of the result will be short. -chunksOf :: Int -> Seq a -> Seq (Seq a) -chunksOf n xs | n <= 0 = - if null xs - then empty - else error "chunksOf: A non-empty sequence can only be broken up into positively-sized chunks." -chunksOf 1 s = fmap singleton s -chunksOf n s = splitMap (uncheckedSplitAt . (*n)) const most (replicate numReps ()) - >< if null end then empty else singleton end - where - (numReps, endLength) = length s `quotRem` n - (most, end) = splitAt (length s - endLength) s - --- | /O(n)/. Returns a sequence of all suffixes of this sequence, --- longest first. For example, --- --- > tails (fromList "abc") = fromList [fromList "abc", fromList "bc", fromList "c", fromList ""] --- --- Evaluating the /i/th suffix takes /O(log(min(i, n-i)))/, but evaluating --- every suffix in the sequence takes /O(n)/ due to sharing. -tails :: Seq a -> Seq (Seq a) -tails (Seq xs) = Seq (tailsTree (Elem . Seq) xs) |> empty - --- | /O(n)/. Returns a sequence of all prefixes of this sequence, --- shortest first. For example, --- --- > inits (fromList "abc") = fromList [fromList "", fromList "a", fromList "ab", fromList "abc"] --- --- Evaluating the /i/th prefix takes /O(log(min(i, n-i)))/, but evaluating --- every prefix in the sequence takes /O(n)/ due to sharing. -inits :: Seq a -> Seq (Seq a) -inits (Seq xs) = empty <| Seq (initsTree (Elem . Seq) xs) - --- This implementation of tails (and, analogously, inits) has the --- following algorithmic advantages: --- Evaluating each tail in the sequence takes linear total time, --- which is better than we could say for --- @fromList [drop n xs | n <- [0..length xs]]@. --- Evaluating any individual tail takes logarithmic time, which is --- better than we can say for either --- @scanr (<|) empty xs@ or @iterateN (length xs + 1) (\ xs -> let _ :< xs' = viewl xs in xs') xs@. --- --- Moreover, if we actually look at every tail in the sequence, the --- following benchmarks demonstrate that this implementation is modestly --- faster than any of the above: --- --- Times (ms) --- min mean +/-sd median max --- Seq.tails: 21.986 24.961 10.169 22.417 86.485 --- scanr: 85.392 87.942 2.488 87.425 100.217 --- iterateN: 29.952 31.245 1.574 30.412 37.268 --- --- The algorithm for tails (and, analogously, inits) is as follows: --- --- A Node in the FingerTree of tails is constructed by evaluating the --- corresponding tail of the FingerTree of Nodes, considering the first --- Node in this tail, and constructing a Node in which each tail of this --- Node is made to be the prefix of the remaining tree. This ends up --- working quite elegantly, as the remainder of the tail of the FingerTree --- of Nodes becomes the middle of a new tail, the suffix of the Node is --- the prefix, and the suffix of the original tree is retained. --- --- In particular, evaluating the /i/th tail involves making as --- many partial evaluations as the Node depth of the /i/th element. --- In addition, when we evaluate the /i/th tail, and we also evaluate --- the /j/th tail, and /m/ Nodes are on the path to both /i/ and /j/, --- each of those /m/ evaluations are shared between the computation of --- the /i/th and /j/th tails. --- --- wasserman.louis@gmail.com, 7/16/09 - -tailsDigit :: Digit a -> Digit (Digit a) -tailsDigit (One a) = One (One a) -tailsDigit (Two a b) = Two (Two a b) (One b) -tailsDigit (Three a b c) = Three (Three a b c) (Two b c) (One c) -tailsDigit (Four a b c d) = Four (Four a b c d) (Three b c d) (Two c d) (One d) - -initsDigit :: Digit a -> Digit (Digit a) -initsDigit (One a) = One (One a) -initsDigit (Two a b) = Two (One a) (Two a b) -initsDigit (Three a b c) = Three (One a) (Two a b) (Three a b c) -initsDigit (Four a b c d) = Four (One a) (Two a b) (Three a b c) (Four a b c d) - -tailsNode :: Node a -> Node (Digit a) -tailsNode (Node2 s a b) = Node2 s (Two a b) (One b) -tailsNode (Node3 s a b c) = Node3 s (Three a b c) (Two b c) (One c) - -initsNode :: Node a -> Node (Digit a) -initsNode (Node2 s a b) = Node2 s (One a) (Two a b) -initsNode (Node3 s a b c) = Node3 s (One a) (Two a b) (Three a b c) - -{-# SPECIALIZE tailsTree :: (FingerTree (Elem a) -> Elem b) -> FingerTree (Elem a) -> FingerTree (Elem b) #-} -{-# SPECIALIZE tailsTree :: (FingerTree (Node a) -> Node b) -> FingerTree (Node a) -> FingerTree (Node b) #-} --- | Given a function to apply to tails of a tree, applies that function --- to every tail of the specified tree. -tailsTree :: Sized a => (FingerTree a -> b) -> FingerTree a -> FingerTree b -tailsTree _ EmptyT = EmptyT -tailsTree f (Single x) = Single (f (Single x)) -tailsTree f (Deep n pr m sf) = - Deep n (fmap (\ pr' -> f (deep pr' m sf)) (tailsDigit pr)) - (tailsTree f' m) - (fmap (f . digitToTree) (tailsDigit sf)) - where - f' ms = let ConsLTree node m' = viewLTree ms in - fmap (\ pr' -> f (deep pr' m' sf)) (tailsNode node) - -{-# SPECIALIZE initsTree :: (FingerTree (Elem a) -> Elem b) -> FingerTree (Elem a) -> FingerTree (Elem b) #-} -{-# SPECIALIZE initsTree :: (FingerTree (Node a) -> Node b) -> FingerTree (Node a) -> FingerTree (Node b) #-} --- | Given a function to apply to inits of a tree, applies that function --- to every init of the specified tree. -initsTree :: Sized a => (FingerTree a -> b) -> FingerTree a -> FingerTree b -initsTree _ EmptyT = EmptyT -initsTree f (Single x) = Single (f (Single x)) -initsTree f (Deep n pr m sf) = - Deep n (fmap (f . digitToTree) (initsDigit pr)) - (initsTree f' m) - (fmap (f . deep pr m) (initsDigit sf)) - where - f' ms = let SnocRTree m' node = viewRTree ms in - fmap (\ sf' -> f (deep pr m' sf')) (initsNode node) - -{-# INLINE foldlWithIndex #-} --- | 'foldlWithIndex' is a version of 'foldl' that also provides access --- to the index of each element. -foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b -foldlWithIndex f z xs = foldl (\ g x !i -> f (g (i - 1)) i x) (const z) xs (length xs - 1) - -{-# INLINE foldrWithIndex #-} --- | 'foldrWithIndex' is a version of 'foldr' that also provides access --- to the index of each element. -foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b -foldrWithIndex f z xs = foldr (\ x g !i -> f i x (g (i+1))) (const z) xs 0 - -{-# INLINE listToMaybe' #-} --- 'listToMaybe\'' is a good consumer version of 'listToMaybe'. -listToMaybe' :: [a] -> Maybe a -listToMaybe' = foldr (\ x _ -> Just x) Nothing - --- | /O(i)/ where /i/ is the prefix length. 'takeWhileL', applied --- to a predicate @p@ and a sequence @xs@, returns the longest prefix --- (possibly empty) of @xs@ of elements that satisfy @p@. -takeWhileL :: (a -> Bool) -> Seq a -> Seq a -takeWhileL p = fst . spanl p - --- | /O(i)/ where /i/ is the suffix length. 'takeWhileR', applied --- to a predicate @p@ and a sequence @xs@, returns the longest suffix --- (possibly empty) of @xs@ of elements that satisfy @p@. --- --- @'takeWhileR' p xs@ is equivalent to @'reverse' ('takeWhileL' p ('reverse' xs))@. -takeWhileR :: (a -> Bool) -> Seq a -> Seq a -takeWhileR p = fst . spanr p - --- | /O(i)/ where /i/ is the prefix length. @'dropWhileL' p xs@ returns --- the suffix remaining after @'takeWhileL' p xs@. -dropWhileL :: (a -> Bool) -> Seq a -> Seq a -dropWhileL p = snd . spanl p - --- | /O(i)/ where /i/ is the suffix length. @'dropWhileR' p xs@ returns --- the prefix remaining after @'takeWhileR' p xs@. --- --- @'dropWhileR' p xs@ is equivalent to @'reverse' ('dropWhileL' p ('reverse' xs))@. -dropWhileR :: (a -> Bool) -> Seq a -> Seq a -dropWhileR p = snd . spanr p - --- | /O(i)/ where /i/ is the prefix length. 'spanl', applied to --- a predicate @p@ and a sequence @xs@, returns a pair whose first --- element is the longest prefix (possibly empty) of @xs@ of elements that --- satisfy @p@ and the second element is the remainder of the sequence. -spanl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) -spanl p = breakl (not . p) - --- | /O(i)/ where /i/ is the suffix length. 'spanr', applied to a --- predicate @p@ and a sequence @xs@, returns a pair whose /first/ element --- is the longest /suffix/ (possibly empty) of @xs@ of elements that --- satisfy @p@ and the second element is the remainder of the sequence. -spanr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) -spanr p = breakr (not . p) - -{-# INLINE breakl #-} --- | /O(i)/ where /i/ is the breakpoint index. 'breakl', applied to a --- predicate @p@ and a sequence @xs@, returns a pair whose first element --- is the longest prefix (possibly empty) of @xs@ of elements that --- /do not satisfy/ @p@ and the second element is the remainder of --- the sequence. --- --- @'breakl' p@ is equivalent to @'spanl' (not . p)@. -breakl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) -breakl p xs = foldr (\ i _ -> splitAt i xs) (xs, empty) (findIndicesL p xs) - -{-# INLINE breakr #-} --- | @'breakr' p@ is equivalent to @'spanr' (not . p)@. -breakr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) -breakr p xs = foldr (\ i _ -> flipPair (splitAt (i + 1) xs)) (xs, empty) (findIndicesR p xs) - where flipPair (x, y) = (y, x) - --- | /O(n)/. The 'partition' function takes a predicate @p@ and a --- sequence @xs@ and returns sequences of those elements which do and --- do not satisfy the predicate. -partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a) -partition p = toPair . foldl' part (empty :*: empty) - where - part (xs :*: ys) x - | p x = (xs `snoc'` x) :*: ys - | otherwise = xs :*: (ys `snoc'` x) - --- | /O(n)/. The 'filter' function takes a predicate @p@ and a sequence --- @xs@ and returns a sequence of those elements which satisfy the --- predicate. -filter :: (a -> Bool) -> Seq a -> Seq a -filter p = foldl' (\ xs x -> if p x then xs `snoc'` x else xs) empty - --- Indexing sequences - --- | 'elemIndexL' finds the leftmost index of the specified element, --- if it is present, and otherwise 'Nothing'. -elemIndexL :: Eq a => a -> Seq a -> Maybe Int -elemIndexL x = findIndexL (x ==) - --- | 'elemIndexR' finds the rightmost index of the specified element, --- if it is present, and otherwise 'Nothing'. -elemIndexR :: Eq a => a -> Seq a -> Maybe Int -elemIndexR x = findIndexR (x ==) - --- | 'elemIndicesL' finds the indices of the specified element, from --- left to right (i.e. in ascending order). -elemIndicesL :: Eq a => a -> Seq a -> [Int] -elemIndicesL x = findIndicesL (x ==) - --- | 'elemIndicesR' finds the indices of the specified element, from --- right to left (i.e. in descending order). -elemIndicesR :: Eq a => a -> Seq a -> [Int] -elemIndicesR x = findIndicesR (x ==) - --- | @'findIndexL' p xs@ finds the index of the leftmost element that --- satisfies @p@, if any exist. -findIndexL :: (a -> Bool) -> Seq a -> Maybe Int -findIndexL p = listToMaybe' . findIndicesL p - --- | @'findIndexR' p xs@ finds the index of the rightmost element that --- satisfies @p@, if any exist. -findIndexR :: (a -> Bool) -> Seq a -> Maybe Int -findIndexR p = listToMaybe' . findIndicesR p - -{-# INLINE findIndicesL #-} --- | @'findIndicesL' p@ finds all indices of elements that satisfy @p@, --- in ascending order. -findIndicesL :: (a -> Bool) -> Seq a -> [Int] -#if __GLASGOW_HASKELL__ -findIndicesL p xs = build (\ c n -> let g i x z = if p x then c i z else z in - foldrWithIndex g n xs) -#else -findIndicesL p xs = foldrWithIndex g [] xs - where g i x is = if p x then i:is else is -#endif - -{-# INLINE findIndicesR #-} --- | @'findIndicesR' p@ finds all indices of elements that satisfy @p@, --- in descending order. -findIndicesR :: (a -> Bool) -> Seq a -> [Int] -#if __GLASGOW_HASKELL__ -findIndicesR p xs = build (\ c n -> - let g z i x = if p x then c i z else z in foldlWithIndex g n xs) -#else -findIndicesR p xs = foldlWithIndex g [] xs - where g is i x = if p x then i:is else is -#endif - ------------------------------------------------------------------------- --- Lists ------------------------------------------------------------------------- - --- The implementation below is based on an idea by Ross Paterson and --- implemented by Lennart Spitzner. It avoids the rebuilding the original --- (|>)-based implementation suffered from. It also avoids the excessive pair --- allocations Paterson's implementation suffered from. --- --- David Feuer suggested building in nine-element chunks, which reduces --- intermediate conses from around (1/2)*n to around (1/8)*n with a concomitant --- improvement in benchmark constant factors. In fact, it should be even --- better to work in chunks of 27 `Elem`s and chunks of three `Node`s, rather --- than nine of each, but it seems hard to avoid a code explosion with --- such large chunks. --- --- Paterson's code can be seen, for example, in --- https://github.com/haskell/containers/blob/74034b3244fa4817c7bef1202e639b887a975d9e/Data/Sequence.hs#L3532 --- --- Given a list --- --- [1..302] --- --- the original code forms Three 1 2 3 | [node3 4 5 6, node3 7 8 9, node3 10 11 --- 12, ...] | Two 301 302 --- --- Then it recurses on the middle list. The middle lists become successively --- shorter as their elements become successively deeper nodes. --- --- The original implementation of the list shortener, getNodes, included the --- recursive step - --- getNodes s x1 (x2:x3:x4:xs) = (Node3 s x1 x2 x3:ns, d) --- where (ns, d) = getNodes s x4 xs - --- This allocates a cons and a lazy pair at each 3-element step. It relies on --- the Haskell implementation using Wadler's technique, described in "Fixing --- some space leaks with a garbage collector" --- http://homepages.inf.ed.ac.uk/wadler/papers/leak/leak.ps.gz, to repeatedly --- simplify the `d` thunk. Although GHC uses this GC trick, heap profiling at --- least appears to indicate that the pair constructors and conses build up --- with this implementation. --- --- Spitzner's implementation uses a similar approach, but replaces the middle --- list, in each level, with a customized stream type that finishes off with --- the final digit in that level and (since it works in nines) in the one --- above. To work around the nested tree structure, the overall computation is --- structured using continuation-passing style, with a function that, at the --- bottom of the tree, deals with a stream that terminates in a nested-pair --- representation of the entire right side of the tree. Perhaps someone will --- eventually find a less mind-bending way to accomplish this. - --- | /O(n)/. Create a sequence from a finite list of elements. --- There is a function 'toList' in the opposite direction for all --- instances of the 'Foldable' class, including 'Seq'. -fromList :: [a] -> Seq a --- Note: we can avoid map_elem if we wish by scattering --- Elem applications throughout mkTreeE and getNodesE, but --- it gets a bit hard to read. -fromList = Seq . mkTree . map_elem - where -#ifdef __GLASGOW_HASKELL__ - mkTree :: forall a' . [Elem a'] -> FingerTree (Elem a') -#else - mkTree :: [Elem a] -> FingerTree (Elem a) -#endif - mkTree [] = EmptyT - mkTree [x1] = Single x1 - mkTree [x1, x2] = Deep 2 (One x1) EmptyT (One x2) - mkTree [x1, x2, x3] = Deep 3 (Two x1 x2) EmptyT (One x3) - mkTree [x1, x2, x3, x4] = Deep 4 (Two x1 x2) EmptyT (Two x3 x4) - mkTree [x1, x2, x3, x4, x5] = Deep 5 (Three x1 x2 x3) EmptyT (Two x4 x5) - mkTree [x1, x2, x3, x4, x5, x6] = - Deep 6 (Three x1 x2 x3) EmptyT (Three x4 x5 x6) - mkTree [x1, x2, x3, x4, x5, x6, x7] = - Deep 7 (Two x1 x2) (Single (Node3 3 x3 x4 x5)) (Two x6 x7) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8] = - Deep 8 (Three x1 x2 x3) (Single (Node3 3 x4 x5 x6)) (Two x7 x8) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9] = - Deep 9 (Three x1 x2 x3) (Single (Node3 3 x4 x5 x6)) (Three x7 x8 x9) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, y0, y1] = - Deep 10 (Two x1 x2) - (Deep 6 (One (Node3 3 x3 x4 x5)) EmptyT (One (Node3 3 x6 x7 x8))) - (Two y0 y1) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1] = - Deep 11 (Three x1 x2 x3) - (Deep 6 (One (Node3 3 x4 x5 x6)) EmptyT (One (Node3 3 x7 x8 x9))) - (Two y0 y1) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2] = - Deep 12 (Three x1 x2 x3) - (Deep 6 (One (Node3 3 x4 x5 x6)) EmptyT (One (Node3 3 x7 x8 x9))) - (Three y0 y1 y2) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, y0, y1, y2, y3, y4] = - Deep 13 (Two x1 x2) - (Deep 9 (Two (Node3 3 x3 x4 x5) (Node3 3 x6 x7 x8)) EmptyT (One (Node3 3 y0 y1 y2))) - (Two y3 y4) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2, y3, y4] = - Deep 14 (Three x1 x2 x3) - (Deep 9 (Two (Node3 3 x4 x5 x6) (Node3 3 x7 x8 x9)) EmptyT (One (Node3 3 y0 y1 y2))) - (Two y3 y4) - mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2, y3, y4, y5] = - Deep 15 (Three x1 x2 x3) - (Deep 9 (Two (Node3 3 x4 x5 x6) (Node3 3 x7 x8 x9)) EmptyT (One (Node3 3 y0 y1 y2))) - (Three y3 y4 y5) - mkTree (x1:x2:x3:x4:x5:x6:x7:x8:x9:y0:y1:y2:y3:y4:y5:y6:xs) = - mkTreeC cont 9 (getNodes 3 (Node3 3 y3 y4 y5) y6 xs) - where - d2 = Three x1 x2 x3 - d1 = Three (Node3 3 x4 x5 x6) (Node3 3 x7 x8 x9) (Node3 3 y0 y1 y2) -#ifdef __GLASGOW_HASKELL__ - cont :: (Digit (Node (Elem a')), Digit (Elem a')) -> FingerTree (Node (Node (Elem a'))) -> FingerTree (Elem a') -#endif - cont (!r1, !r2) !sub = - let !sub1 = Deep (9 + size r1 + size sub) d1 sub r1 - in Deep (3 + size r2 + size sub1) d2 sub1 r2 - - getNodes :: forall a . Int - -> Node a - -> a - -> [a] - -> ListFinal (Node (Node a)) (Digit (Node a), Digit a) - getNodes !_ n1 x1 [] = LFinal (One n1, One x1) - getNodes _ n1 x1 [x2] = LFinal (One n1, Two x1 x2) - getNodes _ n1 x1 [x2, x3] = LFinal (One n1, Three x1 x2 x3) - getNodes s n1 x1 [x2, x3, x4] = LFinal (Two n1 (Node3 s x1 x2 x3), One x4) - getNodes s n1 x1 [x2, x3, x4, x5] = LFinal (Two n1 (Node3 s x1 x2 x3), Two x4 x5) - getNodes s n1 x1 [x2, x3, x4, x5, x6] = LFinal (Two n1 (Node3 s x1 x2 x3), Three x4 x5 x6) - getNodes s n1 x1 [x2, x3, x4, x5, x6, x7] = LFinal (Three n1 (Node3 s x1 x2 x3) (Node3 s x4 x5 x6), One x7) - getNodes s n1 x1 [x2, x3, x4, x5, x6, x7, x8] = LFinal (Three n1 (Node3 s x1 x2 x3) (Node3 s x4 x5 x6), Two x7 x8) - getNodes s n1 x1 [x2, x3, x4, x5, x6, x7, x8, x9] = LFinal (Three n1 (Node3 s x1 x2 x3) (Node3 s x4 x5 x6), Three x7 x8 x9) - getNodes s n1 x1 (x2:x3:x4:x5:x6:x7:x8:x9:x10:xs) = LCons n10 (getNodes s (Node3 s x7 x8 x9) x10 xs) - where !n2 = Node3 s x1 x2 x3 - !n3 = Node3 s x4 x5 x6 - !n10 = Node3 (3*s) n1 n2 n3 - - mkTreeC :: -#ifdef __GLASGOW_HASKELL__ - forall a b c . -#endif - (b -> FingerTree (Node a) -> c) - -> Int - -> ListFinal (Node a) b - -> c - mkTreeC cont !_ (LFinal b) = - cont b EmptyT - mkTreeC cont _ (LCons x1 (LFinal b)) = - cont b (Single x1) - mkTreeC cont s (LCons x1 (LCons x2 (LFinal b))) = - cont b (Deep (2*s) (One x1) EmptyT (One x2)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LFinal b)))) = - cont b (Deep (3*s) (Two x1 x2) EmptyT (One x3)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LFinal b))))) = - cont b (Deep (4*s) (Two x1 x2) EmptyT (Two x3 x4)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LFinal b)))))) = - cont b (Deep (5*s) (Three x1 x2 x3) EmptyT (Two x4 x5)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LFinal b))))))) = - cont b (Deep (6*s) (Three x1 x2 x3) EmptyT (Three x4 x5 x6)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LFinal b)))))))) = - cont b (Deep (7*s) (Two x1 x2) (Single (Node3 (3*s) x3 x4 x5)) (Two x6 x7)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LFinal b))))))))) = - cont b (Deep (8*s) (Three x1 x2 x3) (Single (Node3 (3*s) x4 x5 x6)) (Two x7 x8)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LFinal b)))))))))) = - cont b (Deep (9*s) (Three x1 x2 x3) (Single (Node3 (3*s) x4 x5 x6)) (Three x7 x8 x9)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons y0 (LCons y1 (LFinal b))))))))))) = - cont b (Deep (10*s) (Two x1 x2) (Deep (6*s) (One (Node3 (3*s) x3 x4 x5)) EmptyT (One (Node3 (3*s) x6 x7 x8))) (Two y0 y1)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LFinal b)))))))))))) = - cont b (Deep (11*s) (Three x1 x2 x3) (Deep (6*s) (One (Node3 (3*s) x4 x5 x6)) EmptyT (One (Node3 (3*s) x7 x8 x9))) (Two y0 y1)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LFinal b))))))))))))) = - cont b (Deep (12*s) (Three x1 x2 x3) (Deep (6*s) (One (Node3 (3*s) x4 x5 x6)) EmptyT (One (Node3 (3*s) x7 x8 x9))) (Three y0 y1 y2)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LFinal b)))))))))))))) = - cont b (Deep (13*s) (Two x1 x2) (Deep (9*s) (Two (Node3 (3*s) x3 x4 x5) (Node3 (3*s) x6 x7 x8)) EmptyT (One (Node3 (3*s) y0 y1 y2))) (Two y3 y4)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LFinal b))))))))))))))) = - cont b (Deep (14*s) (Three x1 x2 x3) (Deep (9*s) (Two (Node3 (3*s) x4 x5 x6) (Node3 (3*s) x7 x8 x9)) EmptyT (One (Node3 (3*s) y0 y1 y2))) (Two y3 y4)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LCons y5 (LFinal b)))))))))))))))) = - cont b (Deep (15*s) (Three x1 x2 x3) (Deep (9*s) (Two (Node3 (3*s) x4 x5 x6) (Node3 (3*s) x7 x8 x9)) EmptyT (One (Node3 (3*s) y0 y1 y2))) (Three y3 y4 y5)) - mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LCons y5 (LCons y6 xs)))))))))))))))) = - mkTreeC cont2 (9*s) (getNodesC (3*s) (Node3 (3*s) y3 y4 y5) y6 xs) - where -#ifdef __GLASGOW_HASKELL__ - cont2 :: (b, Digit (Node (Node a)), Digit (Node a)) -> FingerTree (Node (Node (Node a))) -> c -#endif - cont2 (b, r1, r2) !sub = - let d2 = Three x1 x2 x3 - d1 = Three (Node3 (3*s) x4 x5 x6) (Node3 (3*s) x7 x8 x9) (Node3 (3*s) y0 y1 y2) - !sub1 = Deep (9*s + size r1 + size sub) d1 sub r1 - in cont b $! Deep (3*s + size r2 + size sub1) d2 sub1 r2 - - getNodesC :: Int - -> Node a - -> a - -> ListFinal a b - -> ListFinal (Node (Node a)) (b, Digit (Node a), Digit a) - getNodesC !_ n1 x1 (LFinal b) = LFinal $ (b, One n1, One x1) - getNodesC _ n1 x1 (LCons x2 (LFinal b)) = LFinal $ (b, One n1, Two x1 x2) - getNodesC _ n1 x1 (LCons x2 (LCons x3 (LFinal b))) = LFinal $ (b, One n1, Three x1 x2 x3) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LFinal b)))) = - let !n2 = Node3 s x1 x2 x3 - in LFinal $ (b, Two n1 n2, One x4) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LFinal b))))) = - let !n2 = Node3 s x1 x2 x3 - in LFinal $ (b, Two n1 n2, Two x4 x5) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LFinal b)))))) = - let !n2 = Node3 s x1 x2 x3 - in LFinal $ (b, Two n1 n2, Three x4 x5 x6) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LFinal b))))))) = - let !n2 = Node3 s x1 x2 x3 - !n3 = Node3 s x4 x5 x6 - in LFinal $ (b, Three n1 n2 n3, One x7) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LFinal b)))))))) = - let !n2 = Node3 s x1 x2 x3 - !n3 = Node3 s x4 x5 x6 - in LFinal $ (b, Three n1 n2 n3, Two x7 x8) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LFinal b))))))))) = - let !n2 = Node3 s x1 x2 x3 - !n3 = Node3 s x4 x5 x6 - in LFinal $ (b, Three n1 n2 n3, Three x7 x8 x9) - getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons x10 xs))))))))) = - LCons n10 $ getNodesC s (Node3 s x7 x8 x9) x10 xs - where !n2 = Node3 s x1 x2 x3 - !n3 = Node3 s x4 x5 x6 - !n10 = Node3 (3*s) n1 n2 n3 - - map_elem :: [a] -> [Elem a] -#if __GLASGOW_HASKELL__ >= 708 - map_elem xs = coerce xs -#else - map_elem xs = Data.List.map Elem xs -#endif - {-# INLINE map_elem #-} - --- essentially: Free ((,) a) b. -data ListFinal a cont = LFinal !cont | LCons !a (ListFinal a cont) - -#if __GLASGOW_HASKELL__ >= 708 -instance GHC.Exts.IsList (Seq a) where - type Item (Seq a) = a - fromList = fromList - fromListN = fromList2 - toList = toList -#endif - -#ifdef __GLASGOW_HASKELL__ -instance IsString (Seq Char) where - fromString = fromList -#endif - ------------------------------------------------------------------------- --- Reverse ------------------------------------------------------------------------- - --- | /O(n)/. The reverse of a sequence. -reverse :: Seq a -> Seq a -reverse (Seq xs) = Seq (fmapReverseTree id xs) - -#ifdef __GLASGOW_HASKELL__ -{-# NOINLINE [1] reverse #-} - --- | /O(n)/. Reverse a sequence while mapping over it. This is not --- currently exported, but is used in rewrite rules. -fmapReverse :: (a -> b) -> Seq a -> Seq b -fmapReverse f (Seq xs) = Seq (fmapReverseTree (lift_elem f) xs) - where - lift_elem :: (a -> b) -> (Elem a -> Elem b) -#if __GLASGOW_HASKELL__ >= 708 - lift_elem = coerce -#else - lift_elem g (Elem a) = Elem (g a) -#endif - --- If we're mapping over a sequence, we can reverse it at the same time --- at no extra charge. -{-# RULES -"fmapSeq/reverse" forall f xs . fmapSeq f (reverse xs) = fmapReverse f xs -"reverse/fmapSeq" forall f xs . reverse (fmapSeq f xs) = fmapReverse f xs - #-} -#endif - -fmapReverseTree :: (a -> b) -> FingerTree a -> FingerTree b -fmapReverseTree _ EmptyT = EmptyT -fmapReverseTree f (Single x) = Single (f x) -fmapReverseTree f (Deep s pr m sf) = - Deep s (reverseDigit f sf) - (fmapReverseTree (reverseNode f) m) - (reverseDigit f pr) - -{-# INLINE reverseDigit #-} -reverseDigit :: (a -> b) -> Digit a -> Digit b -reverseDigit f (One a) = One (f a) -reverseDigit f (Two a b) = Two (f b) (f a) -reverseDigit f (Three a b c) = Three (f c) (f b) (f a) -reverseDigit f (Four a b c d) = Four (f d) (f c) (f b) (f a) - -reverseNode :: (a -> b) -> Node a -> Node b -reverseNode f (Node2 s a b) = Node2 s (f b) (f a) -reverseNode f (Node3 s a b c) = Node3 s (f c) (f b) (f a) - ------------------------------------------------------------------------- --- Mapping with a splittable value ------------------------------------------------------------------------- - --- For zipping, it is useful to build a result by --- traversing a sequence while splitting up something else. For zipping, we --- traverse the first sequence while splitting up the second. --- --- What makes all this crazy code a good idea: --- --- Suppose we zip together two sequences of the same length: --- --- zs = zip xs ys --- --- We want to get reasonably fast indexing into zs immediately, rather than --- needing to construct the entire thing first, as the previous implementation --- required. The first aspect is that we build the result "outside-in" or --- "top-down", rather than left to right. That gives us access to both ends --- quickly. But that's not enough, by itself, to give immediate access to the --- center of zs. For that, we need to be able to skip over larger segments of --- zs, delaying their construction until we actually need them. The way we do --- this is to traverse xs, while splitting up ys according to the structure of --- xs. If we have a Deep _ pr m sf, we split ys into three pieces, and hand off --- one piece to the prefix, one to the middle, and one to the suffix of the --- result. The key point is that we don't need to actually do anything further --- with those pieces until we actually need them; the computations to split --- them up further and zip them with their matching pieces can be delayed until --- they're actually needed. We do the same thing for Digits (splitting into --- between one and four pieces) and Nodes (splitting into two or three). The --- ultimate result is that we can index into, or split at, any location in zs --- in polylogarithmic time *immediately*, while still being able to force all --- the thunks in O(n) time. --- --- Benchmark info, and alternatives: --- --- The old zipping code used mapAccumL to traverse the first sequence while --- cutting down the second sequence one piece at a time. --- --- An alternative way to express that basic idea is to convert both sequences --- to lists, zip the lists, and then convert the result back to a sequence. --- I'll call this the "listy" implementation. --- --- I benchmarked two operations: Each started by zipping two sequences --- constructed with replicate and/or fromList. The first would then immediately --- index into the result. The second would apply deepseq to force the entire --- result. The new implementation worked much better than either of the others --- on the immediate indexing test, as expected. It also worked better than the --- old implementation for all the deepseq tests. For short sequences, the listy --- implementation outperformed all the others on the deepseq test. However, the --- splitting implementation caught up and surpassed it once the sequences grew --- long enough. It seems likely that by avoiding rebuilding, it interacts --- better with the cache hierarchy. --- --- David Feuer, with some guidance from Carter Schonwald, December 2014 - --- | /O(n)/. Constructs a new sequence with the same structure as an existing --- sequence using a user-supplied mapping function along with a splittable --- value and a way to split it. The value is split up lazily according to the --- structure of the sequence, so one piece of the value is distributed to each --- element of the sequence. The caller should provide a splitter function that --- takes a number, @n@, and a splittable value, breaks off a chunk of size @n@ --- from the value, and returns that chunk and the remainder as a pair. The --- following examples will hopefully make the usage clear: --- --- > zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c --- > zipWith f s1 s2 = splitMap splitAt (\b a -> f a (b `index` 0)) s2' s1' --- > where --- > minLen = min (length s1) (length s2) --- > s1' = take minLen s1 --- > s2' = take minLen s2 --- --- > mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b --- > mapWithIndex f = splitMap (\n i -> (i, n+i)) f 0 -#ifdef __GLASGOW_HASKELL__ --- We use ScopedTypeVariables to improve performance and make --- performance less sensitive to minor changes. - --- We INLINE this so GHC can see that the function passed in is --- strict in its Int argument. -{-# INLINE splitMap #-} -splitMap :: forall s a' b' . (Int -> s -> (s,s)) -> (s -> a' -> b') -> s -> Seq a' -> Seq b' -splitMap splt f0 s0 (Seq xs0) = Seq $ splitMapTreeE (\s' (Elem a) -> Elem (f0 s' a)) s0 xs0 - where - {-# INLINE splitMapTreeE #-} - splitMapTreeE :: (s -> Elem y -> b) -> s -> FingerTree (Elem y) -> FingerTree b - splitMapTreeE _ _ EmptyT = EmptyT - splitMapTreeE f s (Single xs) = Single $ f s xs - splitMapTreeE f s (Deep n pr m sf) = Deep n (splitMapDigit f prs pr) (splitMapTreeN (\eta1 eta2 -> splitMapNode f eta1 eta2) ms m) (splitMapDigit f sfs sf) - where - !spr = size pr - !sm = n - spr - size sf - (prs, r) = splt spr s - (ms, sfs) = splt sm r - - splitMapTreeN :: (s -> Node a -> b) -> s -> FingerTree (Node a) -> FingerTree b - splitMapTreeN _ _ EmptyT = EmptyT - splitMapTreeN f s (Single xs) = Single $ f s xs - splitMapTreeN f s (Deep n pr m sf) = Deep n (splitMapDigit f prs pr) (splitMapTreeN (\eta1 eta2 -> splitMapNode f eta1 eta2) ms m) (splitMapDigit f sfs sf) - where - (prs, r) = splt (size pr) s - (ms, sfs) = splt (size m) r - - {-# INLINE splitMapDigit #-} - splitMapDigit :: Sized a => (s -> a -> b) -> s -> Digit a -> Digit b - splitMapDigit f s (One a) = One (f s a) - splitMapDigit f s (Two a b) = Two (f first a) (f second b) - where - (first, second) = splt (size a) s - splitMapDigit f s (Three a b c) = Three (f first a) (f second b) (f third c) - where - (first, r) = splt (size a) s - (second, third) = splt (size b) r - splitMapDigit f s (Four a b c d) = Four (f first a) (f second b) (f third c) (f fourth d) - where - (first, s') = splt (size a) s - (middle, fourth) = splt (size b + size c) s' - (second, third) = splt (size b) middle - - {-# INLINE splitMapNode #-} - splitMapNode :: Sized a => (s -> a -> b) -> s -> Node a -> Node b - splitMapNode f s (Node2 ns a b) = Node2 ns (f first a) (f second b) - where - (first, second) = splt (size a) s - splitMapNode f s (Node3 ns a b c) = Node3 ns (f first a) (f second b) (f third c) - where - (first, r) = splt (size a) s - (second, third) = splt (size b) r - -#else --- Implementation without ScopedTypeVariables--somewhat slower, --- and much more sensitive to minor changes in various places. - -{-# INLINE splitMap #-} -splitMap :: (Int -> s -> (s,s)) -> (s -> a -> b) -> s -> Seq a -> Seq b -splitMap splt' f0 s0 (Seq xs0) = Seq $ splitMapTreeE splt' (\s' (Elem a) -> Elem (f0 s' a)) s0 xs0 - -{-# INLINE splitMapTreeE #-} -splitMapTreeE :: (Int -> s -> (s,s)) -> (s -> Elem y -> b) -> s -> FingerTree (Elem y) -> FingerTree b -splitMapTreeE _ _ _ EmptyT = EmptyT -splitMapTreeE _ f s (Single xs) = Single $ f s xs -splitMapTreeE splt f s (Deep n pr m sf) = Deep n (splitMapDigit splt f prs pr) (splitMapTreeN splt (\eta1 eta2 -> splitMapNode splt f eta1 eta2) ms m) (splitMapDigit splt f sfs sf) - where - !spr = size pr - sm = n - spr - size sf - (prs, r) = splt spr s - (ms, sfs) = splt sm r - -splitMapTreeN :: (Int -> s -> (s,s)) -> (s -> Node a -> b) -> s -> FingerTree (Node a) -> FingerTree b -splitMapTreeN _ _ _ EmptyT = EmptyT -splitMapTreeN _ f s (Single xs) = Single $ f s xs -splitMapTreeN splt f s (Deep n pr m sf) = Deep n (splitMapDigit splt f prs pr) (splitMapTreeN splt (\eta1 eta2 -> splitMapNode splt f eta1 eta2) ms m) (splitMapDigit splt f sfs sf) - where - (prs, r) = splt (size pr) s - (ms, sfs) = splt (size m) r - -{-# INLINE splitMapDigit #-} -splitMapDigit :: Sized a => (Int -> s -> (s,s)) -> (s -> a -> b) -> s -> Digit a -> Digit b -splitMapDigit _ f s (One a) = One (f s a) -splitMapDigit splt f s (Two a b) = Two (f first a) (f second b) - where - (first, second) = splt (size a) s -splitMapDigit splt f s (Three a b c) = Three (f first a) (f second b) (f third c) - where - (first, r) = splt (size a) s - (second, third) = splt (size b) r -splitMapDigit splt f s (Four a b c d) = Four (f first a) (f second b) (f third c) (f fourth d) - where - (first, s') = splt (size a) s - (middle, fourth) = splt (size b + size c) s' - (second, third) = splt (size b) middle - -{-# INLINE splitMapNode #-} -splitMapNode :: Sized a => (Int -> s -> (s,s)) -> (s -> a -> b) -> s -> Node a -> Node b -splitMapNode splt f s (Node2 ns a b) = Node2 ns (f first a) (f second b) - where - (first, second) = splt (size a) s -splitMapNode splt f s (Node3 ns a b c) = Node3 ns (f first a) (f second b) (f third c) - where - (first, r) = splt (size a) s - (second, third) = splt (size b) r -#endif - -getSingleton :: Seq a -> a -getSingleton (Seq (Single (Elem a))) = a -getSingleton _ = error "getSingleton: Not a singleton." - ------------------------------------------------------------------------- --- Zipping ------------------------------------------------------------------------- - --- | /O(min(n1,n2))/. 'zip' takes two sequences and returns a sequence --- of corresponding pairs. If one input is short, excess elements are --- discarded from the right end of the longer sequence. -zip :: Seq a -> Seq b -> Seq (a, b) -zip = zipWith (,) - --- | /O(min(n1,n2))/. 'zipWith' generalizes 'zip' by zipping with the --- function given as the first argument, instead of a tupling function. --- For example, @zipWith (+)@ is applied to two sequences to take the --- sequence of corresponding sums. -zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c -zipWith f s1 s2 = zipWith' f s1' s2' - where - minLen = min (length s1) (length s2) - s1' = take minLen s1 - s2' = take minLen s2 - --- | A version of zipWith that assumes the sequences have the same length. -zipWith' :: (a -> b -> c) -> Seq a -> Seq b -> Seq c -zipWith' f s1 s2 = splitMap uncheckedSplitAt (\s a -> f a (getSingleton s)) s2 s1 - --- | /O(min(n1,n2,n3))/. 'zip3' takes three sequences and returns a --- sequence of triples, analogous to 'zip'. -zip3 :: Seq a -> Seq b -> Seq c -> Seq (a,b,c) -zip3 = zipWith3 (,,) - --- | /O(min(n1,n2,n3))/. 'zipWith3' takes a function which combines --- three elements, as well as three sequences and returns a sequence of --- their point-wise combinations, analogous to 'zipWith'. -zipWith3 :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d -zipWith3 f s1 s2 s3 = zipWith' ($) (zipWith' f s1' s2') s3' - where - minLen = minimum [length s1, length s2, length s3] - s1' = take minLen s1 - s2' = take minLen s2 - s3' = take minLen s3 - -zipWith3' :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d -zipWith3' f s1 s2 s3 = zipWith' ($) (zipWith' f s1 s2) s3 - --- | /O(min(n1,n2,n3,n4))/. 'zip4' takes four sequences and returns a --- sequence of quadruples, analogous to 'zip'. -zip4 :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a,b,c,d) -zip4 = zipWith4 (,,,) - --- | /O(min(n1,n2,n3,n4))/. 'zipWith4' takes a function which combines --- four elements, as well as four sequences and returns a sequence of --- their point-wise combinations, analogous to 'zipWith'. -zipWith4 :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e -zipWith4 f s1 s2 s3 s4 = zipWith' ($) (zipWith3' f s1' s2' s3') s4' - where - minLen = minimum [length s1, length s2, length s3, length s4] - s1' = take minLen s1 - s2' = take minLen s2 - s3' = take minLen s3 - s4' = take minLen s4 - ------------------------------------------------------------------------- --- Sorting --- --- sort and sortBy are implemented by simple deforestations of --- \ xs -> fromList2 (length xs) . Data.List.sortBy cmp . toList --- which does not get deforested automatically, it would appear. --- --- Unstable sorting is performed by a heap sort implementation based on --- pairing heaps. Because the internal structure of sequences is quite --- varied, it is difficult to get blocks of elements of roughly the same --- length, which would improve merge sort performance. Pairing heaps, --- on the other hand, are relatively resistant to the effects of merging --- heaps of wildly different sizes, as guaranteed by its amortized --- constant-time merge operation. Moreover, extensive use of SpecConstr --- transformations can be done on pairing heaps, especially when we're --- only constructing them to immediately be unrolled. --- --- On purely random sequences of length 50000, with no RTS options, --- I get the following statistics, in which heapsort is about 42.5% --- faster: (all comparisons done with -O2) --- --- Times (ms) min mean +/-sd median max --- to/from list: 103.802 108.572 7.487 106.436 143.339 --- unstable heapsort: 60.686 62.968 4.275 61.187 79.151 --- --- Heapsort, it would seem, is less of a memory hog than Data.List.sortBy. --- The gap is narrowed when more memory is available, but heapsort still --- wins, 15% faster, with +RTS -H128m: --- --- Times (ms) min mean +/-sd median max --- to/from list: 42.692 45.074 2.596 44.600 56.601 --- unstable heapsort: 37.100 38.344 3.043 37.715 55.526 --- --- In addition, on strictly increasing sequences the gap is even wider --- than normal; heapsort is 68.5% faster with no RTS options: --- Times (ms) min mean +/-sd median max --- to/from list: 52.236 53.574 1.987 53.034 62.098 --- unstable heapsort: 16.433 16.919 0.931 16.681 21.622 --- --- This may be attributed to the elegant nature of the pairing heap. --- --- wasserman.louis@gmail.com, 7/20/09 ------------------------------------------------------------------------- - --- | /O(n log n)/. 'sort' sorts the specified 'Seq' by the natural --- ordering of its elements. The sort is stable. --- If stability is not required, 'unstableSort' can be considerably --- faster, and in particular uses less memory. -sort :: Ord a => Seq a -> Seq a -sort = sortBy compare - --- | /O(n log n)/. 'sortBy' sorts the specified 'Seq' according to the --- specified comparator. The sort is stable. --- If stability is not required, 'unstableSortBy' can be considerably --- faster, and in particular uses less memory. -sortBy :: (a -> a -> Ordering) -> Seq a -> Seq a -sortBy cmp xs = fromList2 (length xs) (Data.List.sortBy cmp (toList xs)) - --- | /O(n log n)/. 'unstableSort' sorts the specified 'Seq' by --- the natural ordering of its elements, but the sort is not stable. --- This algorithm is frequently faster and uses less memory than 'sort', --- and performs extremely well -- frequently twice as fast as 'sort' -- --- when the sequence is already nearly sorted. -unstableSort :: Ord a => Seq a -> Seq a -unstableSort = unstableSortBy compare - --- | /O(n log n)/. A generalization of 'unstableSort', 'unstableSortBy' --- takes an arbitrary comparator and sorts the specified sequence. --- The sort is not stable. This algorithm is frequently faster and --- uses less memory than 'sortBy', and performs extremely well -- --- frequently twice as fast as 'sortBy' -- when the sequence is already --- nearly sorted. -unstableSortBy :: (a -> a -> Ordering) -> Seq a -> Seq a -unstableSortBy cmp (Seq xs) = - fromList2 (size xs) $ maybe [] (unrollPQ cmp) $ - toPQ cmp (\ (Elem x) -> PQueue x Nil) xs - --- | fromList2, given a list and its length, constructs a completely --- balanced Seq whose elements are that list using the replicateA --- generalization. -fromList2 :: Int -> [a] -> Seq a -fromList2 n = execState (replicateA n (State ht)) - where - ht (x:xs) = (xs, x) - ht [] = error "fromList2: short list" - --- | A 'PQueue' is a simple pairing heap. -data PQueue e = PQueue e (PQL e) -data PQL e = Nil | {-# UNPACK #-} !(PQueue e) :& PQL e - -infixr 8 :& - -#if TESTING - -instance Functor PQueue where - fmap f (PQueue x ts) = PQueue (f x) (fmap f ts) - -instance Functor PQL where - fmap f (q :& qs) = fmap f q :& fmap f qs - fmap _ Nil = Nil - -instance Show e => Show (PQueue e) where - show = unlines . draw . fmap show - --- borrowed wholesale from Data.Tree, as Data.Tree actually depends --- on Data.Sequence -draw :: PQueue String -> [String] -draw (PQueue x ts0) = x : drawSubTrees ts0 - where - drawSubTrees Nil = [] - drawSubTrees (t :& Nil) = - "|" : shift "`- " " " (draw t) - drawSubTrees (t :& ts) = - "|" : shift "+- " "| " (draw t) ++ drawSubTrees ts - - shift first other = Data.List.zipWith (++) (first : repeat other) -#endif - --- | 'unrollPQ', given a comparator function, unrolls a 'PQueue' into --- a sorted list. -unrollPQ :: (e -> e -> Ordering) -> PQueue e -> [e] -unrollPQ cmp = unrollPQ' - where - {-# INLINE unrollPQ' #-} - unrollPQ' (PQueue x ts) = x:mergePQs0 ts - (<+>) = mergePQ cmp - mergePQs0 Nil = [] - mergePQs0 (t :& Nil) = unrollPQ' t - mergePQs0 (t1 :& t2 :& ts) = mergePQs (t1 <+> t2) ts - mergePQs !t ts = case ts of - Nil -> unrollPQ' t - t1 :& Nil -> unrollPQ' (t <+> t1) - t1 :& t2 :& ts' -> mergePQs (t <+> (t1 <+> t2)) ts' - --- | 'toPQ', given an ordering function and a mechanism for queueifying --- elements, converts a 'FingerTree' to a 'PQueue'. -toPQ :: (e -> e -> Ordering) -> (a -> PQueue e) -> FingerTree a -> Maybe (PQueue e) -toPQ _ _ EmptyT = Nothing -toPQ _ f (Single x) = Just (f x) -toPQ cmp f (Deep _ pr m sf) = Just (maybe (pr' <+> sf') ((pr' <+> sf') <+>) (toPQ cmp fNode m)) - where - fDigit digit = case fmap f digit of - One a -> a - Two a b -> a <+> b - Three a b c -> a <+> b <+> c - Four a b c d -> (a <+> b) <+> (c <+> d) - (<+>) = mergePQ cmp - fNode = fDigit . nodeToDigit - pr' = fDigit pr - sf' = fDigit sf - --- | 'mergePQ' merges two 'PQueue's. -mergePQ :: (a -> a -> Ordering) -> PQueue a -> PQueue a -> PQueue a -mergePQ cmp q1@(PQueue x1 ts1) q2@(PQueue x2 ts2) - | cmp x1 x2 == GT = PQueue x2 (q1 :& ts2) - | otherwise = PQueue x1 (q2 :& ts1) diff --git a/Data/Sequence/Internal.hs b/Data/Sequence/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/Sequence/Internal.hs @@ -0,0 +1,4295 @@ +{-# LANGUAGE CPP #-} +#include "containers.h" +{-# LANGUAGE BangPatterns #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE StandaloneDeriving #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE ScopedTypeVariables #-} +#endif +#if __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Trustworthy #-} +#endif +#if __GLASGOW_HASKELL__ >= 702 +{-# LANGUAGE DeriveGeneric #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE TypeFamilies #-} +#endif +#ifdef DEFINE_PATTERN_SYNONYMS +{-# LANGUAGE PatternSynonyms #-} +{-# LANGUAGE ViewPatterns #-} +#endif + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Sequence.Internal +-- Copyright : (c) Ross Paterson 2005 +-- (c) Louis Wasserman 2009 +-- (c) Bertram Felgenhauer, David Feuer, Ross Paterson, and +-- Milan Straka 2014 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : experimental +-- Portability : portable +-- +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. +-- +-- = Description +-- +-- General purpose finite sequences. +-- Apart from being finite and having strict operations, sequences +-- also differ from lists in supporting a wider variety of operations +-- efficiently. +-- +-- An amortized running time is given for each operation, with /n/ referring +-- to the length of the sequence and /i/ being the integral index used by +-- some operations. These bounds hold even in a persistent (shared) setting. +-- +-- The implementation uses 2-3 finger trees annotated with sizes, +-- as described in section 4.2 of +-- +-- * Ralf Hinze and Ross Paterson, +-- \"Finger trees: a simple general-purpose data structure\", +-- /Journal of Functional Programming/ 16:2 (2006) pp 197-217. +-- +-- +-- /Note/: Many of these operations have the same names as similar +-- operations on lists in the "Prelude". The ambiguity may be resolved +-- using either qualification or the @hiding@ clause. +-- +-- /Warning/: The size of a 'Seq' must not exceed @maxBound::Int@. Violation +-- of this condition is not detected and if the size limit is exceeded, the +-- behaviour of the sequence is undefined. This is unlikely to occur in most +-- applications, but some care may be required when using '><', '<*>', '*>', or +-- '>>', particularly repeatedly and particularly in combination with +-- 'replicate' or 'fromFunction'. +-- +----------------------------------------------------------------------------- + +module Data.Sequence.Internal ( + Elem(..), FingerTree(..), Node(..), Digit(..), Sized(..), MaybeForce, +#if defined(DEFINE_PATTERN_SYNONYMS) + Seq (.., Empty, (:<|), (:|>)), +#else + Seq (..), +#endif + + -- * Construction + empty, -- :: Seq a + singleton, -- :: a -> Seq a + (<|), -- :: a -> Seq a -> Seq a + (|>), -- :: Seq a -> a -> Seq a + (><), -- :: Seq a -> Seq a -> Seq a + fromList, -- :: [a] -> Seq a + fromFunction, -- :: Int -> (Int -> a) -> Seq a + fromArray, -- :: Ix i => Array i a -> Seq a + -- ** Repetition + replicate, -- :: Int -> a -> Seq a + replicateA, -- :: Applicative f => Int -> f a -> f (Seq a) + replicateM, -- :: Monad m => Int -> m a -> m (Seq a) + cycleTaking, -- :: Int -> Seq a -> Seq a + -- ** Iterative construction + iterateN, -- :: Int -> (a -> a) -> a -> Seq a + unfoldr, -- :: (b -> Maybe (a, b)) -> b -> Seq a + unfoldl, -- :: (b -> Maybe (b, a)) -> b -> Seq a + -- * Deconstruction + -- | Additional functions for deconstructing sequences are available + -- via the 'Foldable' instance of 'Seq'. + + -- ** Queries + null, -- :: Seq a -> Bool + length, -- :: Seq a -> Int + -- ** Views + ViewL(..), + viewl, -- :: Seq a -> ViewL a + ViewR(..), + viewr, -- :: Seq a -> ViewR a + -- * Scans + scanl, -- :: (a -> b -> a) -> a -> Seq b -> Seq a + scanl1, -- :: (a -> a -> a) -> Seq a -> Seq a + scanr, -- :: (a -> b -> b) -> b -> Seq a -> Seq b + scanr1, -- :: (a -> a -> a) -> Seq a -> Seq a + -- * Sublists + tails, -- :: Seq a -> Seq (Seq a) + inits, -- :: Seq a -> Seq (Seq a) + chunksOf, -- :: Int -> Seq a -> Seq (Seq a) + -- ** Sequential searches + takeWhileL, -- :: (a -> Bool) -> Seq a -> Seq a + takeWhileR, -- :: (a -> Bool) -> Seq a -> Seq a + dropWhileL, -- :: (a -> Bool) -> Seq a -> Seq a + dropWhileR, -- :: (a -> Bool) -> Seq a -> Seq a + spanl, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) + spanr, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) + breakl, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) + breakr, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) + partition, -- :: (a -> Bool) -> Seq a -> (Seq a, Seq a) + filter, -- :: (a -> Bool) -> Seq a -> Seq a + -- * Sorting + sort, -- :: Ord a => Seq a -> Seq a + sortBy, -- :: (a -> a -> Ordering) -> Seq a -> Seq a + unstableSort, -- :: Ord a => Seq a -> Seq a + unstableSortBy, -- :: (a -> a -> Ordering) -> Seq a -> Seq a + -- * Indexing + lookup, -- :: Int -> Seq a -> Maybe a + (!?), -- :: Seq a -> Int -> Maybe a + index, -- :: Seq a -> Int -> a + adjust, -- :: (a -> a) -> Int -> Seq a -> Seq a + adjust', -- :: (a -> a) -> Int -> Seq a -> Seq a + update, -- :: Int -> a -> Seq a -> Seq a + take, -- :: Int -> Seq a -> Seq a + drop, -- :: Int -> Seq a -> Seq a + insertAt, -- :: Int -> a -> Seq a -> Seq a + deleteAt, -- :: Int -> Seq a -> Seq a + splitAt, -- :: Int -> Seq a -> (Seq a, Seq a) + -- ** Indexing with predicates + -- | These functions perform sequential searches from the left + -- or right ends of the sequence, returning indices of matching + -- elements. + elemIndexL, -- :: Eq a => a -> Seq a -> Maybe Int + elemIndicesL, -- :: Eq a => a -> Seq a -> [Int] + elemIndexR, -- :: Eq a => a -> Seq a -> Maybe Int + elemIndicesR, -- :: Eq a => a -> Seq a -> [Int] + findIndexL, -- :: (a -> Bool) -> Seq a -> Maybe Int + findIndicesL, -- :: (a -> Bool) -> Seq a -> [Int] + findIndexR, -- :: (a -> Bool) -> Seq a -> Maybe Int + findIndicesR, -- :: (a -> Bool) -> Seq a -> [Int] + -- * Folds + -- | General folds are available via the 'Foldable' instance of 'Seq'. + foldMapWithIndex, -- :: Monoid m => (Int -> a -> m) -> Seq a -> m + foldlWithIndex, -- :: (b -> Int -> a -> b) -> b -> Seq a -> b + foldrWithIndex, -- :: (Int -> a -> b -> b) -> b -> Seq a -> b + -- * Transformations + mapWithIndex, -- :: (Int -> a -> b) -> Seq a -> Seq b + traverseWithIndex, -- :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) + reverse, -- :: Seq a -> Seq a + intersperse, -- :: a -> Seq a -> Seq a + -- ** Zips + zip, -- :: Seq a -> Seq b -> Seq (a, b) + zipWith, -- :: (a -> b -> c) -> Seq a -> Seq b -> Seq c + zip3, -- :: Seq a -> Seq b -> Seq c -> Seq (a, b, c) + zipWith3, -- :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d + zip4, -- :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a, b, c, d) + zipWith4, -- :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e +#ifdef TESTING + deep, + node2, + node3, +#endif + ) where + +import Prelude hiding ( + Functor(..), +#if MIN_VERSION_base(4,8,0) + Applicative, (<$>), foldMap, Monoid, +#endif + null, length, lookup, take, drop, splitAt, foldl, foldl1, foldr, foldr1, + scanl, scanl1, scanr, scanr1, replicate, zip, zipWith, zip3, zipWith3, + takeWhile, dropWhile, iterate, reverse, filter, mapM, sum, all) +import qualified Data.List +import Control.Applicative (Applicative(..), (<$>), (<**>), Alternative, + WrappedMonad(..), liftA, liftA2, liftA3) +import qualified Control.Applicative as Applicative (Alternative(..)) +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (MonadPlus(..), ap) +import Data.Monoid (Monoid(..)) +import Data.Functor (Functor(..)) +#if MIN_VERSION_base(4,6,0) +import Data.Foldable (Foldable(foldl, foldl1, foldr, foldr1, foldMap, foldl', foldr'), toList) +#else +import Data.Foldable (Foldable(foldl, foldl1, foldr, foldr1, foldMap), foldl', toList) +#endif + +#if MIN_VERSION_base(4,9,0) +import qualified Data.Semigroup as Semigroup +import Data.Functor.Classes +#endif +import Data.Traversable +import Data.Typeable + +-- GHC specific stuff +#ifdef __GLASGOW_HASKELL__ +import GHC.Exts (build) +import Text.Read (Lexeme(Ident), lexP, parens, prec, + readPrec, readListPrec, readListPrecDefault) +import Data.Data +import Data.String (IsString(..)) +#endif +#if __GLASGOW_HASKELL__ >= 706 +import GHC.Generics (Generic, Generic1) +#elif __GLASGOW_HASKELL__ >= 702 +import GHC.Generics (Generic) +#endif + +-- Array stuff, with GHC.Arr on GHC +import Data.Array (Ix, Array) +import qualified Data.Array +#ifdef __GLASGOW_HASKELL__ +import qualified GHC.Arr +#endif + +-- Coercion on GHC 7.8+ +#if __GLASGOW_HASKELL__ >= 708 +import Data.Coerce +import qualified GHC.Exts +#else +#endif + +-- Identity functor on base 4.8 (GHC 7.10+) +#if MIN_VERSION_base(4,8,0) +import Data.Functor.Identity (Identity(..)) +#endif + +#if !MIN_VERSION_base(4,8,0) +import Data.Word (Word) +#endif + +import Utils.Containers.Internal.StrictPair (StrictPair (..), toPair) + +default () + +-- We define our own copy here, for Monoid only, even though this +-- is now a Semigroup operator in base. The essential reason is that +-- we have absolutely no use for semigroups in this module. Everything +-- that needs to sum things up requires a Monoid constraint to deal +-- with empty sequences. I'm not sure if there's a risk of walking +-- through dictionaries to reach <> from Monoid, but I see no reason +-- to risk it. +infixr 6 <> +(<>) :: Monoid m => m -> m -> m +(<>) = mappend +{-# INLINE (<>) #-} + +infixr 5 `consTree` +infixl 5 `snocTree` +infixr 5 `appendTree0` + +infixr 5 >< +infixr 5 <|, :< +infixl 5 |>, :> + +#ifdef DEFINE_PATTERN_SYNONYMS +infixr 5 :<| +infixl 5 :|> + +-- TODO: Once GHC implements some way to prevent non-exhaustive +-- pattern match warnings for pattern synonyms, we should be +-- sure to take advantage of that. + +-- | A pattern synonym matching an empty sequence. +pattern Empty :: Seq a +pattern Empty = Seq EmptyT + +-- | A pattern synonym viewing the front of a non-empty +-- sequence. +pattern (:<|) :: a -> Seq a -> Seq a +pattern x :<| xs <- (viewl -> x :< xs) + where + x :<| xs = x <| xs + +-- | A pattern synonym viewing the rear of a non-empty +-- sequence. +pattern (:|>) :: Seq a -> a -> Seq a +pattern xs :|> x <- (viewr -> xs :> x) + where + xs :|> x = xs |> x +#endif + +class Sized a where + size :: a -> Int + +-- In much the same way that Sized lets us handle the +-- sizes of elements and nodes uniformly, MaybeForce lets +-- us handle their strictness (or lack thereof) uniformly. +-- We can `mseq` something and not have to worry about +-- whether it's an element or a node. +class MaybeForce a where + maybeRwhnf :: a -> () + +mseq :: MaybeForce a => a -> b -> b +mseq a b = case maybeRwhnf a of () -> b +{-# INLINE mseq #-} + +infixr 0 $!? +($!?) :: MaybeForce a => (a -> b) -> a -> b +f $!? a = case maybeRwhnf a of () -> f a +{-# INLINE ($!?) #-} + +instance MaybeForce (Elem a) where + maybeRwhnf _ = () + {-# INLINE maybeRwhnf #-} + +instance MaybeForce (Node a) where + maybeRwhnf !_ = () + {-# INLINE maybeRwhnf #-} + +-- A wrapper making mseq = seq +newtype ForceBox a = ForceBox a +instance MaybeForce (ForceBox a) where + maybeRwhnf !_ = () +instance Sized (ForceBox a) where + size _ = 1 + +-- | General-purpose finite sequences. +newtype Seq a = Seq (FingerTree (Elem a)) + +instance Functor Seq where + fmap = fmapSeq +#ifdef __GLASGOW_HASKELL__ + x <$ s = replicate (length s) x +#endif + +fmapSeq :: (a -> b) -> Seq a -> Seq b +fmapSeq f (Seq xs) = Seq (fmap (fmap f) xs) +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] fmapSeq #-} +{-# RULES +"fmapSeq/fmapSeq" forall f g xs . fmapSeq f (fmapSeq g xs) = fmapSeq (f . g) xs + #-} +#endif +#if __GLASGOW_HASKELL__ >= 709 +-- Safe coercions were introduced in 7.8, but did not work well with RULES yet. +{-# RULES +"fmapSeq/coerce" fmapSeq coerce = coerce + #-} +#endif + +instance Foldable Seq where + foldMap f (Seq xs) = foldMap (foldMap f) xs +#if __GLASGOW_HASKELL__ >= 708 + foldr f z (Seq xs) = foldr (coerce f) z xs + foldr' f z (Seq xs) = foldr' (coerce f) z xs +#else + foldr f z (Seq xs) = foldr (flip (foldr f)) z xs +#if MIN_VERSION_base(4,6,0) + foldr' f z (Seq xs) = foldr' (flip (foldr' f)) z xs +#endif +#endif + foldl f z (Seq xs) = foldl (foldl f) z xs +#if MIN_VERSION_base(4,6,0) + foldl' f z (Seq xs) = foldl' (foldl' f) z xs +#endif + + foldr1 f (Seq xs) = getElem (foldr1 f' xs) + where f' (Elem x) (Elem y) = Elem (f x y) + + foldl1 f (Seq xs) = getElem (foldl1 f' xs) + where f' (Elem x) (Elem y) = Elem (f x y) + +#if MIN_VERSION_base(4,8,0) + length = length + {-# INLINE length #-} + null = null + {-# INLINE null #-} +#endif + +#if __GLASGOW_HASKELL__ >= 708 +-- The natural definition of traverse, used for implementations that don't +-- support coercions, `fmap`s into each `Elem`, then `fmap`s again over the +-- result to turn it from a `FingerTree` to a `Seq`. None of this mapping is +-- necessary! We could avoid it without coercions, I believe, by writing a +-- bunch of traversal functions to deal with the `Elem` stuff specially (for +-- FingerTrees, Digits, and Nodes), but using coercions we only need to +-- duplicate code at the FingerTree level. We coerce the `Seq a` to a +-- `FingerTree a`, stripping off all the Elem junk, then use a weird FingerTree +-- traversing function that coerces back to Seq within the functor. +instance Traversable Seq where + traverse f xs = traverseFTE f (coerce xs) + +traverseFTE :: Applicative f => (a -> f b) -> FingerTree a -> f (Seq b) +traverseFTE _f EmptyT = pure empty +traverseFTE f (Single x) = Seq . Single . Elem <$> f x +traverseFTE f (Deep s pr m sf) = + (\pr' m' sf' -> coerce $ Deep s pr' m' sf') <$> + traverse f pr <*> traverse (traverse f) m <*> traverse f sf +#else +instance Traversable Seq where + traverse f (Seq xs) = Seq <$> traverse (traverse f) xs +#endif + +instance NFData a => NFData (Seq a) where + rnf (Seq xs) = rnf xs + +instance Monad Seq where + return = pure + xs >>= f = foldl' add empty xs + where add ys x = ys >< f x + (>>) = (*>) + +instance Applicative Seq where + pure = singleton + xs *> ys = cycleNTimes (length xs) ys + + fs <*> xs@(Seq xsFT) = case viewl fs of + EmptyL -> empty + firstf :< fs' -> case viewr fs' of + EmptyR -> fmap firstf xs + Seq fs''FT :> lastf -> case rigidify xsFT of + RigidEmpty -> empty + RigidOne (Elem x) -> fmap ($x) fs + RigidTwo (Elem x1) (Elem x2) -> + Seq $ ap2FT firstf fs''FT lastf (x1, x2) + RigidThree (Elem x1) (Elem x2) (Elem x3) -> + Seq $ ap3FT firstf fs''FT lastf (x1, x2, x3) + RigidFull r@(Rigid s pr _m sf) -> Seq $ + Deep (s * length fs) + (fmap (fmap firstf) (nodeToDigit pr)) + (aptyMiddle (fmap firstf) (fmap lastf) fmap fs''FT r) + (fmap (fmap lastf) (nodeToDigit sf)) + + +ap2FT :: (a -> b) -> FingerTree (Elem (a->b)) -> (a -> b) -> (a,a) -> FingerTree (Elem b) +ap2FT firstf fs lastf (x,y) = + Deep (size fs * 2 + 4) + (Two (Elem $ firstf x) (Elem $ firstf y)) + (mapMulFT 2 (\(Elem f) -> Node2 2 (Elem (f x)) (Elem (f y))) fs) + (Two (Elem $ lastf x) (Elem $ lastf y)) + +ap3FT :: (a -> b) -> FingerTree (Elem (a->b)) -> (a -> b) -> (a,a,a) -> FingerTree (Elem b) +ap3FT firstf fs lastf (x,y,z) = Deep (size fs * 3 + 6) + (Three (Elem $ firstf x) (Elem $ firstf y) (Elem $ firstf z)) + (mapMulFT 3 (\(Elem f) -> Node3 3 (Elem (f x)) (Elem (f y)) (Elem (f z))) fs) + (Three (Elem $ lastf x) (Elem $ lastf y) (Elem $ lastf z)) + + +data Rigidified a = RigidEmpty + | RigidOne a + | RigidTwo a a + | RigidThree a a a + | RigidFull (Rigid a) +#ifdef TESTING + deriving Show +#endif + +-- | A finger tree whose top level has only Two and/or Three digits, and whose +-- other levels have only One and Two digits. A Rigid tree is precisely what one +-- gets by unzipping/inverting a 2-3 tree, so it is precisely what we need to +-- turn a finger tree into in order to transform it into a 2-3 tree. +data Rigid a = Rigid {-# UNPACK #-} !Int !(Digit23 a) (Thin (Node a)) !(Digit23 a) +#ifdef TESTING + deriving Show +#endif + +-- | A finger tree whose digits are all ones and twos +data Thin a = EmptyTh + | SingleTh a + | DeepTh {-# UNPACK #-} !Int !(Digit12 a) (Thin (Node a)) !(Digit12 a) +#ifdef TESTING + deriving Show +#endif + +data Digit12 a = One12 a | Two12 a a +#ifdef TESTING + deriving Show +#endif + +-- | Sometimes, we want to emphasize that we are viewing a node as a top-level +-- digit of a 'Rigid' tree. +type Digit23 a = Node a + +-- | 'aptyMiddle' does most of the hard work of computing @fs<*>xs@. It +-- produces the center part of a finger tree, with a prefix corresponding to +-- the prefix of @xs@ and a suffix corresponding to the suffix of @xs@ omitted; +-- the missing suffix and prefix are added by the caller. For the recursive +-- call, it squashes the prefix and the suffix into the center tree. Once it +-- gets to the bottom, it turns the tree into a 2-3 tree, applies 'mapMulFT' to +-- produce the main body, and glues all the pieces together. +-- +-- 'map23' itself is a bit horrifying because of the nested types involved. Its +-- job is to map over the *elements* of a 2-3 tree, rather than the subtrees. +-- If we used a higher-order nested type with MPTC, we could probably use a +-- class, but as it is we have to build up 'map23' explicitly through the +-- recursion. +aptyMiddle + :: (c -> d) + -> (c -> d) + -> ((a -> b) -> c -> d) + -> FingerTree (Elem (a -> b)) + -> Rigid c + -> FingerTree (Node d) + +-- Not at the bottom yet + +aptyMiddle firstf + lastf + map23 + fs + (Rigid s pr (DeepTh sm prm mm sfm) sf) + = Deep (sm + s * (size fs + 1)) -- note: sm = s - size pr - size sf + (fmap (fmap firstf) (digit12ToDigit prm)) + (aptyMiddle (fmap firstf) + (fmap lastf) + (fmap . map23) + fs + (Rigid s (squashL pr prm) mm (squashR sfm sf))) + (fmap (fmap lastf) (digit12ToDigit sfm)) + +-- At the bottom + +aptyMiddle firstf + lastf + map23 + fs + (Rigid s pr EmptyTh sf) + = deep + (One (fmap firstf sf)) + (mapMulFT s (\(Elem f) -> fmap (fmap (map23 f)) converted) fs) + (One (fmap lastf pr)) + where converted = node2 pr sf + +aptyMiddle firstf + lastf + map23 + fs + (Rigid s pr (SingleTh q) sf) + = deep + (Two (fmap firstf q) (fmap firstf sf)) + (mapMulFT s (\(Elem f) -> fmap (fmap (map23 f)) converted) fs) + (Two (fmap lastf pr) (fmap lastf q)) + where converted = node3 pr q sf + +digit12ToDigit :: Digit12 a -> Digit a +digit12ToDigit (One12 a) = One a +digit12ToDigit (Two12 a b) = Two a b + +-- Squash the first argument down onto the left side of the second. +squashL :: Digit23 a -> Digit12 (Node a) -> Digit23 (Node a) +squashL m (One12 n) = node2 m n +squashL m (Two12 n1 n2) = node3 m n1 n2 + +-- Squash the second argument down onto the right side of the first +squashR :: Digit12 (Node a) -> Digit23 a -> Digit23 (Node a) +squashR (One12 n) m = node2 n m +squashR (Two12 n1 n2) m = node3 n1 n2 m + + +-- | /O(m*n)/ (incremental) Takes an /O(m)/ function and a finger tree of size +-- /n/ and maps the function over the tree leaves. Unlike the usual 'fmap', the +-- function is applied to the "leaves" of the 'FingerTree' (i.e., given a +-- @FingerTree (Elem a)@, it applies the function to elements of type @Elem +-- a@), replacing the leaves with subtrees of at least the same height, e.g., +-- @Node(Node(Elem y))@. The multiplier argument serves to make the annotations +-- match up properly. +mapMulFT :: Int -> (a -> b) -> FingerTree a -> FingerTree b +mapMulFT _ _ EmptyT = EmptyT +mapMulFT _mul f (Single a) = Single (f a) +mapMulFT mul f (Deep s pr m sf) = Deep (mul * s) (fmap f pr) (mapMulFT mul (mapMulNode mul f) m) (fmap f sf) + +mapMulNode :: Int -> (a -> b) -> Node a -> Node b +mapMulNode mul f (Node2 s a b) = Node2 (mul * s) (f a) (f b) +mapMulNode mul f (Node3 s a b c) = Node3 (mul * s) (f a) (f b) (f c) + +-- | /O(log n)/ (incremental) Takes the extra flexibility out of a 'FingerTree' +-- to make it a genuine 2-3 finger tree. The result of 'rigidify' will have +-- only two and three digits at the top level and only one and two +-- digits elsewhere. If the tree has fewer than four elements, 'rigidify' +-- will simply extract them, and will not build a tree. +rigidify :: FingerTree (Elem a) -> Rigidified (Elem a) +-- The patterns below just fix up the top level of the tree; 'rigidify' +-- delegates the hard work to 'thin'. + +rigidify EmptyT = RigidEmpty + +rigidify (Single q) = RigidOne q + +-- The left digit is Two or Three +rigidify (Deep s (Two a b) m sf) = rigidifyRight s (node2 a b) m sf +rigidify (Deep s (Three a b c) m sf) = rigidifyRight s (node3 a b c) m sf + +-- The left digit is Four +rigidify (Deep s (Four a b c d) m sf) = rigidifyRight s (node2 a b) (node2 c d `consTree` m) sf + +-- The left digit is One +rigidify (Deep s (One a) m sf) = case viewLTree m of + ConsLTree (Node2 _ b c) m' -> rigidifyRight s (node3 a b c) m' sf + ConsLTree (Node3 _ b c d) m' -> rigidifyRight s (node2 a b) (node2 c d `consTree` m') sf + EmptyLTree -> case sf of + One b -> RigidTwo a b + Two b c -> RigidThree a b c + Three b c d -> RigidFull $ Rigid s (node2 a b) EmptyTh (node2 c d) + Four b c d e -> RigidFull $ Rigid s (node3 a b c) EmptyTh (node2 d e) + +-- | /O(log n)/ (incremental) Takes a tree whose left side has been rigidified +-- and finishes the job. +rigidifyRight :: Int -> Digit23 (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> Rigidified (Elem a) + +-- The right digit is Two, Three, or Four +rigidifyRight s pr m (Two a b) = RigidFull $ Rigid s pr (thin m) (node2 a b) +rigidifyRight s pr m (Three a b c) = RigidFull $ Rigid s pr (thin m) (node3 a b c) +rigidifyRight s pr m (Four a b c d) = RigidFull $ Rigid s pr (thin $ m `snocTree` node2 a b) (node2 c d) + +-- The right digit is One +rigidifyRight s pr m (One e) = case viewRTree m of + SnocRTree m' (Node2 _ a b) -> RigidFull $ Rigid s pr (thin m') (node3 a b e) + SnocRTree m' (Node3 _ a b c) -> RigidFull $ Rigid s pr (thin $ m' `snocTree` node2 a b) (node2 c e) + EmptyRTree -> case pr of + Node2 _ a b -> RigidThree a b e + Node3 _ a b c -> RigidFull $ Rigid s (node2 a b) EmptyTh (node2 c e) + +-- | /O(log n)/ (incremental) Rejigger a finger tree so the digits are all ones +-- and twos. +thin :: Sized a => FingerTree a -> Thin a +-- Note that 'thin12' will produce a 'DeepTh' constructor immediately before +-- recursively calling 'thin'. +thin EmptyT = EmptyTh +thin (Single a) = SingleTh a +thin (Deep s pr m sf) = + case pr of + One a -> thin12 s (One12 a) m sf + Two a b -> thin12 s (Two12 a b) m sf + Three a b c -> thin12 s (One12 a) (node2 b c `consTree` m) sf + Four a b c d -> thin12 s (Two12 a b) (node2 c d `consTree` m) sf + +thin12 :: Sized a => Int -> Digit12 a -> FingerTree (Node a) -> Digit a -> Thin a +thin12 s pr m (One a) = DeepTh s pr (thin m) (One12 a) +thin12 s pr m (Two a b) = DeepTh s pr (thin m) (Two12 a b) +thin12 s pr m (Three a b c) = DeepTh s pr (thin $ m `snocTree` node2 a b) (One12 c) +thin12 s pr m (Four a b c d) = DeepTh s pr (thin $ m `snocTree` node2 a b) (Two12 c d) + +-- | Intersperse an element between the elements of a sequence. +-- +-- @ +-- intersperse a empty = empty +-- intersperse a (singleton x) = singleton x +-- intersperse a (fromList [x,y]) = fromList [x,a,y] +-- intersperse a (fromList [x,y,z]) = fromList [x,a,y,a,z] +-- @ +-- +-- @since 0.5.8 +intersperse :: a -> Seq a -> Seq a +intersperse y xs = case viewl xs of + EmptyL -> empty + p :< ps -> p <| (ps <**> (const y <| singleton id)) +-- We used to use +-- +-- intersperse y xs = drop 1 $ xs <**> (const y <| singleton id) +-- +-- but if length xs = ((maxBound :: Int) `quot` 2) + 1 then +-- +-- length (xs <**> (const y <| singleton id)) will wrap around to negative +-- and the drop won't work. The new implementation can produce a result +-- right up to maxBound :: Int + +instance MonadPlus Seq where + mzero = empty + mplus = (><) + +instance Alternative Seq where + empty = empty + (<|>) = (><) + +instance Eq a => Eq (Seq a) where + xs == ys = length xs == length ys && toList xs == toList ys + +instance Ord a => Ord (Seq a) where + compare xs ys = compare (toList xs) (toList ys) + +#ifdef TESTING +instance Show a => Show (Seq a) where + showsPrec p (Seq x) = showsPrec p x +#else +instance Show a => Show (Seq a) where + showsPrec p xs = showParen (p > 10) $ + showString "fromList " . shows (toList xs) +#endif + +#if MIN_VERSION_base(4,9,0) +instance Show1 Seq where + liftShowsPrec _shwsPrc shwList p xs = showParen (p > 10) $ + showString "fromList " . shwList (toList xs) + +instance Eq1 Seq where + liftEq eq xs ys = length xs == length ys && liftEq eq (toList xs) (toList ys) + +instance Ord1 Seq where + liftCompare cmp xs ys = liftCompare cmp (toList xs) (toList ys) +#endif + +instance Read a => Read (Seq a) 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 + +#if MIN_VERSION_base(4,9,0) +instance Read1 Seq where + liftReadsPrec _rp readLst p = readParen (p > 10) $ \r -> do + ("fromList",s) <- lex r + (xs,t) <- readLst s + pure (fromList xs, t) +#endif + +instance Monoid (Seq a) where + mempty = empty + mappend = (><) + +#if MIN_VERSION_base(4,9,0) +instance Semigroup.Semigroup (Seq a) where + (<>) = (><) +#endif + +INSTANCE_TYPEABLE1(Seq) + +#if __GLASGOW_HASKELL__ +instance Data a => Data (Seq a) where + gfoldl f z s = case viewl s of + EmptyL -> z empty + x :< xs -> z (<|) `f` x `f` xs + + gunfold k z c = case constrIndex c of + 1 -> z empty + 2 -> k (k (z (<|))) + _ -> error "gunfold" + + toConstr xs + | null xs = emptyConstr + | otherwise = consConstr + + dataTypeOf _ = seqDataType + + dataCast1 f = gcast1 f + +emptyConstr, consConstr :: Constr +emptyConstr = mkConstr seqDataType "empty" [] Prefix +consConstr = mkConstr seqDataType "<|" [] Infix + +seqDataType :: DataType +seqDataType = mkDataType "Data.Sequence.Seq" [emptyConstr, consConstr] +#endif + +-- Finger trees + +data FingerTree a + = EmptyT + | Single a + | Deep {-# UNPACK #-} !Int !(Digit a) (FingerTree (Node a)) !(Digit a) +#ifdef TESTING + deriving Show +#endif + +instance Sized a => Sized (FingerTree a) where + {-# SPECIALIZE instance Sized (FingerTree (Elem a)) #-} + {-# SPECIALIZE instance Sized (FingerTree (Node a)) #-} + size EmptyT = 0 + size (Single x) = size x + size (Deep v _ _ _) = v + +instance Foldable FingerTree where + foldMap _ EmptyT = mempty + foldMap f (Single x) = f x + foldMap f (Deep _ pr m sf) = + foldMap f pr <> foldMap (foldMap f) m <> foldMap f sf + + foldr _ z EmptyT = z + foldr f z (Single x) = x `f` z + foldr f z (Deep _ pr m sf) = + foldr f (foldr (flip (foldr f)) (foldr f z sf) m) pr + + foldl _ z EmptyT = z + foldl f z (Single x) = z `f` x + foldl f z (Deep _ pr m sf) = + foldl f (foldl (foldl f) (foldl f z pr) m) sf + +#if MIN_VERSION_base(4,6,0) + foldr' _ z EmptyT = z + foldr' f z (Single x) = f x z + foldr' f z (Deep _ pr m sf) = foldr' f mres pr + where !sfRes = foldr' f z sf + !mres = foldr' (flip (foldr' f)) sfRes m + + foldl' _ z EmptyT = z + foldl' f z (Single x) = z `f` x + foldl' f z (Deep _ pr m sf) = foldl' f mres sf + where !prRes = foldl' f z pr + !mres = foldl' (foldl' f) prRes m +#endif + + foldr1 _ EmptyT = error "foldr1: empty sequence" + foldr1 _ (Single x) = x + foldr1 f (Deep _ pr m sf) = + foldr f (foldr (flip (foldr f)) (foldr1 f sf) m) pr + + foldl1 _ EmptyT = error "foldl1: empty sequence" + foldl1 _ (Single x) = x + foldl1 f (Deep _ pr m sf) = + foldl f (foldl (foldl f) (foldl1 f pr) m) sf + +instance Functor FingerTree where + fmap _ EmptyT = EmptyT + fmap f (Single x) = Single (f x) + fmap f (Deep v pr m sf) = + Deep v (fmap f pr) (fmap (fmap f) m) (fmap f sf) + +instance Traversable FingerTree where + traverse _ EmptyT = pure EmptyT + traverse f (Single x) = Single <$> f x + traverse f (Deep v pr m sf) = + deep' v <$> traverse f pr <*> traverse (traverse f) m <*> + traverse f sf + +instance NFData a => NFData (FingerTree a) where + rnf EmptyT = () + rnf (Single x) = rnf x + rnf (Deep _ pr m sf) = rnf pr `seq` rnf sf `seq` rnf m + +{-# INLINE deep #-} +deep :: Sized a => Digit a -> FingerTree (Node a) -> Digit a -> FingerTree a +deep pr m sf = Deep (size pr + size m + size sf) pr m sf + +{-# INLINE pullL #-} +pullL :: Int -> FingerTree (Node a) -> Digit a -> FingerTree a +pullL s m sf = case viewLTree m of + EmptyLTree -> digitToTree' s sf + ConsLTree pr m' -> Deep s (nodeToDigit pr) m' sf + +{-# INLINE pullR #-} +pullR :: Int -> Digit a -> FingerTree (Node a) -> FingerTree a +pullR s pr m = case viewRTree m of + EmptyRTree -> digitToTree' s pr + SnocRTree m' sf -> Deep s pr m' (nodeToDigit sf) + +-- Digits + +data Digit a + = One a + | Two a a + | Three a a a + | Four a a a a +#ifdef TESTING + deriving Show +#endif + +instance Foldable Digit where + foldMap f (One a) = f a + foldMap f (Two a b) = f a <> f b + foldMap f (Three a b c) = f a <> f b <> f c + foldMap f (Four a b c d) = f a <> f b <> f c <> f d + + foldr f z (One a) = a `f` z + foldr f z (Two a b) = a `f` (b `f` z) + foldr f z (Three a b c) = a `f` (b `f` (c `f` z)) + foldr f z (Four a b c d) = a `f` (b `f` (c `f` (d `f` z))) + + foldl f z (One a) = z `f` a + foldl f z (Two a b) = (z `f` a) `f` b + foldl f z (Three a b c) = ((z `f` a) `f` b) `f` c + foldl f z (Four a b c d) = (((z `f` a) `f` b) `f` c) `f` d + +#if MIN_VERSION_base(4,6,0) + foldr' f z (One a) = a `f` z + foldr' f z (Two a b) = f a $! f b z + foldr' f z (Three a b c) = f a $! f b $! f c z + foldr' f z (Four a b c d) = f a $! f b $! f c $! f d z + + foldl' f z (One a) = f z a + foldl' f z (Two a b) = (f $! f z a) b + foldl' f z (Three a b c) = (f $! (f $! f z a) b) c + foldl' f z (Four a b c d) = (f $! (f $! (f $! f z a) b) c) d +#endif + + foldr1 _ (One a) = a + foldr1 f (Two a b) = a `f` b + foldr1 f (Three a b c) = a `f` (b `f` c) + foldr1 f (Four a b c d) = a `f` (b `f` (c `f` d)) + + foldl1 _ (One a) = a + foldl1 f (Two a b) = a `f` b + foldl1 f (Three a b c) = (a `f` b) `f` c + foldl1 f (Four a b c d) = ((a `f` b) `f` c) `f` d + +instance Functor Digit where + {-# INLINE fmap #-} + fmap f (One a) = One (f a) + fmap f (Two a b) = Two (f a) (f b) + fmap f (Three a b c) = Three (f a) (f b) (f c) + fmap f (Four a b c d) = Four (f a) (f b) (f c) (f d) + +instance Traversable Digit where + {-# INLINE traverse #-} + traverse f (One a) = One <$> f a + traverse f (Two a b) = Two <$> f a <*> f b + traverse f (Three a b c) = Three <$> f a <*> f b <*> f c + traverse f (Four a b c d) = Four <$> f a <*> f b <*> f c <*> f d + +instance NFData a => NFData (Digit a) where + rnf (One a) = rnf a + rnf (Two a b) = rnf a `seq` rnf b + rnf (Three a b c) = rnf a `seq` rnf b `seq` rnf c + rnf (Four a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d + +instance Sized a => Sized (Digit a) where + {-# INLINE size #-} + size = foldl1 (+) . fmap size + +{-# SPECIALIZE digitToTree :: Digit (Elem a) -> FingerTree (Elem a) #-} +{-# SPECIALIZE digitToTree :: Digit (Node a) -> FingerTree (Node a) #-} +digitToTree :: Sized a => Digit a -> FingerTree a +digitToTree (One a) = Single a +digitToTree (Two a b) = deep (One a) EmptyT (One b) +digitToTree (Three a b c) = deep (Two a b) EmptyT (One c) +digitToTree (Four a b c d) = deep (Two a b) EmptyT (Two c d) + +-- | Given the size of a digit and the digit itself, efficiently converts +-- it to a FingerTree. +digitToTree' :: Int -> Digit a -> FingerTree a +digitToTree' n (Four a b c d) = Deep n (Two a b) EmptyT (Two c d) +digitToTree' n (Three a b c) = Deep n (Two a b) EmptyT (One c) +digitToTree' n (Two a b) = Deep n (One a) EmptyT (One b) +digitToTree' !_n (One a) = Single a + +-- Nodes + +data Node a + = Node2 {-# UNPACK #-} !Int a a + | Node3 {-# UNPACK #-} !Int a a a +#ifdef TESTING + deriving Show +#endif + +-- Sometimes, we need to apply a Node2, Node3, or Deep constructor +-- to a size and pass the result to a function. If we calculate, +-- say, `Node2 n <$> x <*> y`, then according to -ddump-simpl, +-- GHC boxes up `n`, passes it to the strict constructor for `Node2`, +-- and passes the result to `fmap`. Using `node2'` instead prevents +-- this, forming a closure with the unboxed size. +{-# INLINE node2' #-} +node2' :: Int -> a -> a -> Node a +node2' !s = \a b -> Node2 s a b + +{-# INLINE node3' #-} +node3' :: Int -> a -> a -> a -> Node a +node3' !s = \a b c -> Node3 s a b c + +{-# INLINE deep' #-} +deep' :: Int -> Digit a -> FingerTree (Node a) -> Digit a -> FingerTree a +deep' !s = \pr m sf -> Deep s pr m sf + +instance Foldable Node where + foldMap f (Node2 _ a b) = f a <> f b + foldMap f (Node3 _ a b c) = f a <> f b <> f c + + foldr f z (Node2 _ a b) = a `f` (b `f` z) + foldr f z (Node3 _ a b c) = a `f` (b `f` (c `f` z)) + + foldl f z (Node2 _ a b) = (z `f` a) `f` b + foldl f z (Node3 _ a b c) = ((z `f` a) `f` b) `f` c + +#if MIN_VERSION_base(4,6,0) + foldr' f z (Node2 _ a b) = f a $! f b z + foldr' f z (Node3 _ a b c) = f a $! f b $! f c z + + foldl' f z (Node2 _ a b) = (f $! f z a) b + foldl' f z (Node3 _ a b c) = (f $! (f $! f z a) b) c +#endif + +instance Functor Node where + {-# INLINE fmap #-} + fmap f (Node2 v a b) = Node2 v (f a) (f b) + fmap f (Node3 v a b c) = Node3 v (f a) (f b) (f c) + +instance Traversable Node where + {-# INLINE traverse #-} + traverse f (Node2 v a b) = node2' v <$> f a <*> f b + traverse f (Node3 v a b c) = node3' v <$> f a <*> f b <*> f c + +instance NFData a => NFData (Node a) where + rnf (Node2 _ a b) = rnf a `seq` rnf b + rnf (Node3 _ a b c) = rnf a `seq` rnf b `seq` rnf c + +instance Sized (Node a) where + size (Node2 v _ _) = v + size (Node3 v _ _ _) = v + +{-# INLINE node2 #-} +node2 :: Sized a => a -> a -> Node a +node2 a b = Node2 (size a + size b) a b + +{-# INLINE node3 #-} +node3 :: Sized a => a -> a -> a -> Node a +node3 a b c = Node3 (size a + size b + size c) a b c + +nodeToDigit :: Node a -> Digit a +nodeToDigit (Node2 _ a b) = Two a b +nodeToDigit (Node3 _ a b c) = Three a b c + +-- Elements + +newtype Elem a = Elem { getElem :: a } +#ifdef TESTING + deriving Show +#endif + +instance Sized (Elem a) where + size _ = 1 + +instance Functor Elem where +#if __GLASGOW_HASKELL__ >= 708 +-- This cuts the time for <*> by around a fifth. + fmap = coerce +#else + fmap f (Elem x) = Elem (f x) +#endif + +instance Foldable Elem where + foldr f z (Elem x) = f x z +#if __GLASGOW_HASKELL__ >= 708 + foldMap = coerce + foldl = coerce + foldl' = coerce +#else + foldMap f (Elem x) = f x + foldl f z (Elem x) = f z x +#if MIN_VERSION_base(4,6,0) + foldl' f z (Elem x) = f z x +#endif +#endif + +instance Traversable Elem where + traverse f (Elem x) = Elem <$> f x + +instance NFData a => NFData (Elem a) where + rnf (Elem x) = rnf x + +------------------------------------------------------- +-- Applicative construction +------------------------------------------------------- +#if !MIN_VERSION_base(4,8,0) +newtype Identity a = Identity {runIdentity :: a} + +instance Functor Identity where + fmap f (Identity x) = Identity (f x) + +instance Applicative Identity where + pure = Identity + Identity f <*> Identity x = Identity (f x) +#endif + +-- | This is essentially a clone of Control.Monad.State.Strict. +newtype State s a = State {runState :: s -> (s, a)} + +instance Functor (State s) where + fmap = liftA + +instance Monad (State s) where + {-# INLINE return #-} + {-# INLINE (>>=) #-} + return = pure + m >>= k = State $ \ s -> case runState m s of + (s', x) -> runState (k x) s' + +instance Applicative (State s) where + {-# INLINE pure #-} + pure x = State $ \ s -> (s, x) + (<*>) = ap + +execState :: State s a -> s -> a +execState m x = snd (runState m x) + +-- | 'applicativeTree' takes an Applicative-wrapped construction of a +-- piece of a FingerTree, assumed to always have the same size (which +-- is put in the second argument), and replicates it as many times as +-- specified. This is a generalization of 'replicateA', which itself +-- is a generalization of many Data.Sequence methods. +{-# SPECIALIZE applicativeTree :: Int -> Int -> State s a -> State s (FingerTree a) #-} +{-# SPECIALIZE applicativeTree :: Int -> Int -> Identity a -> Identity (FingerTree a) #-} +-- Special note: the Identity specialization automatically does node sharing, +-- reducing memory usage of the resulting tree to /O(log n)/. +applicativeTree :: Applicative f => Int -> Int -> f a -> f (FingerTree a) +applicativeTree n !mSize m = case n of + 0 -> pure EmptyT + 1 -> fmap Single m + 2 -> deepA one emptyTree one + 3 -> deepA two emptyTree one + 4 -> deepA two emptyTree two + 5 -> deepA three emptyTree two + 6 -> deepA three emptyTree three + _ -> case n `quotRem` 3 of + (q,0) -> deepA three (applicativeTree (q - 2) mSize' n3) three + (q,1) -> deepA two (applicativeTree (q - 1) mSize' n3) two + (q,_) -> deepA three (applicativeTree (q - 1) mSize' n3) two + where !mSize' = 3 * mSize + n3 = liftA3 (node3' mSize') m m m + where + one = fmap One m + two = liftA2 Two m m + three = liftA3 Three m m m + deepA = liftA3 (deep' (n * mSize)) + emptyTree = pure EmptyT + +------------------------------------------------------------------------ +-- Construction +------------------------------------------------------------------------ + +-- | /O(1)/. The empty sequence. +empty :: Seq a +empty = Seq EmptyT + +-- | /O(1)/. A singleton sequence. +singleton :: a -> Seq a +singleton x = Seq (Single (Elem x)) + +-- | /O(log n)/. @replicate n x@ is a sequence consisting of @n@ copies of @x@. +replicate :: Int -> a -> Seq a +replicate n x + | n >= 0 = runIdentity (replicateA n (Identity x)) + | otherwise = error "replicate takes a nonnegative integer argument" + +-- | 'replicateA' is an 'Applicative' version of 'replicate', and makes +-- /O(log n)/ calls to '<*>' and 'pure'. +-- +-- > replicateA n x = sequenceA (replicate n x) +replicateA :: Applicative f => Int -> f a -> f (Seq a) +replicateA n x + | n >= 0 = Seq <$> applicativeTree n 1 (Elem <$> x) + | otherwise = error "replicateA takes a nonnegative integer argument" + +-- | 'replicateM' is a sequence counterpart of 'Control.Monad.replicateM'. +-- +-- > replicateM n x = sequence (replicate n x) +replicateM :: Monad m => Int -> m a -> m (Seq a) +replicateM n x + | n >= 0 = unwrapMonad (replicateA n (WrapMonad x)) + | otherwise = error "replicateM takes a nonnegative integer argument" + +-- | /O(log(k))/. @'cycleTaking' k xs@ forms a sequence of length @k@ by +-- repeatedly concatenating @xs@ with itself. @xs@ may only be empty if +-- @k@ is 0. +-- +-- prop> cycleTaking k = fromList . take k . cycle . toList + +-- If you wish to concatenate a non-empty sequence @xs@ with itself precisely +-- @k@ times, you can use @cycleTaking (k * length xs)@ or just +-- @replicate k () *> xs@. +-- +-- @since 0.5.8 +cycleTaking :: Int -> Seq a -> Seq a +cycleTaking n !_xs | n <= 0 = empty +cycleTaking _n xs | null xs = error "cycleTaking cannot take a positive number of elements from an empty cycle." +cycleTaking n xs = cycleNTimes reps xs >< take final xs + where + (reps, final) = n `quotRem` length xs + +-- | /O(log(kn))/. @'cycleNTimes' k xs@ concatenates @k@ copies of @xs@. This +-- operation uses time and additional space logarithmic in the size of its +-- result. +cycleNTimes :: Int -> Seq a -> Seq a +cycleNTimes n !xs + | n <= 0 = empty + | n == 1 = xs +cycleNTimes n (Seq xsFT) = case rigidify xsFT of + RigidEmpty -> empty + RigidOne (Elem x) -> replicate n x + RigidTwo x1 x2 -> Seq $ + Deep (n*2) pair + (runIdentity $ applicativeTree (n-2) 2 (Identity (node2 x1 x2))) + pair + where pair = Two x1 x2 + RigidThree x1 x2 x3 -> Seq $ + Deep (n*3) triple + (runIdentity $ applicativeTree (n-2) 3 (Identity (node3 x1 x2 x3))) + triple + where triple = Three x1 x2 x3 + RigidFull r@(Rigid s pr _m sf) -> Seq $ + Deep (n*s) + (nodeToDigit pr) + (cycleNMiddle (n-2) r) + (nodeToDigit sf) + +cycleNMiddle + :: Int + -> Rigid c + -> FingerTree (Node c) + +-- Not at the bottom yet + +cycleNMiddle !n + (Rigid s pr (DeepTh sm prm mm sfm) sf) + = Deep (sm + s * (n + 1)) -- note: sm = s - size pr - size sf + (digit12ToDigit prm) + (cycleNMiddle n + (Rigid s (squashL pr prm) mm (squashR sfm sf))) + (digit12ToDigit sfm) + +-- At the bottom + +cycleNMiddle n + (Rigid s pr EmptyTh sf) + = deep + (One sf) + (runIdentity $ applicativeTree n s (Identity converted)) + (One pr) + where converted = node2 pr sf + +cycleNMiddle n + (Rigid s pr (SingleTh q) sf) + = deep + (Two q sf) + (runIdentity $ applicativeTree n s (Identity converted)) + (Two pr q) + where converted = node3 pr q sf + + +-- | /O(1)/. Add an element to the left end of a sequence. +-- Mnemonic: a triangle with the single element at the pointy end. +(<|) :: a -> Seq a -> Seq a +x <| Seq xs = Seq (Elem x `consTree` xs) + +{-# SPECIALIZE consTree :: Elem a -> FingerTree (Elem a) -> FingerTree (Elem a) #-} +{-# SPECIALIZE consTree :: Node a -> FingerTree (Node a) -> FingerTree (Node a) #-} +consTree :: Sized a => a -> FingerTree a -> FingerTree a +consTree a EmptyT = Single a +consTree a (Single b) = deep (One a) EmptyT (One b) +-- As described in the paper, we force the middle of a tree +-- *before* consing onto it; this preserves the amortized +-- bounds but prevents repeated consing from building up +-- gigantic suspensions. +consTree a (Deep s (Four b c d e) m sf) = m `seq` + Deep (size a + s) (Two a b) (node3 c d e `consTree` m) sf +consTree a (Deep s (Three b c d) m sf) = + Deep (size a + s) (Four a b c d) m sf +consTree a (Deep s (Two b c) m sf) = + Deep (size a + s) (Three a b c) m sf +consTree a (Deep s (One b) m sf) = + Deep (size a + s) (Two a b) m sf + +cons' :: a -> Seq a -> Seq a +cons' x (Seq xs) = Seq (Elem x `consTree'` xs) + +snoc' :: Seq a -> a -> Seq a +snoc' (Seq xs) x = Seq (xs `snocTree'` Elem x) + +{-# SPECIALIZE consTree' :: Elem a -> FingerTree (Elem a) -> FingerTree (Elem a) #-} +{-# SPECIALIZE consTree' :: Node a -> FingerTree (Node a) -> FingerTree (Node a) #-} +consTree' :: Sized a => a -> FingerTree a -> FingerTree a +consTree' a EmptyT = Single a +consTree' a (Single b) = deep (One a) EmptyT (One b) +-- As described in the paper, we force the middle of a tree +-- *before* consing onto it; this preserves the amortized +-- bounds but prevents repeated consing from building up +-- gigantic suspensions. +consTree' a (Deep s (Four b c d e) m sf) = + Deep (size a + s) (Two a b) m' sf + where !m' = abc `consTree'` m + !abc = node3 c d e +consTree' a (Deep s (Three b c d) m sf) = + Deep (size a + s) (Four a b c d) m sf +consTree' a (Deep s (Two b c) m sf) = + Deep (size a + s) (Three a b c) m sf +consTree' a (Deep s (One b) m sf) = + Deep (size a + s) (Two a b) m sf + +-- | /O(1)/. Add an element to the right end of a sequence. +-- Mnemonic: a triangle with the single element at the pointy end. +(|>) :: Seq a -> a -> Seq a +Seq xs |> x = Seq (xs `snocTree` Elem x) + +{-# SPECIALIZE snocTree :: FingerTree (Elem a) -> Elem a -> FingerTree (Elem a) #-} +{-# SPECIALIZE snocTree :: FingerTree (Node a) -> Node a -> FingerTree (Node a) #-} +snocTree :: Sized a => FingerTree a -> a -> FingerTree a +snocTree EmptyT a = Single a +snocTree (Single a) b = deep (One a) EmptyT (One b) +-- See note on `seq` in `consTree`. +snocTree (Deep s pr m (Four a b c d)) e = m `seq` + Deep (s + size e) pr (m `snocTree` node3 a b c) (Two d e) +snocTree (Deep s pr m (Three a b c)) d = + Deep (s + size d) pr m (Four a b c d) +snocTree (Deep s pr m (Two a b)) c = + Deep (s + size c) pr m (Three a b c) +snocTree (Deep s pr m (One a)) b = + Deep (s + size b) pr m (Two a b) + +{-# SPECIALIZE snocTree' :: FingerTree (Elem a) -> Elem a -> FingerTree (Elem a) #-} +{-# SPECIALIZE snocTree' :: FingerTree (Node a) -> Node a -> FingerTree (Node a) #-} +snocTree' :: Sized a => FingerTree a -> a -> FingerTree a +snocTree' EmptyT a = Single a +snocTree' (Single a) b = deep (One a) EmptyT (One b) +-- See note on `seq` in `consTree`. +snocTree' (Deep s pr m (Four a b c d)) e = + Deep (s + size e) pr m' (Two d e) + where !m' = m `snocTree'` abc + !abc = node3 a b c +snocTree' (Deep s pr m (Three a b c)) d = + Deep (s + size d) pr m (Four a b c d) +snocTree' (Deep s pr m (Two a b)) c = + Deep (s + size c) pr m (Three a b c) +snocTree' (Deep s pr m (One a)) b = + Deep (s + size b) pr m (Two a b) + +-- | /O(log(min(n1,n2)))/. Concatenate two sequences. +(><) :: Seq a -> Seq a -> Seq a +Seq xs >< Seq ys = Seq (appendTree0 xs ys) + +-- The appendTree/addDigits gunk below is machine generated + +appendTree0 :: FingerTree (Elem a) -> FingerTree (Elem a) -> FingerTree (Elem a) +appendTree0 EmptyT xs = + xs +appendTree0 xs EmptyT = + xs +appendTree0 (Single x) xs = + x `consTree` xs +appendTree0 xs (Single x) = + xs `snocTree` x +appendTree0 (Deep s1 pr1 m1 sf1) (Deep s2 pr2 m2 sf2) = + Deep (s1 + s2) pr1 m sf2 + where !m = addDigits0 m1 sf1 pr2 m2 + +addDigits0 :: FingerTree (Node (Elem a)) -> Digit (Elem a) -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> FingerTree (Node (Elem a)) +addDigits0 m1 (One a) (One b) m2 = + appendTree1 m1 (node2 a b) m2 +addDigits0 m1 (One a) (Two b c) m2 = + appendTree1 m1 (node3 a b c) m2 +addDigits0 m1 (One a) (Three b c d) m2 = + appendTree2 m1 (node2 a b) (node2 c d) m2 +addDigits0 m1 (One a) (Four b c d e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits0 m1 (Two a b) (One c) m2 = + appendTree1 m1 (node3 a b c) m2 +addDigits0 m1 (Two a b) (Two c d) m2 = + appendTree2 m1 (node2 a b) (node2 c d) m2 +addDigits0 m1 (Two a b) (Three c d e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits0 m1 (Two a b) (Four c d e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits0 m1 (Three a b c) (One d) m2 = + appendTree2 m1 (node2 a b) (node2 c d) m2 +addDigits0 m1 (Three a b c) (Two d e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits0 m1 (Three a b c) (Three d e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits0 m1 (Three a b c) (Four d e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits0 m1 (Four a b c d) (One e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits0 m1 (Four a b c d) (Two e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits0 m1 (Four a b c d) (Three e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits0 m1 (Four a b c d) (Four e f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 + +appendTree1 :: FingerTree (Node a) -> Node a -> FingerTree (Node a) -> FingerTree (Node a) +appendTree1 EmptyT !a xs = + a `consTree` xs +appendTree1 xs !a EmptyT = + xs `snocTree` a +appendTree1 (Single x) !a xs = + x `consTree` a `consTree` xs +appendTree1 xs !a (Single x) = + xs `snocTree` a `snocTree` x +appendTree1 (Deep s1 pr1 m1 sf1) a (Deep s2 pr2 m2 sf2) = + Deep (s1 + size a + s2) pr1 m sf2 + where !m = addDigits1 m1 sf1 a pr2 m2 + +addDigits1 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) +addDigits1 m1 (One a) b (One c) m2 = + appendTree1 m1 (node3 a b c) m2 +addDigits1 m1 (One a) b (Two c d) m2 = + appendTree2 m1 (node2 a b) (node2 c d) m2 +addDigits1 m1 (One a) b (Three c d e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits1 m1 (One a) b (Four c d e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits1 m1 (Two a b) c (One d) m2 = + appendTree2 m1 (node2 a b) (node2 c d) m2 +addDigits1 m1 (Two a b) c (Two d e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits1 m1 (Two a b) c (Three d e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits1 m1 (Two a b) c (Four d e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits1 m1 (Three a b c) d (One e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits1 m1 (Three a b c) d (Two e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits1 m1 (Three a b c) d (Three e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits1 m1 (Three a b c) d (Four e f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits1 m1 (Four a b c d) e (One f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits1 m1 (Four a b c d) e (Two f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits1 m1 (Four a b c d) e (Three f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits1 m1 (Four a b c d) e (Four f g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 + +appendTree2 :: FingerTree (Node a) -> Node a -> Node a -> FingerTree (Node a) -> FingerTree (Node a) +appendTree2 EmptyT !a !b xs = + a `consTree` b `consTree` xs +appendTree2 xs !a !b EmptyT = + xs `snocTree` a `snocTree` b +appendTree2 (Single x) a b xs = + x `consTree` a `consTree` b `consTree` xs +appendTree2 xs a b (Single x) = + xs `snocTree` a `snocTree` b `snocTree` x +appendTree2 (Deep s1 pr1 m1 sf1) a b (Deep s2 pr2 m2 sf2) = + Deep (s1 + size a + size b + s2) pr1 m sf2 + where !m = addDigits2 m1 sf1 a b pr2 m2 + +addDigits2 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) +addDigits2 m1 (One a) b c (One d) m2 = + appendTree2 m1 (node2 a b) (node2 c d) m2 +addDigits2 m1 (One a) b c (Two d e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits2 m1 (One a) b c (Three d e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits2 m1 (One a) b c (Four d e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits2 m1 (Two a b) c d (One e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits2 m1 (Two a b) c d (Two e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits2 m1 (Two a b) c d (Three e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits2 m1 (Two a b) c d (Four e f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits2 m1 (Three a b c) d e (One f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits2 m1 (Three a b c) d e (Two f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits2 m1 (Three a b c) d e (Three f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits2 m1 (Three a b c) d e (Four f g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits2 m1 (Four a b c d) e f (One g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits2 m1 (Four a b c d) e f (Two g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits2 m1 (Four a b c d) e f (Three g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits2 m1 (Four a b c d) e f (Four g h i j) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 + +appendTree3 :: FingerTree (Node a) -> Node a -> Node a -> Node a -> FingerTree (Node a) -> FingerTree (Node a) +appendTree3 EmptyT !a !b !c xs = + a `consTree` b `consTree` c `consTree` xs +appendTree3 xs !a !b !c EmptyT = + xs `snocTree` a `snocTree` b `snocTree` c +appendTree3 (Single x) a b c xs = + x `consTree` a `consTree` b `consTree` c `consTree` xs +appendTree3 xs a b c (Single x) = + xs `snocTree` a `snocTree` b `snocTree` c `snocTree` x +appendTree3 (Deep s1 pr1 m1 sf1) a b c (Deep s2 pr2 m2 sf2) = + Deep (s1 + size a + size b + size c + s2) pr1 m sf2 + where !m = addDigits3 m1 sf1 a b c pr2 m2 + +addDigits3 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Node a -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) +addDigits3 m1 (One a) !b !c !d (One e) m2 = + appendTree2 m1 (node3 a b c) (node2 d e) m2 +addDigits3 m1 (One a) b c d (Two e f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits3 m1 (One a) b c d (Three e f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits3 m1 (One a) b c d (Four e f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits3 m1 (Two a b) !c !d !e (One f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits3 m1 (Two a b) c d e (Two f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits3 m1 (Two a b) c d e (Three f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits3 m1 (Two a b) c d e (Four f g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits3 m1 (Three a b c) !d !e !f (One g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits3 m1 (Three a b c) d e f (Two g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits3 m1 (Three a b c) d e f (Three g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits3 m1 (Three a b c) d e f (Four g h i j) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 +addDigits3 m1 (Four a b c d) !e !f !g (One h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits3 m1 (Four a b c d) e f g (Two h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits3 m1 (Four a b c d) e f g (Three h i j) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 +addDigits3 m1 (Four a b c d) e f g (Four h i j k) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node2 j k) m2 + +appendTree4 :: FingerTree (Node a) -> Node a -> Node a -> Node a -> Node a -> FingerTree (Node a) -> FingerTree (Node a) +appendTree4 EmptyT !a !b !c !d xs = + a `consTree` b `consTree` c `consTree` d `consTree` xs +appendTree4 xs !a !b !c !d EmptyT = + xs `snocTree` a `snocTree` b `snocTree` c `snocTree` d +appendTree4 (Single x) a b c d xs = + x `consTree` a `consTree` b `consTree` c `consTree` d `consTree` xs +appendTree4 xs a b c d (Single x) = + xs `snocTree` a `snocTree` b `snocTree` c `snocTree` d `snocTree` x +appendTree4 (Deep s1 pr1 m1 sf1) a b c d (Deep s2 pr2 m2 sf2) = + Deep (s1 + size a + size b + size c + size d + s2) pr1 m sf2 + where !m = addDigits4 m1 sf1 a b c d pr2 m2 + +addDigits4 :: FingerTree (Node (Node a)) -> Digit (Node a) -> Node a -> Node a -> Node a -> Node a -> Digit (Node a) -> FingerTree (Node (Node a)) -> FingerTree (Node (Node a)) +addDigits4 m1 (One a) !b !c !d !e (One f) m2 = + appendTree2 m1 (node3 a b c) (node3 d e f) m2 +addDigits4 m1 (One a) b c d e (Two f g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits4 m1 (One a) b c d e (Three f g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits4 m1 (One a) b c d e (Four f g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits4 m1 (Two a b) !c !d !e !f (One g) m2 = + appendTree3 m1 (node3 a b c) (node2 d e) (node2 f g) m2 +addDigits4 m1 (Two a b) c d e f (Two g h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits4 m1 (Two a b) c d e f (Three g h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits4 m1 (Two a b) c d e f (Four g h i j) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 +addDigits4 m1 (Three a b c) !d !e !f !g (One h) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node2 g h) m2 +addDigits4 m1 (Three a b c) d e f g (Two h i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits4 m1 (Three a b c) d e f g (Three h i j) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 +addDigits4 m1 (Three a b c) d e f g (Four h i j k) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node2 j k) m2 +addDigits4 m1 (Four a b c d) !e !f !g !h (One i) m2 = + appendTree3 m1 (node3 a b c) (node3 d e f) (node3 g h i) m2 +addDigits4 m1 (Four a b c d) !e !f !g !h (Two i j) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node2 g h) (node2 i j) m2 +addDigits4 m1 (Four a b c d) !e !f !g !h (Three i j k) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node2 j k) m2 +addDigits4 m1 (Four a b c d) !e !f !g !h (Four i j k l) m2 = + appendTree4 m1 (node3 a b c) (node3 d e f) (node3 g h i) (node3 j k l) m2 + +-- | Builds a sequence from a seed value. Takes time linear in the +-- number of generated elements. /WARNING:/ If the number of generated +-- elements is infinite, this method will not terminate. +unfoldr :: (b -> Maybe (a, b)) -> b -> Seq a +unfoldr f = unfoldr' empty + -- uses tail recursion rather than, for instance, the List implementation. + where unfoldr' !as b = maybe as (\ (a, b') -> unfoldr' (as `snoc'` a) b') (f b) + +-- | @'unfoldl' f x@ is equivalent to @'reverse' ('unfoldr' ('fmap' swap . f) x)@. +unfoldl :: (b -> Maybe (b, a)) -> b -> Seq a +unfoldl f = unfoldl' empty + where unfoldl' !as b = maybe as (\ (b', a) -> unfoldl' (a `cons'` as) b') (f b) + +-- | /O(n)/. Constructs a sequence by repeated application of a function +-- to a seed value. +-- +-- > iterateN n f x = fromList (Prelude.take n (Prelude.iterate f x)) +iterateN :: Int -> (a -> a) -> a -> Seq a +iterateN n f x + | n >= 0 = replicateA n (State (\ y -> (f y, y))) `execState` x + | otherwise = error "iterateN takes a nonnegative integer argument" + +------------------------------------------------------------------------ +-- Deconstruction +------------------------------------------------------------------------ + +-- | /O(1)/. Is this the empty sequence? +null :: Seq a -> Bool +null (Seq EmptyT) = True +null _ = False + +-- | /O(1)/. The number of elements in the sequence. +length :: Seq a -> Int +length (Seq xs) = size xs + +-- Views + +data ViewLTree a = ConsLTree a (FingerTree a) | EmptyLTree +data ViewRTree a = SnocRTree (FingerTree a) a | EmptyRTree + +-- | View of the left end of a sequence. +data ViewL a + = EmptyL -- ^ empty sequence + | a :< Seq a -- ^ leftmost element and the rest of the sequence + deriving (Eq, Ord, Show, Read) + +#if __GLASGOW_HASKELL__ +deriving instance Data a => Data (ViewL a) +#endif +#if __GLASGOW_HASKELL__ >= 706 +deriving instance Generic1 ViewL +#endif +#if __GLASGOW_HASKELL__ >= 702 +deriving instance Generic (ViewL a) +#endif + +INSTANCE_TYPEABLE1(ViewL) + +instance Functor ViewL where + {-# INLINE fmap #-} + fmap _ EmptyL = EmptyL + fmap f (x :< xs) = f x :< fmap f xs + +instance Foldable ViewL where + foldr _ z EmptyL = z + foldr f z (x :< xs) = f x (foldr f z xs) + + foldl _ z EmptyL = z + foldl f z (x :< xs) = foldl f (f z x) xs + + foldl1 _ EmptyL = error "foldl1: empty view" + foldl1 f (x :< xs) = foldl f x xs + +#if MIN_VERSION_base(4,8,0) + null EmptyL = True + null (_ :< _) = False + + length EmptyL = 0 + length (_ :< xs) = 1 + length xs +#endif + +instance Traversable ViewL where + traverse _ EmptyL = pure EmptyL + traverse f (x :< xs) = (:<) <$> f x <*> traverse f xs + +-- | /O(1)/. Analyse the left end of a sequence. +viewl :: Seq a -> ViewL a +viewl (Seq xs) = case viewLTree xs of + EmptyLTree -> EmptyL + ConsLTree (Elem x) xs' -> x :< Seq xs' + +{-# SPECIALIZE viewLTree :: FingerTree (Elem a) -> ViewLTree (Elem a) #-} +{-# SPECIALIZE viewLTree :: FingerTree (Node a) -> ViewLTree (Node a) #-} +viewLTree :: Sized a => FingerTree a -> ViewLTree a +viewLTree EmptyT = EmptyLTree +viewLTree (Single a) = ConsLTree a EmptyT +viewLTree (Deep s (One a) m sf) = ConsLTree a (pullL (s - size a) m sf) +viewLTree (Deep s (Two a b) m sf) = + ConsLTree a (Deep (s - size a) (One b) m sf) +viewLTree (Deep s (Three a b c) m sf) = + ConsLTree a (Deep (s - size a) (Two b c) m sf) +viewLTree (Deep s (Four a b c d) m sf) = + ConsLTree a (Deep (s - size a) (Three b c d) m sf) + +-- | View of the right end of a sequence. +data ViewR a + = EmptyR -- ^ empty sequence + | Seq a :> a -- ^ the sequence minus the rightmost element, + -- and the rightmost element + deriving (Eq, Ord, Show, Read) + +#if __GLASGOW_HASKELL__ +deriving instance Data a => Data (ViewR a) +#endif +#if __GLASGOW_HASKELL__ >= 706 +deriving instance Generic1 ViewR +#endif +#if __GLASGOW_HASKELL__ >= 702 +deriving instance Generic (ViewR a) +#endif + +INSTANCE_TYPEABLE1(ViewR) + +instance Functor ViewR where + {-# INLINE fmap #-} + fmap _ EmptyR = EmptyR + fmap f (xs :> x) = fmap f xs :> f x + +instance Foldable ViewR where + foldMap _ EmptyR = mempty + foldMap f (xs :> x) = foldMap f xs <> f x + + foldr _ z EmptyR = z + foldr f z (xs :> x) = foldr f (f x z) xs + + foldl _ z EmptyR = z + foldl f z (xs :> x) = foldl f z xs `f` x + + foldr1 _ EmptyR = error "foldr1: empty view" + foldr1 f (xs :> x) = foldr f x xs +#if MIN_VERSION_base(4,8,0) + null EmptyR = True + null (_ :> _) = False + + length EmptyR = 0 + length (xs :> _) = length xs + 1 +#endif + +instance Traversable ViewR where + traverse _ EmptyR = pure EmptyR + traverse f (xs :> x) = (:>) <$> traverse f xs <*> f x + +-- | /O(1)/. Analyse the right end of a sequence. +viewr :: Seq a -> ViewR a +viewr (Seq xs) = case viewRTree xs of + EmptyRTree -> EmptyR + SnocRTree xs' (Elem x) -> Seq xs' :> x + +{-# SPECIALIZE viewRTree :: FingerTree (Elem a) -> ViewRTree (Elem a) #-} +{-# SPECIALIZE viewRTree :: FingerTree (Node a) -> ViewRTree (Node a) #-} +viewRTree :: Sized a => FingerTree a -> ViewRTree a +viewRTree EmptyT = EmptyRTree +viewRTree (Single z) = SnocRTree EmptyT z +viewRTree (Deep s pr m (One z)) = SnocRTree (pullR (s - size z) pr m) z +viewRTree (Deep s pr m (Two y z)) = + SnocRTree (Deep (s - size z) pr m (One y)) z +viewRTree (Deep s pr m (Three x y z)) = + SnocRTree (Deep (s - size z) pr m (Two x y)) z +viewRTree (Deep s pr m (Four w x y z)) = + SnocRTree (Deep (s - size z) pr m (Three w x y)) z + +------------------------------------------------------------------------ +-- Scans +-- +-- These are not particularly complex applications of the Traversable +-- functor, though making the correspondence with Data.List exact +-- requires the use of (<|) and (|>). +-- +-- Note that save for the single (<|) or (|>), we maintain the original +-- structure of the Seq, not having to do any restructuring of our own. +-- +-- wasserman.louis@gmail.com, 5/23/09 +------------------------------------------------------------------------ + +-- | 'scanl' is similar to 'foldl', but returns a sequence of reduced +-- values from the left: +-- +-- > scanl f z (fromList [x1, x2, ...]) = fromList [z, z `f` x1, (z `f` x1) `f` x2, ...] +scanl :: (a -> b -> a) -> a -> Seq b -> Seq a +scanl f z0 xs = z0 <| snd (mapAccumL (\ x z -> let x' = f x z in (x', x')) z0 xs) + +-- | 'scanl1' is a variant of 'scanl' that has no starting value argument: +-- +-- > scanl1 f (fromList [x1, x2, ...]) = fromList [x1, x1 `f` x2, ...] +scanl1 :: (a -> a -> a) -> Seq a -> Seq a +scanl1 f xs = case viewl xs of + EmptyL -> error "scanl1 takes a nonempty sequence as an argument" + x :< xs' -> scanl f x xs' + +-- | 'scanr' is the right-to-left dual of 'scanl'. +scanr :: (a -> b -> b) -> b -> Seq a -> Seq b +scanr f z0 xs = snd (mapAccumR (\ z x -> let z' = f x z in (z', z')) z0 xs) |> z0 + +-- | 'scanr1' is a variant of 'scanr' that has no starting value argument. +scanr1 :: (a -> a -> a) -> Seq a -> Seq a +scanr1 f xs = case viewr xs of + EmptyR -> error "scanr1 takes a nonempty sequence as an argument" + xs' :> x -> scanr f x xs' + +-- Indexing + +-- | /O(log(min(i,n-i)))/. The element at the specified position, +-- counting from 0. The argument should thus be a non-negative +-- integer less than the size of the sequence. +-- If the position is out of range, 'index' fails with an error. +-- +-- prop> xs `index` i = toList xs !! i +-- +-- Caution: 'index' necessarily delays retrieving the requested +-- element until the result is forced. It can therefore lead to a space +-- leak if the result is stored, unforced, in another structure. To retrieve +-- an element immediately without forcing it, use 'lookup' or '(!?)'. +index :: Seq a -> Int -> a +index (Seq xs) i + -- See note on unsigned arithmetic in splitAt + | fromIntegral i < (fromIntegral (size xs) :: Word) = case lookupTree i xs of + Place _ (Elem x) -> x + | otherwise = error "index out of bounds" + +-- | /O(log(min(i,n-i)))/. The element at the specified position, +-- counting from 0. If the specified position is negative or at +-- least the length of the sequence, 'lookup' returns 'Nothing'. +-- +-- prop> 0 <= i < length xs ==> lookup i xs == Just (toList xs !! i) +-- prop> i < 0 || i >= length xs ==> lookup i xs = Nothing +-- +-- Unlike 'index', this can be used to retrieve an element without +-- forcing it. For example, to insert the fifth element of a sequence +-- @xs@ into a 'Data.Map.Lazy.Map' @m@ at key @k@, you could use +-- +-- @ +-- case lookup 5 xs of +-- Nothing -> m +-- Just x -> 'Data.Map.Lazy.insert' k x m +-- @ +-- +-- @since 0.5.8 +lookup :: Int -> Seq a -> Maybe a +lookup i (Seq xs) + -- Note: we perform the lookup *before* applying the Just constructor + -- to ensure that we don't hold a reference to the whole sequence in + -- a thunk. If we applied the Just constructor around the case, the + -- actual lookup wouldn't be performed unless and until the value was + -- forced. + | fromIntegral i < (fromIntegral (size xs) :: Word) = case lookupTree i xs of + Place _ (Elem x) -> Just x + | otherwise = Nothing + +-- | /O(log(min(i,n-i)))/. A flipped, infix version of `lookup`. +-- +-- @since 0.5.8 +(!?) :: Seq a -> Int -> Maybe a +(!?) = flip lookup + +data Place a = Place {-# UNPACK #-} !Int a +#ifdef TESTING + deriving Show +#endif + +{-# SPECIALIZE lookupTree :: Int -> FingerTree (Elem a) -> Place (Elem a) #-} +{-# SPECIALIZE lookupTree :: Int -> FingerTree (Node a) -> Place (Node a) #-} +lookupTree :: Sized a => Int -> FingerTree a -> Place a +lookupTree !_ EmptyT = error "lookupTree of empty tree" +lookupTree i (Single x) = Place i x +lookupTree i (Deep _ pr m sf) + | i < spr = lookupDigit i pr + | i < spm = case lookupTree (i - spr) m of + Place i' xs -> lookupNode i' xs + | otherwise = lookupDigit (i - spm) sf + where + spr = size pr + spm = spr + size m + +{-# SPECIALIZE lookupNode :: Int -> Node (Elem a) -> Place (Elem a) #-} +{-# SPECIALIZE lookupNode :: Int -> Node (Node a) -> Place (Node a) #-} +lookupNode :: Sized a => Int -> Node a -> Place a +lookupNode i (Node2 _ a b) + | i < sa = Place i a + | otherwise = Place (i - sa) b + where + sa = size a +lookupNode i (Node3 _ a b c) + | i < sa = Place i a + | i < sab = Place (i - sa) b + | otherwise = Place (i - sab) c + where + sa = size a + sab = sa + size b + +{-# SPECIALIZE lookupDigit :: Int -> Digit (Elem a) -> Place (Elem a) #-} +{-# SPECIALIZE lookupDigit :: Int -> Digit (Node a) -> Place (Node a) #-} +lookupDigit :: Sized a => Int -> Digit a -> Place a +lookupDigit i (One a) = Place i a +lookupDigit i (Two a b) + | i < sa = Place i a + | otherwise = Place (i - sa) b + where + sa = size a +lookupDigit i (Three a b c) + | i < sa = Place i a + | i < sab = Place (i - sa) b + | otherwise = Place (i - sab) c + where + sa = size a + sab = sa + size b +lookupDigit i (Four a b c d) + | i < sa = Place i a + | i < sab = Place (i - sa) b + | i < sabc = Place (i - sab) c + | otherwise = Place (i - sabc) d + where + sa = size a + sab = sa + size b + sabc = sab + size c + +-- | /O(log(min(i,n-i)))/. Replace the element at the specified position. +-- If the position is out of range, the original sequence is returned. +update :: Int -> a -> Seq a -> Seq a +update i x (Seq xs) + -- See note on unsigned arithmetic in splitAt + | fromIntegral i < (fromIntegral (size xs) :: Word) = Seq (updateTree (Elem x) i xs) + | otherwise = Seq xs + +-- It seems a shame to copy the implementation of the top layer of +-- `adjust` instead of just using `update i x = adjust (const x) i`. +-- With the latter implementation, updating the same position many +-- times could lead to silly thunks building up around that position. +-- The thunks will each look like @const v a@, where @v@ is the new +-- value and @a@ the old. +updateTree :: Elem a -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) +updateTree _ !_ EmptyT = EmptyT -- Unreachable +updateTree v _i (Single _) = Single v +updateTree v i (Deep s pr m sf) + | i < spr = Deep s (updateDigit v i pr) m sf + | i < spm = let !m' = adjustTree (updateNode v) (i - spr) m + in Deep s pr m' sf + | otherwise = Deep s pr m (updateDigit v (i - spm) sf) + where + spr = size pr + spm = spr + size m + +updateNode :: Elem a -> Int -> Node (Elem a) -> Node (Elem a) +updateNode v i (Node2 s a b) + | i < sa = Node2 s v b + | otherwise = Node2 s a v + where + sa = size a +updateNode v i (Node3 s a b c) + | i < sa = Node3 s v b c + | i < sab = Node3 s a v c + | otherwise = Node3 s a b v + where + sa = size a + sab = sa + size b + +updateDigit :: Elem a -> Int -> Digit (Elem a) -> Digit (Elem a) +updateDigit v !_i (One _) = One v +updateDigit v i (Two a b) + | i < sa = Two v b + | otherwise = Two a v + where + sa = size a +updateDigit v i (Three a b c) + | i < sa = Three v b c + | i < sab = Three a v c + | otherwise = Three a b v + where + sa = size a + sab = sa + size b +updateDigit v i (Four a b c d) + | i < sa = Four v b c d + | i < sab = Four a v c d + | i < sabc = Four a b v d + | otherwise = Four a b c v + where + sa = size a + sab = sa + size b + sabc = sab + size c + +-- | /O(log(min(i,n-i)))/. Update the element at the specified position. If +-- the position is out of range, the original sequence is returned. 'adjust' +-- can lead to poor performance and even memory leaks, because it does not +-- force the new value before installing it in the sequence. 'adjust'' should +-- usually be preferred. +adjust :: (a -> a) -> Int -> Seq a -> Seq a +adjust f i (Seq xs) + -- See note on unsigned arithmetic in splitAt + | fromIntegral i < (fromIntegral (size xs) :: Word) = Seq (adjustTree (`seq` fmap f) i xs) + | otherwise = Seq xs + +-- | /O(log(min(i,n-i)))/. Update the element at the specified position. +-- If the position is out of range, the original sequence is returned. +-- The new value is forced before it is installed in the sequence. +-- +-- @ +-- adjust' f i xs = +-- case xs !? i of +-- Nothing -> xs +-- Just x -> let !x' = f x +-- in update i x' xs +-- @ +-- +-- @since 0.5.8 +adjust' :: forall a . (a -> a) -> Int -> Seq a -> Seq a +#if __GLASGOW_HASKELL__ >= 708 +adjust' f i xs + -- See note on unsigned arithmetic in splitAt + | fromIntegral i < (fromIntegral (length xs) :: Word) = + coerce $ adjustTree (\ !_k (ForceBox a) -> ForceBox (f a)) i (coerce xs) + | otherwise = xs +#else +-- This is inefficient, but fixing it would take a lot of fuss and bother +-- for little immediate gain. We can deal with that when we have another +-- Haskell implementation to worry about. +adjust' f i xs = + case xs !? i of + Nothing -> xs + Just x -> let !x' = f x + in update i x' xs +#endif + +{-# SPECIALIZE adjustTree :: (Int -> ForceBox a -> ForceBox a) -> Int -> FingerTree (ForceBox a) -> FingerTree (ForceBox a) #-} +{-# SPECIALIZE adjustTree :: (Int -> Elem a -> Elem a) -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) #-} +{-# SPECIALIZE adjustTree :: (Int -> Node a -> Node a) -> Int -> FingerTree (Node a) -> FingerTree (Node a) #-} +adjustTree :: (Sized a, MaybeForce a) => (Int -> a -> a) -> + Int -> FingerTree a -> FingerTree a +adjustTree _ !_ EmptyT = EmptyT -- Unreachable +adjustTree f i (Single x) = Single $!? f i x +adjustTree f i (Deep s pr m sf) + | i < spr = Deep s (adjustDigit f i pr) m sf + | i < spm = let !m' = adjustTree (adjustNode f) (i - spr) m + in Deep s pr m' sf + | otherwise = Deep s pr m (adjustDigit f (i - spm) sf) + where + spr = size pr + spm = spr + size m + +{-# SPECIALIZE adjustNode :: (Int -> Elem a -> Elem a) -> Int -> Node (Elem a) -> Node (Elem a) #-} +{-# SPECIALIZE adjustNode :: (Int -> Node a -> Node a) -> Int -> Node (Node a) -> Node (Node a) #-} +adjustNode :: (Sized a, MaybeForce a) => (Int -> a -> a) -> Int -> Node a -> Node a +adjustNode f i (Node2 s a b) + | i < sa = let fia = f i a in fia `mseq` Node2 s fia b + | otherwise = let fisab = f (i - sa) b in fisab `mseq` Node2 s a fisab + where + sa = size a +adjustNode f i (Node3 s a b c) + | i < sa = let fia = f i a in fia `mseq` Node3 s fia b c + | i < sab = let fisab = f (i - sa) b in fisab `mseq` Node3 s a fisab c + | otherwise = let fisabc = f (i - sab) c in fisabc `mseq` Node3 s a b fisabc + where + sa = size a + sab = sa + size b + +{-# SPECIALIZE adjustDigit :: (Int -> Elem a -> Elem a) -> Int -> Digit (Elem a) -> Digit (Elem a) #-} +{-# SPECIALIZE adjustDigit :: (Int -> Node a -> Node a) -> Int -> Digit (Node a) -> Digit (Node a) #-} +adjustDigit :: (Sized a, MaybeForce a) => (Int -> a -> a) -> Int -> Digit a -> Digit a +adjustDigit f !i (One a) = One $!? f i a +adjustDigit f i (Two a b) + | i < sa = let fia = f i a in fia `mseq` Two fia b + | otherwise = let fisab = f (i - sa) b in fisab `mseq` Two a fisab + where + sa = size a +adjustDigit f i (Three a b c) + | i < sa = let fia = f i a in fia `mseq` Three fia b c + | i < sab = let fisab = f (i - sa) b in fisab `mseq` Three a fisab c + | otherwise = let fisabc = f (i - sab) c in fisabc `mseq` Three a b fisabc + where + sa = size a + sab = sa + size b +adjustDigit f i (Four a b c d) + | i < sa = let fia = f i a in fia `mseq` Four fia b c d + | i < sab = let fisab = f (i - sa) b in fisab `mseq` Four a fisab c d + | i < sabc = let fisabc = f (i - sab) c in fisabc `mseq` Four a b fisabc d + | otherwise = let fisabcd = f (i - sabc) d in fisabcd `mseq` Four a b c fisabcd + where + sa = size a + sab = sa + size b + sabc = sab + size c + +-- | /O(log(min(i,n-i)))/. @'insertAt' i x xs@ inserts @x@ into @xs@ +-- at the index @i@, shifting the rest of the sequence over. +-- +-- @ +-- insertAt 2 x (fromList [a,b,c,d]) = fromList [a,b,x,c,d] +-- insertAt 4 x (fromList [a,b,c,d]) = insertAt 10 x (fromList [a,b,c,d]) +-- = fromList [a,b,c,d,x] +-- @ +-- +-- prop> insertAt i x xs = take i xs >< singleton x >< drop i xs +-- +-- @since 0.5.8 +insertAt :: Int -> a -> Seq a -> Seq a +insertAt i a s@(Seq xs) + | fromIntegral i < (fromIntegral (size xs) :: Word) + = Seq (insTree (`seq` InsTwo (Elem a)) i xs) + | i <= 0 = a <| s + | otherwise = s |> a + +data Ins a = InsOne a | InsTwo a a + +{-# SPECIALIZE insTree :: (Int -> Elem a -> Ins (Elem a)) -> Int -> FingerTree (Elem a) -> FingerTree (Elem a) #-} +{-# SPECIALIZE insTree :: (Int -> Node a -> Ins (Node a)) -> Int -> FingerTree (Node a) -> FingerTree (Node a) #-} +insTree :: Sized a => (Int -> a -> Ins a) -> + Int -> FingerTree a -> FingerTree a +insTree _ !_ EmptyT = EmptyT -- Unreachable +insTree f i (Single x) = case f i x of + InsOne x' -> Single x' + InsTwo m n -> deep (One m) EmptyT (One n) +insTree f i (Deep s pr m sf) + | i < spr = case insLeftDigit f i pr of + InsLeftDig pr' -> Deep (s + 1) pr' m sf + InsDigNode pr' n -> m `seq` Deep (s + 1) pr' (n `consTree` m) sf + | i < spm = let !m' = insTree (insNode f) (i - spr) m + in Deep (s + 1) pr m' sf + | otherwise = case insRightDigit f (i - spm) sf of + InsRightDig sf' -> Deep (s + 1) pr m sf' + InsNodeDig n sf' -> m `seq` Deep (s + 1) pr (m `snocTree` n) sf' + where + spr = size pr + spm = spr + size m + +{-# SPECIALIZE insNode :: (Int -> Elem a -> Ins (Elem a)) -> Int -> Node (Elem a) -> Ins (Node (Elem a)) #-} +{-# SPECIALIZE insNode :: (Int -> Node a -> Ins (Node a)) -> Int -> Node (Node a) -> Ins (Node (Node a)) #-} +insNode :: Sized a => (Int -> a -> Ins a) -> Int -> Node a -> Ins (Node a) +insNode f i (Node2 s a b) + | i < sa = case f i a of + InsOne n -> InsOne $ Node2 (s + 1) n b + InsTwo m n -> InsOne $ Node3 (s + 1) m n b + | otherwise = case f (i - sa) b of + InsOne n -> InsOne $ Node2 (s + 1) a n + InsTwo m n -> InsOne $ Node3 (s + 1) a m n + where sa = size a +insNode f i (Node3 s a b c) + | i < sa = case f i a of + InsOne n -> InsOne $ Node3 (s + 1) n b c + InsTwo m n -> InsTwo (Node2 (sa + 1) m n) (Node2 (s - sa) b c) + | i < sab = case f (i - sa) b of + InsOne n -> InsOne $ Node3 (s + 1) a n c + InsTwo m n -> InsTwo am nc + where !am = node2 a m + !nc = node2 n c + | otherwise = case f (i - sab) c of + InsOne n -> InsOne $ Node3 (s + 1) a b n + InsTwo m n -> InsTwo (Node2 sab a b) (Node2 (s - sab + 1) m n) + where sa = size a + sab = sa + size b + +data InsDigNode a = InsLeftDig !(Digit a) | InsDigNode !(Digit a) !(Node a) +{-# SPECIALIZE insLeftDigit :: (Int -> Elem a -> Ins (Elem a)) -> Int -> Digit (Elem a) -> InsDigNode (Elem a) #-} +{-# SPECIALIZE insLeftDigit :: (Int -> Node a -> Ins (Node a)) -> Int -> Digit (Node a) -> InsDigNode (Node a) #-} +insLeftDigit :: Sized a => (Int -> a -> Ins a) -> Int -> Digit a -> InsDigNode a +insLeftDigit f !i (One a) = case f i a of + InsOne a' -> InsLeftDig $ One a' + InsTwo a1 a2 -> InsLeftDig $ Two a1 a2 +insLeftDigit f i (Two a b) + | i < sa = case f i a of + InsOne a' -> InsLeftDig $ Two a' b + InsTwo a1 a2 -> InsLeftDig $ Three a1 a2 b + | otherwise = case f (i - sa) b of + InsOne b' -> InsLeftDig $ Two a b' + InsTwo b1 b2 -> InsLeftDig $ Three a b1 b2 + where sa = size a +insLeftDigit f i (Three a b c) + | i < sa = case f i a of + InsOne a' -> InsLeftDig $ Three a' b c + InsTwo a1 a2 -> InsLeftDig $ Four a1 a2 b c + | i < sab = case f (i - sa) b of + InsOne b' -> InsLeftDig $ Three a b' c + InsTwo b1 b2 -> InsLeftDig $ Four a b1 b2 c + | otherwise = case f (i - sab) c of + InsOne c' -> InsLeftDig $ Three a b c' + InsTwo c1 c2 -> InsLeftDig $ Four a b c1 c2 + where sa = size a + sab = sa + size b +insLeftDigit f i (Four a b c d) + | i < sa = case f i a of + InsOne a' -> InsLeftDig $ Four a' b c d + InsTwo a1 a2 -> InsDigNode (Two a1 a2) (node3 b c d) + | i < sab = case f (i - sa) b of + InsOne b' -> InsLeftDig $ Four a b' c d + InsTwo b1 b2 -> InsDigNode (Two a b1) (node3 b2 c d) + | i < sabc = case f (i - sab) c of + InsOne c' -> InsLeftDig $ Four a b c' d + InsTwo c1 c2 -> InsDigNode (Two a b) (node3 c1 c2 d) + | otherwise = case f (i - sabc) d of + InsOne d' -> InsLeftDig $ Four a b c d' + InsTwo d1 d2 -> InsDigNode (Two a b) (node3 c d1 d2) + where sa = size a + sab = sa + size b + sabc = sab + size c + +data InsNodeDig a = InsRightDig !(Digit a) | InsNodeDig !(Node a) !(Digit a) +{-# SPECIALIZE insRightDigit :: (Int -> Elem a -> Ins (Elem a)) -> Int -> Digit (Elem a) -> InsNodeDig (Elem a) #-} +{-# SPECIALIZE insRightDigit :: (Int -> Node a -> Ins (Node a)) -> Int -> Digit (Node a) -> InsNodeDig (Node a) #-} +insRightDigit :: Sized a => (Int -> a -> Ins a) -> Int -> Digit a -> InsNodeDig a +insRightDigit f !i (One a) = case f i a of + InsOne a' -> InsRightDig $ One a' + InsTwo a1 a2 -> InsRightDig $ Two a1 a2 +insRightDigit f i (Two a b) + | i < sa = case f i a of + InsOne a' -> InsRightDig $ Two a' b + InsTwo a1 a2 -> InsRightDig $ Three a1 a2 b + | otherwise = case f (i - sa) b of + InsOne b' -> InsRightDig $ Two a b' + InsTwo b1 b2 -> InsRightDig $ Three a b1 b2 + where sa = size a +insRightDigit f i (Three a b c) + | i < sa = case f i a of + InsOne a' -> InsRightDig $ Three a' b c + InsTwo a1 a2 -> InsRightDig $ Four a1 a2 b c + | i < sab = case f (i - sa) b of + InsOne b' -> InsRightDig $ Three a b' c + InsTwo b1 b2 -> InsRightDig $ Four a b1 b2 c + | otherwise = case f (i - sab) c of + InsOne c' -> InsRightDig $ Three a b c' + InsTwo c1 c2 -> InsRightDig $ Four a b c1 c2 + where sa = size a + sab = sa + size b +insRightDigit f i (Four a b c d) + | i < sa = case f i a of + InsOne a' -> InsRightDig $ Four a' b c d + InsTwo a1 a2 -> InsNodeDig (node3 a1 a2 b) (Two c d) + | i < sab = case f (i - sa) b of + InsOne b' -> InsRightDig $ Four a b' c d + InsTwo b1 b2 -> InsNodeDig (node3 a b1 b2) (Two c d) + | i < sabc = case f (i - sab) c of + InsOne c' -> InsRightDig $ Four a b c' d + InsTwo c1 c2 -> InsNodeDig (node3 a b c1) (Two c2 d) + | otherwise = case f (i - sabc) d of + InsOne d' -> InsRightDig $ Four a b c d' + InsTwo d1 d2 -> InsNodeDig (node3 a b c) (Two d1 d2) + where sa = size a + sab = sa + size b + sabc = sab + size c + +-- | /O(log(min(i,n-i)))/. Delete the element of a sequence at a given +-- index. Return the original sequence if the index is out of range. +-- +-- @ +-- deleteAt 2 [a,b,c,d] = [a,b,d] +-- deleteAt 4 [a,b,c,d] = deleteAt (-1) [a,b,c,d] = [a,b,c,d] +-- @ +-- +-- @since 0.5.8 +deleteAt :: Int -> Seq a -> Seq a +deleteAt i (Seq xs) + | fromIntegral i < (fromIntegral (size xs) :: Word) = Seq $ delTreeE i xs + | otherwise = Seq xs + +delTreeE :: Int -> FingerTree (Elem a) -> FingerTree (Elem a) +delTreeE !_i EmptyT = EmptyT -- Unreachable +delTreeE _i Single{} = EmptyT +delTreeE i (Deep s pr m sf) + | i < spr = delLeftDigitE i s pr m sf + | i < spm = case delTree delNodeE (i - spr) m of + FullTree m' -> Deep (s - 1) pr m' sf + DefectTree e -> delRebuildMiddle (s - 1) pr e sf + | otherwise = delRightDigitE (i - spm) s pr m sf + where spr = size pr + spm = spr + size m + +delNodeE :: Int -> Node (Elem a) -> Del (Elem a) +delNodeE i (Node3 _ a b c) = case i of + 0 -> Full $ Node2 2 b c + 1 -> Full $ Node2 2 a c + _ -> Full $ Node2 2 a b +delNodeE i (Node2 _ a b) = case i of + 0 -> Defect b + _ -> Defect a + + +delLeftDigitE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) +delLeftDigitE !_i s One{} m sf = pullL (s - 1) m sf +delLeftDigitE i s (Two a b) m sf + | i == 0 = Deep (s - 1) (One b) m sf + | otherwise = Deep (s - 1) (One a) m sf +delLeftDigitE i s (Three a b c) m sf + | i == 0 = Deep (s - 1) (Two b c) m sf + | i == 1 = Deep (s - 1) (Two a c) m sf + | otherwise = Deep (s - 1) (Two a b) m sf +delLeftDigitE i s (Four a b c d) m sf + | i == 0 = Deep (s - 1) (Three b c d) m sf + | i == 1 = Deep (s - 1) (Three a c d) m sf + | i == 2 = Deep (s - 1) (Three a b d) m sf + | otherwise = Deep (s - 1) (Three a b c) m sf + +delRightDigitE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> FingerTree (Elem a) +delRightDigitE !_i s pr m One{} = pullR (s - 1) pr m +delRightDigitE i s pr m (Two a b) + | i == 0 = Deep (s - 1) pr m (One b) + | otherwise = Deep (s - 1) pr m (One a) +delRightDigitE i s pr m (Three a b c) + | i == 0 = Deep (s - 1) pr m (Two b c) + | i == 1 = Deep (s - 1) pr m (Two a c) + | otherwise = deep pr m (Two a b) +delRightDigitE i s pr m (Four a b c d) + | i == 0 = Deep (s - 1) pr m (Three b c d) + | i == 1 = Deep (s - 1) pr m (Three a c d) + | i == 2 = Deep (s - 1) pr m (Three a b d) + | otherwise = Deep (s - 1) pr m (Three a b c) + +data DelTree a = FullTree !(FingerTree (Node a)) | DefectTree a + +{-# SPECIALIZE delTree :: (Int -> Node (Elem a) -> Del (Elem a)) -> Int -> FingerTree (Node (Elem a)) -> DelTree (Elem a) #-} +{-# SPECIALIZE delTree :: (Int -> Node (Node a) -> Del (Node a)) -> Int -> FingerTree (Node (Node a)) -> DelTree (Node a) #-} +delTree :: Sized a => (Int -> Node a -> Del a) -> Int -> FingerTree (Node a) -> DelTree a +delTree _f !_i EmptyT = FullTree EmptyT -- Unreachable +delTree f i (Single a) = case f i a of + Full a' -> FullTree (Single a') + Defect e -> DefectTree e +delTree f i (Deep s pr m sf) + | i < spr = case delDigit f i pr of + FullDig pr' -> FullTree $ Deep (s - 1) pr' m sf + DefectDig e -> case viewLTree m of + EmptyLTree -> FullTree $ delRebuildRightDigit (s - 1) e sf + ConsLTree n m' -> FullTree $ delRebuildLeftSide (s - 1) e n m' sf + | i < spm = case delTree (delNode f) (i - spr) m of + FullTree m' -> FullTree (Deep (s - 1) pr m' sf) + DefectTree e -> FullTree $ delRebuildMiddle (s - 1) pr e sf + | otherwise = case delDigit f (i - spm) sf of + FullDig sf' -> FullTree $ Deep (s - 1) pr m sf' + DefectDig e -> case viewRTree m of + EmptyRTree -> FullTree $ delRebuildLeftDigit (s - 1) pr e + SnocRTree m' n -> FullTree $ delRebuildRightSide (s - 1) pr m' n e + where spr = size pr + spm = spr + size m + +data Del a = Full !(Node a) | Defect a + +{-# SPECIALIZE delNode :: (Int -> Node (Elem a) -> Del (Elem a)) -> Int -> Node (Node (Elem a)) -> Del (Node (Elem a)) #-} +{-# SPECIALIZE delNode :: (Int -> Node (Node a) -> Del (Node a)) -> Int -> Node (Node (Node a)) -> Del (Node (Node a)) #-} +delNode :: Sized a => (Int -> Node a -> Del a) -> Int -> Node (Node a) -> Del (Node a) +delNode f i (Node3 s a b c) + | i < sa = case f i a of + Full a' -> Full $ Node3 (s - 1) a' b c + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> Full $ Node3 (s - 1) (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) c + where !sx = size x + Node2 sxy x y -> Full $ Node2 (s - 1) (Node3 (sxy + se) e x y) c + | i < sab = case f (i - sa) b of + Full b' -> Full $ Node3 (s - 1) a b' c + Defect e -> let !se = size e in case a of + Node3 sxyz x y z -> Full $ Node3 (s - 1) (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) c + where !sz = size z + Node2 sxy x y -> Full $ Node2 (s - 1) (Node3 (sxy + se) x y e) c + | otherwise = case f (i - sab) c of + Full c' -> Full $ Node3 (s - 1) a b c' + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> Full $ Node3 (s - 1) a (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) + where !sz = size z + Node2 sxy x y -> Full $ Node2 (s - 1) a (Node3 (sxy + se) x y e) + where sa = size a + sab = sa + size b +delNode f i (Node2 s a b) + | i < sa = case f i a of + Full a' -> Full $ Node2 (s - 1) a' b + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> Full $ Node2 (s - 1) (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) + where !sx = size x + Node2 _ x y -> Defect $ Node3 (s - 1) e x y + | otherwise = case f (i - sa) b of + Full b' -> Full $ Node2 (s - 1) a b' + Defect e -> let !se = size e in case a of + Node3 sxyz x y z -> Full $ Node2 (s - 1) (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) + where !sz = size z + Node2 _ x y -> Defect $ Node3 (s - 1) x y e + where sa = size a + +{-# SPECIALIZE delRebuildRightDigit :: Int -> Elem a -> Digit (Node (Elem a)) -> FingerTree (Node (Elem a)) #-} +{-# SPECIALIZE delRebuildRightDigit :: Int -> Node a -> Digit (Node (Node a)) -> FingerTree (Node (Node a)) #-} +delRebuildRightDigit :: Sized a => Int -> a -> Digit (Node a) -> FingerTree (Node a) +delRebuildRightDigit s p (One a) = let !sp = size p in case a of + Node3 sxyz x y z -> Deep s (One (Node2 (sp + sx) p x)) EmptyT (One (Node2 (sxyz - sx) y z)) + where !sx = size x + Node2 sxy x y -> Single (Node3 (sp + sxy) p x y) +delRebuildRightDigit s p (Two a b) = let !sp = size p in case a of + Node3 sxyz x y z -> Deep s (Two (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z)) EmptyT (One b) + where !sx = size x + Node2 sxy x y -> Deep s (One (Node3 (sp + sxy) p x y)) EmptyT (One b) +delRebuildRightDigit s p (Three a b c) = let !sp = size p in case a of + Node3 sxyz x y z -> Deep s (Two (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z)) EmptyT (Two b c) + where !sx = size x + Node2 sxy x y -> Deep s (Two (Node3 (sp + sxy) p x y) b) EmptyT (One c) +delRebuildRightDigit s p (Four a b c d) = let !sp = size p in case a of + Node3 sxyz x y z -> Deep s (Three (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z) b) EmptyT (Two c d) + where !sx = size x + Node2 sxy x y -> Deep s (Two (Node3 (sp + sxy) p x y) b) EmptyT (Two c d) + +{-# SPECIALIZE delRebuildLeftDigit :: Int -> Digit (Node (Elem a)) -> Elem a -> FingerTree (Node (Elem a)) #-} +{-# SPECIALIZE delRebuildLeftDigit :: Int -> Digit (Node (Node a)) -> Node a -> FingerTree (Node (Node a)) #-} +delRebuildLeftDigit :: Sized a => Int -> Digit (Node a) -> a -> FingerTree (Node a) +delRebuildLeftDigit s (One a) p = let !sp = size p in case a of + Node3 sxyz x y z -> Deep s (One (Node2 (sxyz - sz) x y)) EmptyT (One (Node2 (sz + sp) z p)) + where !sz = size z + Node2 sxy x y -> Single (Node3 (sxy + sp) x y p) +delRebuildLeftDigit s (Two a b) p = let !sp = size p in case b of + Node3 sxyz x y z -> Deep s (Two a (Node2 (sxyz - sz) x y)) EmptyT (One (Node2 (sz + sp) z p)) + where !sz = size z + Node2 sxy x y -> Deep s (One a) EmptyT (One (Node3 (sxy + sp) x y p)) +delRebuildLeftDigit s (Three a b c) p = let !sp = size p in case c of + Node3 sxyz x y z -> Deep s (Two a b) EmptyT (Two (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) + where !sz = size z + Node2 sxy x y -> Deep s (Two a b) EmptyT (One (Node3 (sxy + sp) x y p)) +delRebuildLeftDigit s (Four a b c d) p = let !sp = size p in case d of + Node3 sxyz x y z -> Deep s (Three a b c) EmptyT (Two (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) + where !sz = size z + Node2 sxy x y -> Deep s (Two a b) EmptyT (Two c (Node3 (sxy + sp) x y p)) + +delRebuildLeftSide :: Sized a + => Int -> a -> Node (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) + -> FingerTree (Node a) +delRebuildLeftSide s p (Node2 _ a b) m sf = let !sp = size p in case a of + Node2 sxy x y -> Deep s (Two (Node3 (sp + sxy) p x y) b) m sf + Node3 sxyz x y z -> Deep s (Three (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z) b) m sf + where !sx = size x +delRebuildLeftSide s p (Node3 _ a b c) m sf = let !sp = size p in case a of + Node2 sxy x y -> Deep s (Three (Node3 (sp + sxy) p x y) b c) m sf + Node3 sxyz x y z -> Deep s (Four (Node2 (sp + sx) p x) (Node2 (sxyz - sx) y z) b c) m sf + where !sx = size x + +delRebuildRightSide :: Sized a + => Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Node (Node a) -> a + -> FingerTree (Node a) +delRebuildRightSide s pr m (Node2 _ a b) p = let !sp = size p in case b of + Node2 sxy x y -> Deep s pr m (Two a (Node3 (sxy + sp) x y p)) + Node3 sxyz x y z -> Deep s pr m (Three a (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) + where !sz = size z +delRebuildRightSide s pr m (Node3 _ a b c) p = let !sp = size p in case c of + Node2 sxy x y -> Deep s pr m (Three a b (Node3 (sxy + sp) x y p)) + Node3 sxyz x y z -> Deep s pr m (Four a b (Node2 (sxyz - sz) x y) (Node2 (sz + sp) z p)) + where !sz = size z + +delRebuildMiddle :: Sized a + => Int -> Digit a -> a -> Digit a + -> FingerTree a +delRebuildMiddle s (One a) e sf = Deep s (Two a e) EmptyT sf +delRebuildMiddle s (Two a b) e sf = Deep s (Three a b e) EmptyT sf +delRebuildMiddle s (Three a b c) e sf = Deep s (Four a b c e) EmptyT sf +delRebuildMiddle s (Four a b c d) e sf = Deep s (Two a b) (Single (node3 c d e)) sf + +data DelDig a = FullDig !(Digit (Node a)) | DefectDig a + +{-# SPECIALIZE delDigit :: (Int -> Node (Elem a) -> Del (Elem a)) -> Int -> Digit (Node (Elem a)) -> DelDig (Elem a) #-} +{-# SPECIALIZE delDigit :: (Int -> Node (Node a) -> Del (Node a)) -> Int -> Digit (Node (Node a)) -> DelDig (Node a) #-} +delDigit :: Sized a => (Int -> Node a -> Del a) -> Int -> Digit (Node a) -> DelDig a +delDigit f !i (One a) = case f i a of + Full a' -> FullDig $ One a' + Defect e -> DefectDig e +delDigit f i (Two a b) + | i < sa = case f i a of + Full a' -> FullDig $ Two a' b + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> FullDig $ Two (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) + where !sx = size x + Node2 sxy x y -> FullDig $ One (Node3 (se + sxy) e x y) + | otherwise = case f (i - sa) b of + Full b' -> FullDig $ Two a b' + Defect e -> let !se = size e in case a of + Node3 sxyz x y z -> FullDig $ Two (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) + where !sz = size z + Node2 sxy x y -> FullDig $ One (Node3 (sxy + se) x y e) + where sa = size a +delDigit f i (Three a b c) + | i < sa = case f i a of + Full a' -> FullDig $ Three a' b c + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> FullDig $ Three (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) c + where !sx = size x + Node2 sxy x y -> FullDig $ Two (Node3 (se + sxy) e x y) c + | i < sab = case f (i - sa) b of + Full b' -> FullDig $ Three a b' c + Defect e -> let !se = size e in case a of + Node3 sxyz x y z -> FullDig $ Three (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) c + where !sz = size z + Node2 sxy x y -> FullDig $ Two (Node3 (sxy + se) x y e) c + | otherwise = case f (i - sab) c of + Full c' -> FullDig $ Three a b c' + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> FullDig $ Three a (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) + where !sz = size z + Node2 sxy x y -> FullDig $ Two a (Node3 (sxy + se) x y e) + where sa = size a + sab = sa + size b +delDigit f i (Four a b c d) + | i < sa = case f i a of + Full a' -> FullDig $ Four a' b c d + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> FullDig $ Four (Node2 (se + sx) e x) (Node2 (sxyz - sx) y z) c d + where !sx = size x + Node2 sxy x y -> FullDig $ Three (Node3 (se + sxy) e x y) c d + | i < sab = case f (i - sa) b of + Full b' -> FullDig $ Four a b' c d + Defect e -> let !se = size e in case a of + Node3 sxyz x y z -> FullDig $ Four (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) c d + where !sz = size z + Node2 sxy x y -> FullDig $ Three (Node3 (sxy + se) x y e) c d + | i < sabc = case f (i - sab) c of + Full c' -> FullDig $ Four a b c' d + Defect e -> let !se = size e in case b of + Node3 sxyz x y z -> FullDig $ Four a (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) d + where !sz = size z + Node2 sxy x y -> FullDig $ Three a (Node3 (sxy + se) x y e) d + | otherwise = case f (i - sabc) d of + Full d' -> FullDig $ Four a b c d' + Defect e -> let !se = size e in case c of + Node3 sxyz x y z -> FullDig $ Four a b (Node2 (sxyz - sz) x y) (Node2 (sz + se) z e) + where !sz = size z + Node2 sxy x y -> FullDig $ Three a b (Node3 (sxy + se) x y e) + where sa = size a + sab = sa + size b + sabc = sab + size c + + +-- | /O(n)/. A generalization of 'fmap', 'mapWithIndex' takes a mapping +-- function that also depends on the element's index, and applies it to every +-- element in the sequence. +mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b +mapWithIndex f' (Seq xs') = Seq $ mapWithIndexTree (\s (Elem a) -> Elem (f' s a)) 0 xs' + where + {-# SPECIALIZE mapWithIndexTree :: (Int -> Elem y -> b) -> Int -> FingerTree (Elem y) -> FingerTree b #-} + {-# SPECIALIZE mapWithIndexTree :: (Int -> Node y -> b) -> Int -> FingerTree (Node y) -> FingerTree b #-} + mapWithIndexTree :: Sized a => (Int -> a -> b) -> Int -> FingerTree a -> FingerTree b + mapWithIndexTree _ !_s EmptyT = EmptyT + mapWithIndexTree f s (Single xs) = Single $ f s xs + mapWithIndexTree f s (Deep n pr m sf) = + Deep n + (mapWithIndexDigit f s pr) + (mapWithIndexTree (mapWithIndexNode f) sPspr m) + (mapWithIndexDigit f sPsprm sf) + where + !sPspr = s + size pr + !sPsprm = sPspr + size m + + {-# SPECIALIZE mapWithIndexDigit :: (Int -> Elem y -> b) -> Int -> Digit (Elem y) -> Digit b #-} + {-# SPECIALIZE mapWithIndexDigit :: (Int -> Node y -> b) -> Int -> Digit (Node y) -> Digit b #-} + mapWithIndexDigit :: Sized a => (Int -> a -> b) -> Int -> Digit a -> Digit b + mapWithIndexDigit f !s (One a) = One (f s a) + mapWithIndexDigit f s (Two a b) = Two (f s a) (f sPsa b) + where + !sPsa = s + size a + mapWithIndexDigit f s (Three a b c) = + Three (f s a) (f sPsa b) (f sPsab c) + where + !sPsa = s + size a + !sPsab = sPsa + size b + mapWithIndexDigit f s (Four a b c d) = + Four (f s a) (f sPsa b) (f sPsab c) (f sPsabc d) + where + !sPsa = s + size a + !sPsab = sPsa + size b + !sPsabc = sPsab + size c + + {-# SPECIALIZE mapWithIndexNode :: (Int -> Elem y -> b) -> Int -> Node (Elem y) -> Node b #-} + {-# SPECIALIZE mapWithIndexNode :: (Int -> Node y -> b) -> Int -> Node (Node y) -> Node b #-} + mapWithIndexNode :: Sized a => (Int -> a -> b) -> Int -> Node a -> Node b + mapWithIndexNode f s (Node2 ns a b) = Node2 ns (f s a) (f sPsa b) + where + !sPsa = s + size a + mapWithIndexNode f s (Node3 ns a b c) = + Node3 ns (f s a) (f sPsa b) (f sPsab c) + where + !sPsa = s + size a + !sPsab = sPsa + size b + +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] mapWithIndex #-} +{-# RULES +"mapWithIndex/mapWithIndex" forall f g xs . mapWithIndex f (mapWithIndex g xs) = + mapWithIndex (\k a -> f k (g k a)) xs +"mapWithIndex/fmapSeq" forall f g xs . mapWithIndex f (fmapSeq g xs) = + mapWithIndex (\k a -> f k (g a)) xs +"fmapSeq/mapWithIndex" forall f g xs . fmapSeq f (mapWithIndex g xs) = + mapWithIndex (\k a -> f (g k a)) xs + #-} +#endif + + +-- | /O(n)/. A generalization of 'foldMap', 'foldMapWithIndex' takes a folding +-- function that also depends on the element's index, and applies it to every +-- element in the sequence. +-- +-- @since 0.5.8 +foldMapWithIndex :: Monoid m => (Int -> a -> m) -> Seq a -> m +foldMapWithIndex f' (Seq xs') = foldMapWithIndexTreeE (lift_elem f') 0 xs' + where + lift_elem :: (Int -> a -> m) -> (Int -> Elem a -> m) +#if __GLASGOW_HASKELL__ >= 708 + lift_elem g = coerce g +#else + lift_elem g = \s (Elem a) -> g s a +#endif + {-# INLINE lift_elem #-} +-- We have to specialize these functions by hand, unfortunately, because +-- GHC does not specialize until *all* instances are determined. +-- Although the Sized instance is known at compile time, the Monoid +-- instance generally is not. + foldMapWithIndexTreeE :: Monoid m => (Int -> Elem a -> m) -> Int -> FingerTree (Elem a) -> m + foldMapWithIndexTreeE _ !_s EmptyT = mempty + foldMapWithIndexTreeE f s (Single xs) = f s xs + foldMapWithIndexTreeE f s (Deep _ pr m sf) = + foldMapWithIndexDigitE f s pr <> + foldMapWithIndexTreeN (foldMapWithIndexNodeE f) sPspr m <> + foldMapWithIndexDigitE f sPsprm sf + where + !sPspr = s + size pr + !sPsprm = sPspr + size m + + foldMapWithIndexTreeN :: Monoid m => (Int -> Node a -> m) -> Int -> FingerTree (Node a) -> m + foldMapWithIndexTreeN _ !_s EmptyT = mempty + foldMapWithIndexTreeN f s (Single xs) = f s xs + foldMapWithIndexTreeN f s (Deep _ pr m sf) = + foldMapWithIndexDigitN f s pr <> + foldMapWithIndexTreeN (foldMapWithIndexNodeN f) sPspr m <> + foldMapWithIndexDigitN f sPsprm sf + where + !sPspr = s + size pr + !sPsprm = sPspr + size m + + foldMapWithIndexDigitE :: Monoid m => (Int -> Elem a -> m) -> Int -> Digit (Elem a) -> m + foldMapWithIndexDigitE f i t = foldMapWithIndexDigit f i t + + foldMapWithIndexDigitN :: Monoid m => (Int -> Node a -> m) -> Int -> Digit (Node a) -> m + foldMapWithIndexDigitN f i t = foldMapWithIndexDigit f i t + + {-# INLINE foldMapWithIndexDigit #-} + foldMapWithIndexDigit :: (Monoid m, Sized a) => (Int -> a -> m) -> Int -> Digit a -> m + foldMapWithIndexDigit f !s (One a) = f s a + foldMapWithIndexDigit f s (Two a b) = f s a <> f sPsa b + where + !sPsa = s + size a + foldMapWithIndexDigit f s (Three a b c) = + f s a <> f sPsa b <> f sPsab c + where + !sPsa = s + size a + !sPsab = sPsa + size b + foldMapWithIndexDigit f s (Four a b c d) = + f s a <> f sPsa b <> f sPsab c <> f sPsabc d + where + !sPsa = s + size a + !sPsab = sPsa + size b + !sPsabc = sPsab + size c + + foldMapWithIndexNodeE :: Monoid m => (Int -> Elem a -> m) -> Int -> Node (Elem a) -> m + foldMapWithIndexNodeE f i t = foldMapWithIndexNode f i t + + foldMapWithIndexNodeN :: Monoid m => (Int -> Node a -> m) -> Int -> Node (Node a) -> m + foldMapWithIndexNodeN f i t = foldMapWithIndexNode f i t + + {-# INLINE foldMapWithIndexNode #-} + foldMapWithIndexNode :: (Monoid m, Sized a) => (Int -> a -> m) -> Int -> Node a -> m + foldMapWithIndexNode f !s (Node2 _ a b) = f s a <> f sPsa b + where + !sPsa = s + size a + foldMapWithIndexNode f s (Node3 _ a b c) = + f s a <> f sPsa b <> f sPsab c + where + !sPsa = s + size a + !sPsab = sPsa + size b + +#if __GLASGOW_HASKELL__ +{-# INLINABLE foldMapWithIndex #-} +#endif + +-- | 'traverseWithIndex' is a version of 'traverse' that also offers +-- access to the index of each element. +-- +-- @since 0.5.8 +traverseWithIndex :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) +traverseWithIndex f' (Seq xs') = Seq <$> traverseWithIndexTreeE (\s (Elem a) -> Elem <$> f' s a) 0 xs' + where +-- We have to specialize these functions by hand, unfortunately, because +-- GHC does not specialize until *all* instances are determined. +-- Although the Sized instance is known at compile time, the Applicative +-- instance generally is not. + traverseWithIndexTreeE :: Applicative f => (Int -> Elem a -> f b) -> Int -> FingerTree (Elem a) -> f (FingerTree b) + traverseWithIndexTreeE _ !_s EmptyT = pure EmptyT + traverseWithIndexTreeE f s (Single xs) = Single <$> f s xs + traverseWithIndexTreeE f s (Deep n pr m sf) = + deep' n <$> + traverseWithIndexDigitE f s pr <*> + traverseWithIndexTreeN (traverseWithIndexNodeE f) sPspr m <*> + traverseWithIndexDigitE f sPsprm sf + where + !sPspr = s + size pr + !sPsprm = sPspr + size m + + traverseWithIndexTreeN :: Applicative f => (Int -> Node a -> f b) -> Int -> FingerTree (Node a) -> f (FingerTree b) + traverseWithIndexTreeN _ !_s EmptyT = pure EmptyT + traverseWithIndexTreeN f s (Single xs) = Single <$> f s xs + traverseWithIndexTreeN f s (Deep n pr m sf) = + deep' n <$> + traverseWithIndexDigitN f s pr <*> + traverseWithIndexTreeN (traverseWithIndexNodeN f) sPspr m <*> + traverseWithIndexDigitN f sPsprm sf + where + !sPspr = s + size pr + !sPsprm = sPspr + size m + + traverseWithIndexDigitE :: Applicative f => (Int -> Elem a -> f b) -> Int -> Digit (Elem a) -> f (Digit b) + traverseWithIndexDigitE f i t = traverseWithIndexDigit f i t + + traverseWithIndexDigitN :: Applicative f => (Int -> Node a -> f b) -> Int -> Digit (Node a) -> f (Digit b) + traverseWithIndexDigitN f i t = traverseWithIndexDigit f i t + + {-# INLINE traverseWithIndexDigit #-} + traverseWithIndexDigit :: (Applicative f, Sized a) => (Int -> a -> f b) -> Int -> Digit a -> f (Digit b) + traverseWithIndexDigit f !s (One a) = One <$> f s a + traverseWithIndexDigit f s (Two a b) = Two <$> f s a <*> f sPsa b + where + !sPsa = s + size a + traverseWithIndexDigit f s (Three a b c) = + Three <$> f s a <*> f sPsa b <*> f sPsab c + where + !sPsa = s + size a + !sPsab = sPsa + size b + traverseWithIndexDigit f s (Four a b c d) = + Four <$> f s a <*> f sPsa b <*> f sPsab c <*> f sPsabc d + where + !sPsa = s + size a + !sPsab = sPsa + size b + !sPsabc = sPsab + size c + + traverseWithIndexNodeE :: Applicative f => (Int -> Elem a -> f b) -> Int -> Node (Elem a) -> f (Node b) + traverseWithIndexNodeE f i t = traverseWithIndexNode f i t + + traverseWithIndexNodeN :: Applicative f => (Int -> Node a -> f b) -> Int -> Node (Node a) -> f (Node b) + traverseWithIndexNodeN f i t = traverseWithIndexNode f i t + + {-# INLINE traverseWithIndexNode #-} + traverseWithIndexNode :: (Applicative f, Sized a) => (Int -> a -> f b) -> Int -> Node a -> f (Node b) + traverseWithIndexNode f !s (Node2 ns a b) = node2' ns <$> f s a <*> f sPsa b + where + !sPsa = s + size a + traverseWithIndexNode f s (Node3 ns a b c) = + node3' ns <$> f s a <*> f sPsa b <*> f sPsab c + where + !sPsa = s + size a + !sPsab = sPsa + size b + + +{-# NOINLINE [1] traverseWithIndex #-} +#ifdef __GLASGOW_HASKELL__ +{-# RULES +"travWithIndex/mapWithIndex" forall f g xs . traverseWithIndex f (mapWithIndex g xs) = + traverseWithIndex (\k a -> f k (g k a)) xs +"travWithIndex/fmapSeq" forall f g xs . traverseWithIndex f (fmapSeq g xs) = + traverseWithIndex (\k a -> f k (g a)) xs + #-} +#endif +{- +It might be nice to be able to rewrite + +traverseWithIndex f (fromFunction i g) +to +replicateAWithIndex i (\k -> f k (g k)) +and +traverse f (fromFunction i g) +to +replicateAWithIndex i (f . g) + +but we don't have replicateAWithIndex as yet. + +We might wish for a rule like +"fmapSeq/travWithIndex" forall f g xs . fmapSeq f <$> traverseWithIndex g xs = + traverseWithIndex (\k a -> f <$> g k a) xs +Unfortunately, this rule could screw up the inliner's treatment of +fmap in general, and it also relies on the arbitrary Functor being +valid. +-} + + +-- | /O(n)/. Convert a given sequence length and a function representing that +-- sequence into a sequence. +fromFunction :: Int -> (Int -> a) -> Seq a +fromFunction len f | len < 0 = error "Data.Sequence.fromFunction called with negative len" + | len == 0 = empty + | otherwise = Seq $ create (lift_elem f) 1 0 len + where + create :: (Int -> a) -> Int -> Int -> Int -> FingerTree a + create b{-tree_builder-} !s{-tree_size-} !i{-start_index-} trees = case trees of + 1 -> Single $ b i + 2 -> Deep (2*s) (One (b i)) EmptyT (One (b (i+s))) + 3 -> Deep (3*s) (createTwo i) EmptyT (One (b (i+2*s))) + 4 -> Deep (4*s) (createTwo i) EmptyT (createTwo (i+2*s)) + 5 -> Deep (5*s) (createThree i) EmptyT (createTwo (i+3*s)) + 6 -> Deep (6*s) (createThree i) EmptyT (createThree (i+3*s)) + _ -> case trees `quotRem` 3 of + (trees', 1) -> Deep (trees*s) (createTwo i) + (create mb (3*s) (i+2*s) (trees'-1)) + (createTwo (i+(2+3*(trees'-1))*s)) + (trees', 2) -> Deep (trees*s) (createThree i) + (create mb (3*s) (i+3*s) (trees'-1)) + (createTwo (i+(3+3*(trees'-1))*s)) + (trees', _) -> Deep (trees*s) (createThree i) + (create mb (3*s) (i+3*s) (trees'-2)) + (createThree (i+(3+3*(trees'-2))*s)) + where + createTwo j = Two (b j) (b (j + s)) + {-# INLINE createTwo #-} + createThree j = Three (b j) (b (j + s)) (b (j + 2*s)) + {-# INLINE createThree #-} + mb j = Node3 (3*s) (b j) (b (j + s)) (b (j + 2*s)) + {-# INLINE mb #-} + + lift_elem :: (Int -> a) -> (Int -> Elem a) +#if __GLASGOW_HASKELL__ >= 708 + lift_elem g = coerce g +#else + lift_elem g = Elem . g +#endif + {-# INLINE lift_elem #-} + +-- | /O(n)/. Create a sequence consisting of the elements of an 'Array'. +-- Note that the resulting sequence elements may be evaluated lazily (as on GHC), +-- so you must force the entire structure to be sure that the original array +-- can be garbage-collected. +fromArray :: Ix i => Array i a -> Seq a +#ifdef __GLASGOW_HASKELL__ +fromArray a = fromFunction (GHC.Arr.numElements a) (GHC.Arr.unsafeAt a) + where + -- The following definition uses (Ix i) constraing, which is needed for the + -- other fromArray definition. + _ = Data.Array.rangeSize (Data.Array.bounds a) +#else +fromArray a = fromList2 (Data.Array.rangeSize (Data.Array.bounds a)) (Data.Array.elems a) +#endif + +-- Splitting + +-- | /O(log(min(i,n-i)))/. The first @i@ elements of a sequence. +-- If @i@ is negative, @'take' i s@ yields the empty sequence. +-- If the sequence contains fewer than @i@ elements, the whole sequence +-- is returned. +take :: Int -> Seq a -> Seq a +take i xs@(Seq t) + -- See note on unsigned arithmetic in splitAt + | fromIntegral i - 1 < (fromIntegral (length xs) - 1 :: Word) = + Seq (takeTreeE i t) + | i <= 0 = empty + | otherwise = xs + +takeTreeE :: Int -> FingerTree (Elem a) -> FingerTree (Elem a) +takeTreeE !_i EmptyT = EmptyT +takeTreeE i t@(Single _) + | i <= 0 = EmptyT + | otherwise = t +takeTreeE i (Deep s pr m sf) + | i < spr = takePrefixE i pr + | i < spm = case takeTreeN im m of + ml :*: xs -> takeMiddleE (im - size ml) spr pr ml xs + | otherwise = takeSuffixE (i - spm) s pr m sf + where + spr = size pr + spm = spr + size m + im = i - spr + +takeTreeN :: Int -> FingerTree (Node a) -> StrictPair (FingerTree (Node a)) (Node a) +takeTreeN !_i EmptyT = error "takeTreeN of empty tree" +takeTreeN _i (Single x) = EmptyT :*: x +takeTreeN i (Deep s pr m sf) + | i < spr = takePrefixN i pr + | i < spm = case takeTreeN im m of + ml :*: xs -> takeMiddleN (im - size ml) spr pr ml xs + | otherwise = takeSuffixN (i - spm) s pr m sf where + spr = size pr + spm = spr + size m + im = i - spr + +takeMiddleN :: Int -> Int + -> Digit (Node a) -> FingerTree (Node (Node a)) -> Node (Node a) + -> StrictPair (FingerTree (Node a)) (Node a) +takeMiddleN i spr pr ml (Node2 _ a b) + | i < sa = pullR sprml pr ml :*: a + | otherwise = Deep sprmla pr ml (One a) :*: b + where + sa = size a + sprml = spr + size ml + sprmla = sa + sprml +takeMiddleN i spr pr ml (Node3 _ a b c) + | i < sa = pullR sprml pr ml :*: a + | i < sab = Deep sprmla pr ml (One a) :*: b + | otherwise = Deep sprmlab pr ml (Two a b) :*: c + where + sa = size a + sab = sa + size b + sprml = spr + size ml + sprmla = sa + sprml + sprmlab = sprmla + size b + +takeMiddleE :: Int -> Int + -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Node (Elem a) + -> FingerTree (Elem a) +takeMiddleE i spr pr ml (Node2 _ a _) + | i < 1 = pullR sprml pr ml + | otherwise = Deep sprmla pr ml (One a) + where + sprml = spr + size ml + sprmla = 1 + sprml +takeMiddleE i spr pr ml (Node3 _ a b _) + | i < 1 = pullR sprml pr ml + | i < 2 = Deep sprmla pr ml (One a) + | otherwise = Deep sprmlab pr ml (Two a b) + where + sprml = spr + size ml + sprmla = 1 + sprml + sprmlab = sprmla + 1 + +takePrefixE :: Int -> Digit (Elem a) -> FingerTree (Elem a) +takePrefixE !_i (One _) = EmptyT +takePrefixE i (Two a _) + | i < 1 = EmptyT + | otherwise = Single a +takePrefixE i (Three a b _) + | i < 1 = EmptyT + | i < 2 = Single a + | otherwise = Deep 2 (One a) EmptyT (One b) +takePrefixE i (Four a b c _) + | i < 1 = EmptyT + | i < 2 = Single a + | i < 3 = Deep 2 (One a) EmptyT (One b) + | otherwise = Deep 3 (Two a b) EmptyT (One c) + +takePrefixN :: Int -> Digit (Node a) + -> StrictPair (FingerTree (Node a)) (Node a) +takePrefixN !_i (One a) = EmptyT :*: a +takePrefixN i (Two a b) + | i < sa = EmptyT :*: a + | otherwise = Single a :*: b + where + sa = size a +takePrefixN i (Three a b c) + | i < sa = EmptyT :*: a + | i < sab = Single a :*: b + | otherwise = Deep sab (One a) EmptyT (One b) :*: c + where + sa = size a + sab = sa + size b +takePrefixN i (Four a b c d) + | i < sa = EmptyT :*: a + | i < sab = Single a :*: b + | i < sabc = Deep sab (One a) EmptyT (One b) :*: c + | otherwise = Deep sabc (Two a b) EmptyT (One c) :*: d + where + sa = size a + sab = sa + size b + sabc = sab + size c + +takeSuffixE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> + FingerTree (Elem a) +takeSuffixE !_i !s pr m (One _) = pullR (s - 1) pr m +takeSuffixE i s pr m (Two a _) + | i < 1 = pullR (s - 2) pr m + | otherwise = Deep (s - 1) pr m (One a) +takeSuffixE i s pr m (Three a b _) + | i < 1 = pullR (s - 3) pr m + | i < 2 = Deep (s - 2) pr m (One a) + | otherwise = Deep (s - 1) pr m (Two a b) +takeSuffixE i s pr m (Four a b c _) + | i < 1 = pullR (s - 4) pr m + | i < 2 = Deep (s - 3) pr m (One a) + | i < 3 = Deep (s - 2) pr m (Two a b) + | otherwise = Deep (s - 1) pr m (Three a b c) + +takeSuffixN :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> + StrictPair (FingerTree (Node a)) (Node a) +takeSuffixN !_i !s pr m (One a) = pullR (s - size a) pr m :*: a +takeSuffixN i s pr m (Two a b) + | i < sa = pullR (s - sa - size b) pr m :*: a + | otherwise = Deep (s - size b) pr m (One a) :*: b + where + sa = size a +takeSuffixN i s pr m (Three a b c) + | i < sa = pullR (s - sab - size c) pr m :*: a + | i < sab = Deep (s - size b - size c) pr m (One a) :*: b + | otherwise = Deep (s - size c) pr m (Two a b) :*: c + where + sa = size a + sab = sa + size b +takeSuffixN i s pr m (Four a b c d) + | i < sa = pullR (s - sa - sbcd) pr m :*: a + | i < sab = Deep (s - sbcd) pr m (One a) :*: b + | i < sabc = Deep (s - scd) pr m (Two a b) :*: c + | otherwise = Deep (s - sd) pr m (Three a b c) :*: d + where + sa = size a + sab = sa + size b + sabc = sab + size c + sd = size d + scd = size c + sd + sbcd = size b + scd + +-- | /O(log(min(i,n-i)))/. Elements of a sequence after the first @i@. +-- If @i@ is negative, @'drop' i s@ yields the whole sequence. +-- If the sequence contains fewer than @i@ elements, the empty sequence +-- is returned. +drop :: Int -> Seq a -> Seq a +drop i xs@(Seq t) + -- See note on unsigned arithmetic in splitAt + | fromIntegral i - 1 < (fromIntegral (length xs) - 1 :: Word) = + Seq (takeTreeER (length xs - i) t) + | i <= 0 = xs + | otherwise = empty + +-- We implement `drop` using a "take from the rear" strategy. There's no +-- particular technical reason for this; it just lets us reuse the arithmetic +-- from `take` (which itself reuses the arithmetic from `splitAt`) instead of +-- figuring it out from scratch and ending up with lots of off-by-one errors. +takeTreeER :: Int -> FingerTree (Elem a) -> FingerTree (Elem a) +takeTreeER !_i EmptyT = EmptyT +takeTreeER i t@(Single _) + | i <= 0 = EmptyT + | otherwise = t +takeTreeER i (Deep s pr m sf) + | i < ssf = takeSuffixER i sf + | i < ssm = case takeTreeNR im m of + xs :*: mr -> takeMiddleER (im - size mr) ssf xs mr sf + | otherwise = takePrefixER (i - ssm) s pr m sf + where + ssf = size sf + ssm = ssf + size m + im = i - ssf + +takeTreeNR :: Int -> FingerTree (Node a) -> StrictPair (Node a) (FingerTree (Node a)) +takeTreeNR !_i EmptyT = error "takeTreeNR of empty tree" +takeTreeNR _i (Single x) = x :*: EmptyT +takeTreeNR i (Deep s pr m sf) + | i < ssf = takeSuffixNR i sf + | i < ssm = case takeTreeNR im m of + xs :*: mr -> takeMiddleNR (im - size mr) ssf xs mr sf + | otherwise = takePrefixNR (i - ssm) s pr m sf where + ssf = size sf + ssm = ssf + size m + im = i - ssf + +takeMiddleNR :: Int -> Int + -> Node (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) + -> StrictPair (Node a) (FingerTree (Node a)) +takeMiddleNR i ssf (Node2 _ a b) mr sf + | i < sb = b :*: pullL ssfmr mr sf + | otherwise = a :*: Deep ssfmrb (One b) mr sf + where + sb = size b + ssfmr = ssf + size mr + ssfmrb = sb + ssfmr +takeMiddleNR i ssf (Node3 _ a b c) mr sf + | i < sc = c :*: pullL ssfmr mr sf + | i < sbc = b :*: Deep ssfmrc (One c) mr sf + | otherwise = a :*: Deep ssfmrbc (Two b c) mr sf + where + sc = size c + sbc = sc + size b + ssfmr = ssf + size mr + ssfmrc = sc + ssfmr + ssfmrbc = ssfmrc + size b + +takeMiddleER :: Int -> Int + -> Node (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) + -> FingerTree (Elem a) +takeMiddleER i ssf (Node2 _ _ b) mr sf + | i < 1 = pullL ssfmr mr sf + | otherwise = Deep ssfmrb (One b) mr sf + where + ssfmr = ssf + size mr + ssfmrb = 1 + ssfmr +takeMiddleER i ssf (Node3 _ _ b c) mr sf + | i < 1 = pullL ssfmr mr sf + | i < 2 = Deep ssfmrc (One c) mr sf + | otherwise = Deep ssfmrbc (Two b c) mr sf + where + ssfmr = ssf + size mr + ssfmrc = 1 + ssfmr + ssfmrbc = ssfmr + 2 + +takeSuffixER :: Int -> Digit (Elem a) -> FingerTree (Elem a) +takeSuffixER !_i (One _) = EmptyT +takeSuffixER i (Two _ b) + | i < 1 = EmptyT + | otherwise = Single b +takeSuffixER i (Three _ b c) + | i < 1 = EmptyT + | i < 2 = Single c + | otherwise = Deep 2 (One b) EmptyT (One c) +takeSuffixER i (Four _ b c d) + | i < 1 = EmptyT + | i < 2 = Single d + | i < 3 = Deep 2 (One c) EmptyT (One d) + | otherwise = Deep 3 (Two b c) EmptyT (One d) + +takeSuffixNR :: Int -> Digit (Node a) + -> StrictPair (Node a) (FingerTree (Node a)) +takeSuffixNR !_i (One a) = a :*: EmptyT +takeSuffixNR i (Two a b) + | i < sb = b :*: EmptyT + | otherwise = a :*: Single b + where + sb = size b +takeSuffixNR i (Three a b c) + | i < sc = c :*: EmptyT + | i < sbc = b :*: Single c + | otherwise = a :*: Deep sbc (One b) EmptyT (One c) + where + sc = size c + sbc = sc + size b +takeSuffixNR i (Four a b c d) + | i < sd = d :*: EmptyT + | i < scd = c :*: Single d + | i < sbcd = b :*: Deep scd (One c) EmptyT (One d) + | otherwise = a :*: Deep sbcd (Two b c) EmptyT (One d) + where + sd = size d + scd = sd + size c + sbcd = scd + size b + +takePrefixER :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> + FingerTree (Elem a) +takePrefixER !_i !s (One _) m sf = pullL (s - 1) m sf +takePrefixER i s (Two _ b) m sf + | i < 1 = pullL (s - 2) m sf + | otherwise = Deep (s - 1) (One b) m sf +takePrefixER i s (Three _ b c) m sf + | i < 1 = pullL (s - 3) m sf + | i < 2 = Deep (s - 2) (One c) m sf + | otherwise = Deep (s - 1) (Two b c) m sf +takePrefixER i s (Four _ b c d) m sf + | i < 1 = pullL (s - 4) m sf + | i < 2 = Deep (s - 3) (One d) m sf + | i < 3 = Deep (s - 2) (Two c d) m sf + | otherwise = Deep (s - 1) (Three b c d) m sf + +takePrefixNR :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> + StrictPair (Node a) (FingerTree (Node a)) +takePrefixNR !_i !s (One a) m sf = a :*: pullL (s - size a) m sf +takePrefixNR i s (Two a b) m sf + | i < sb = b :*: pullL (s - sb - size a) m sf + | otherwise = a :*: Deep (s - size a) (One b) m sf + where + sb = size b +takePrefixNR i s (Three a b c) m sf + | i < sc = c :*: pullL (s - sbc - size a) m sf + | i < sbc = b :*: Deep (s - size b - size a) (One c) m sf + | otherwise = a :*: Deep (s - size a) (Two b c) m sf + where + sc = size c + sbc = sc + size b +takePrefixNR i s (Four a b c d) m sf + | i < sd = d :*: pullL (s - sd - sabc) m sf + | i < scd = c :*: Deep (s - sabc) (One d) m sf + | i < sbcd = b :*: Deep (s - sab) (Two c d) m sf + | otherwise = a :*: Deep (s - sa) (Three b c d) m sf + where + sa = size a + sab = sa + size b + sabc = sab + size c + sd = size d + scd = size c + sd + sbcd = size b + scd + +-- | /O(log(min(i,n-i)))/. Split a sequence at a given position. +-- @'splitAt' i s = ('take' i s, 'drop' i s)@. +splitAt :: Int -> Seq a -> (Seq a, Seq a) +splitAt i xs@(Seq t) + -- We use an unsigned comparison to make the common case + -- faster. This only works because our representation of + -- sizes as (signed) Ints gives us a free high bit to play + -- with. Note also that there's no sharing to lose in the + -- case that the length is 0. + | fromIntegral i - 1 < (fromIntegral (length xs) - 1 :: Word) = + case splitTreeE i t of + l :*: r -> (Seq l, Seq r) + | i <= 0 = (empty, xs) + | otherwise = (xs, empty) + +-- | /O(log(min(i,n-i))) A version of 'splitAt' that does not attempt to +-- enhance sharing when the split point is less than or equal to 0, and that +-- gives completely wrong answers when the split point is at least the length +-- of the sequence, unless the sequence is a singleton. This is used to +-- implement zipWith and chunksOf, which are extremely sensitive to the cost of +-- splitting very short sequences. There is just enough of a speed increase to +-- make this worth the trouble. +uncheckedSplitAt :: Int -> Seq a -> (Seq a, Seq a) +uncheckedSplitAt i (Seq xs) = case splitTreeE i xs of + l :*: r -> (Seq l, Seq r) + +data Split a = Split !(FingerTree (Node a)) !(Node a) !(FingerTree (Node a)) +#ifdef TESTING + deriving Show +#endif + +splitTreeE :: Int -> FingerTree (Elem a) -> StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) +splitTreeE !_i EmptyT = EmptyT :*: EmptyT +splitTreeE i t@(Single _) + | i <= 0 = EmptyT :*: t + | otherwise = t :*: EmptyT +splitTreeE i (Deep s pr m sf) + | i < spr = splitPrefixE i s pr m sf + | i < spm = case splitTreeN im m of + Split ml xs mr -> splitMiddleE (im - size ml) s spr pr ml xs mr sf + | otherwise = splitSuffixE (i - spm) s pr m sf + where + spr = size pr + spm = spr + size m + im = i - spr + +splitTreeN :: Int -> FingerTree (Node a) -> Split a +splitTreeN !_i EmptyT = error "splitTreeN of empty tree" +splitTreeN _i (Single x) = Split EmptyT x EmptyT +splitTreeN i (Deep s pr m sf) + | i < spr = splitPrefixN i s pr m sf + | i < spm = case splitTreeN im m of + Split ml xs mr -> splitMiddleN (im - size ml) s spr pr ml xs mr sf + | otherwise = splitSuffixN (i - spm) s pr m sf where + spr = size pr + spm = spr + size m + im = i - spr + +splitMiddleN :: Int -> Int -> Int + -> Digit (Node a) -> FingerTree (Node (Node a)) -> Node (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) + -> Split a +splitMiddleN i s spr pr ml (Node2 _ a b) mr sf + | i < sa = Split (pullR sprml pr ml) a (Deep (s - sprmla) (One b) mr sf) + | otherwise = Split (Deep sprmla pr ml (One a)) b (pullL (s - sprmla - size b) mr sf) + where + sa = size a + sprml = spr + size ml + sprmla = sa + sprml +splitMiddleN i s spr pr ml (Node3 _ a b c) mr sf + | i < sa = Split (pullR sprml pr ml) a (Deep (s - sprmla) (Two b c) mr sf) + | i < sab = Split (Deep sprmla pr ml (One a)) b (Deep (s - sprmlab) (One c) mr sf) + | otherwise = Split (Deep sprmlab pr ml (Two a b)) c (pullL (s - sprmlab - size c) mr sf) + where + sa = size a + sab = sa + size b + sprml = spr + size ml + sprmla = sa + sprml + sprmlab = sprmla + size b + +splitMiddleE :: Int -> Int -> Int + -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Node (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) + -> StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) +splitMiddleE i s spr pr ml (Node2 _ a b) mr sf + | i < 1 = pullR sprml pr ml :*: Deep (s - sprml) (Two a b) mr sf + | otherwise = Deep sprmla pr ml (One a) :*: Deep (s - sprmla) (One b) mr sf + where + sprml = spr + size ml + sprmla = 1 + sprml +splitMiddleE i s spr pr ml (Node3 _ a b c) mr sf = case i of + 0 -> pullR sprml pr ml :*: Deep (s - sprml) (Three a b c) mr sf + 1 -> Deep sprmla pr ml (One a) :*: Deep (s - sprmla) (Two b c) mr sf + _ -> Deep sprmlab pr ml (Two a b) :*: Deep (s - sprmlab) (One c) mr sf + where + sprml = spr + size ml + sprmla = 1 + sprml + sprmlab = sprmla + 1 + +splitPrefixE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> + StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) +splitPrefixE !_i !s (One a) m sf = EmptyT :*: Deep s (One a) m sf +splitPrefixE i s (Two a b) m sf = case i of + 0 -> EmptyT :*: Deep s (Two a b) m sf + _ -> Single a :*: Deep (s - 1) (One b) m sf +splitPrefixE i s (Three a b c) m sf = case i of + 0 -> EmptyT :*: Deep s (Three a b c) m sf + 1 -> Single a :*: Deep (s - 1) (Two b c) m sf + _ -> Deep 2 (One a) EmptyT (One b) :*: Deep (s - 2) (One c) m sf +splitPrefixE i s (Four a b c d) m sf = case i of + 0 -> EmptyT :*: Deep s (Four a b c d) m sf + 1 -> Single a :*: Deep (s - 1) (Three b c d) m sf + 2 -> Deep 2 (One a) EmptyT (One b) :*: Deep (s - 2) (Two c d) m sf + _ -> Deep 3 (Two a b) EmptyT (One c) :*: Deep (s - 3) (One d) m sf + +splitPrefixN :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> + Split a +splitPrefixN !_i !s (One a) m sf = Split EmptyT a (pullL (s - size a) m sf) +splitPrefixN i s (Two a b) m sf + | i < sa = Split EmptyT a (Deep (s - sa) (One b) m sf) + | otherwise = Split (Single a) b (pullL (s - sa - size b) m sf) + where + sa = size a +splitPrefixN i s (Three a b c) m sf + | i < sa = Split EmptyT a (Deep (s - sa) (Two b c) m sf) + | i < sab = Split (Single a) b (Deep (s - sab) (One c) m sf) + | otherwise = Split (Deep sab (One a) EmptyT (One b)) c (pullL (s - sab - size c) m sf) + where + sa = size a + sab = sa + size b +splitPrefixN i s (Four a b c d) m sf + | i < sa = Split EmptyT a $ Deep (s - sa) (Three b c d) m sf + | i < sab = Split (Single a) b $ Deep (s - sab) (Two c d) m sf + | i < sabc = Split (Deep sab (One a) EmptyT (One b)) c $ Deep (s - sabc) (One d) m sf + | otherwise = Split (Deep sabc (Two a b) EmptyT (One c)) d $ pullL (s - sabc - size d) m sf + where + sa = size a + sab = sa + size b + sabc = sab + size c + +splitSuffixE :: Int -> Int -> Digit (Elem a) -> FingerTree (Node (Elem a)) -> Digit (Elem a) -> + StrictPair (FingerTree (Elem a)) (FingerTree (Elem a)) +splitSuffixE !_i !s pr m (One a) = pullR (s - 1) pr m :*: Single a +splitSuffixE i s pr m (Two a b) = case i of + 0 -> pullR (s - 2) pr m :*: Deep 2 (One a) EmptyT (One b) + _ -> Deep (s - 1) pr m (One a) :*: Single b +splitSuffixE i s pr m (Three a b c) = case i of + 0 -> pullR (s - 3) pr m :*: Deep 3 (Two a b) EmptyT (One c) + 1 -> Deep (s - 2) pr m (One a) :*: Deep 2 (One b) EmptyT (One c) + _ -> Deep (s - 1) pr m (Two a b) :*: Single c +splitSuffixE i s pr m (Four a b c d) = case i of + 0 -> pullR (s - 4) pr m :*: Deep 4 (Two a b) EmptyT (Two c d) + 1 -> Deep (s - 3) pr m (One a) :*: Deep 3 (Two b c) EmptyT (One d) + 2 -> Deep (s - 2) pr m (Two a b) :*: Deep 2 (One c) EmptyT (One d) + _ -> Deep (s - 1) pr m (Three a b c) :*: Single d + +splitSuffixN :: Int -> Int -> Digit (Node a) -> FingerTree (Node (Node a)) -> Digit (Node a) -> + Split a +splitSuffixN !_i !s pr m (One a) = Split (pullR (s - size a) pr m) a EmptyT +splitSuffixN i s pr m (Two a b) + | i < sa = Split (pullR (s - sa - size b) pr m) a (Single b) + | otherwise = Split (Deep (s - size b) pr m (One a)) b EmptyT + where + sa = size a +splitSuffixN i s pr m (Three a b c) + | i < sa = Split (pullR (s - sab - size c) pr m) a (deep (One b) EmptyT (One c)) + | i < sab = Split (Deep (s - size b - size c) pr m (One a)) b (Single c) + | otherwise = Split (Deep (s - size c) pr m (Two a b)) c EmptyT + where + sa = size a + sab = sa + size b +splitSuffixN i s pr m (Four a b c d) + | i < sa = Split (pullR (s - sa - sbcd) pr m) a (Deep sbcd (Two b c) EmptyT (One d)) + | i < sab = Split (Deep (s - sbcd) pr m (One a)) b (Deep scd (One c) EmptyT (One d)) + | i < sabc = Split (Deep (s - scd) pr m (Two a b)) c (Single d) + | otherwise = Split (Deep (s - sd) pr m (Three a b c)) d EmptyT + where + sa = size a + sab = sa + size b + sabc = sab + size c + sd = size d + scd = size c + sd + sbcd = size b + scd + +-- | /O(n)/. @chunksOf n xs@ splits @xs@ into chunks of size @n>0@. +-- If @n@ does not divide the length of @xs@ evenly, then the last element +-- of the result will be short. +chunksOf :: Int -> Seq a -> Seq (Seq a) +chunksOf n xs | n <= 0 = + if null xs + then empty + else error "chunksOf: A non-empty sequence can only be broken up into positively-sized chunks." +chunksOf 1 s = fmap singleton s +chunksOf n s = splitMap (uncheckedSplitAt . (*n)) const most (replicate numReps ()) + >< if null end then empty else singleton end + where + (numReps, endLength) = length s `quotRem` n + (most, end) = splitAt (length s - endLength) s + +-- | /O(n)/. Returns a sequence of all suffixes of this sequence, +-- longest first. For example, +-- +-- > tails (fromList "abc") = fromList [fromList "abc", fromList "bc", fromList "c", fromList ""] +-- +-- Evaluating the /i/th suffix takes /O(log(min(i, n-i)))/, but evaluating +-- every suffix in the sequence takes /O(n)/ due to sharing. +tails :: Seq a -> Seq (Seq a) +tails (Seq xs) = Seq (tailsTree (Elem . Seq) xs) |> empty + +-- | /O(n)/. Returns a sequence of all prefixes of this sequence, +-- shortest first. For example, +-- +-- > inits (fromList "abc") = fromList [fromList "", fromList "a", fromList "ab", fromList "abc"] +-- +-- Evaluating the /i/th prefix takes /O(log(min(i, n-i)))/, but evaluating +-- every prefix in the sequence takes /O(n)/ due to sharing. +inits :: Seq a -> Seq (Seq a) +inits (Seq xs) = empty <| Seq (initsTree (Elem . Seq) xs) + +-- This implementation of tails (and, analogously, inits) has the +-- following algorithmic advantages: +-- Evaluating each tail in the sequence takes linear total time, +-- which is better than we could say for +-- @fromList [drop n xs | n <- [0..length xs]]@. +-- Evaluating any individual tail takes logarithmic time, which is +-- better than we can say for either +-- @scanr (<|) empty xs@ or @iterateN (length xs + 1) (\ xs -> let _ :< xs' = viewl xs in xs') xs@. +-- +-- Moreover, if we actually look at every tail in the sequence, the +-- following benchmarks demonstrate that this implementation is modestly +-- faster than any of the above: +-- +-- Times (ms) +-- min mean +/-sd median max +-- Seq.tails: 21.986 24.961 10.169 22.417 86.485 +-- scanr: 85.392 87.942 2.488 87.425 100.217 +-- iterateN: 29.952 31.245 1.574 30.412 37.268 +-- +-- The algorithm for tails (and, analogously, inits) is as follows: +-- +-- A Node in the FingerTree of tails is constructed by evaluating the +-- corresponding tail of the FingerTree of Nodes, considering the first +-- Node in this tail, and constructing a Node in which each tail of this +-- Node is made to be the prefix of the remaining tree. This ends up +-- working quite elegantly, as the remainder of the tail of the FingerTree +-- of Nodes becomes the middle of a new tail, the suffix of the Node is +-- the prefix, and the suffix of the original tree is retained. +-- +-- In particular, evaluating the /i/th tail involves making as +-- many partial evaluations as the Node depth of the /i/th element. +-- In addition, when we evaluate the /i/th tail, and we also evaluate +-- the /j/th tail, and /m/ Nodes are on the path to both /i/ and /j/, +-- each of those /m/ evaluations are shared between the computation of +-- the /i/th and /j/th tails. +-- +-- wasserman.louis@gmail.com, 7/16/09 + +tailsDigit :: Digit a -> Digit (Digit a) +tailsDigit (One a) = One (One a) +tailsDigit (Two a b) = Two (Two a b) (One b) +tailsDigit (Three a b c) = Three (Three a b c) (Two b c) (One c) +tailsDigit (Four a b c d) = Four (Four a b c d) (Three b c d) (Two c d) (One d) + +initsDigit :: Digit a -> Digit (Digit a) +initsDigit (One a) = One (One a) +initsDigit (Two a b) = Two (One a) (Two a b) +initsDigit (Three a b c) = Three (One a) (Two a b) (Three a b c) +initsDigit (Four a b c d) = Four (One a) (Two a b) (Three a b c) (Four a b c d) + +tailsNode :: Node a -> Node (Digit a) +tailsNode (Node2 s a b) = Node2 s (Two a b) (One b) +tailsNode (Node3 s a b c) = Node3 s (Three a b c) (Two b c) (One c) + +initsNode :: Node a -> Node (Digit a) +initsNode (Node2 s a b) = Node2 s (One a) (Two a b) +initsNode (Node3 s a b c) = Node3 s (One a) (Two a b) (Three a b c) + +{-# SPECIALIZE tailsTree :: (FingerTree (Elem a) -> Elem b) -> FingerTree (Elem a) -> FingerTree (Elem b) #-} +{-# SPECIALIZE tailsTree :: (FingerTree (Node a) -> Node b) -> FingerTree (Node a) -> FingerTree (Node b) #-} +-- | Given a function to apply to tails of a tree, applies that function +-- to every tail of the specified tree. +tailsTree :: Sized a => (FingerTree a -> b) -> FingerTree a -> FingerTree b +tailsTree _ EmptyT = EmptyT +tailsTree f (Single x) = Single (f (Single x)) +tailsTree f (Deep n pr m sf) = + Deep n (fmap (\ pr' -> f (deep pr' m sf)) (tailsDigit pr)) + (tailsTree f' m) + (fmap (f . digitToTree) (tailsDigit sf)) + where + f' ms = let ConsLTree node m' = viewLTree ms in + fmap (\ pr' -> f (deep pr' m' sf)) (tailsNode node) + +{-# SPECIALIZE initsTree :: (FingerTree (Elem a) -> Elem b) -> FingerTree (Elem a) -> FingerTree (Elem b) #-} +{-# SPECIALIZE initsTree :: (FingerTree (Node a) -> Node b) -> FingerTree (Node a) -> FingerTree (Node b) #-} +-- | Given a function to apply to inits of a tree, applies that function +-- to every init of the specified tree. +initsTree :: Sized a => (FingerTree a -> b) -> FingerTree a -> FingerTree b +initsTree _ EmptyT = EmptyT +initsTree f (Single x) = Single (f (Single x)) +initsTree f (Deep n pr m sf) = + Deep n (fmap (f . digitToTree) (initsDigit pr)) + (initsTree f' m) + (fmap (f . deep pr m) (initsDigit sf)) + where + f' ms = let SnocRTree m' node = viewRTree ms in + fmap (\ sf' -> f (deep pr m' sf')) (initsNode node) + +{-# INLINE foldlWithIndex #-} +-- | 'foldlWithIndex' is a version of 'foldl' that also provides access +-- to the index of each element. +foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b +foldlWithIndex f z xs = foldl (\ g x !i -> f (g (i - 1)) i x) (const z) xs (length xs - 1) + +{-# INLINE foldrWithIndex #-} +-- | 'foldrWithIndex' is a version of 'foldr' that also provides access +-- to the index of each element. +foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b +foldrWithIndex f z xs = foldr (\ x g !i -> f i x (g (i+1))) (const z) xs 0 + +{-# INLINE listToMaybe' #-} +-- 'listToMaybe\'' is a good consumer version of 'listToMaybe'. +listToMaybe' :: [a] -> Maybe a +listToMaybe' = foldr (\ x _ -> Just x) Nothing + +-- | /O(i)/ where /i/ is the prefix length. 'takeWhileL', applied +-- to a predicate @p@ and a sequence @xs@, returns the longest prefix +-- (possibly empty) of @xs@ of elements that satisfy @p@. +takeWhileL :: (a -> Bool) -> Seq a -> Seq a +takeWhileL p = fst . spanl p + +-- | /O(i)/ where /i/ is the suffix length. 'takeWhileR', applied +-- to a predicate @p@ and a sequence @xs@, returns the longest suffix +-- (possibly empty) of @xs@ of elements that satisfy @p@. +-- +-- @'takeWhileR' p xs@ is equivalent to @'reverse' ('takeWhileL' p ('reverse' xs))@. +takeWhileR :: (a -> Bool) -> Seq a -> Seq a +takeWhileR p = fst . spanr p + +-- | /O(i)/ where /i/ is the prefix length. @'dropWhileL' p xs@ returns +-- the suffix remaining after @'takeWhileL' p xs@. +dropWhileL :: (a -> Bool) -> Seq a -> Seq a +dropWhileL p = snd . spanl p + +-- | /O(i)/ where /i/ is the suffix length. @'dropWhileR' p xs@ returns +-- the prefix remaining after @'takeWhileR' p xs@. +-- +-- @'dropWhileR' p xs@ is equivalent to @'reverse' ('dropWhileL' p ('reverse' xs))@. +dropWhileR :: (a -> Bool) -> Seq a -> Seq a +dropWhileR p = snd . spanr p + +-- | /O(i)/ where /i/ is the prefix length. 'spanl', applied to +-- a predicate @p@ and a sequence @xs@, returns a pair whose first +-- element is the longest prefix (possibly empty) of @xs@ of elements that +-- satisfy @p@ and the second element is the remainder of the sequence. +spanl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) +spanl p = breakl (not . p) + +-- | /O(i)/ where /i/ is the suffix length. 'spanr', applied to a +-- predicate @p@ and a sequence @xs@, returns a pair whose /first/ element +-- is the longest /suffix/ (possibly empty) of @xs@ of elements that +-- satisfy @p@ and the second element is the remainder of the sequence. +spanr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) +spanr p = breakr (not . p) + +{-# INLINE breakl #-} +-- | /O(i)/ where /i/ is the breakpoint index. 'breakl', applied to a +-- predicate @p@ and a sequence @xs@, returns a pair whose first element +-- is the longest prefix (possibly empty) of @xs@ of elements that +-- /do not satisfy/ @p@ and the second element is the remainder of +-- the sequence. +-- +-- @'breakl' p@ is equivalent to @'spanl' (not . p)@. +breakl :: (a -> Bool) -> Seq a -> (Seq a, Seq a) +breakl p xs = foldr (\ i _ -> splitAt i xs) (xs, empty) (findIndicesL p xs) + +{-# INLINE breakr #-} +-- | @'breakr' p@ is equivalent to @'spanr' (not . p)@. +breakr :: (a -> Bool) -> Seq a -> (Seq a, Seq a) +breakr p xs = foldr (\ i _ -> flipPair (splitAt (i + 1) xs)) (xs, empty) (findIndicesR p xs) + where flipPair (x, y) = (y, x) + +-- | /O(n)/. The 'partition' function takes a predicate @p@ and a +-- sequence @xs@ and returns sequences of those elements which do and +-- do not satisfy the predicate. +partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a) +partition p = toPair . foldl' part (empty :*: empty) + where + part (xs :*: ys) x + | p x = (xs `snoc'` x) :*: ys + | otherwise = xs :*: (ys `snoc'` x) + +-- | /O(n)/. The 'filter' function takes a predicate @p@ and a sequence +-- @xs@ and returns a sequence of those elements which satisfy the +-- predicate. +filter :: (a -> Bool) -> Seq a -> Seq a +filter p = foldl' (\ xs x -> if p x then xs `snoc'` x else xs) empty + +-- Indexing sequences + +-- | 'elemIndexL' finds the leftmost index of the specified element, +-- if it is present, and otherwise 'Nothing'. +elemIndexL :: Eq a => a -> Seq a -> Maybe Int +elemIndexL x = findIndexL (x ==) + +-- | 'elemIndexR' finds the rightmost index of the specified element, +-- if it is present, and otherwise 'Nothing'. +elemIndexR :: Eq a => a -> Seq a -> Maybe Int +elemIndexR x = findIndexR (x ==) + +-- | 'elemIndicesL' finds the indices of the specified element, from +-- left to right (i.e. in ascending order). +elemIndicesL :: Eq a => a -> Seq a -> [Int] +elemIndicesL x = findIndicesL (x ==) + +-- | 'elemIndicesR' finds the indices of the specified element, from +-- right to left (i.e. in descending order). +elemIndicesR :: Eq a => a -> Seq a -> [Int] +elemIndicesR x = findIndicesR (x ==) + +-- | @'findIndexL' p xs@ finds the index of the leftmost element that +-- satisfies @p@, if any exist. +findIndexL :: (a -> Bool) -> Seq a -> Maybe Int +findIndexL p = listToMaybe' . findIndicesL p + +-- | @'findIndexR' p xs@ finds the index of the rightmost element that +-- satisfies @p@, if any exist. +findIndexR :: (a -> Bool) -> Seq a -> Maybe Int +findIndexR p = listToMaybe' . findIndicesR p + +{-# INLINE findIndicesL #-} +-- | @'findIndicesL' p@ finds all indices of elements that satisfy @p@, +-- in ascending order. +findIndicesL :: (a -> Bool) -> Seq a -> [Int] +#if __GLASGOW_HASKELL__ +findIndicesL p xs = build (\ c n -> let g i x z = if p x then c i z else z in + foldrWithIndex g n xs) +#else +findIndicesL p xs = foldrWithIndex g [] xs + where g i x is = if p x then i:is else is +#endif + +{-# INLINE findIndicesR #-} +-- | @'findIndicesR' p@ finds all indices of elements that satisfy @p@, +-- in descending order. +findIndicesR :: (a -> Bool) -> Seq a -> [Int] +#if __GLASGOW_HASKELL__ +findIndicesR p xs = build (\ c n -> + let g z i x = if p x then c i z else z in foldlWithIndex g n xs) +#else +findIndicesR p xs = foldlWithIndex g [] xs + where g is i x = if p x then i:is else is +#endif + +------------------------------------------------------------------------ +-- Lists +------------------------------------------------------------------------ + +-- The implementation below is based on an idea by Ross Paterson and +-- implemented by Lennart Spitzner. It avoids the rebuilding the original +-- (|>)-based implementation suffered from. It also avoids the excessive pair +-- allocations Paterson's implementation suffered from. +-- +-- David Feuer suggested building in nine-element chunks, which reduces +-- intermediate conses from around (1/2)*n to around (1/8)*n with a concomitant +-- improvement in benchmark constant factors. In fact, it should be even +-- better to work in chunks of 27 `Elem`s and chunks of three `Node`s, rather +-- than nine of each, but it seems hard to avoid a code explosion with +-- such large chunks. +-- +-- Paterson's code can be seen, for example, in +-- https://github.com/haskell/containers/blob/74034b3244fa4817c7bef1202e639b887a975d9e/Data/Sequence.hs#L3532 +-- +-- Given a list +-- +-- [1..302] +-- +-- the original code forms Three 1 2 3 | [node3 4 5 6, node3 7 8 9, node3 10 11 +-- 12, ...] | Two 301 302 +-- +-- Then it recurses on the middle list. The middle lists become successively +-- shorter as their elements become successively deeper nodes. +-- +-- The original implementation of the list shortener, getNodes, included the +-- recursive step + +-- getNodes s x1 (x2:x3:x4:xs) = (Node3 s x1 x2 x3:ns, d) +-- where (ns, d) = getNodes s x4 xs + +-- This allocates a cons and a lazy pair at each 3-element step. It relies on +-- the Haskell implementation using Wadler's technique, described in "Fixing +-- some space leaks with a garbage collector" +-- http://homepages.inf.ed.ac.uk/wadler/papers/leak/leak.ps.gz, to repeatedly +-- simplify the `d` thunk. Although GHC uses this GC trick, heap profiling at +-- least appears to indicate that the pair constructors and conses build up +-- with this implementation. +-- +-- Spitzner's implementation uses a similar approach, but replaces the middle +-- list, in each level, with a customized stream type that finishes off with +-- the final digit in that level and (since it works in nines) in the one +-- above. To work around the nested tree structure, the overall computation is +-- structured using continuation-passing style, with a function that, at the +-- bottom of the tree, deals with a stream that terminates in a nested-pair +-- representation of the entire right side of the tree. Perhaps someone will +-- eventually find a less mind-bending way to accomplish this. + +-- | /O(n)/. Create a sequence from a finite list of elements. +-- There is a function 'toList' in the opposite direction for all +-- instances of the 'Foldable' class, including 'Seq'. +fromList :: [a] -> Seq a +-- Note: we can avoid map_elem if we wish by scattering +-- Elem applications throughout mkTreeE and getNodesE, but +-- it gets a bit hard to read. +fromList = Seq . mkTree . map_elem + where +#ifdef __GLASGOW_HASKELL__ + mkTree :: forall a' . [Elem a'] -> FingerTree (Elem a') +#else + mkTree :: [Elem a] -> FingerTree (Elem a) +#endif + mkTree [] = EmptyT + mkTree [x1] = Single x1 + mkTree [x1, x2] = Deep 2 (One x1) EmptyT (One x2) + mkTree [x1, x2, x3] = Deep 3 (Two x1 x2) EmptyT (One x3) + mkTree [x1, x2, x3, x4] = Deep 4 (Two x1 x2) EmptyT (Two x3 x4) + mkTree [x1, x2, x3, x4, x5] = Deep 5 (Three x1 x2 x3) EmptyT (Two x4 x5) + mkTree [x1, x2, x3, x4, x5, x6] = + Deep 6 (Three x1 x2 x3) EmptyT (Three x4 x5 x6) + mkTree [x1, x2, x3, x4, x5, x6, x7] = + Deep 7 (Two x1 x2) (Single (Node3 3 x3 x4 x5)) (Two x6 x7) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8] = + Deep 8 (Three x1 x2 x3) (Single (Node3 3 x4 x5 x6)) (Two x7 x8) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9] = + Deep 9 (Three x1 x2 x3) (Single (Node3 3 x4 x5 x6)) (Three x7 x8 x9) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, y0, y1] = + Deep 10 (Two x1 x2) + (Deep 6 (One (Node3 3 x3 x4 x5)) EmptyT (One (Node3 3 x6 x7 x8))) + (Two y0 y1) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1] = + Deep 11 (Three x1 x2 x3) + (Deep 6 (One (Node3 3 x4 x5 x6)) EmptyT (One (Node3 3 x7 x8 x9))) + (Two y0 y1) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2] = + Deep 12 (Three x1 x2 x3) + (Deep 6 (One (Node3 3 x4 x5 x6)) EmptyT (One (Node3 3 x7 x8 x9))) + (Three y0 y1 y2) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, y0, y1, y2, y3, y4] = + Deep 13 (Two x1 x2) + (Deep 9 (Two (Node3 3 x3 x4 x5) (Node3 3 x6 x7 x8)) EmptyT (One (Node3 3 y0 y1 y2))) + (Two y3 y4) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2, y3, y4] = + Deep 14 (Three x1 x2 x3) + (Deep 9 (Two (Node3 3 x4 x5 x6) (Node3 3 x7 x8 x9)) EmptyT (One (Node3 3 y0 y1 y2))) + (Two y3 y4) + mkTree [x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2, y3, y4, y5] = + Deep 15 (Three x1 x2 x3) + (Deep 9 (Two (Node3 3 x4 x5 x6) (Node3 3 x7 x8 x9)) EmptyT (One (Node3 3 y0 y1 y2))) + (Three y3 y4 y5) + mkTree (x1:x2:x3:x4:x5:x6:x7:x8:x9:y0:y1:y2:y3:y4:y5:y6:xs) = + mkTreeC cont 9 (getNodes 3 (Node3 3 y3 y4 y5) y6 xs) + where + d2 = Three x1 x2 x3 + d1 = Three (Node3 3 x4 x5 x6) (Node3 3 x7 x8 x9) (Node3 3 y0 y1 y2) +#ifdef __GLASGOW_HASKELL__ + cont :: (Digit (Node (Elem a')), Digit (Elem a')) -> FingerTree (Node (Node (Elem a'))) -> FingerTree (Elem a') +#endif + cont (!r1, !r2) !sub = + let !sub1 = Deep (9 + size r1 + size sub) d1 sub r1 + in Deep (3 + size r2 + size sub1) d2 sub1 r2 + + getNodes :: forall a . Int + -> Node a + -> a + -> [a] + -> ListFinal (Node (Node a)) (Digit (Node a), Digit a) + getNodes !_ n1 x1 [] = LFinal (One n1, One x1) + getNodes _ n1 x1 [x2] = LFinal (One n1, Two x1 x2) + getNodes _ n1 x1 [x2, x3] = LFinal (One n1, Three x1 x2 x3) + getNodes s n1 x1 [x2, x3, x4] = LFinal (Two n1 (Node3 s x1 x2 x3), One x4) + getNodes s n1 x1 [x2, x3, x4, x5] = LFinal (Two n1 (Node3 s x1 x2 x3), Two x4 x5) + getNodes s n1 x1 [x2, x3, x4, x5, x6] = LFinal (Two n1 (Node3 s x1 x2 x3), Three x4 x5 x6) + getNodes s n1 x1 [x2, x3, x4, x5, x6, x7] = LFinal (Three n1 (Node3 s x1 x2 x3) (Node3 s x4 x5 x6), One x7) + getNodes s n1 x1 [x2, x3, x4, x5, x6, x7, x8] = LFinal (Three n1 (Node3 s x1 x2 x3) (Node3 s x4 x5 x6), Two x7 x8) + getNodes s n1 x1 [x2, x3, x4, x5, x6, x7, x8, x9] = LFinal (Three n1 (Node3 s x1 x2 x3) (Node3 s x4 x5 x6), Three x7 x8 x9) + getNodes s n1 x1 (x2:x3:x4:x5:x6:x7:x8:x9:x10:xs) = LCons n10 (getNodes s (Node3 s x7 x8 x9) x10 xs) + where !n2 = Node3 s x1 x2 x3 + !n3 = Node3 s x4 x5 x6 + !n10 = Node3 (3*s) n1 n2 n3 + + mkTreeC :: +#ifdef __GLASGOW_HASKELL__ + forall a b c . +#endif + (b -> FingerTree (Node a) -> c) + -> Int + -> ListFinal (Node a) b + -> c + mkTreeC cont !_ (LFinal b) = + cont b EmptyT + mkTreeC cont _ (LCons x1 (LFinal b)) = + cont b (Single x1) + mkTreeC cont s (LCons x1 (LCons x2 (LFinal b))) = + cont b (Deep (2*s) (One x1) EmptyT (One x2)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LFinal b)))) = + cont b (Deep (3*s) (Two x1 x2) EmptyT (One x3)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LFinal b))))) = + cont b (Deep (4*s) (Two x1 x2) EmptyT (Two x3 x4)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LFinal b)))))) = + cont b (Deep (5*s) (Three x1 x2 x3) EmptyT (Two x4 x5)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LFinal b))))))) = + cont b (Deep (6*s) (Three x1 x2 x3) EmptyT (Three x4 x5 x6)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LFinal b)))))))) = + cont b (Deep (7*s) (Two x1 x2) (Single (Node3 (3*s) x3 x4 x5)) (Two x6 x7)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LFinal b))))))))) = + cont b (Deep (8*s) (Three x1 x2 x3) (Single (Node3 (3*s) x4 x5 x6)) (Two x7 x8)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LFinal b)))))))))) = + cont b (Deep (9*s) (Three x1 x2 x3) (Single (Node3 (3*s) x4 x5 x6)) (Three x7 x8 x9)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons y0 (LCons y1 (LFinal b))))))))))) = + cont b (Deep (10*s) (Two x1 x2) (Deep (6*s) (One (Node3 (3*s) x3 x4 x5)) EmptyT (One (Node3 (3*s) x6 x7 x8))) (Two y0 y1)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LFinal b)))))))))))) = + cont b (Deep (11*s) (Three x1 x2 x3) (Deep (6*s) (One (Node3 (3*s) x4 x5 x6)) EmptyT (One (Node3 (3*s) x7 x8 x9))) (Two y0 y1)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LFinal b))))))))))))) = + cont b (Deep (12*s) (Three x1 x2 x3) (Deep (6*s) (One (Node3 (3*s) x4 x5 x6)) EmptyT (One (Node3 (3*s) x7 x8 x9))) (Three y0 y1 y2)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LFinal b)))))))))))))) = + cont b (Deep (13*s) (Two x1 x2) (Deep (9*s) (Two (Node3 (3*s) x3 x4 x5) (Node3 (3*s) x6 x7 x8)) EmptyT (One (Node3 (3*s) y0 y1 y2))) (Two y3 y4)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LFinal b))))))))))))))) = + cont b (Deep (14*s) (Three x1 x2 x3) (Deep (9*s) (Two (Node3 (3*s) x4 x5 x6) (Node3 (3*s) x7 x8 x9)) EmptyT (One (Node3 (3*s) y0 y1 y2))) (Two y3 y4)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LCons y5 (LFinal b)))))))))))))))) = + cont b (Deep (15*s) (Three x1 x2 x3) (Deep (9*s) (Two (Node3 (3*s) x4 x5 x6) (Node3 (3*s) x7 x8 x9)) EmptyT (One (Node3 (3*s) y0 y1 y2))) (Three y3 y4 y5)) + mkTreeC cont s (LCons x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons y0 (LCons y1 (LCons y2 (LCons y3 (LCons y4 (LCons y5 (LCons y6 xs)))))))))))))))) = + mkTreeC cont2 (9*s) (getNodesC (3*s) (Node3 (3*s) y3 y4 y5) y6 xs) + where +#ifdef __GLASGOW_HASKELL__ + cont2 :: (b, Digit (Node (Node a)), Digit (Node a)) -> FingerTree (Node (Node (Node a))) -> c +#endif + cont2 (b, r1, r2) !sub = + let d2 = Three x1 x2 x3 + d1 = Three (Node3 (3*s) x4 x5 x6) (Node3 (3*s) x7 x8 x9) (Node3 (3*s) y0 y1 y2) + !sub1 = Deep (9*s + size r1 + size sub) d1 sub r1 + in cont b $! Deep (3*s + size r2 + size sub1) d2 sub1 r2 + + getNodesC :: Int + -> Node a + -> a + -> ListFinal a b + -> ListFinal (Node (Node a)) (b, Digit (Node a), Digit a) + getNodesC !_ n1 x1 (LFinal b) = LFinal $ (b, One n1, One x1) + getNodesC _ n1 x1 (LCons x2 (LFinal b)) = LFinal $ (b, One n1, Two x1 x2) + getNodesC _ n1 x1 (LCons x2 (LCons x3 (LFinal b))) = LFinal $ (b, One n1, Three x1 x2 x3) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LFinal b)))) = + let !n2 = Node3 s x1 x2 x3 + in LFinal $ (b, Two n1 n2, One x4) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LFinal b))))) = + let !n2 = Node3 s x1 x2 x3 + in LFinal $ (b, Two n1 n2, Two x4 x5) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LFinal b)))))) = + let !n2 = Node3 s x1 x2 x3 + in LFinal $ (b, Two n1 n2, Three x4 x5 x6) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LFinal b))))))) = + let !n2 = Node3 s x1 x2 x3 + !n3 = Node3 s x4 x5 x6 + in LFinal $ (b, Three n1 n2 n3, One x7) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LFinal b)))))))) = + let !n2 = Node3 s x1 x2 x3 + !n3 = Node3 s x4 x5 x6 + in LFinal $ (b, Three n1 n2 n3, Two x7 x8) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LFinal b))))))))) = + let !n2 = Node3 s x1 x2 x3 + !n3 = Node3 s x4 x5 x6 + in LFinal $ (b, Three n1 n2 n3, Three x7 x8 x9) + getNodesC s n1 x1 (LCons x2 (LCons x3 (LCons x4 (LCons x5 (LCons x6 (LCons x7 (LCons x8 (LCons x9 (LCons x10 xs))))))))) = + LCons n10 $ getNodesC s (Node3 s x7 x8 x9) x10 xs + where !n2 = Node3 s x1 x2 x3 + !n3 = Node3 s x4 x5 x6 + !n10 = Node3 (3*s) n1 n2 n3 + + map_elem :: [a] -> [Elem a] +#if __GLASGOW_HASKELL__ >= 708 + map_elem xs = coerce xs +#else + map_elem xs = Data.List.map Elem xs +#endif + {-# INLINE map_elem #-} + +-- essentially: Free ((,) a) b. +data ListFinal a cont = LFinal !cont | LCons !a (ListFinal a cont) + +#if __GLASGOW_HASKELL__ >= 708 +instance GHC.Exts.IsList (Seq a) where + type Item (Seq a) = a + fromList = fromList + fromListN = fromList2 + toList = toList +#endif + +#ifdef __GLASGOW_HASKELL__ +instance IsString (Seq Char) where + fromString = fromList +#endif + +------------------------------------------------------------------------ +-- Reverse +------------------------------------------------------------------------ + +-- | /O(n)/. The reverse of a sequence. +reverse :: Seq a -> Seq a +reverse (Seq xs) = Seq (fmapReverseTree id xs) + +#ifdef __GLASGOW_HASKELL__ +{-# NOINLINE [1] reverse #-} + +-- | /O(n)/. Reverse a sequence while mapping over it. This is not +-- currently exported, but is used in rewrite rules. +fmapReverse :: (a -> b) -> Seq a -> Seq b +fmapReverse f (Seq xs) = Seq (fmapReverseTree (lift_elem f) xs) + where + lift_elem :: (a -> b) -> (Elem a -> Elem b) +#if __GLASGOW_HASKELL__ >= 708 + lift_elem = coerce +#else + lift_elem g (Elem a) = Elem (g a) +#endif + +-- If we're mapping over a sequence, we can reverse it at the same time +-- at no extra charge. +{-# RULES +"fmapSeq/reverse" forall f xs . fmapSeq f (reverse xs) = fmapReverse f xs +"reverse/fmapSeq" forall f xs . reverse (fmapSeq f xs) = fmapReverse f xs + #-} +#endif + +fmapReverseTree :: (a -> b) -> FingerTree a -> FingerTree b +fmapReverseTree _ EmptyT = EmptyT +fmapReverseTree f (Single x) = Single (f x) +fmapReverseTree f (Deep s pr m sf) = + Deep s (reverseDigit f sf) + (fmapReverseTree (reverseNode f) m) + (reverseDigit f pr) + +{-# INLINE reverseDigit #-} +reverseDigit :: (a -> b) -> Digit a -> Digit b +reverseDigit f (One a) = One (f a) +reverseDigit f (Two a b) = Two (f b) (f a) +reverseDigit f (Three a b c) = Three (f c) (f b) (f a) +reverseDigit f (Four a b c d) = Four (f d) (f c) (f b) (f a) + +reverseNode :: (a -> b) -> Node a -> Node b +reverseNode f (Node2 s a b) = Node2 s (f b) (f a) +reverseNode f (Node3 s a b c) = Node3 s (f c) (f b) (f a) + +------------------------------------------------------------------------ +-- Mapping with a splittable value +------------------------------------------------------------------------ + +-- For zipping, it is useful to build a result by +-- traversing a sequence while splitting up something else. For zipping, we +-- traverse the first sequence while splitting up the second. +-- +-- What makes all this crazy code a good idea: +-- +-- Suppose we zip together two sequences of the same length: +-- +-- zs = zip xs ys +-- +-- We want to get reasonably fast indexing into zs immediately, rather than +-- needing to construct the entire thing first, as the previous implementation +-- required. The first aspect is that we build the result "outside-in" or +-- "top-down", rather than left to right. That gives us access to both ends +-- quickly. But that's not enough, by itself, to give immediate access to the +-- center of zs. For that, we need to be able to skip over larger segments of +-- zs, delaying their construction until we actually need them. The way we do +-- this is to traverse xs, while splitting up ys according to the structure of +-- xs. If we have a Deep _ pr m sf, we split ys into three pieces, and hand off +-- one piece to the prefix, one to the middle, and one to the suffix of the +-- result. The key point is that we don't need to actually do anything further +-- with those pieces until we actually need them; the computations to split +-- them up further and zip them with their matching pieces can be delayed until +-- they're actually needed. We do the same thing for Digits (splitting into +-- between one and four pieces) and Nodes (splitting into two or three). The +-- ultimate result is that we can index into, or split at, any location in zs +-- in polylogarithmic time *immediately*, while still being able to force all +-- the thunks in O(n) time. +-- +-- Benchmark info, and alternatives: +-- +-- The old zipping code used mapAccumL to traverse the first sequence while +-- cutting down the second sequence one piece at a time. +-- +-- An alternative way to express that basic idea is to convert both sequences +-- to lists, zip the lists, and then convert the result back to a sequence. +-- I'll call this the "listy" implementation. +-- +-- I benchmarked two operations: Each started by zipping two sequences +-- constructed with replicate and/or fromList. The first would then immediately +-- index into the result. The second would apply deepseq to force the entire +-- result. The new implementation worked much better than either of the others +-- on the immediate indexing test, as expected. It also worked better than the +-- old implementation for all the deepseq tests. For short sequences, the listy +-- implementation outperformed all the others on the deepseq test. However, the +-- splitting implementation caught up and surpassed it once the sequences grew +-- long enough. It seems likely that by avoiding rebuilding, it interacts +-- better with the cache hierarchy. +-- +-- David Feuer, with some guidance from Carter Schonwald, December 2014 + +-- | /O(n)/. Constructs a new sequence with the same structure as an existing +-- sequence using a user-supplied mapping function along with a splittable +-- value and a way to split it. The value is split up lazily according to the +-- structure of the sequence, so one piece of the value is distributed to each +-- element of the sequence. The caller should provide a splitter function that +-- takes a number, @n@, and a splittable value, breaks off a chunk of size @n@ +-- from the value, and returns that chunk and the remainder as a pair. The +-- following examples will hopefully make the usage clear: +-- +-- > zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c +-- > zipWith f s1 s2 = splitMap splitAt (\b a -> f a (b `index` 0)) s2' s1' +-- > where +-- > minLen = min (length s1) (length s2) +-- > s1' = take minLen s1 +-- > s2' = take minLen s2 +-- +-- > mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b +-- > mapWithIndex f = splitMap (\n i -> (i, n+i)) f 0 +#ifdef __GLASGOW_HASKELL__ +-- We use ScopedTypeVariables to improve performance and make +-- performance less sensitive to minor changes. + +-- We INLINE this so GHC can see that the function passed in is +-- strict in its Int argument. +{-# INLINE splitMap #-} +splitMap :: forall s a' b' . (Int -> s -> (s,s)) -> (s -> a' -> b') -> s -> Seq a' -> Seq b' +splitMap splt f0 s0 (Seq xs0) = Seq $ splitMapTreeE (\s' (Elem a) -> Elem (f0 s' a)) s0 xs0 + where + {-# INLINE splitMapTreeE #-} + splitMapTreeE :: (s -> Elem y -> b) -> s -> FingerTree (Elem y) -> FingerTree b + splitMapTreeE _ _ EmptyT = EmptyT + splitMapTreeE f s (Single xs) = Single $ f s xs + splitMapTreeE f s (Deep n pr m sf) = Deep n (splitMapDigit f prs pr) (splitMapTreeN (\eta1 eta2 -> splitMapNode f eta1 eta2) ms m) (splitMapDigit f sfs sf) + where + !spr = size pr + !sm = n - spr - size sf + (prs, r) = splt spr s + (ms, sfs) = splt sm r + + splitMapTreeN :: (s -> Node a -> b) -> s -> FingerTree (Node a) -> FingerTree b + splitMapTreeN _ _ EmptyT = EmptyT + splitMapTreeN f s (Single xs) = Single $ f s xs + splitMapTreeN f s (Deep n pr m sf) = Deep n (splitMapDigit f prs pr) (splitMapTreeN (\eta1 eta2 -> splitMapNode f eta1 eta2) ms m) (splitMapDigit f sfs sf) + where + (prs, r) = splt (size pr) s + (ms, sfs) = splt (size m) r + + {-# INLINE splitMapDigit #-} + splitMapDigit :: Sized a => (s -> a -> b) -> s -> Digit a -> Digit b + splitMapDigit f s (One a) = One (f s a) + splitMapDigit f s (Two a b) = Two (f first a) (f second b) + where + (first, second) = splt (size a) s + splitMapDigit f s (Three a b c) = Three (f first a) (f second b) (f third c) + where + (first, r) = splt (size a) s + (second, third) = splt (size b) r + splitMapDigit f s (Four a b c d) = Four (f first a) (f second b) (f third c) (f fourth d) + where + (first, s') = splt (size a) s + (middle, fourth) = splt (size b + size c) s' + (second, third) = splt (size b) middle + + {-# INLINE splitMapNode #-} + splitMapNode :: Sized a => (s -> a -> b) -> s -> Node a -> Node b + splitMapNode f s (Node2 ns a b) = Node2 ns (f first a) (f second b) + where + (first, second) = splt (size a) s + splitMapNode f s (Node3 ns a b c) = Node3 ns (f first a) (f second b) (f third c) + where + (first, r) = splt (size a) s + (second, third) = splt (size b) r + +#else +-- Implementation without ScopedTypeVariables--somewhat slower, +-- and much more sensitive to minor changes in various places. + +{-# INLINE splitMap #-} +splitMap :: (Int -> s -> (s,s)) -> (s -> a -> b) -> s -> Seq a -> Seq b +splitMap splt' f0 s0 (Seq xs0) = Seq $ splitMapTreeE splt' (\s' (Elem a) -> Elem (f0 s' a)) s0 xs0 + +{-# INLINE splitMapTreeE #-} +splitMapTreeE :: (Int -> s -> (s,s)) -> (s -> Elem y -> b) -> s -> FingerTree (Elem y) -> FingerTree b +splitMapTreeE _ _ _ EmptyT = EmptyT +splitMapTreeE _ f s (Single xs) = Single $ f s xs +splitMapTreeE splt f s (Deep n pr m sf) = Deep n (splitMapDigit splt f prs pr) (splitMapTreeN splt (\eta1 eta2 -> splitMapNode splt f eta1 eta2) ms m) (splitMapDigit splt f sfs sf) + where + !spr = size pr + sm = n - spr - size sf + (prs, r) = splt spr s + (ms, sfs) = splt sm r + +splitMapTreeN :: (Int -> s -> (s,s)) -> (s -> Node a -> b) -> s -> FingerTree (Node a) -> FingerTree b +splitMapTreeN _ _ _ EmptyT = EmptyT +splitMapTreeN _ f s (Single xs) = Single $ f s xs +splitMapTreeN splt f s (Deep n pr m sf) = Deep n (splitMapDigit splt f prs pr) (splitMapTreeN splt (\eta1 eta2 -> splitMapNode splt f eta1 eta2) ms m) (splitMapDigit splt f sfs sf) + where + (prs, r) = splt (size pr) s + (ms, sfs) = splt (size m) r + +{-# INLINE splitMapDigit #-} +splitMapDigit :: Sized a => (Int -> s -> (s,s)) -> (s -> a -> b) -> s -> Digit a -> Digit b +splitMapDigit _ f s (One a) = One (f s a) +splitMapDigit splt f s (Two a b) = Two (f first a) (f second b) + where + (first, second) = splt (size a) s +splitMapDigit splt f s (Three a b c) = Three (f first a) (f second b) (f third c) + where + (first, r) = splt (size a) s + (second, third) = splt (size b) r +splitMapDigit splt f s (Four a b c d) = Four (f first a) (f second b) (f third c) (f fourth d) + where + (first, s') = splt (size a) s + (middle, fourth) = splt (size b + size c) s' + (second, third) = splt (size b) middle + +{-# INLINE splitMapNode #-} +splitMapNode :: Sized a => (Int -> s -> (s,s)) -> (s -> a -> b) -> s -> Node a -> Node b +splitMapNode splt f s (Node2 ns a b) = Node2 ns (f first a) (f second b) + where + (first, second) = splt (size a) s +splitMapNode splt f s (Node3 ns a b c) = Node3 ns (f first a) (f second b) (f third c) + where + (first, r) = splt (size a) s + (second, third) = splt (size b) r +#endif + +getSingleton :: Seq a -> a +getSingleton (Seq (Single (Elem a))) = a +getSingleton _ = error "getSingleton: Not a singleton." + +------------------------------------------------------------------------ +-- Zipping +------------------------------------------------------------------------ + +-- | /O(min(n1,n2))/. 'zip' takes two sequences and returns a sequence +-- of corresponding pairs. If one input is short, excess elements are +-- discarded from the right end of the longer sequence. +zip :: Seq a -> Seq b -> Seq (a, b) +zip = zipWith (,) + +-- | /O(min(n1,n2))/. 'zipWith' generalizes 'zip' by zipping with the +-- function given as the first argument, instead of a tupling function. +-- For example, @zipWith (+)@ is applied to two sequences to take the +-- sequence of corresponding sums. +zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c +zipWith f s1 s2 = zipWith' f s1' s2' + where + minLen = min (length s1) (length s2) + s1' = take minLen s1 + s2' = take minLen s2 + +-- | A version of zipWith that assumes the sequences have the same length. +zipWith' :: (a -> b -> c) -> Seq a -> Seq b -> Seq c +zipWith' f s1 s2 = splitMap uncheckedSplitAt (\s a -> f a (getSingleton s)) s2 s1 + +-- | /O(min(n1,n2,n3))/. 'zip3' takes three sequences and returns a +-- sequence of triples, analogous to 'zip'. +zip3 :: Seq a -> Seq b -> Seq c -> Seq (a,b,c) +zip3 = zipWith3 (,,) + +-- | /O(min(n1,n2,n3))/. 'zipWith3' takes a function which combines +-- three elements, as well as three sequences and returns a sequence of +-- their point-wise combinations, analogous to 'zipWith'. +zipWith3 :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d +zipWith3 f s1 s2 s3 = zipWith' ($) (zipWith' f s1' s2') s3' + where + minLen = minimum [length s1, length s2, length s3] + s1' = take minLen s1 + s2' = take minLen s2 + s3' = take minLen s3 + +zipWith3' :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d +zipWith3' f s1 s2 s3 = zipWith' ($) (zipWith' f s1 s2) s3 + +-- | /O(min(n1,n2,n3,n4))/. 'zip4' takes four sequences and returns a +-- sequence of quadruples, analogous to 'zip'. +zip4 :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a,b,c,d) +zip4 = zipWith4 (,,,) + +-- | /O(min(n1,n2,n3,n4))/. 'zipWith4' takes a function which combines +-- four elements, as well as four sequences and returns a sequence of +-- their point-wise combinations, analogous to 'zipWith'. +zipWith4 :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e +zipWith4 f s1 s2 s3 s4 = zipWith' ($) (zipWith3' f s1' s2' s3') s4' + where + minLen = minimum [length s1, length s2, length s3, length s4] + s1' = take minLen s1 + s2' = take minLen s2 + s3' = take minLen s3 + s4' = take minLen s4 + +------------------------------------------------------------------------ +-- Sorting +-- +-- sort and sortBy are implemented by simple deforestations of +-- \ xs -> fromList2 (length xs) . Data.List.sortBy cmp . toList +-- which does not get deforested automatically, it would appear. +-- +-- Unstable sorting is performed by a heap sort implementation based on +-- pairing heaps. Because the internal structure of sequences is quite +-- varied, it is difficult to get blocks of elements of roughly the same +-- length, which would improve merge sort performance. Pairing heaps, +-- on the other hand, are relatively resistant to the effects of merging +-- heaps of wildly different sizes, as guaranteed by its amortized +-- constant-time merge operation. Moreover, extensive use of SpecConstr +-- transformations can be done on pairing heaps, especially when we're +-- only constructing them to immediately be unrolled. +-- +-- On purely random sequences of length 50000, with no RTS options, +-- I get the following statistics, in which heapsort is about 42.5% +-- faster: (all comparisons done with -O2) +-- +-- Times (ms) min mean +/-sd median max +-- to/from list: 103.802 108.572 7.487 106.436 143.339 +-- unstable heapsort: 60.686 62.968 4.275 61.187 79.151 +-- +-- Heapsort, it would seem, is less of a memory hog than Data.List.sortBy. +-- The gap is narrowed when more memory is available, but heapsort still +-- wins, 15% faster, with +RTS -H128m: +-- +-- Times (ms) min mean +/-sd median max +-- to/from list: 42.692 45.074 2.596 44.600 56.601 +-- unstable heapsort: 37.100 38.344 3.043 37.715 55.526 +-- +-- In addition, on strictly increasing sequences the gap is even wider +-- than normal; heapsort is 68.5% faster with no RTS options: +-- Times (ms) min mean +/-sd median max +-- to/from list: 52.236 53.574 1.987 53.034 62.098 +-- unstable heapsort: 16.433 16.919 0.931 16.681 21.622 +-- +-- This may be attributed to the elegant nature of the pairing heap. +-- +-- wasserman.louis@gmail.com, 7/20/09 +------------------------------------------------------------------------ + +-- | /O(n log n)/. 'sort' sorts the specified 'Seq' by the natural +-- ordering of its elements. The sort is stable. +-- If stability is not required, 'unstableSort' can be considerably +-- faster, and in particular uses less memory. +sort :: Ord a => Seq a -> Seq a +sort = sortBy compare + +-- | /O(n log n)/. 'sortBy' sorts the specified 'Seq' according to the +-- specified comparator. The sort is stable. +-- If stability is not required, 'unstableSortBy' can be considerably +-- faster, and in particular uses less memory. +sortBy :: (a -> a -> Ordering) -> Seq a -> Seq a +sortBy cmp xs = fromList2 (length xs) (Data.List.sortBy cmp (toList xs)) + +-- | /O(n log n)/. 'unstableSort' sorts the specified 'Seq' by +-- the natural ordering of its elements, but the sort is not stable. +-- This algorithm is frequently faster and uses less memory than 'sort', +-- and performs extremely well -- frequently twice as fast as 'sort' -- +-- when the sequence is already nearly sorted. +unstableSort :: Ord a => Seq a -> Seq a +unstableSort = unstableSortBy compare + +-- | /O(n log n)/. A generalization of 'unstableSort', 'unstableSortBy' +-- takes an arbitrary comparator and sorts the specified sequence. +-- The sort is not stable. This algorithm is frequently faster and +-- uses less memory than 'sortBy', and performs extremely well -- +-- frequently twice as fast as 'sortBy' -- when the sequence is already +-- nearly sorted. +unstableSortBy :: (a -> a -> Ordering) -> Seq a -> Seq a +unstableSortBy cmp (Seq xs) = + fromList2 (size xs) $ maybe [] (unrollPQ cmp) $ + toPQ cmp (\ (Elem x) -> PQueue x Nil) xs + +-- | fromList2, given a list and its length, constructs a completely +-- balanced Seq whose elements are that list using the replicateA +-- generalization. +fromList2 :: Int -> [a] -> Seq a +fromList2 n = execState (replicateA n (State ht)) + where + ht (x:xs) = (xs, x) + ht [] = error "fromList2: short list" + +-- | A 'PQueue' is a simple pairing heap. +data PQueue e = PQueue e (PQL e) +data PQL e = Nil | {-# UNPACK #-} !(PQueue e) :& PQL e + +infixr 8 :& + +#ifdef TESTING + +instance Functor PQueue where + fmap f (PQueue x ts) = PQueue (f x) (fmap f ts) + +instance Functor PQL where + fmap f (q :& qs) = fmap f q :& fmap f qs + fmap _ Nil = Nil + +instance Show e => Show (PQueue e) where + show = unlines . draw . fmap show + +-- borrowed wholesale from Data.Tree, as Data.Tree actually depends +-- on Data.Sequence +draw :: PQueue String -> [String] +draw (PQueue x ts0) = x : drawSubTrees ts0 + where + drawSubTrees Nil = [] + drawSubTrees (t :& Nil) = + "|" : shift "`- " " " (draw t) + drawSubTrees (t :& ts) = + "|" : shift "+- " "| " (draw t) ++ drawSubTrees ts + + shift first other = Data.List.zipWith (++) (first : repeat other) +#endif + +-- | 'unrollPQ', given a comparator function, unrolls a 'PQueue' into +-- a sorted list. +unrollPQ :: (e -> e -> Ordering) -> PQueue e -> [e] +unrollPQ cmp = unrollPQ' + where + {-# INLINE unrollPQ' #-} + unrollPQ' (PQueue x ts) = x:mergePQs0 ts + (<+>) = mergePQ cmp + mergePQs0 Nil = [] + mergePQs0 (t :& Nil) = unrollPQ' t + mergePQs0 (t1 :& t2 :& ts) = mergePQs (t1 <+> t2) ts + mergePQs !t ts = case ts of + Nil -> unrollPQ' t + t1 :& Nil -> unrollPQ' (t <+> t1) + t1 :& t2 :& ts' -> mergePQs (t <+> (t1 <+> t2)) ts' + +-- | 'toPQ', given an ordering function and a mechanism for queueifying +-- elements, converts a 'FingerTree' to a 'PQueue'. +toPQ :: (e -> e -> Ordering) -> (a -> PQueue e) -> FingerTree a -> Maybe (PQueue e) +toPQ _ _ EmptyT = Nothing +toPQ _ f (Single x) = Just (f x) +toPQ cmp f (Deep _ pr m sf) = Just (maybe (pr' <+> sf') ((pr' <+> sf') <+>) (toPQ cmp fNode m)) + where + fDigit digit = case fmap f digit of + One a -> a + Two a b -> a <+> b + Three a b c -> a <+> b <+> c + Four a b c d -> (a <+> b) <+> (c <+> d) + (<+>) = mergePQ cmp + fNode = fDigit . nodeToDigit + pr' = fDigit pr + sf' = fDigit sf + +-- | 'mergePQ' merges two 'PQueue's. +mergePQ :: (a -> a -> Ordering) -> PQueue a -> PQueue a -> PQueue a +mergePQ cmp q1@(PQueue x1 ts1) q2@(PQueue x2 ts2) + | cmp x1 x2 == GT = PQueue x2 (q1 :& ts2) + | otherwise = PQueue x1 (q2 :& ts1) diff --git a/Data/Set.hs b/Data/Set.hs --- a/Data/Set.hs +++ b/Data/Set.hs @@ -121,6 +121,8 @@ , fold -- * Min\/Max + , lookupMin + , lookupMax , findMin , findMax , deleteMin @@ -159,7 +161,7 @@ #endif ) where -import Data.Set.Base as S +import Data.Set.Internal as S -- $strictness -- diff --git a/Data/Set/Base.hs b/Data/Set/Base.hs deleted file mode 100644 --- a/Data/Set/Base.hs +++ /dev/null @@ -1,1680 +0,0 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} -#endif -#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Trustworthy #-} -#endif -#if __GLASGOW_HASKELL__ >= 708 -{-# LANGUAGE RoleAnnotations #-} -{-# LANGUAGE TypeFamilies #-} -#endif - -#include "containers.h" - -{-# OPTIONS_HADDOCK hide #-} - ------------------------------------------------------------------------------ --- | --- Module : Data.Set.Base --- Copyright : (c) Daan Leijen 2002 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : provisional --- Portability : portable --- --- An efficient implementation of sets. --- --- These modules are intended to be imported qualified, to avoid name --- clashes with Prelude functions, e.g. --- --- > import Data.Set (Set) --- > import qualified Data.Set as Set --- --- The implementation of 'Set' is based on /size balanced/ binary trees (or --- trees of /bounded balance/) as described by: --- --- * Stephen Adams, \"/Efficient sets: a balancing act/\", --- Journal of Functional Programming 3(4):553-562, October 1993, --- . --- * J. Nievergelt and E.M. Reingold, --- \"/Binary search trees of bounded balance/\", --- SIAM journal of computing 2(1), March 1973. --- --- Bounds for 'union', 'intersection', and 'difference' are as given --- by --- --- * Guy Blelloch, Daniel Ferizovic, and Yihan Sun, --- \"/Just Join for Parallel Ordered Sets/\", --- . --- --- Note that the implementation is /left-biased/ -- the elements of a --- first argument are always preferred to the second, for example in --- 'union' or 'insert'. Of course, left-biasing can only be observed --- when equality is an equivalence relation instead of structural --- equality. --- --- /Warning/: The size of the set must not exceed @maxBound::Int@. Violation of --- this condition is not detected and if the size limit is exceeded, the --- behavior of the set is completely undefined. ------------------------------------------------------------------------------ - --- [Note: Using INLINABLE] --- ~~~~~~~~~~~~~~~~~~~~~~~ --- It is crucial to the performance that the functions specialize on the Ord --- type when possible. GHC 7.0 and higher does this by itself when it sees th --- unfolding of a function -- that is why all public functions are marked --- INLINABLE (that exposes the unfolding). - - --- [Note: Using INLINE] --- ~~~~~~~~~~~~~~~~~~~~ --- For other compilers and GHC pre 7.0, we mark some of the functions INLINE. --- We mark the functions that just navigate down the tree (lookup, insert, --- delete and similar). That navigation code gets inlined and thus specialized --- when possible. There is a price to pay -- code growth. The code INLINED is --- therefore only the tree navigation, all the real work (rebalancing) is not --- INLINED by using a NOINLINE. --- --- All methods marked INLINE have to be nonrecursive -- a 'go' function doing --- the real work is provided. - - --- [Note: Type of local 'go' function] --- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- If the local 'go' function uses an Ord class, it sometimes heap-allocates --- the Ord dictionary when the 'go' function does not have explicit type. --- In that case we give 'go' explicit type. But this slightly decrease --- performance, as the resulting 'go' function can float out to top level. - - --- [Note: Local 'go' functions and capturing] --- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- As opposed to IntSet, when 'go' function captures an argument, increased --- heap-allocation can occur: sometimes in a polymorphic function, the 'go' --- floats out of its enclosing function and then it heap-allocates the --- dictionary and the argument. Maybe it floats out too late and strictness --- analyzer cannot see that these could be passed on stack. - --- [Note: Order of constructors] --- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ --- The order of constructors of Set matters when considering performance. --- Currently in GHC 7.0, when type has 2 constructors, a forward conditional --- jump is made when successfully matching second constructor. Successful match --- of first constructor results in the forward jump not taken. --- On GHC 7.0, reordering constructors from Tip | Bin to Bin | Tip --- improves the benchmark by up to 10% on x86. - -module Data.Set.Base ( - -- * Set type - Set(..) -- instance Eq,Ord,Show,Read,Data,Typeable - - -- * Operators - , (\\) - - -- * Query - , null - , size - , member - , notMember - , lookupLT - , lookupGT - , lookupLE - , lookupGE - , isSubsetOf - , isProperSubsetOf - - -- * Construction - , empty - , singleton - , insert - , delete - - -- * Combine - , union - , unions - , difference - , intersection - - -- * Filter - , filter - , takeWhileAntitone - , dropWhileAntitone - , spanAntitone - , partition - , split - , splitMember - , splitRoot - - -- * Indexed - , lookupIndex - , findIndex - , elemAt - , deleteAt - , take - , drop - , splitAt - - -- * Map - , map - , mapMonotonic - - -- * 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 - , fromDescList - , fromDistinctDescList - - -- * Debugging - , showTree - , showTreeWith - , valid - - -- Internals (for testing) - , bin - , balanced - , link - , merge - ) where - -import Prelude hiding (filter,foldl,foldr,null,map,take,drop,splitAt) -import qualified Data.List as List -import Data.Bits (shiftL, shiftR) -#if !MIN_VERSION_base(4,8,0) -import Data.Monoid (Monoid(..)) -#endif -#if MIN_VERSION_base(4,9,0) -import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) -#endif -import qualified Data.Foldable as Foldable -import Data.Typeable -import Control.DeepSeq (NFData(rnf)) - -import Data.Utils.StrictFold -import Data.Utils.StrictPair -import Data.Utils.PtrEquality - -#if __GLASGOW_HASKELL__ -import GHC.Exts ( build ) -#if __GLASGOW_HASKELL__ >= 708 -import qualified GHC.Exts as GHCExts -#endif -import Text.Read -import Data.Data -#endif - - -{-------------------------------------------------------------------- - Operators ---------------------------------------------------------------------} -infixl 9 \\ -- - --- | /O(m*log(n\/m+1)), m <= n/. See 'difference'. -(\\) :: Ord a => Set a -> Set a -> Set a -m1 \\ m2 = difference m1 m2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE (\\) #-} -#endif - -{-------------------------------------------------------------------- - Sets are size balanced trees ---------------------------------------------------------------------} --- | A set of values @a@. - --- See Note: Order of constructors -data Set a = Bin {-# UNPACK #-} !Size !a !(Set a) !(Set a) - | Tip - -type Size = Int - -#if __GLASGOW_HASKELL__ >= 708 -type role Set nominal -#endif - -instance Ord a => Monoid (Set a) where - mempty = empty - mconcat = unions -#if !(MIN_VERSION_base(4,9,0)) - mappend = union -#else - mappend = (<>) - -instance Ord a => Semigroup (Set a) where - (<>) = union - stimes = stimesIdempotentMonoid -#endif - - -instance Foldable.Foldable Set where - fold = go - where go Tip = mempty - go (Bin 1 k _ _) = k - go (Bin _ k l r) = go l `mappend` (k `mappend` go r) - {-# INLINABLE fold #-} - foldr = foldr - {-# INLINE foldr #-} - foldl = foldl - {-# INLINE foldl #-} - foldMap f t = go t - where go Tip = mempty - go (Bin 1 k _ _) = f k - go (Bin _ k l r) = go l `mappend` (f k `mappend` go r) - {-# INLINE foldMap #-} - -#if MIN_VERSION_base(4,6,0) - foldl' = foldl' - {-# INLINE foldl' #-} - foldr' = foldr' - {-# INLINE foldr' #-} -#endif -#if MIN_VERSION_base(4,8,0) - length = size - {-# INLINE length #-} - null = null - {-# INLINE null #-} - toList = toList - {-# INLINE toList #-} - elem = go - where go !_ Tip = False - go x (Bin _ y l r) = x == y || go x l || go x r - {-# INLINABLE elem #-} - minimum = findMin - {-# INLINE minimum #-} - maximum = findMax - {-# INLINE maximum #-} - sum = foldl' (+) 0 - {-# INLINABLE sum #-} - product = foldl' (*) 1 - {-# INLINABLE product #-} -#endif - - -#if __GLASGOW_HASKELL__ - -{-------------------------------------------------------------------- - A Data instance ---------------------------------------------------------------------} - --- This instance preserves data abstraction at the cost of inefficiency. --- We provide limited reflection services for the sake of data abstraction. - -instance (Data a, Ord a) => Data (Set a) where - gfoldl f z set = z fromList `f` (toList set) - toConstr _ = fromListConstr - gunfold k z c = case constrIndex c of - 1 -> k (z fromList) - _ -> error "gunfold" - dataTypeOf _ = setDataType - dataCast1 f = gcast1 f - -fromListConstr :: Constr -fromListConstr = mkConstr setDataType "fromList" [] Prefix - -setDataType :: DataType -setDataType = mkDataType "Data.Set.Base.Set" [fromListConstr] - -#endif - -{-------------------------------------------------------------------- - Query ---------------------------------------------------------------------} --- | /O(1)/. Is this the empty set? -null :: Set a -> Bool -null Tip = True -null (Bin {}) = False -{-# INLINE null #-} - --- | /O(1)/. The number of elements in the set. -size :: Set a -> Int -size Tip = 0 -size (Bin sz _ _ _) = sz -{-# INLINE size #-} - --- | /O(log n)/. Is the element in the set? -member :: Ord a => a -> Set a -> Bool -member = go - where - go !_ Tip = False - go x (Bin _ y l r) = case compare x y of - LT -> go x l - GT -> go x r - EQ -> True -#if __GLASGOW_HASKELL__ -{-# INLINABLE member #-} -#else -{-# INLINE member #-} -#endif - --- | /O(log n)/. Is the element not in the set? -notMember :: Ord a => a -> Set a -> Bool -notMember a t = not $ member a t -#if __GLASGOW_HASKELL__ -{-# INLINABLE notMember #-} -#else -{-# INLINE notMember #-} -#endif - --- | /O(log n)/. Find largest element smaller than the given one. --- --- > lookupLT 3 (fromList [3, 5]) == Nothing --- > lookupLT 5 (fromList [3, 5]) == Just 3 -lookupLT :: Ord a => a -> Set a -> Maybe a -lookupLT = goNothing - where - goNothing !_ Tip = Nothing - goNothing x (Bin _ y l r) | x <= y = goNothing x l - | otherwise = goJust x y r - - goJust !_ best Tip = Just best - goJust x best (Bin _ y l r) | x <= y = goJust x best l - | otherwise = goJust x y r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupLT #-} -#else -{-# INLINE lookupLT #-} -#endif - --- | /O(log n)/. Find smallest element greater than the given one. --- --- > lookupGT 4 (fromList [3, 5]) == Just 5 --- > lookupGT 5 (fromList [3, 5]) == Nothing -lookupGT :: Ord a => a -> Set a -> Maybe a -lookupGT = goNothing - where - goNothing !_ Tip = Nothing - goNothing x (Bin _ y l r) | x < y = goJust x y l - | otherwise = goNothing x r - - goJust !_ best Tip = Just best - goJust x best (Bin _ y l r) | x < y = goJust x y l - | otherwise = goJust x best r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupGT #-} -#else -{-# INLINE lookupGT #-} -#endif - --- | /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 -lookupLE :: Ord a => a -> Set a -> Maybe a -lookupLE = goNothing - where - goNothing !_ Tip = Nothing - goNothing x (Bin _ y l r) = case compare x y of LT -> goNothing x l - EQ -> Just y - GT -> goJust x y r - - goJust !_ best Tip = Just best - goJust x best (Bin _ y l r) = case compare x y of LT -> goJust x best l - EQ -> Just y - GT -> goJust x y r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupLE #-} -#else -{-# INLINE lookupLE #-} -#endif - --- | /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 -lookupGE :: Ord a => a -> Set a -> Maybe a -lookupGE = goNothing - where - goNothing !_ Tip = Nothing - goNothing x (Bin _ y l r) = case compare x y of LT -> goJust x y l - EQ -> Just y - GT -> goNothing x r - - goJust !_ best Tip = Just best - goJust x best (Bin _ y l r) = case compare x y of LT -> goJust x y l - EQ -> Just y - GT -> goJust x best r -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupGE #-} -#else -{-# INLINE lookupGE #-} -#endif - -{-------------------------------------------------------------------- - Construction ---------------------------------------------------------------------} --- | /O(1)/. The empty set. -empty :: Set a -empty = Tip -{-# INLINE empty #-} - --- | /O(1)/. Create a singleton set. -singleton :: a -> Set a -singleton x = Bin 1 x Tip Tip -{-# INLINE singleton #-} - -{-------------------------------------------------------------------- - Insertion, Deletion ---------------------------------------------------------------------} --- | /O(log n)/. Insert an element in a set. --- If the set already contains an element equal to the given value, --- it is replaced with the new value. - --- See Note: Type of local 'go' function -insert :: Ord a => a -> Set a -> Set a -insert = go - where - go :: Ord a => a -> Set a -> Set a - go !x Tip = singleton x - go !x t@(Bin sz y l r) = case compare x y of - LT | l' `ptrEq` l -> t - | otherwise -> balanceL y l' r - where !l' = go x l - GT | r' `ptrEq` r -> t - | otherwise -> balanceR y l r' - where !r' = go x r - EQ | x `ptrEq` y -> t - | otherwise -> Bin sz x l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE insert #-} -#else -{-# INLINE insert #-} -#endif - --- Insert an element to the set only if it is not in the set. --- Used by `union`. - --- See Note: Type of local 'go' function -insertR :: Ord a => a -> Set a -> Set a -insertR = go - where - go :: Ord a => a -> Set a -> Set a - go !x Tip = singleton x - go !x t@(Bin _ y l r) = case compare x y of - LT | l' `ptrEq` l -> t - | otherwise -> balanceL y l' r - where !l' = go x l - GT | r' `ptrEq` r -> t - | otherwise -> balanceR y l r' - where !r' = go x r - EQ -> t -#if __GLASGOW_HASKELL__ -{-# INLINABLE insertR #-} -#else -{-# INLINE insertR #-} -#endif - --- | /O(log n)/. Delete an element from a set. - --- See Note: Type of local 'go' function -delete :: Ord a => a -> Set a -> Set a -delete = go - where - go :: Ord a => a -> Set a -> Set a - go !_ Tip = Tip - go x t@(Bin _ y l r) = case compare x y of - LT | l' `ptrEq` l -> t - | otherwise -> balanceR y l' r - where !l' = go x l - GT | r' `ptrEq` r -> t - | otherwise -> balanceL y l r' - where !r' = go x r - EQ -> glue l r -#if __GLASGOW_HASKELL__ -{-# INLINABLE delete #-} -#else -{-# INLINE delete #-} -#endif - -{-------------------------------------------------------------------- - Subset ---------------------------------------------------------------------} --- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal). -isProperSubsetOf :: Ord a => Set a -> Set a -> Bool -isProperSubsetOf s1 s2 - = (size s1 < size s2) && (isSubsetOf s1 s2) -#if __GLASGOW_HASKELL__ -{-# INLINABLE isProperSubsetOf #-} -#endif - - --- | /O(n+m)/. Is this a subset? --- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@. -isSubsetOf :: Ord a => Set a -> Set a -> Bool -isSubsetOf t1 t2 - = (size t1 <= size t2) && (isSubsetOfX t1 t2) -#if __GLASGOW_HASKELL__ -{-# INLINABLE isSubsetOf #-} -#endif - -isSubsetOfX :: Ord a => Set a -> Set a -> Bool -isSubsetOfX Tip _ = True -isSubsetOfX _ Tip = False -isSubsetOfX (Bin _ x l r) t - = found && isSubsetOfX l lt && isSubsetOfX r gt - where - (lt,found,gt) = splitMember x t -#if __GLASGOW_HASKELL__ -{-# INLINABLE isSubsetOfX #-} -#endif - - -{-------------------------------------------------------------------- - Minimal, Maximal ---------------------------------------------------------------------} --- | /O(log n)/. The minimal element of a set. -findMin :: Set a -> a -findMin (Bin _ x Tip _) = x -findMin (Bin _ _ l _) = findMin l -findMin Tip = error "Set.findMin: empty set has no minimal element" - --- | /O(log n)/. The maximal element of a set. -findMax :: Set a -> a -findMax (Bin _ x _ Tip) = x -findMax (Bin _ _ _ r) = findMax r -findMax Tip = error "Set.findMax: empty set has no maximal element" - --- | /O(log n)/. Delete the minimal element. Returns an empty set if the set is empty. -deleteMin :: Set a -> Set a -deleteMin (Bin _ _ Tip r) = r -deleteMin (Bin _ x l r) = balanceR x (deleteMin l) r -deleteMin Tip = Tip - --- | /O(log n)/. Delete the maximal element. Returns an empty set if the set is empty. -deleteMax :: Set a -> Set a -deleteMax (Bin _ _ l Tip) = l -deleteMax (Bin _ x l r) = balanceL x l (deleteMax r) -deleteMax Tip = Tip - -{-------------------------------------------------------------------- - Union. ---------------------------------------------------------------------} --- | The union of a list of sets: (@'unions' == 'foldl' 'union' 'empty'@). -unions :: Ord a => [Set a] -> Set a -unions = foldlStrict union empty -#if __GLASGOW_HASKELL__ -{-# INLINABLE unions #-} -#endif - --- | /O(m*log(n/m + 1)), m <= n/. The union of two sets, preferring the first set when --- equal elements are encountered. -union :: Ord a => Set a -> Set a -> Set a -union t1 Tip = t1 -union t1 (Bin _ x Tip Tip) = insertR x t1 -union (Bin _ x Tip Tip) t2 = insert x t2 -union Tip t2 = t2 -union t1@(Bin _ x l1 r1) t2 = case splitS x t2 of - (l2 :*: r2) - | l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 -> t1 - | otherwise -> link x l1l2 r1r2 - where !l1l2 = union l1 l2 - !r1r2 = union r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE union #-} -#endif - -{-------------------------------------------------------------------- - Difference ---------------------------------------------------------------------} --- | /O(m*log(n/m + 1)), m <= n/. Difference of two sets. -difference :: Ord a => Set a -> Set a -> Set a -difference Tip _ = Tip -difference t1 Tip = t1 -difference t1 (Bin _ x l2 r2) = case split x t1 of - (l1, r1) - | size l1l2 + size r1r2 == size t1 -> t1 - | otherwise -> merge l1l2 r1r2 - where !l1l2 = difference l1 l2 - !r1r2 = difference r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE difference #-} -#endif - -{-------------------------------------------------------------------- - Intersection ---------------------------------------------------------------------} --- | /O(m*log(n/m + 1)), m <= n/. The intersection of two sets. --- Elements of the result come from the first set, so for example --- --- > import qualified Data.Set as S --- > data AB = A | B deriving Show --- > instance Ord AB where compare _ _ = EQ --- > instance Eq AB where _ == _ = True --- > main = print (S.singleton A `S.intersection` S.singleton B, --- > S.singleton B `S.intersection` S.singleton A) --- --- prints @(fromList [A],fromList [B])@. -intersection :: Ord a => Set a -> Set a -> Set a -intersection Tip _ = Tip -intersection _ Tip = Tip -intersection t1@(Bin _ x l1 r1) t2 - | b = if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 - then t1 - else link x l1l2 r1r2 - | otherwise = merge l1l2 r1r2 - where - !(l2, b, r2) = splitMember x t2 - !l1l2 = intersection l1 l2 - !r1r2 = intersection r1 r2 -#if __GLASGOW_HASKELL__ -{-# INLINABLE intersection #-} -#endif - -{-------------------------------------------------------------------- - Filter and partition ---------------------------------------------------------------------} --- | /O(n)/. Filter all elements that satisfy the predicate. -filter :: (a -> Bool) -> Set a -> Set a -filter _ Tip = Tip -filter p t@(Bin _ x l r) - | p x = if l `ptrEq` l' && r `ptrEq` r' - then t - else link x l' r' - | otherwise = merge l' r' - where - !l' = filter p l - !r' = filter p r - --- | /O(n)/. Partition the set into two sets, one with all elements that satisfy --- the predicate and one with all elements that don't satisfy the predicate. --- See also 'split'. -partition :: (a -> Bool) -> Set a -> (Set a,Set a) -partition p0 t0 = toPair $ go p0 t0 - where - go _ Tip = (Tip :*: Tip) - go p t@(Bin _ x l r) = case (go p l, go p r) of - ((l1 :*: l2), (r1 :*: r2)) - | p x -> (if l1 `ptrEq` l && r1 `ptrEq` r - then t - else link x l1 r1) :*: merge l2 r2 - | otherwise -> merge l1 r1 :*: - (if l2 `ptrEq` l && r2 `ptrEq` r - then t - else link x l2 r2) - -{---------------------------------------------------------------------- - Map -----------------------------------------------------------------------} - --- | /O(n*log n)/. --- @'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 :: Ord b => (a->b) -> Set a -> Set b -map f = fromList . List.map f . toList -#if __GLASGOW_HASKELL__ -{-# INLINABLE map #-} -#endif - --- | /O(n)/. The --- --- @'mapMonotonic' f s == 'map' f s@, but works only when @f@ is strictly increasing. --- /The precondition is not checked./ --- Semi-formally, we have: --- --- > and [x < y ==> f x < f y | x <- ls, y <- ls] --- > ==> mapMonotonic f s == map f s --- > where ls = toList s - -mapMonotonic :: (a->b) -> Set a -> Set b -mapMonotonic _ Tip = Tip -mapMonotonic f (Bin sz x l r) = Bin sz (f x) (mapMonotonic f l) (mapMonotonic f r) - -{-------------------------------------------------------------------- - 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 :: (a -> b -> b) -> b -> Set a -> 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 :: (a -> b -> b) -> b -> Set a -> b -foldr f z = go z - where - go z' Tip = z' - go z' (Bin _ x l r) = go (f x (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' :: (a -> b -> b) -> b -> Set a -> b -foldr' f z = go z - where - go !z' Tip = z' - go z' (Bin _ x l r) = go (f x (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 -> b -> a) -> a -> Set b -> a -foldl f z = go z - where - go z' Tip = z' - go z' (Bin _ x l r) = go (f (go z' l) x) 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 -> b -> a) -> a -> Set b -> a -foldl' f z = go z - where - go !z' Tip = z' - go z' (Bin _ x l r) = go (f (go z' l) x) r -{-# INLINE foldl' #-} - -{-------------------------------------------------------------------- - List variations ---------------------------------------------------------------------} --- | /O(n)/. An alias of 'toAscList'. The elements of a set in ascending order. --- Subject to list fusion. -elems :: Set a -> [a] -elems = toAscList - -{-------------------------------------------------------------------- - Lists ---------------------------------------------------------------------} -#if __GLASGOW_HASKELL__ >= 708 -instance (Ord a) => GHCExts.IsList (Set a) where - type Item (Set a) = a - fromList = fromList - toList = toList -#endif - --- | /O(n)/. Convert the set to a list of elements. Subject to list fusion. -toList :: Set a -> [a] -toList = toAscList - --- | /O(n)/. Convert the set to an ascending list of elements. Subject to list fusion. -toAscList :: Set a -> [a] -toAscList = foldr (:) [] - --- | /O(n)/. Convert the set to a descending list of elements. Subject to list --- fusion. -toDescList :: Set a -> [a] -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 :: (a -> b -> b) -> b -> Set a -> b -foldrFB = foldr -{-# INLINE[0] foldrFB #-} -foldlFB :: (a -> b -> a) -> a -> Set b -> 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 "Set.toAscList" [~1] forall s . toAscList s = build (\c n -> foldrFB c n s) #-} -{-# RULES "Set.toAscListBack" [1] foldrFB (:) [] = toAscList #-} -{-# RULES "Set.toDescList" [~1] forall s . toDescList s = build (\c n -> foldlFB (\xs x -> c x xs) n s) #-} -{-# RULES "Set.toDescListBack" [1] foldlFB (\xs x -> x : xs) [] = toDescList #-} -#endif - --- | /O(n*log n)/. Create a set from a list of elements. --- --- If the elements are ordered, a linear-time implementation is used, --- with the performance equal to 'fromDistinctAscList'. - --- For some reason, when 'singleton' is used in fromList or in --- create, it is not inlined, so we inline it manually. -fromList :: Ord a => [a] -> Set a -fromList [] = Tip -fromList [x] = Bin 1 x Tip Tip -fromList (x0 : xs0) | not_ordered x0 xs0 = fromList' (Bin 1 x0 Tip Tip) xs0 - | otherwise = go (1::Int) (Bin 1 x0 Tip Tip) xs0 - where - not_ordered _ [] = False - not_ordered x (y : _) = x >= y - {-# INLINE not_ordered #-} - - fromList' t0 xs = foldlStrict ins t0 xs - where ins t x = insert x t - - go !_ t [] = t - go _ t [x] = insertMax x t - go s l xs@(x : xss) | not_ordered x xss = fromList' l xs - | otherwise = case create s xss of - (r, ys, []) -> go (s `shiftL` 1) (link x l r) ys - (r, _, ys) -> fromList' (link x l r) ys - - -- The create is returning a triple (tree, xs, ys). Both xs and ys - -- represent not yet processed elements and only one of them can be nonempty. - -- If ys is nonempty, the keys in ys are not ordered with respect to tree - -- and must be inserted using fromList'. Otherwise the keys have been - -- ordered so far. - create !_ [] = (Tip, [], []) - create s xs@(x : xss) - | s == 1 = if not_ordered x xss then (Bin 1 x Tip Tip, [], xss) - else (Bin 1 x Tip Tip, xss, []) - | otherwise = case create (s `shiftR` 1) xs of - res@(_, [], _) -> res - (l, [y], zs) -> (insertMax y l, [], zs) - (l, ys@(y:yss), _) | not_ordered y yss -> (l, [], ys) - | otherwise -> case create (s `shiftR` 1) yss of - (r, zs, ws) -> (link y l r, zs, ws) -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromList #-} -#endif - -{-------------------------------------------------------------------- - Building trees from ascending/descending lists can be done in linear time. - - Note that if [xs] is ascending that: - fromAscList xs == fromList xs ---------------------------------------------------------------------} --- | /O(n)/. Build a set from an ascending list in linear time. --- /The precondition (input list is ascending) is not checked./ -fromAscList :: Eq a => [a] -> Set a -fromAscList xs = fromDistinctAscList (combineEq xs) -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromAscList #-} -#endif - --- | /O(n)/. Build a set from a descending list in linear time. --- /The precondition (input list is descending) is not checked./ -fromDescList :: Eq a => [a] -> Set a -fromDescList xs = fromDistinctDescList (combineEq xs) -#if __GLASGOW_HASKELL__ -{-# INLINABLE fromDescList #-} -#endif - --- [combineEq xs] combines equal elements with [const] in an ordered list [xs] --- --- TODO: combineEq allocates an intermediate list. It *should* be better to --- make fromAscListBy and fromDescListBy the fundamental operations, and to --- implement the rest using those. -combineEq :: Eq a => [a] -> [a] -combineEq [] = [] -combineEq (x : xs) = combineEq' x xs - where - combineEq' z [] = [z] - combineEq' z (y:ys) - | z == y = combineEq' z ys - | otherwise = z : combineEq' y ys - --- | /O(n)/. Build a set from an ascending list of distinct elements in linear time. --- /The precondition (input list is strictly ascending) is not checked./ - --- For some reason, when 'singleton' is used in fromDistinctAscList or in --- create, it is not inlined, so we inline it manually. -fromDistinctAscList :: [a] -> Set a -fromDistinctAscList [] = Tip -fromDistinctAscList (x0 : xs0) = go (1::Int) (Bin 1 x0 Tip Tip) xs0 - where - go !_ t [] = t - go s l (x : xs) = case create s xs of - (r :*: ys) -> go (s `shiftL` 1) (link x l r) ys - - create !_ [] = (Tip :*: []) - create s xs@(x : xs') - | s == 1 = (Bin 1 x Tip Tip :*: xs') - | otherwise = case create (s `shiftR` 1) xs of - res@(_ :*: []) -> res - (l :*: (y:ys)) -> case create (s `shiftR` 1) ys of - (r :*: zs) -> (link y l r :*: zs) - --- | /O(n)/. Build a set from a descending list of distinct elements in linear time. --- /The precondition (input list is strictly descending) is not checked./ - --- For some reason, when 'singleton' is used in fromDistinctDescList or in --- create, it is not inlined, so we inline it manually. -fromDistinctDescList :: [a] -> Set a -fromDistinctDescList [] = Tip -fromDistinctDescList (x0 : xs0) = go (1::Int) (Bin 1 x0 Tip Tip) xs0 - where - go !_ t [] = t - go s r (x : xs) = case create s xs of - (l :*: ys) -> go (s `shiftL` 1) (link x l r) ys - - create !_ [] = (Tip :*: []) - create s xs@(x : xs') - | s == 1 = (Bin 1 x Tip Tip :*: xs') - | otherwise = case create (s `shiftR` 1) xs of - res@(_ :*: []) -> res - (r :*: (y:ys)) -> case create (s `shiftR` 1) ys of - (l :*: zs) -> (link y l r :*: zs) - -{-------------------------------------------------------------------- - Eq converts the set to a list. In a lazy setting, this - actually seems one of the faster methods to compare two trees - and it is certainly the simplest :-) ---------------------------------------------------------------------} -instance Eq a => Eq (Set a) where - t1 == t2 = (size t1 == size t2) && (toAscList t1 == toAscList t2) - -{-------------------------------------------------------------------- - Ord ---------------------------------------------------------------------} - -instance Ord a => Ord (Set a) where - compare s1 s2 = compare (toAscList s1) (toAscList s2) - -{-------------------------------------------------------------------- - Show ---------------------------------------------------------------------} -instance Show a => Show (Set a) where - showsPrec p xs = showParen (p > 10) $ - showString "fromList " . shows (toList xs) - -{-------------------------------------------------------------------- - Read ---------------------------------------------------------------------} -instance (Read a, Ord a) => Read (Set a) 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/Data ---------------------------------------------------------------------} - -INSTANCE_TYPEABLE1(Set) - -{-------------------------------------------------------------------- - NFData ---------------------------------------------------------------------} - -instance NFData a => NFData (Set a) where - rnf Tip = () - rnf (Bin _ y l r) = rnf y `seq` rnf l `seq` rnf r - -{-------------------------------------------------------------------- - Split ---------------------------------------------------------------------} --- | /O(log n)/. 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 :: Ord a => a -> Set a -> (Set a,Set a) -split x t = toPair $ splitS x t -{-# INLINABLE split #-} - -splitS :: Ord a => a -> Set a -> StrictPair (Set a) (Set a) -splitS _ Tip = (Tip :*: Tip) -splitS x (Bin _ y l r) - = case compare x y of - LT -> let (lt :*: gt) = splitS x l in (lt :*: link y gt r) - GT -> let (lt :*: gt) = splitS x r in (link y l lt :*: gt) - EQ -> (l :*: r) -{-# INLINABLE splitS #-} - --- | /O(log n)/. Performs a 'split' but also returns whether the pivot --- element was found in the original set. -splitMember :: Ord a => a -> Set a -> (Set a,Bool,Set a) -splitMember _ Tip = (Tip, False, Tip) -splitMember x (Bin _ y l r) - = case compare x y of - LT -> let (lt, found, gt) = splitMember x l - !gt' = link y gt r - in (lt, found, gt') - GT -> let (lt, found, gt) = splitMember x r - !lt' = link y l lt - in (lt', found, gt) - EQ -> (l, True, r) -#if __GLASGOW_HASKELL__ -{-# INLINABLE splitMember #-} -#endif - -{-------------------------------------------------------------------- - Indexing ---------------------------------------------------------------------} - --- | /O(log n)/. Return the /index/ of an element, which is its zero-based --- index in the sorted sequence of elements. The index is a number from /0/ up --- to, but not including, the 'size' of the set. Calls 'error' when the element --- is not a 'member' of the set. --- --- > findIndex 2 (fromList [5,3]) Error: element is not in the set --- > findIndex 3 (fromList [5,3]) == 0 --- > findIndex 5 (fromList [5,3]) == 1 --- > findIndex 6 (fromList [5,3]) Error: element is not in the set - --- See Note: Type of local 'go' function -findIndex :: Ord a => a -> Set a -> Int -findIndex = go 0 - where - go :: Ord a => Int -> a -> Set a -> Int - go !_ !_ Tip = error "Set.findIndex: element is not in the set" - go idx x (Bin _ kx l r) = case compare x kx of - LT -> go idx x l - GT -> go (idx + size l + 1) x r - EQ -> idx + size l -#if __GLASGOW_HASKELL__ -{-# INLINABLE findIndex #-} -#endif - --- | /O(log n)/. Lookup the /index/ of an element, which is its zero-based index in --- the sorted sequence of elements. The index is a number from /0/ up to, but not --- including, the 'size' of the set. --- --- > isJust (lookupIndex 2 (fromList [5,3])) == False --- > fromJust (lookupIndex 3 (fromList [5,3])) == 0 --- > fromJust (lookupIndex 5 (fromList [5,3])) == 1 --- > isJust (lookupIndex 6 (fromList [5,3])) == False - --- See Note: Type of local 'go' function -lookupIndex :: Ord a => a -> Set a -> Maybe Int -lookupIndex = go 0 - where - go :: Ord a => Int -> a -> Set a -> Maybe Int - go !_ !_ Tip = Nothing - go idx x (Bin _ kx l r) = case compare x kx of - LT -> go idx x l - GT -> go (idx + size l + 1) x r - EQ -> Just $! idx + size l -#if __GLASGOW_HASKELL__ -{-# INLINABLE lookupIndex #-} -#endif - --- | /O(log n)/. Retrieve an element by its /index/, i.e. by its zero-based --- index in the sorted sequence of elements. If the /index/ is out of range (less --- than zero, greater or equal to 'size' of the set), 'error' is called. --- --- > elemAt 0 (fromList [5,3]) == 3 --- > elemAt 1 (fromList [5,3]) == 5 --- > elemAt 2 (fromList [5,3]) Error: index out of range - -elemAt :: Int -> Set a -> a -elemAt !_ Tip = error "Set.elemAt: index out of range" -elemAt i (Bin _ x l r) - = case compare i sizeL of - LT -> elemAt i l - GT -> elemAt (i-sizeL-1) r - EQ -> x - where - sizeL = size l - --- | /O(log n)/. Delete the element at /index/, i.e. by its zero-based index in --- the sorted sequence of elements. If the /index/ is out of range (less than zero, --- greater or equal to 'size' of the set), 'error' is called. --- --- > deleteAt 0 (fromList [5,3]) == singleton 5 --- > deleteAt 1 (fromList [5,3]) == singleton 3 --- > deleteAt 2 (fromList [5,3]) Error: index out of range --- > deleteAt (-1) (fromList [5,3]) Error: index out of range - -deleteAt :: Int -> Set a -> Set a -deleteAt !i t = - case t of - Tip -> error "Set.deleteAt: index out of range" - Bin _ x l r -> case compare i sizeL of - LT -> balanceR x (deleteAt i l) r - GT -> balanceL x l (deleteAt (i-sizeL-1) r) - EQ -> glue l r - where - sizeL = size l - --- | Take a given number of elements in order, beginning --- with the smallest ones. --- --- @ --- take n = 'fromDistinctAscList' . 'Prelude.take' n . 'toAscList' --- @ -take :: Int -> Set a -> Set a -take i m | i >= size m = m -take i0 m0 = go i0 m0 - where - go i !_ | i <= 0 = Tip - go !_ Tip = Tip - go i (Bin _ x l r) = - case compare i sizeL of - LT -> go i l - GT -> link x l (go (i - sizeL - 1) r) - EQ -> l - where sizeL = size l - --- | Drop a given number of elements in order, beginning --- with the smallest ones. --- --- @ --- drop n = 'fromDistinctAscList' . 'Prelude.drop' n . 'toAscList' --- @ -drop :: Int -> Set a -> Set a -drop i m | i >= size m = Tip -drop i0 m0 = go i0 m0 - where - go i m | i <= 0 = m - go !_ Tip = Tip - go i (Bin _ x l r) = - case compare i sizeL of - LT -> link x (go i l) r - GT -> go (i - sizeL - 1) r - EQ -> insertMin x r - where sizeL = size l - --- | /O(log n)/. Split a set at a particular index. --- --- @ --- splitAt !n !xs = ('take' n xs, 'drop' n xs) --- @ -splitAt :: Int -> Set a -> (Set a, Set a) -splitAt i0 m0 - | i0 >= size m0 = (m0, Tip) - | otherwise = toPair $ go i0 m0 - where - go i m | i <= 0 = Tip :*: m - go !_ Tip = Tip :*: Tip - go i (Bin _ x l r) - = case compare i sizeL of - LT -> case go i l of - ll :*: lr -> ll :*: link x lr r - GT -> case go (i - sizeL - 1) r of - rl :*: rr -> link x l rl :*: rr - EQ -> l :*: insertMin x r - where sizeL = size l - --- | /O(log n)/. Take while a predicate on the elements holds. --- The user is responsible for ensuring that for all elements @j@ and @k@ in the set, --- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. --- --- @ --- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' p . 'toList' --- takeWhileAntitone p = 'filter' p --- @ - -takeWhileAntitone :: (a -> Bool) -> Set a -> Set a -takeWhileAntitone _ Tip = Tip -takeWhileAntitone p (Bin _ x l r) - | p x = link x l (takeWhileAntitone p r) - | otherwise = takeWhileAntitone p l - --- | /O(log n)/. Drop while a predicate on the elements holds. --- The user is responsible for ensuring that for all elements @j@ and @k@ in the set, --- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. --- --- @ --- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' p . 'toList' --- dropWhileAntitone p = 'filter' (not . p) --- @ - -dropWhileAntitone :: (a -> Bool) -> Set a -> Set a -dropWhileAntitone _ Tip = Tip -dropWhileAntitone p (Bin _ x l r) - | p x = dropWhileAntitone p r - | otherwise = link x (dropWhileAntitone p l) r - --- | /O(log n)/. Divide a set at the point where a predicate on the elements stops holding. --- The user is responsible for ensuring that for all elements @j@ and @k@ in the set, --- @j \< k ==\> p j \>= p k@. --- --- @ --- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs) --- spanAntitone p xs = partition p xs --- @ --- --- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the set --- at some /unspecified/ point where the predicate switches from holding to not --- holding (where the predicate is seen to hold before the first element and to fail --- after the last element). - -spanAntitone :: (a -> Bool) -> Set a -> (Set a, Set a) -spanAntitone p0 m = toPair (go p0 m) - where - go _ Tip = Tip :*: Tip - go p (Bin _ x l r) - | p x = let u :*: v = go p r in link x l u :*: v - | otherwise = let u :*: v = go p l in u :*: link x v r - - -{-------------------------------------------------------------------- - Utility functions that maintain the balance properties of the tree. - All constructors assume that all values in [l] < [x] and all values - in [r] > [x], and that [l] and [r] are valid trees. - - In order of sophistication: - [Bin sz x l r] The type constructor. - [bin x l r] Maintains the correct size, assumes that both [l] - and [r] are balanced with respect to each other. - [balance x l r] Restores the balance and size. - Assumes that the original tree was balanced and - that [l] or [r] has changed by at most one element. - [link x l r] Restores balance and size. - - Furthermore, we can construct a new tree from two trees. Both operations - assume that all values in [l] < all values in [r] and that [l] and [r] - are valid: - [glue l r] Glues [l] and [r] together. Assumes that [l] and - [r] are already balanced with respect to each other. - [merge l r] Merges two trees and restores balance. ---------------------------------------------------------------------} - -{-------------------------------------------------------------------- - Link ---------------------------------------------------------------------} -link :: a -> Set a -> Set a -> Set a -link x Tip r = insertMin x r -link x l Tip = insertMax x l -link x l@(Bin sizeL y ly ry) r@(Bin sizeR z lz rz) - | delta*sizeL < sizeR = balanceL z (link x l lz) rz - | delta*sizeR < sizeL = balanceR y ly (link x ry r) - | otherwise = bin x l r - - --- insertMin and insertMax don't perform potentially expensive comparisons. -insertMax,insertMin :: a -> Set a -> Set a -insertMax x t - = case t of - Tip -> singleton x - Bin _ y l r - -> balanceR y l (insertMax x r) - -insertMin x t - = case t of - Tip -> singleton x - Bin _ y l r - -> balanceL y (insertMin x l) r - -{-------------------------------------------------------------------- - [merge l r]: merges two trees. ---------------------------------------------------------------------} -merge :: Set a -> Set a -> Set a -merge Tip r = r -merge l Tip = l -merge l@(Bin sizeL x lx rx) r@(Bin sizeR y ly ry) - | delta*sizeL < sizeR = balanceL y (merge l ly) ry - | delta*sizeR < sizeL = balanceR x lx (merge rx r) - | otherwise = glue l r - -{-------------------------------------------------------------------- - [glue l r]: glues two trees together. - Assumes that [l] and [r] are already balanced with respect to each other. ---------------------------------------------------------------------} -glue :: Set a -> Set a -> Set a -glue Tip r = r -glue l Tip = l -glue l r - | size l > size r = let (m,l') = deleteFindMax l in balanceR m l' r - | otherwise = let (m,r') = deleteFindMin r in balanceL m l r' - --- | /O(log n)/. Delete and find the minimal element. --- --- > deleteFindMin set = (findMin set, deleteMin set) - -deleteFindMin :: Set a -> (a,Set a) -deleteFindMin t - = case t of - Bin _ x Tip r -> (x,r) - Bin _ x l r -> let (xm,l') = deleteFindMin l in (xm,balanceR x l' r) - Tip -> (error "Set.deleteFindMin: can not return the minimal element of an empty set", Tip) - --- | /O(log n)/. Delete and find the maximal element. --- --- > deleteFindMax set = (findMax set, deleteMax set) -deleteFindMax :: Set a -> (a,Set a) -deleteFindMax t - = case t of - Bin _ x l Tip -> (x,l) - Bin _ x l r -> let (xm,r') = deleteFindMax r in (xm,balanceL x l r') - Tip -> (error "Set.deleteFindMax: can not return the maximal element of an empty set", Tip) - --- | /O(log n)/. Retrieves the minimal key of the set, and the set --- stripped of that element, or 'Nothing' if passed an empty set. -minView :: Set a -> Maybe (a, Set a) -minView Tip = Nothing -minView x = Just (deleteFindMin x) - --- | /O(log n)/. Retrieves the maximal key of the set, and the set --- stripped of that element, or 'Nothing' if passed an empty set. -maxView :: Set a -> Maybe (a, Set a) -maxView Tip = Nothing -maxView x = Just (deleteFindMax x) - -{-------------------------------------------------------------------- - [balance x l r] balances two trees with value x. - The sizes of the trees should balance after decreasing the - size of one of them. (a rotation). - - [delta] is the maximal relative difference between the sizes of - two trees, it corresponds with the [w] in Adams' paper. - [ratio] is the ratio between an outer and inner sibling of the - heavier subtree in an unbalanced setting. It determines - whether a double or single rotation should be performed - to restore balance. It is correspondes with the inverse - of $\alpha$ in Adam's article. - - Note that according to the Adam's paper: - - [delta] should be larger than 4.646 with a [ratio] of 2. - - [delta] should be larger than 3.745 with a [ratio] of 1.534. - - But the Adam's paper is errorneous: - - it can be proved that for delta=2 and delta>=5 there does - not exist any ratio that would work - - delta=4.5 and ratio=2 does not work - - That leaves two reasonable variants, delta=3 and delta=4, - both with ratio=2. - - - A lower [delta] leads to a more 'perfectly' balanced tree. - - A higher [delta] performs less rebalancing. - - In the benchmarks, delta=3 is faster on insert operations, - and delta=4 has slightly better deletes. As the insert speedup - is larger, we currently use delta=3. - ---------------------------------------------------------------------} -delta,ratio :: Int -delta = 3 -ratio = 2 - --- The balance function is equivalent to the following: --- --- balance :: a -> Set a -> Set a -> Set a --- balance x l r --- | sizeL + sizeR <= 1 = Bin sizeX x l r --- | sizeR > delta*sizeL = rotateL x l r --- | sizeL > delta*sizeR = rotateR x l r --- | otherwise = Bin sizeX x l r --- where --- sizeL = size l --- sizeR = size r --- sizeX = sizeL + sizeR + 1 --- --- rotateL :: a -> Set a -> Set a -> Set a --- rotateL x l r@(Bin _ _ ly ry) | size ly < ratio*size ry = singleL x l r --- | otherwise = doubleL x l r --- rotateR :: a -> Set a -> Set a -> Set a --- rotateR x l@(Bin _ _ ly ry) r | size ry < ratio*size ly = singleR x l r --- | otherwise = doubleR x l r --- --- singleL, singleR :: a -> Set a -> Set a -> Set a --- singleL x1 t1 (Bin _ x2 t2 t3) = bin x2 (bin x1 t1 t2) t3 --- singleR x1 (Bin _ x2 t1 t2) t3 = bin x2 t1 (bin x1 t2 t3) --- --- doubleL, doubleR :: a -> Set a -> Set a -> Set a --- doubleL x1 t1 (Bin _ x2 (Bin _ x3 t2 t3) t4) = bin x3 (bin x1 t1 t2) (bin x2 t3 t4) --- doubleR x1 (Bin _ x2 t1 (Bin _ x3 t2 t3)) t4 = bin x3 (bin x2 t1 t2) (bin x1 t3 t4) --- --- It is only written in such a way that every node is pattern-matched only once. --- --- Only balanceL and balanceR are needed at the moment, so balance is not here anymore. --- In case it is needed, it can be found in Data.Map. - --- Functions balanceL and balanceR are specialised versions of balance. --- balanceL only checks whether the left subtree is too big, --- balanceR only checks whether the right subtree is too big. - --- balanceL is called when left subtree might have been inserted to or when --- right subtree might have been deleted from. -balanceL :: a -> Set a -> Set a -> Set a -balanceL x l r = case r of - Tip -> case l of - Tip -> Bin 1 x Tip Tip - (Bin _ _ Tip Tip) -> Bin 2 x l Tip - (Bin _ lx Tip (Bin _ lrx _ _)) -> Bin 3 lrx (Bin 1 lx Tip Tip) (Bin 1 x Tip Tip) - (Bin _ lx ll@(Bin _ _ _ _) Tip) -> Bin 3 lx ll (Bin 1 x Tip Tip) - (Bin ls lx ll@(Bin lls _ _ _) lr@(Bin lrs lrx lrl lrr)) - | lrs < ratio*lls -> Bin (1+ls) lx ll (Bin (1+lrs) x lr Tip) - | otherwise -> Bin (1+ls) lrx (Bin (1+lls+size lrl) lx ll lrl) (Bin (1+size lrr) x lrr Tip) - - (Bin rs _ _ _) -> case l of - Tip -> Bin (1+rs) x Tip r - - (Bin ls lx ll lr) - | ls > delta*rs -> case (ll, lr) of - (Bin lls _ _ _, Bin lrs lrx lrl lrr) - | lrs < ratio*lls -> Bin (1+ls+rs) lx ll (Bin (1+rs+lrs) x lr r) - | otherwise -> Bin (1+ls+rs) lrx (Bin (1+lls+size lrl) lx ll lrl) (Bin (1+rs+size lrr) x lrr r) - (_, _) -> error "Failure in Data.Map.balanceL" - | otherwise -> Bin (1+ls+rs) x l r -{-# NOINLINE balanceL #-} - --- balanceR is called when right subtree might have been inserted to or when --- left subtree might have been deleted from. -balanceR :: a -> Set a -> Set a -> Set a -balanceR x l r = case l of - Tip -> case r of - Tip -> Bin 1 x Tip Tip - (Bin _ _ Tip Tip) -> Bin 2 x Tip r - (Bin _ rx Tip rr@(Bin _ _ _ _)) -> Bin 3 rx (Bin 1 x Tip Tip) rr - (Bin _ rx (Bin _ rlx _ _) Tip) -> Bin 3 rlx (Bin 1 x Tip Tip) (Bin 1 rx Tip Tip) - (Bin rs rx rl@(Bin rls rlx rll rlr) rr@(Bin rrs _ _ _)) - | rls < ratio*rrs -> Bin (1+rs) rx (Bin (1+rls) x Tip rl) rr - | otherwise -> Bin (1+rs) rlx (Bin (1+size rll) x Tip rll) (Bin (1+rrs+size rlr) rx rlr rr) - - (Bin ls _ _ _) -> case r of - Tip -> Bin (1+ls) x l Tip - - (Bin rs rx rl rr) - | rs > delta*ls -> case (rl, rr) of - (Bin rls rlx rll rlr, Bin rrs _ _ _) - | rls < ratio*rrs -> Bin (1+ls+rs) rx (Bin (1+ls+rls) x l rl) rr - | otherwise -> Bin (1+ls+rs) rlx (Bin (1+ls+size rll) x l rll) (Bin (1+rrs+size rlr) rx rlr rr) - (_, _) -> error "Failure in Data.Map.balanceR" - | otherwise -> Bin (1+ls+rs) x l r -{-# NOINLINE balanceR #-} - -{-------------------------------------------------------------------- - The bin constructor maintains the size of the tree ---------------------------------------------------------------------} -bin :: a -> Set a -> Set a -> Set a -bin x l r - = Bin (size l + size r + 1) x l r -{-# INLINE bin #-} - - -{-------------------------------------------------------------------- - Utilities ---------------------------------------------------------------------} - --- | /O(1)/. Decompose a set into pieces based on the structure of the underlying --- tree. This function is useful for consuming a set in parallel. --- --- No guarantee is made as to the sizes of the pieces; an internal, but --- deterministic process determines this. However, it is guaranteed that the pieces --- returned will be in ascending order (all elements in the first subset less than all --- elements in the second, and so on). --- --- Examples: --- --- > splitRoot (fromList [1..6]) == --- > [fromList [1,2,3],fromList [4],fromList [5,6]] --- --- > splitRoot empty == [] --- --- Note that the current implementation does not return more than three subsets, --- but you should not depend on this behaviour because it can change in the --- future without notice. -splitRoot :: Set a -> [Set a] -splitRoot orig = - case orig of - Tip -> [] - Bin _ v l r -> [l, singleton v, r] -{-# INLINE splitRoot #-} - - -{-------------------------------------------------------------------- - Debugging ---------------------------------------------------------------------} --- | /O(n)/. Show the tree that implements the set. The tree is shown --- in a compressed, hanging format. -showTree :: Show a => Set a -> 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. - -> Set> putStrLn $ showTreeWith True False $ fromDistinctAscList [1..5] -> 4 -> +--2 -> | +--1 -> | +--3 -> +--5 -> -> Set> putStrLn $ showTreeWith True True $ fromDistinctAscList [1..5] -> 4 -> | -> +--2 -> | | -> | +--1 -> | | -> | +--3 -> | -> +--5 -> -> Set> putStrLn $ showTreeWith False True $ fromDistinctAscList [1..5] -> +--5 -> | -> 4 -> | -> | +--3 -> | | -> +--2 -> | -> +--1 - --} -showTreeWith :: Show a => Bool -> Bool -> Set a -> String -showTreeWith hang wide t - | hang = (showsTreeHang wide [] t) "" - | otherwise = (showsTree wide [] [] t) "" - -showsTree :: Show a => Bool -> [String] -> [String] -> Set a -> ShowS -showsTree wide lbars rbars t - = case t of - Tip -> showsBars lbars . showString "|\n" - Bin _ x Tip Tip - -> showsBars lbars . shows x . showString "\n" - Bin _ x l r - -> showsTree wide (withBar rbars) (withEmpty rbars) r . - showWide wide rbars . - showsBars lbars . shows x . showString "\n" . - showWide wide lbars . - showsTree wide (withEmpty lbars) (withBar lbars) l - -showsTreeHang :: Show a => Bool -> [String] -> Set a -> ShowS -showsTreeHang wide bars t - = case t of - Tip -> showsBars bars . showString "|\n" - Bin _ x Tip Tip - -> showsBars bars . shows x . showString "\n" - Bin _ x l r - -> showsBars bars . shows x . showString "\n" . - showWide wide bars . - showsTreeHang wide (withBar bars) l . - showWide wide bars . - showsTreeHang wide (withEmpty bars) r - -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 - -node :: String -node = "+--" - -withBar, withEmpty :: [String] -> [String] -withBar bars = "| ":bars -withEmpty bars = " ":bars - -{-------------------------------------------------------------------- - Assertions ---------------------------------------------------------------------} --- | /O(n)/. Test if the internal set structure is valid. -valid :: Ord a => Set a -> Bool -valid t - = balanced t && ordered t && validsize t - -ordered :: Ord a => Set a -> Bool -ordered t - = bounded (const True) (const True) t - where - bounded lo hi t' - = case t' of - Tip -> True - Bin _ x l r -> (lo x) && (hi x) && bounded lo (x) hi r - -balanced :: Set a -> Bool -balanced t - = case t of - Tip -> True - Bin _ _ l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) && - balanced l && balanced r - -validsize :: Set a -> Bool -validsize t - = (realsize t == Just (size t)) - where - realsize t' - = case t' of - Tip -> Just 0 - Bin sz _ l r -> case (realsize l,realsize r) of - (Just n,Just m) | n+m+1 == sz -> Just sz - _ -> Nothing diff --git a/Data/Set/Internal.hs b/Data/Set/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/Set/Internal.hs @@ -0,0 +1,1753 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE PatternGuards #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Trustworthy #-} +#endif +#if __GLASGOW_HASKELL__ >= 708 +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE TypeFamilies #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Data.Set.Internal +-- Copyright : (c) Daan Leijen 2002 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. +-- +-- = Description +-- +-- An efficient implementation of sets. +-- +-- These modules are intended to be imported qualified, to avoid name +-- clashes with Prelude functions, e.g. +-- +-- > import Data.Set (Set) +-- > import qualified Data.Set as Set +-- +-- The implementation of 'Set' is based on /size balanced/ binary trees (or +-- trees of /bounded balance/) as described by: +-- +-- * Stephen Adams, \"/Efficient sets: a balancing act/\", +-- Journal of Functional Programming 3(4):553-562, October 1993, +-- . +-- * J. Nievergelt and E.M. Reingold, +-- \"/Binary search trees of bounded balance/\", +-- SIAM journal of computing 2(1), March 1973. +-- +-- Bounds for 'union', 'intersection', and 'difference' are as given +-- by +-- +-- * Guy Blelloch, Daniel Ferizovic, and Yihan Sun, +-- \"/Just Join for Parallel Ordered Sets/\", +-- . +-- +-- Note that the implementation is /left-biased/ -- the elements of a +-- first argument are always preferred to the second, for example in +-- 'union' or 'insert'. Of course, left-biasing can only be observed +-- when equality is an equivalence relation instead of structural +-- equality. +-- +-- /Warning/: The size of the set must not exceed @maxBound::Int@. Violation of +-- this condition is not detected and if the size limit is exceeded, the +-- behavior of the set is completely undefined. +----------------------------------------------------------------------------- + +-- [Note: Using INLINABLE] +-- ~~~~~~~~~~~~~~~~~~~~~~~ +-- It is crucial to the performance that the functions specialize on the Ord +-- type when possible. GHC 7.0 and higher does this by itself when it sees th +-- unfolding of a function -- that is why all public functions are marked +-- INLINABLE (that exposes the unfolding). + + +-- [Note: Using INLINE] +-- ~~~~~~~~~~~~~~~~~~~~ +-- For other compilers and GHC pre 7.0, we mark some of the functions INLINE. +-- We mark the functions that just navigate down the tree (lookup, insert, +-- delete and similar). That navigation code gets inlined and thus specialized +-- when possible. There is a price to pay -- code growth. The code INLINED is +-- therefore only the tree navigation, all the real work (rebalancing) is not +-- INLINED by using a NOINLINE. +-- +-- All methods marked INLINE have to be nonrecursive -- a 'go' function doing +-- the real work is provided. + + +-- [Note: Type of local 'go' function] +-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +-- If the local 'go' function uses an Ord class, it sometimes heap-allocates +-- the Ord dictionary when the 'go' function does not have explicit type. +-- In that case we give 'go' explicit type. But this slightly decrease +-- performance, as the resulting 'go' function can float out to top level. + + +-- [Note: Local 'go' functions and capturing] +-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +-- As opposed to IntSet, when 'go' function captures an argument, increased +-- heap-allocation can occur: sometimes in a polymorphic function, the 'go' +-- floats out of its enclosing function and then it heap-allocates the +-- dictionary and the argument. Maybe it floats out too late and strictness +-- analyzer cannot see that these could be passed on stack. + +-- [Note: Order of constructors] +-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +-- The order of constructors of Set matters when considering performance. +-- Currently in GHC 7.0, when type has 2 constructors, a forward conditional +-- jump is made when successfully matching second constructor. Successful match +-- of first constructor results in the forward jump not taken. +-- On GHC 7.0, reordering constructors from Tip | Bin to Bin | Tip +-- improves the benchmark by up to 10% on x86. + +module Data.Set.Internal ( + -- * Set type + Set(..) -- instance Eq,Ord,Show,Read,Data,Typeable + + -- * Operators + , (\\) + + -- * Query + , null + , size + , member + , notMember + , lookupLT + , lookupGT + , lookupLE + , lookupGE + , isSubsetOf + , isProperSubsetOf + + -- * Construction + , empty + , singleton + , insert + , delete + + -- * Combine + , union + , unions + , difference + , intersection + + -- * Filter + , filter + , takeWhileAntitone + , dropWhileAntitone + , spanAntitone + , partition + , split + , splitMember + , splitRoot + + -- * Indexed + , lookupIndex + , findIndex + , elemAt + , deleteAt + , take + , drop + , splitAt + + -- * Map + , map + , mapMonotonic + + -- * Folds + , foldr + , foldl + -- ** Strict folds + , foldr' + , foldl' + -- ** Legacy folds + , fold + + -- * Min\/Max + , lookupMin + , lookupMax + , findMin + , findMax + , deleteMin + , deleteMax + , deleteFindMin + , deleteFindMax + , maxView + , minView + + -- * Conversion + + -- ** List + , elems + , toList + , fromList + + -- ** Ordered list + , toAscList + , toDescList + , fromAscList + , fromDistinctAscList + , fromDescList + , fromDistinctDescList + + -- * Debugging + , showTree + , showTreeWith + , valid + + -- Internals (for testing) + , bin + , balanced + , link + , merge + ) where + +import Prelude hiding (filter,foldl,foldr,null,map,take,drop,splitAt) +import qualified Data.List as List +import Data.Bits (shiftL, shiftR) +#if !MIN_VERSION_base(4,8,0) +import Data.Monoid (Monoid(..)) +#endif +#if MIN_VERSION_base(4,9,0) +import Data.Semigroup (Semigroup((<>), stimes), stimesIdempotentMonoid) +import Data.Functor.Classes +#endif +import qualified Data.Foldable as Foldable +import Data.Typeable +import Control.DeepSeq (NFData(rnf)) + +import Utils.Containers.Internal.StrictFold +import Utils.Containers.Internal.StrictPair +import Utils.Containers.Internal.PtrEquality + +#if __GLASGOW_HASKELL__ +import GHC.Exts ( build ) +#if __GLASGOW_HASKELL__ >= 708 +import qualified GHC.Exts as GHCExts +#endif +import Text.Read +import Data.Data +#endif + + +{-------------------------------------------------------------------- + Operators +--------------------------------------------------------------------} +infixl 9 \\ -- + +-- | /O(m*log(n\/m+1)), m <= n/. See 'difference'. +(\\) :: Ord a => Set a -> Set a -> Set a +m1 \\ m2 = difference m1 m2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE (\\) #-} +#endif + +{-------------------------------------------------------------------- + Sets are size balanced trees +--------------------------------------------------------------------} +-- | A set of values @a@. + +-- See Note: Order of constructors +data Set a = Bin {-# UNPACK #-} !Size !a !(Set a) !(Set a) + | Tip + +type Size = Int + +#if __GLASGOW_HASKELL__ >= 708 +type role Set nominal +#endif + +instance Ord a => Monoid (Set a) where + mempty = empty + mconcat = unions +#if !(MIN_VERSION_base(4,9,0)) + mappend = union +#else + mappend = (<>) + +instance Ord a => Semigroup (Set a) where + (<>) = union + stimes = stimesIdempotentMonoid +#endif + + +instance Foldable.Foldable Set where + fold = go + where go Tip = mempty + go (Bin 1 k _ _) = k + go (Bin _ k l r) = go l `mappend` (k `mappend` go r) + {-# INLINABLE fold #-} + foldr = foldr + {-# INLINE foldr #-} + foldl = foldl + {-# INLINE foldl #-} + foldMap f t = go t + where go Tip = mempty + go (Bin 1 k _ _) = f k + go (Bin _ k l r) = go l `mappend` (f k `mappend` go r) + {-# INLINE foldMap #-} + +#if MIN_VERSION_base(4,6,0) + foldl' = foldl' + {-# INLINE foldl' #-} + foldr' = foldr' + {-# INLINE foldr' #-} +#endif +#if MIN_VERSION_base(4,8,0) + length = size + {-# INLINE length #-} + null = null + {-# INLINE null #-} + toList = toList + {-# INLINE toList #-} + elem = go + where go !_ Tip = False + go x (Bin _ y l r) = x == y || go x l || go x r + {-# INLINABLE elem #-} + minimum = findMin + {-# INLINE minimum #-} + maximum = findMax + {-# INLINE maximum #-} + sum = foldl' (+) 0 + {-# INLINABLE sum #-} + product = foldl' (*) 1 + {-# INLINABLE product #-} +#endif + + +#if __GLASGOW_HASKELL__ + +{-------------------------------------------------------------------- + A Data instance +--------------------------------------------------------------------} + +-- This instance preserves data abstraction at the cost of inefficiency. +-- We provide limited reflection services for the sake of data abstraction. + +instance (Data a, Ord a) => Data (Set a) where + gfoldl f z set = z fromList `f` (toList set) + toConstr _ = fromListConstr + gunfold k z c = case constrIndex c of + 1 -> k (z fromList) + _ -> error "gunfold" + dataTypeOf _ = setDataType + dataCast1 f = gcast1 f + +fromListConstr :: Constr +fromListConstr = mkConstr setDataType "fromList" [] Prefix + +setDataType :: DataType +setDataType = mkDataType "Data.Set.Internal.Set" [fromListConstr] + +#endif + +{-------------------------------------------------------------------- + Query +--------------------------------------------------------------------} +-- | /O(1)/. Is this the empty set? +null :: Set a -> Bool +null Tip = True +null (Bin {}) = False +{-# INLINE null #-} + +-- | /O(1)/. The number of elements in the set. +size :: Set a -> Int +size Tip = 0 +size (Bin sz _ _ _) = sz +{-# INLINE size #-} + +-- | /O(log n)/. Is the element in the set? +member :: Ord a => a -> Set a -> Bool +member = go + where + go !_ Tip = False + go x (Bin _ y l r) = case compare x y of + LT -> go x l + GT -> go x r + EQ -> True +#if __GLASGOW_HASKELL__ +{-# INLINABLE member #-} +#else +{-# INLINE member #-} +#endif + +-- | /O(log n)/. Is the element not in the set? +notMember :: Ord a => a -> Set a -> Bool +notMember a t = not $ member a t +#if __GLASGOW_HASKELL__ +{-# INLINABLE notMember #-} +#else +{-# INLINE notMember #-} +#endif + +-- | /O(log n)/. Find largest element smaller than the given one. +-- +-- > lookupLT 3 (fromList [3, 5]) == Nothing +-- > lookupLT 5 (fromList [3, 5]) == Just 3 +lookupLT :: Ord a => a -> Set a -> Maybe a +lookupLT = goNothing + where + goNothing !_ Tip = Nothing + goNothing x (Bin _ y l r) | x <= y = goNothing x l + | otherwise = goJust x y r + + goJust !_ best Tip = Just best + goJust x best (Bin _ y l r) | x <= y = goJust x best l + | otherwise = goJust x y r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupLT #-} +#else +{-# INLINE lookupLT #-} +#endif + +-- | /O(log n)/. Find smallest element greater than the given one. +-- +-- > lookupGT 4 (fromList [3, 5]) == Just 5 +-- > lookupGT 5 (fromList [3, 5]) == Nothing +lookupGT :: Ord a => a -> Set a -> Maybe a +lookupGT = goNothing + where + goNothing !_ Tip = Nothing + goNothing x (Bin _ y l r) | x < y = goJust x y l + | otherwise = goNothing x r + + goJust !_ best Tip = Just best + goJust x best (Bin _ y l r) | x < y = goJust x y l + | otherwise = goJust x best r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupGT #-} +#else +{-# INLINE lookupGT #-} +#endif + +-- | /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 +lookupLE :: Ord a => a -> Set a -> Maybe a +lookupLE = goNothing + where + goNothing !_ Tip = Nothing + goNothing x (Bin _ y l r) = case compare x y of LT -> goNothing x l + EQ -> Just y + GT -> goJust x y r + + goJust !_ best Tip = Just best + goJust x best (Bin _ y l r) = case compare x y of LT -> goJust x best l + EQ -> Just y + GT -> goJust x y r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupLE #-} +#else +{-# INLINE lookupLE #-} +#endif + +-- | /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 +lookupGE :: Ord a => a -> Set a -> Maybe a +lookupGE = goNothing + where + goNothing !_ Tip = Nothing + goNothing x (Bin _ y l r) = case compare x y of LT -> goJust x y l + EQ -> Just y + GT -> goNothing x r + + goJust !_ best Tip = Just best + goJust x best (Bin _ y l r) = case compare x y of LT -> goJust x y l + EQ -> Just y + GT -> goJust x best r +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupGE #-} +#else +{-# INLINE lookupGE #-} +#endif + +{-------------------------------------------------------------------- + Construction +--------------------------------------------------------------------} +-- | /O(1)/. The empty set. +empty :: Set a +empty = Tip +{-# INLINE empty #-} + +-- | /O(1)/. Create a singleton set. +singleton :: a -> Set a +singleton x = Bin 1 x Tip Tip +{-# INLINE singleton #-} + +{-------------------------------------------------------------------- + Insertion, Deletion +--------------------------------------------------------------------} +-- | /O(log n)/. Insert an element in a set. +-- If the set already contains an element equal to the given value, +-- it is replaced with the new value. + +-- See Note: Type of local 'go' function +insert :: Ord a => a -> Set a -> Set a +insert = go + where + go :: Ord a => a -> Set a -> Set a + go !x Tip = singleton x + go !x t@(Bin sz y l r) = case compare x y of + LT | l' `ptrEq` l -> t + | otherwise -> balanceL y l' r + where !l' = go x l + GT | r' `ptrEq` r -> t + | otherwise -> balanceR y l r' + where !r' = go x r + EQ | x `ptrEq` y -> t + | otherwise -> Bin sz x l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE insert #-} +#else +{-# INLINE insert #-} +#endif + +-- Insert an element to the set only if it is not in the set. +-- Used by `union`. + +-- See Note: Type of local 'go' function +insertR :: Ord a => a -> Set a -> Set a +insertR = go + where + go :: Ord a => a -> Set a -> Set a + go !x Tip = singleton x + go !x t@(Bin _ y l r) = case compare x y of + LT | l' `ptrEq` l -> t + | otherwise -> balanceL y l' r + where !l' = go x l + GT | r' `ptrEq` r -> t + | otherwise -> balanceR y l r' + where !r' = go x r + EQ -> t +#if __GLASGOW_HASKELL__ +{-# INLINABLE insertR #-} +#else +{-# INLINE insertR #-} +#endif + +-- | /O(log n)/. Delete an element from a set. + +-- See Note: Type of local 'go' function +delete :: Ord a => a -> Set a -> Set a +delete = go + where + go :: Ord a => a -> Set a -> Set a + go !_ Tip = Tip + go x t@(Bin _ y l r) = case compare x y of + LT | l' `ptrEq` l -> t + | otherwise -> balanceR y l' r + where !l' = go x l + GT | r' `ptrEq` r -> t + | otherwise -> balanceL y l r' + where !r' = go x r + EQ -> glue l r +#if __GLASGOW_HASKELL__ +{-# INLINABLE delete #-} +#else +{-# INLINE delete #-} +#endif + +{-------------------------------------------------------------------- + Subset +--------------------------------------------------------------------} +-- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal). +isProperSubsetOf :: Ord a => Set a -> Set a -> Bool +isProperSubsetOf s1 s2 + = (size s1 < size s2) && (isSubsetOf s1 s2) +#if __GLASGOW_HASKELL__ +{-# INLINABLE isProperSubsetOf #-} +#endif + + +-- | /O(n+m)/. Is this a subset? +-- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@. +isSubsetOf :: Ord a => Set a -> Set a -> Bool +isSubsetOf t1 t2 + = (size t1 <= size t2) && (isSubsetOfX t1 t2) +#if __GLASGOW_HASKELL__ +{-# INLINABLE isSubsetOf #-} +#endif + +isSubsetOfX :: Ord a => Set a -> Set a -> Bool +isSubsetOfX Tip _ = True +isSubsetOfX _ Tip = False +isSubsetOfX (Bin _ x l r) t + = found && isSubsetOfX l lt && isSubsetOfX r gt + where + (lt,found,gt) = splitMember x t +#if __GLASGOW_HASKELL__ +{-# INLINABLE isSubsetOfX #-} +#endif + + +{-------------------------------------------------------------------- + Minimal, Maximal +--------------------------------------------------------------------} + +-- We perform call-pattern specialization manually on lookupMin +-- and lookupMax. Otherwise, GHC doesn't seem to do it, which is +-- unfortunate if, for example, someone uses findMin or findMax. + +lookupMinSure :: a -> Set a -> a +lookupMinSure x Tip = x +lookupMinSure _ (Bin _ x l _) = lookupMinSure x l + +-- | /O(log n)/. The minimal element of a set. +-- +-- @since 0.5.9 + +lookupMin :: Set a -> Maybe a +lookupMin Tip = Nothing +lookupMin (Bin _ x l _) = Just $! lookupMinSure x l + +-- | /O(log n)/. The minimal element of a set. +findMin :: Set a -> a +findMin t + | Just r <- lookupMin t = r + | otherwise = error "Set.findMin: empty set has no minimal element" + +lookupMaxSure :: a -> Set a -> a +lookupMaxSure x Tip = x +lookupMaxSure _ (Bin _ x _ r) = lookupMaxSure x r + +-- | /O(log n)/. The maximal element of a set. +-- +-- @since 0.5.9 + +lookupMax :: Set a -> Maybe a +lookupMax Tip = Nothing +lookupMax (Bin _ x _ r) = Just $! lookupMaxSure x r + +-- | /O(log n)/. The maximal element of a set. +findMax :: Set a -> a +findMax t + | Just r <- lookupMax t = r + | otherwise = error "Set.findMax: empty set has no maximal element" + +-- | /O(log n)/. Delete the minimal element. Returns an empty set if the set is empty. +deleteMin :: Set a -> Set a +deleteMin (Bin _ _ Tip r) = r +deleteMin (Bin _ x l r) = balanceR x (deleteMin l) r +deleteMin Tip = Tip + +-- | /O(log n)/. Delete the maximal element. Returns an empty set if the set is empty. +deleteMax :: Set a -> Set a +deleteMax (Bin _ _ l Tip) = l +deleteMax (Bin _ x l r) = balanceL x l (deleteMax r) +deleteMax Tip = Tip + +{-------------------------------------------------------------------- + Union. +--------------------------------------------------------------------} +-- | The union of a list of sets: (@'unions' == 'foldl' 'union' 'empty'@). +unions :: Ord a => [Set a] -> Set a +unions = foldlStrict union empty +#if __GLASGOW_HASKELL__ +{-# INLINABLE unions #-} +#endif + +-- | /O(m*log(n/m + 1)), m <= n/. The union of two sets, preferring the first set when +-- equal elements are encountered. +union :: Ord a => Set a -> Set a -> Set a +union t1 Tip = t1 +union t1 (Bin _ x Tip Tip) = insertR x t1 +union (Bin _ x Tip Tip) t2 = insert x t2 +union Tip t2 = t2 +union t1@(Bin _ x l1 r1) t2 = case splitS x t2 of + (l2 :*: r2) + | l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 -> t1 + | otherwise -> link x l1l2 r1r2 + where !l1l2 = union l1 l2 + !r1r2 = union r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE union #-} +#endif + +{-------------------------------------------------------------------- + Difference +--------------------------------------------------------------------} +-- | /O(m*log(n/m + 1)), m <= n/. Difference of two sets. +difference :: Ord a => Set a -> Set a -> Set a +difference Tip _ = Tip +difference t1 Tip = t1 +difference t1 (Bin _ x l2 r2) = case split x t1 of + (l1, r1) + | size l1l2 + size r1r2 == size t1 -> t1 + | otherwise -> merge l1l2 r1r2 + where !l1l2 = difference l1 l2 + !r1r2 = difference r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE difference #-} +#endif + +{-------------------------------------------------------------------- + Intersection +--------------------------------------------------------------------} +-- | /O(m*log(n/m + 1)), m <= n/. The intersection of two sets. +-- Elements of the result come from the first set, so for example +-- +-- > import qualified Data.Set as S +-- > data AB = A | B deriving Show +-- > instance Ord AB where compare _ _ = EQ +-- > instance Eq AB where _ == _ = True +-- > main = print (S.singleton A `S.intersection` S.singleton B, +-- > S.singleton B `S.intersection` S.singleton A) +-- +-- prints @(fromList [A],fromList [B])@. +intersection :: Ord a => Set a -> Set a -> Set a +intersection Tip _ = Tip +intersection _ Tip = Tip +intersection t1@(Bin _ x l1 r1) t2 + | b = if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1 + then t1 + else link x l1l2 r1r2 + | otherwise = merge l1l2 r1r2 + where + !(l2, b, r2) = splitMember x t2 + !l1l2 = intersection l1 l2 + !r1r2 = intersection r1 r2 +#if __GLASGOW_HASKELL__ +{-# INLINABLE intersection #-} +#endif + +{-------------------------------------------------------------------- + Filter and partition +--------------------------------------------------------------------} +-- | /O(n)/. Filter all elements that satisfy the predicate. +filter :: (a -> Bool) -> Set a -> Set a +filter _ Tip = Tip +filter p t@(Bin _ x l r) + | p x = if l `ptrEq` l' && r `ptrEq` r' + then t + else link x l' r' + | otherwise = merge l' r' + where + !l' = filter p l + !r' = filter p r + +-- | /O(n)/. Partition the set into two sets, one with all elements that satisfy +-- the predicate and one with all elements that don't satisfy the predicate. +-- See also 'split'. +partition :: (a -> Bool) -> Set a -> (Set a,Set a) +partition p0 t0 = toPair $ go p0 t0 + where + go _ Tip = (Tip :*: Tip) + go p t@(Bin _ x l r) = case (go p l, go p r) of + ((l1 :*: l2), (r1 :*: r2)) + | p x -> (if l1 `ptrEq` l && r1 `ptrEq` r + then t + else link x l1 r1) :*: merge l2 r2 + | otherwise -> merge l1 r1 :*: + (if l2 `ptrEq` l && r2 `ptrEq` r + then t + else link x l2 r2) + +{---------------------------------------------------------------------- + Map +----------------------------------------------------------------------} + +-- | /O(n*log n)/. +-- @'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 :: Ord b => (a->b) -> Set a -> Set b +map f = fromList . List.map f . toList +#if __GLASGOW_HASKELL__ +{-# INLINABLE map #-} +#endif + +-- | /O(n)/. The +-- +-- @'mapMonotonic' f s == 'map' f s@, but works only when @f@ is strictly increasing. +-- /The precondition is not checked./ +-- Semi-formally, we have: +-- +-- > and [x < y ==> f x < f y | x <- ls, y <- ls] +-- > ==> mapMonotonic f s == map f s +-- > where ls = toList s + +mapMonotonic :: (a->b) -> Set a -> Set b +mapMonotonic _ Tip = Tip +mapMonotonic f (Bin sz x l r) = Bin sz (f x) (mapMonotonic f l) (mapMonotonic f r) + +{-------------------------------------------------------------------- + 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 :: (a -> b -> b) -> b -> Set a -> 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 :: (a -> b -> b) -> b -> Set a -> b +foldr f z = go z + where + go z' Tip = z' + go z' (Bin _ x l r) = go (f x (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' :: (a -> b -> b) -> b -> Set a -> b +foldr' f z = go z + where + go !z' Tip = z' + go z' (Bin _ x l r) = go (f x (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 -> b -> a) -> a -> Set b -> a +foldl f z = go z + where + go z' Tip = z' + go z' (Bin _ x l r) = go (f (go z' l) x) 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 -> b -> a) -> a -> Set b -> a +foldl' f z = go z + where + go !z' Tip = z' + go z' (Bin _ x l r) = go (f (go z' l) x) r +{-# INLINE foldl' #-} + +{-------------------------------------------------------------------- + List variations +--------------------------------------------------------------------} +-- | /O(n)/. An alias of 'toAscList'. The elements of a set in ascending order. +-- Subject to list fusion. +elems :: Set a -> [a] +elems = toAscList + +{-------------------------------------------------------------------- + Lists +--------------------------------------------------------------------} +#if __GLASGOW_HASKELL__ >= 708 +instance (Ord a) => GHCExts.IsList (Set a) where + type Item (Set a) = a + fromList = fromList + toList = toList +#endif + +-- | /O(n)/. Convert the set to a list of elements. Subject to list fusion. +toList :: Set a -> [a] +toList = toAscList + +-- | /O(n)/. Convert the set to an ascending list of elements. Subject to list fusion. +toAscList :: Set a -> [a] +toAscList = foldr (:) [] + +-- | /O(n)/. Convert the set to a descending list of elements. Subject to list +-- fusion. +toDescList :: Set a -> [a] +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 :: (a -> b -> b) -> b -> Set a -> b +foldrFB = foldr +{-# INLINE[0] foldrFB #-} +foldlFB :: (a -> b -> a) -> a -> Set b -> 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 "Set.toAscList" [~1] forall s . toAscList s = build (\c n -> foldrFB c n s) #-} +{-# RULES "Set.toAscListBack" [1] foldrFB (:) [] = toAscList #-} +{-# RULES "Set.toDescList" [~1] forall s . toDescList s = build (\c n -> foldlFB (\xs x -> c x xs) n s) #-} +{-# RULES "Set.toDescListBack" [1] foldlFB (\xs x -> x : xs) [] = toDescList #-} +#endif + +-- | /O(n*log n)/. Create a set from a list of elements. +-- +-- If the elements are ordered, a linear-time implementation is used, +-- with the performance equal to 'fromDistinctAscList'. + +-- For some reason, when 'singleton' is used in fromList or in +-- create, it is not inlined, so we inline it manually. +fromList :: Ord a => [a] -> Set a +fromList [] = Tip +fromList [x] = Bin 1 x Tip Tip +fromList (x0 : xs0) | not_ordered x0 xs0 = fromList' (Bin 1 x0 Tip Tip) xs0 + | otherwise = go (1::Int) (Bin 1 x0 Tip Tip) xs0 + where + not_ordered _ [] = False + not_ordered x (y : _) = x >= y + {-# INLINE not_ordered #-} + + fromList' t0 xs = foldlStrict ins t0 xs + where ins t x = insert x t + + go !_ t [] = t + go _ t [x] = insertMax x t + go s l xs@(x : xss) | not_ordered x xss = fromList' l xs + | otherwise = case create s xss of + (r, ys, []) -> go (s `shiftL` 1) (link x l r) ys + (r, _, ys) -> fromList' (link x l r) ys + + -- The create is returning a triple (tree, xs, ys). Both xs and ys + -- represent not yet processed elements and only one of them can be nonempty. + -- If ys is nonempty, the keys in ys are not ordered with respect to tree + -- and must be inserted using fromList'. Otherwise the keys have been + -- ordered so far. + create !_ [] = (Tip, [], []) + create s xs@(x : xss) + | s == 1 = if not_ordered x xss then (Bin 1 x Tip Tip, [], xss) + else (Bin 1 x Tip Tip, xss, []) + | otherwise = case create (s `shiftR` 1) xs of + res@(_, [], _) -> res + (l, [y], zs) -> (insertMax y l, [], zs) + (l, ys@(y:yss), _) | not_ordered y yss -> (l, [], ys) + | otherwise -> case create (s `shiftR` 1) yss of + (r, zs, ws) -> (link y l r, zs, ws) +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromList #-} +#endif + +{-------------------------------------------------------------------- + Building trees from ascending/descending lists can be done in linear time. + + Note that if [xs] is ascending that: + fromAscList xs == fromList xs +--------------------------------------------------------------------} +-- | /O(n)/. Build a set from an ascending list in linear time. +-- /The precondition (input list is ascending) is not checked./ +fromAscList :: Eq a => [a] -> Set a +fromAscList xs = fromDistinctAscList (combineEq xs) +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromAscList #-} +#endif + +-- | /O(n)/. Build a set from a descending list in linear time. +-- /The precondition (input list is descending) is not checked./ +fromDescList :: Eq a => [a] -> Set a +fromDescList xs = fromDistinctDescList (combineEq xs) +#if __GLASGOW_HASKELL__ +{-# INLINABLE fromDescList #-} +#endif + +-- [combineEq xs] combines equal elements with [const] in an ordered list [xs] +-- +-- TODO: combineEq allocates an intermediate list. It *should* be better to +-- make fromAscListBy and fromDescListBy the fundamental operations, and to +-- implement the rest using those. +combineEq :: Eq a => [a] -> [a] +combineEq [] = [] +combineEq (x : xs) = combineEq' x xs + where + combineEq' z [] = [z] + combineEq' z (y:ys) + | z == y = combineEq' z ys + | otherwise = z : combineEq' y ys + +-- | /O(n)/. Build a set from an ascending list of distinct elements in linear time. +-- /The precondition (input list is strictly ascending) is not checked./ + +-- For some reason, when 'singleton' is used in fromDistinctAscList or in +-- create, it is not inlined, so we inline it manually. +fromDistinctAscList :: [a] -> Set a +fromDistinctAscList [] = Tip +fromDistinctAscList (x0 : xs0) = go (1::Int) (Bin 1 x0 Tip Tip) xs0 + where + go !_ t [] = t + go s l (x : xs) = case create s xs of + (r :*: ys) -> let !t' = link x l r + in go (s `shiftL` 1) t' ys + + create !_ [] = (Tip :*: []) + create s xs@(x : xs') + | s == 1 = (Bin 1 x Tip Tip :*: xs') + | otherwise = case create (s `shiftR` 1) xs of + res@(_ :*: []) -> res + (l :*: (y:ys)) -> case create (s `shiftR` 1) ys of + (r :*: zs) -> (link y l r :*: zs) + +-- | /O(n)/. Build a set from a descending list of distinct elements in linear time. +-- /The precondition (input list is strictly descending) is not checked./ + +-- For some reason, when 'singleton' is used in fromDistinctDescList or in +-- create, it is not inlined, so we inline it manually. +fromDistinctDescList :: [a] -> Set a +fromDistinctDescList [] = Tip +fromDistinctDescList (x0 : xs0) = go (1::Int) (Bin 1 x0 Tip Tip) xs0 + where + go !_ t [] = t + go s r (x : xs) = case create s xs of + (l :*: ys) -> let !t' = link x l r + in go (s `shiftL` 1) t' ys + + create !_ [] = (Tip :*: []) + create s xs@(x : xs') + | s == 1 = (Bin 1 x Tip Tip :*: xs') + | otherwise = case create (s `shiftR` 1) xs of + res@(_ :*: []) -> res + (r :*: (y:ys)) -> case create (s `shiftR` 1) ys of + (l :*: zs) -> (link y l r :*: zs) + +{-------------------------------------------------------------------- + Eq converts the set to a list. In a lazy setting, this + actually seems one of the faster methods to compare two trees + and it is certainly the simplest :-) +--------------------------------------------------------------------} +instance Eq a => Eq (Set a) where + t1 == t2 = (size t1 == size t2) && (toAscList t1 == toAscList t2) + +{-------------------------------------------------------------------- + Ord +--------------------------------------------------------------------} + +instance Ord a => Ord (Set a) where + compare s1 s2 = compare (toAscList s1) (toAscList s2) + +{-------------------------------------------------------------------- + Show +--------------------------------------------------------------------} +instance Show a => Show (Set a) where + showsPrec p xs = showParen (p > 10) $ + showString "fromList " . shows (toList xs) + +#if MIN_VERSION_base(4,9,0) +instance Eq1 Set where + liftEq eq m n = + size m == size n && liftEq eq (toList m) (toList n) + +instance Ord1 Set where + liftCompare cmp m n = + liftCompare cmp (toList m) (toList n) + +instance Show1 Set where + liftShowsPrec sp sl d m = + showsUnaryWith (liftShowsPrec sp sl) "fromList" d (toList m) +#endif + +{-------------------------------------------------------------------- + Read +--------------------------------------------------------------------} +instance (Read a, Ord a) => Read (Set a) 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/Data +--------------------------------------------------------------------} + +INSTANCE_TYPEABLE1(Set) + +{-------------------------------------------------------------------- + NFData +--------------------------------------------------------------------} + +instance NFData a => NFData (Set a) where + rnf Tip = () + rnf (Bin _ y l r) = rnf y `seq` rnf l `seq` rnf r + +{-------------------------------------------------------------------- + Split +--------------------------------------------------------------------} +-- | /O(log n)/. 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 :: Ord a => a -> Set a -> (Set a,Set a) +split x t = toPair $ splitS x t +{-# INLINABLE split #-} + +splitS :: Ord a => a -> Set a -> StrictPair (Set a) (Set a) +splitS _ Tip = (Tip :*: Tip) +splitS x (Bin _ y l r) + = case compare x y of + LT -> let (lt :*: gt) = splitS x l in (lt :*: link y gt r) + GT -> let (lt :*: gt) = splitS x r in (link y l lt :*: gt) + EQ -> (l :*: r) +{-# INLINABLE splitS #-} + +-- | /O(log n)/. Performs a 'split' but also returns whether the pivot +-- element was found in the original set. +splitMember :: Ord a => a -> Set a -> (Set a,Bool,Set a) +splitMember _ Tip = (Tip, False, Tip) +splitMember x (Bin _ y l r) + = case compare x y of + LT -> let (lt, found, gt) = splitMember x l + !gt' = link y gt r + in (lt, found, gt') + GT -> let (lt, found, gt) = splitMember x r + !lt' = link y l lt + in (lt', found, gt) + EQ -> (l, True, r) +#if __GLASGOW_HASKELL__ +{-# INLINABLE splitMember #-} +#endif + +{-------------------------------------------------------------------- + Indexing +--------------------------------------------------------------------} + +-- | /O(log n)/. Return the /index/ of an element, which is its zero-based +-- index in the sorted sequence of elements. The index is a number from /0/ up +-- to, but not including, the 'size' of the set. Calls 'error' when the element +-- is not a 'member' of the set. +-- +-- > findIndex 2 (fromList [5,3]) Error: element is not in the set +-- > findIndex 3 (fromList [5,3]) == 0 +-- > findIndex 5 (fromList [5,3]) == 1 +-- > findIndex 6 (fromList [5,3]) Error: element is not in the set + +-- See Note: Type of local 'go' function +findIndex :: Ord a => a -> Set a -> Int +findIndex = go 0 + where + go :: Ord a => Int -> a -> Set a -> Int + go !_ !_ Tip = error "Set.findIndex: element is not in the set" + go idx x (Bin _ kx l r) = case compare x kx of + LT -> go idx x l + GT -> go (idx + size l + 1) x r + EQ -> idx + size l +#if __GLASGOW_HASKELL__ +{-# INLINABLE findIndex #-} +#endif + +-- | /O(log n)/. Lookup the /index/ of an element, which is its zero-based index in +-- the sorted sequence of elements. The index is a number from /0/ up to, but not +-- including, the 'size' of the set. +-- +-- > isJust (lookupIndex 2 (fromList [5,3])) == False +-- > fromJust (lookupIndex 3 (fromList [5,3])) == 0 +-- > fromJust (lookupIndex 5 (fromList [5,3])) == 1 +-- > isJust (lookupIndex 6 (fromList [5,3])) == False + +-- See Note: Type of local 'go' function +lookupIndex :: Ord a => a -> Set a -> Maybe Int +lookupIndex = go 0 + where + go :: Ord a => Int -> a -> Set a -> Maybe Int + go !_ !_ Tip = Nothing + go idx x (Bin _ kx l r) = case compare x kx of + LT -> go idx x l + GT -> go (idx + size l + 1) x r + EQ -> Just $! idx + size l +#if __GLASGOW_HASKELL__ +{-# INLINABLE lookupIndex #-} +#endif + +-- | /O(log n)/. Retrieve an element by its /index/, i.e. by its zero-based +-- index in the sorted sequence of elements. If the /index/ is out of range (less +-- than zero, greater or equal to 'size' of the set), 'error' is called. +-- +-- > elemAt 0 (fromList [5,3]) == 3 +-- > elemAt 1 (fromList [5,3]) == 5 +-- > elemAt 2 (fromList [5,3]) Error: index out of range + +elemAt :: Int -> Set a -> a +elemAt !_ Tip = error "Set.elemAt: index out of range" +elemAt i (Bin _ x l r) + = case compare i sizeL of + LT -> elemAt i l + GT -> elemAt (i-sizeL-1) r + EQ -> x + where + sizeL = size l + +-- | /O(log n)/. Delete the element at /index/, i.e. by its zero-based index in +-- the sorted sequence of elements. If the /index/ is out of range (less than zero, +-- greater or equal to 'size' of the set), 'error' is called. +-- +-- > deleteAt 0 (fromList [5,3]) == singleton 5 +-- > deleteAt 1 (fromList [5,3]) == singleton 3 +-- > deleteAt 2 (fromList [5,3]) Error: index out of range +-- > deleteAt (-1) (fromList [5,3]) Error: index out of range + +deleteAt :: Int -> Set a -> Set a +deleteAt !i t = + case t of + Tip -> error "Set.deleteAt: index out of range" + Bin _ x l r -> case compare i sizeL of + LT -> balanceR x (deleteAt i l) r + GT -> balanceL x l (deleteAt (i-sizeL-1) r) + EQ -> glue l r + where + sizeL = size l + +-- | Take a given number of elements in order, beginning +-- with the smallest ones. +-- +-- @ +-- take n = 'fromDistinctAscList' . 'Prelude.take' n . 'toAscList' +-- @ +take :: Int -> Set a -> Set a +take i m | i >= size m = m +take i0 m0 = go i0 m0 + where + go i !_ | i <= 0 = Tip + go !_ Tip = Tip + go i (Bin _ x l r) = + case compare i sizeL of + LT -> go i l + GT -> link x l (go (i - sizeL - 1) r) + EQ -> l + where sizeL = size l + +-- | Drop a given number of elements in order, beginning +-- with the smallest ones. +-- +-- @ +-- drop n = 'fromDistinctAscList' . 'Prelude.drop' n . 'toAscList' +-- @ +drop :: Int -> Set a -> Set a +drop i m | i >= size m = Tip +drop i0 m0 = go i0 m0 + where + go i m | i <= 0 = m + go !_ Tip = Tip + go i (Bin _ x l r) = + case compare i sizeL of + LT -> link x (go i l) r + GT -> go (i - sizeL - 1) r + EQ -> insertMin x r + where sizeL = size l + +-- | /O(log n)/. Split a set at a particular index. +-- +-- @ +-- splitAt !n !xs = ('take' n xs, 'drop' n xs) +-- @ +splitAt :: Int -> Set a -> (Set a, Set a) +splitAt i0 m0 + | i0 >= size m0 = (m0, Tip) + | otherwise = toPair $ go i0 m0 + where + go i m | i <= 0 = Tip :*: m + go !_ Tip = Tip :*: Tip + go i (Bin _ x l r) + = case compare i sizeL of + LT -> case go i l of + ll :*: lr -> ll :*: link x lr r + GT -> case go (i - sizeL - 1) r of + rl :*: rr -> link x l rl :*: rr + EQ -> l :*: insertMin x r + where sizeL = size l + +-- | /O(log n)/. Take while a predicate on the elements holds. +-- The user is responsible for ensuring that for all elements @j@ and @k@ in the set, +-- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. +-- +-- @ +-- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' p . 'toList' +-- takeWhileAntitone p = 'filter' p +-- @ + +takeWhileAntitone :: (a -> Bool) -> Set a -> Set a +takeWhileAntitone _ Tip = Tip +takeWhileAntitone p (Bin _ x l r) + | p x = link x l (takeWhileAntitone p r) + | otherwise = takeWhileAntitone p l + +-- | /O(log n)/. Drop while a predicate on the elements holds. +-- The user is responsible for ensuring that for all elements @j@ and @k@ in the set, +-- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'. +-- +-- @ +-- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' p . 'toList' +-- dropWhileAntitone p = 'filter' (not . p) +-- @ + +dropWhileAntitone :: (a -> Bool) -> Set a -> Set a +dropWhileAntitone _ Tip = Tip +dropWhileAntitone p (Bin _ x l r) + | p x = dropWhileAntitone p r + | otherwise = link x (dropWhileAntitone p l) r + +-- | /O(log n)/. Divide a set at the point where a predicate on the elements stops holding. +-- The user is responsible for ensuring that for all elements @j@ and @k@ in the set, +-- @j \< k ==\> p j \>= p k@. +-- +-- @ +-- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs) +-- spanAntitone p xs = partition p xs +-- @ +-- +-- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the set +-- at some /unspecified/ point where the predicate switches from holding to not +-- holding (where the predicate is seen to hold before the first element and to fail +-- after the last element). + +spanAntitone :: (a -> Bool) -> Set a -> (Set a, Set a) +spanAntitone p0 m = toPair (go p0 m) + where + go _ Tip = Tip :*: Tip + go p (Bin _ x l r) + | p x = let u :*: v = go p r in link x l u :*: v + | otherwise = let u :*: v = go p l in u :*: link x v r + + +{-------------------------------------------------------------------- + Utility functions that maintain the balance properties of the tree. + All constructors assume that all values in [l] < [x] and all values + in [r] > [x], and that [l] and [r] are valid trees. + + In order of sophistication: + [Bin sz x l r] The type constructor. + [bin x l r] Maintains the correct size, assumes that both [l] + and [r] are balanced with respect to each other. + [balance x l r] Restores the balance and size. + Assumes that the original tree was balanced and + that [l] or [r] has changed by at most one element. + [link x l r] Restores balance and size. + + Furthermore, we can construct a new tree from two trees. Both operations + assume that all values in [l] < all values in [r] and that [l] and [r] + are valid: + [glue l r] Glues [l] and [r] together. Assumes that [l] and + [r] are already balanced with respect to each other. + [merge l r] Merges two trees and restores balance. +--------------------------------------------------------------------} + +{-------------------------------------------------------------------- + Link +--------------------------------------------------------------------} +link :: a -> Set a -> Set a -> Set a +link x Tip r = insertMin x r +link x l Tip = insertMax x l +link x l@(Bin sizeL y ly ry) r@(Bin sizeR z lz rz) + | delta*sizeL < sizeR = balanceL z (link x l lz) rz + | delta*sizeR < sizeL = balanceR y ly (link x ry r) + | otherwise = bin x l r + + +-- insertMin and insertMax don't perform potentially expensive comparisons. +insertMax,insertMin :: a -> Set a -> Set a +insertMax x t + = case t of + Tip -> singleton x + Bin _ y l r + -> balanceR y l (insertMax x r) + +insertMin x t + = case t of + Tip -> singleton x + Bin _ y l r + -> balanceL y (insertMin x l) r + +{-------------------------------------------------------------------- + [merge l r]: merges two trees. +--------------------------------------------------------------------} +merge :: Set a -> Set a -> Set a +merge Tip r = r +merge l Tip = l +merge l@(Bin sizeL x lx rx) r@(Bin sizeR y ly ry) + | delta*sizeL < sizeR = balanceL y (merge l ly) ry + | delta*sizeR < sizeL = balanceR x lx (merge rx r) + | otherwise = glue l r + +{-------------------------------------------------------------------- + [glue l r]: glues two trees together. + Assumes that [l] and [r] are already balanced with respect to each other. +--------------------------------------------------------------------} +glue :: Set a -> Set a -> Set a +glue Tip r = r +glue l Tip = l +glue l@(Bin sl xl ll lr) r@(Bin sr xr rl rr) + | sl > sr = let !(m :*: l') = maxViewSure xl ll lr in balanceR m l' r + | otherwise = let !(m :*: r') = minViewSure xr rl rr in balanceL m l r' + +-- | /O(log n)/. Delete and find the minimal element. +-- +-- > deleteFindMin set = (findMin set, deleteMin set) + +deleteFindMin :: Set a -> (a,Set a) +deleteFindMin t + | Just r <- minView t = r + | otherwise = (error "Set.deleteFindMin: can not return the minimal element of an empty set", Tip) + +-- | /O(log n)/. Delete and find the maximal element. +-- +-- > deleteFindMax set = (findMax set, deleteMax set) +deleteFindMax :: Set a -> (a,Set a) +deleteFindMax t + | Just r <- maxView t = r + | otherwise = (error "Set.deleteFindMax: can not return the maximal element of an empty set", Tip) + +minViewSure :: a -> Set a -> Set a -> StrictPair a (Set a) +minViewSure = go + where + go x Tip r = x :*: r + go x (Bin _ xl ll lr) r = + case go xl ll lr of + xm :*: l' -> xm :*: balanceR x l' r + +-- | /O(log n)/. Retrieves the minimal key of the set, and the set +-- stripped of that element, or 'Nothing' if passed an empty set. +minView :: Set a -> Maybe (a, Set a) +minView Tip = Nothing +minView (Bin _ x l r) = Just $! toPair $ minViewSure x l r + +maxViewSure :: a -> Set a -> Set a -> StrictPair a (Set a) +maxViewSure = go + where + go x l Tip = x :*: l + go x l (Bin _ xr rl rr) = + case go xr rl rr of + xm :*: r' -> xm :*: balanceL x l r' + +-- | /O(log n)/. Retrieves the maximal key of the set, and the set +-- stripped of that element, or 'Nothing' if passed an empty set. +maxView :: Set a -> Maybe (a, Set a) +maxView Tip = Nothing +maxView (Bin _ x l r) = Just $! toPair $ maxViewSure x l r + +{-------------------------------------------------------------------- + [balance x l r] balances two trees with value x. + The sizes of the trees should balance after decreasing the + size of one of them. (a rotation). + + [delta] is the maximal relative difference between the sizes of + two trees, it corresponds with the [w] in Adams' paper. + [ratio] is the ratio between an outer and inner sibling of the + heavier subtree in an unbalanced setting. It determines + whether a double or single rotation should be performed + to restore balance. It is correspondes with the inverse + of $\alpha$ in Adam's article. + + Note that according to the Adam's paper: + - [delta] should be larger than 4.646 with a [ratio] of 2. + - [delta] should be larger than 3.745 with a [ratio] of 1.534. + + But the Adam's paper is errorneous: + - it can be proved that for delta=2 and delta>=5 there does + not exist any ratio that would work + - delta=4.5 and ratio=2 does not work + + That leaves two reasonable variants, delta=3 and delta=4, + both with ratio=2. + + - A lower [delta] leads to a more 'perfectly' balanced tree. + - A higher [delta] performs less rebalancing. + + In the benchmarks, delta=3 is faster on insert operations, + and delta=4 has slightly better deletes. As the insert speedup + is larger, we currently use delta=3. + +--------------------------------------------------------------------} +delta,ratio :: Int +delta = 3 +ratio = 2 + +-- The balance function is equivalent to the following: +-- +-- balance :: a -> Set a -> Set a -> Set a +-- balance x l r +-- | sizeL + sizeR <= 1 = Bin sizeX x l r +-- | sizeR > delta*sizeL = rotateL x l r +-- | sizeL > delta*sizeR = rotateR x l r +-- | otherwise = Bin sizeX x l r +-- where +-- sizeL = size l +-- sizeR = size r +-- sizeX = sizeL + sizeR + 1 +-- +-- rotateL :: a -> Set a -> Set a -> Set a +-- rotateL x l r@(Bin _ _ ly ry) | size ly < ratio*size ry = singleL x l r +-- | otherwise = doubleL x l r +-- rotateR :: a -> Set a -> Set a -> Set a +-- rotateR x l@(Bin _ _ ly ry) r | size ry < ratio*size ly = singleR x l r +-- | otherwise = doubleR x l r +-- +-- singleL, singleR :: a -> Set a -> Set a -> Set a +-- singleL x1 t1 (Bin _ x2 t2 t3) = bin x2 (bin x1 t1 t2) t3 +-- singleR x1 (Bin _ x2 t1 t2) t3 = bin x2 t1 (bin x1 t2 t3) +-- +-- doubleL, doubleR :: a -> Set a -> Set a -> Set a +-- doubleL x1 t1 (Bin _ x2 (Bin _ x3 t2 t3) t4) = bin x3 (bin x1 t1 t2) (bin x2 t3 t4) +-- doubleR x1 (Bin _ x2 t1 (Bin _ x3 t2 t3)) t4 = bin x3 (bin x2 t1 t2) (bin x1 t3 t4) +-- +-- It is only written in such a way that every node is pattern-matched only once. +-- +-- Only balanceL and balanceR are needed at the moment, so balance is not here anymore. +-- In case it is needed, it can be found in Data.Map. + +-- Functions balanceL and balanceR are specialised versions of balance. +-- balanceL only checks whether the left subtree is too big, +-- balanceR only checks whether the right subtree is too big. + +-- balanceL is called when left subtree might have been inserted to or when +-- right subtree might have been deleted from. +balanceL :: a -> Set a -> Set a -> Set a +balanceL x l r = case r of + Tip -> case l of + Tip -> Bin 1 x Tip Tip + (Bin _ _ Tip Tip) -> Bin 2 x l Tip + (Bin _ lx Tip (Bin _ lrx _ _)) -> Bin 3 lrx (Bin 1 lx Tip Tip) (Bin 1 x Tip Tip) + (Bin _ lx ll@(Bin _ _ _ _) Tip) -> Bin 3 lx ll (Bin 1 x Tip Tip) + (Bin ls lx ll@(Bin lls _ _ _) lr@(Bin lrs lrx lrl lrr)) + | lrs < ratio*lls -> Bin (1+ls) lx ll (Bin (1+lrs) x lr Tip) + | otherwise -> Bin (1+ls) lrx (Bin (1+lls+size lrl) lx ll lrl) (Bin (1+size lrr) x lrr Tip) + + (Bin rs _ _ _) -> case l of + Tip -> Bin (1+rs) x Tip r + + (Bin ls lx ll lr) + | ls > delta*rs -> case (ll, lr) of + (Bin lls _ _ _, Bin lrs lrx lrl lrr) + | lrs < ratio*lls -> Bin (1+ls+rs) lx ll (Bin (1+rs+lrs) x lr r) + | otherwise -> Bin (1+ls+rs) lrx (Bin (1+lls+size lrl) lx ll lrl) (Bin (1+rs+size lrr) x lrr r) + (_, _) -> error "Failure in Data.Map.balanceL" + | otherwise -> Bin (1+ls+rs) x l r +{-# NOINLINE balanceL #-} + +-- balanceR is called when right subtree might have been inserted to or when +-- left subtree might have been deleted from. +balanceR :: a -> Set a -> Set a -> Set a +balanceR x l r = case l of + Tip -> case r of + Tip -> Bin 1 x Tip Tip + (Bin _ _ Tip Tip) -> Bin 2 x Tip r + (Bin _ rx Tip rr@(Bin _ _ _ _)) -> Bin 3 rx (Bin 1 x Tip Tip) rr + (Bin _ rx (Bin _ rlx _ _) Tip) -> Bin 3 rlx (Bin 1 x Tip Tip) (Bin 1 rx Tip Tip) + (Bin rs rx rl@(Bin rls rlx rll rlr) rr@(Bin rrs _ _ _)) + | rls < ratio*rrs -> Bin (1+rs) rx (Bin (1+rls) x Tip rl) rr + | otherwise -> Bin (1+rs) rlx (Bin (1+size rll) x Tip rll) (Bin (1+rrs+size rlr) rx rlr rr) + + (Bin ls _ _ _) -> case r of + Tip -> Bin (1+ls) x l Tip + + (Bin rs rx rl rr) + | rs > delta*ls -> case (rl, rr) of + (Bin rls rlx rll rlr, Bin rrs _ _ _) + | rls < ratio*rrs -> Bin (1+ls+rs) rx (Bin (1+ls+rls) x l rl) rr + | otherwise -> Bin (1+ls+rs) rlx (Bin (1+ls+size rll) x l rll) (Bin (1+rrs+size rlr) rx rlr rr) + (_, _) -> error "Failure in Data.Map.balanceR" + | otherwise -> Bin (1+ls+rs) x l r +{-# NOINLINE balanceR #-} + +{-------------------------------------------------------------------- + The bin constructor maintains the size of the tree +--------------------------------------------------------------------} +bin :: a -> Set a -> Set a -> Set a +bin x l r + = Bin (size l + size r + 1) x l r +{-# INLINE bin #-} + + +{-------------------------------------------------------------------- + Utilities +--------------------------------------------------------------------} + +-- | /O(1)/. Decompose a set into pieces based on the structure of the underlying +-- tree. This function is useful for consuming a set in parallel. +-- +-- No guarantee is made as to the sizes of the pieces; an internal, but +-- deterministic process determines this. However, it is guaranteed that the pieces +-- returned will be in ascending order (all elements in the first subset less than all +-- elements in the second, and so on). +-- +-- Examples: +-- +-- > splitRoot (fromList [1..6]) == +-- > [fromList [1,2,3],fromList [4],fromList [5,6]] +-- +-- > splitRoot empty == [] +-- +-- Note that the current implementation does not return more than three subsets, +-- but you should not depend on this behaviour because it can change in the +-- future without notice. +splitRoot :: Set a -> [Set a] +splitRoot orig = + case orig of + Tip -> [] + Bin _ v l r -> [l, singleton v, r] +{-# INLINE splitRoot #-} + + +{-------------------------------------------------------------------- + Debugging +--------------------------------------------------------------------} +-- | /O(n)/. Show the tree that implements the set. The tree is shown +-- in a compressed, hanging format. +showTree :: Show a => Set a -> 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. + +> Set> putStrLn $ showTreeWith True False $ fromDistinctAscList [1..5] +> 4 +> +--2 +> | +--1 +> | +--3 +> +--5 +> +> Set> putStrLn $ showTreeWith True True $ fromDistinctAscList [1..5] +> 4 +> | +> +--2 +> | | +> | +--1 +> | | +> | +--3 +> | +> +--5 +> +> Set> putStrLn $ showTreeWith False True $ fromDistinctAscList [1..5] +> +--5 +> | +> 4 +> | +> | +--3 +> | | +> +--2 +> | +> +--1 + +-} +showTreeWith :: Show a => Bool -> Bool -> Set a -> String +showTreeWith hang wide t + | hang = (showsTreeHang wide [] t) "" + | otherwise = (showsTree wide [] [] t) "" + +showsTree :: Show a => Bool -> [String] -> [String] -> Set a -> ShowS +showsTree wide lbars rbars t + = case t of + Tip -> showsBars lbars . showString "|\n" + Bin _ x Tip Tip + -> showsBars lbars . shows x . showString "\n" + Bin _ x l r + -> showsTree wide (withBar rbars) (withEmpty rbars) r . + showWide wide rbars . + showsBars lbars . shows x . showString "\n" . + showWide wide lbars . + showsTree wide (withEmpty lbars) (withBar lbars) l + +showsTreeHang :: Show a => Bool -> [String] -> Set a -> ShowS +showsTreeHang wide bars t + = case t of + Tip -> showsBars bars . showString "|\n" + Bin _ x Tip Tip + -> showsBars bars . shows x . showString "\n" + Bin _ x l r + -> showsBars bars . shows x . showString "\n" . + showWide wide bars . + showsTreeHang wide (withBar bars) l . + showWide wide bars . + showsTreeHang wide (withEmpty bars) r + +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 + +node :: String +node = "+--" + +withBar, withEmpty :: [String] -> [String] +withBar bars = "| ":bars +withEmpty bars = " ":bars + +{-------------------------------------------------------------------- + Assertions +--------------------------------------------------------------------} +-- | /O(n)/. Test if the internal set structure is valid. +valid :: Ord a => Set a -> Bool +valid t + = balanced t && ordered t && validsize t + +ordered :: Ord a => Set a -> Bool +ordered t + = bounded (const True) (const True) t + where + bounded lo hi t' + = case t' of + Tip -> True + Bin _ x l r -> (lo x) && (hi x) && bounded lo (x) hi r + +balanced :: Set a -> Bool +balanced t + = case t of + Tip -> True + Bin _ _ l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) && + balanced l && balanced r + +validsize :: Set a -> Bool +validsize t + = (realsize t == Just (size t)) + where + realsize t' + = case t' of + Tip -> Just 0 + Bin sz _ l r -> case (realsize l,realsize r) of + (Just n,Just m) | n+m+1 == sz -> Just sz + _ -> Nothing diff --git a/Data/Tree.hs b/Data/Tree.hs --- a/Data/Tree.hs +++ b/Data/Tree.hs @@ -65,6 +65,11 @@ import Data.Coerce #endif +#if MIN_VERSION_base(4,9,0) +import Data.Functor.Classes +import Data.Semigroup (Semigroup (..)) +#endif + -- | Multi-way trees, also known as /rose trees/. data Tree a = Node { rootLabel :: a, -- ^ label value @@ -82,6 +87,39 @@ deriving (Eq, Read, Show) #endif type Forest a = [Tree a] + +#if MIN_VERSION_base(4,9,0) +instance Eq1 Tree where + liftEq eq = leq + where + leq (Node a fr) (Node a' fr') = eq a a' && liftEq leq fr fr' + +instance Ord1 Tree where + liftCompare cmp = lcomp + where + lcomp (Node a fr) (Node a' fr') = cmp a a' <> liftCompare lcomp fr fr' + +instance Show1 Tree where + liftShowsPrec shw shwl _p (Node a fr) = + showString "Node {rootLabel = " . shw 0 a . showString ", " . + showString "subForest = " . liftShowList shw shwl fr . + showString "}" + +instance Read1 Tree where + liftReadsPrec rd rdl _p = readParen False $ + \s -> do + ("Node", s1) <- lex s + ("{", s2) <- lex s1 + ("rootLabel", s3) <- lex s2 + ("=", s4) <- lex s3 + (a, s5) <- rd 0 s4 + (",", s6) <- lex s5 + ("subForest", s7) <- lex s6 + ("=", s8) <- lex s7 + (fr, s9) <- liftReadList rd rdl s8 + ("}", s10) <- lex s9 + pure (Node a fr, s10) +#endif INSTANCE_TYPEABLE1(Tree) diff --git a/Data/Utils/BitQueue.hs b/Data/Utils/BitQueue.hs deleted file mode 100644 --- a/Data/Utils/BitQueue.hs +++ /dev/null @@ -1,148 +0,0 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE BangPatterns #-} - -#include "containers.h" - -{-# OPTIONS_HADDOCK hide #-} - ------------------------------------------------------------------------------ --- | --- Module : Data.Utils.BitQueue --- Copyright : (c) David Feuer 2016 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : provisional --- Portability : portable --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. --- --- = Description --- --- An extremely light-weight, fast, and limited representation of a string of --- up to (2*WORDSIZE - 2) bits. In fact, there are two representations, --- misleadingly named bit queue builder and bit queue. The builder supports --- only `emptyQB`, creating an empty builder, and `snocQB`, enqueueing a bit. --- The bit queue builder is then turned into a bit queue using `buildQ`, after --- which bits can be removed one by one using `unconsQ`. If the size limit is --- exceeded, further operations will silently produce nonsense. ------------------------------------------------------------------------------ - -module Data.Utils.BitQueue - ( BitQueue - , BitQueueB - , emptyQB - , snocQB - , buildQ - , unconsQ - , toListQ - ) where - -#if !MIN_VERSION_base(4,8,0) -import Data.Word (Word) -#endif -import Data.Utils.BitUtil (shiftLL, shiftRL, wordSize) -import Data.Bits ((.|.), (.&.), testBit) -#if MIN_VERSION_base(4,8,0) -import Data.Bits (countTrailingZeros) -#elif MIN_VERSION_base(4,5,0) -import Data.Bits (popCount) -#endif - -#if !MIN_VERSION_base(4,5,0) --- We could almost certainly improve this fall-back (copied straight from the --- default definition in Data.Bits), but it hardly seems worth the trouble --- to speed things up on GHC 7.4 and below. -countTrailingZeros :: Word -> Int -countTrailingZeros x = go 0 - where - go i | i >= wordSize = i - | testBit x i = i - | otherwise = go (i+1) - -#elif !MIN_VERSION_base(4,8,0) -countTrailingZeros :: Word -> Int -countTrailingZeros x = popCount ((x .&. (-x)) - 1) -{-# INLINE countTrailingZeros #-} -#endif - --- A bit queue builder. We represent a double word using two words --- because we don't currently have access to proper double words. -data BitQueueB = BQB {-# UNPACK #-} !Word - {-# UNPACK #-} !Word - -newtype BitQueue = BQ BitQueueB deriving Show - --- Intended for debugging. -instance Show BitQueueB where - show (BQB hi lo) = "BQ"++ - show (map (testBit hi) [(wordSize - 1),(wordSize - 2)..0] - ++ map (testBit lo) [(wordSize - 1),(wordSize - 2)..0]) - --- | Create an empty bit queue builder. This is represented as a single guard --- bit in the most significant position. -emptyQB :: BitQueueB -emptyQB = BQB (1 `shiftLL` (wordSize - 1)) 0 -{-# INLINE emptyQB #-} - --- Shift the double word to the right by one bit. -shiftQBR1 :: BitQueueB -> BitQueueB -shiftQBR1 (BQB hi lo) = BQB hi' lo' where - lo' = (lo `shiftRL` 1) .|. (hi `shiftLL` (wordSize - 1)) - hi' = hi `shiftRL` 1 -{-# INLINE shiftQBR1 #-} - --- | Enqueue a bit. This works by shifting the queue right one bit, --- then setting the most significant bit as requested. -{-# INLINE snocQB #-} -snocQB :: BitQueueB -> Bool -> BitQueueB -snocQB bq b = case shiftQBR1 bq of - BQB hi lo -> BQB (hi .|. (fromIntegral (fromEnum b) `shiftLL` (wordSize - 1))) lo - --- | Convert a bit queue builder to a bit queue. This shifts in a new --- guard bit on the left, and shifts right until the old guard bit falls --- off. -{-# INLINE buildQ #-} -buildQ :: BitQueueB -> BitQueue -buildQ (BQB hi 0) = BQ (BQB 0 lo') where - zeros = countTrailingZeros hi - lo' = ((hi `shiftRL` 1) .|. (1 `shiftLL` (wordSize - 1))) `shiftRL` zeros -buildQ (BQB hi lo) = BQ (BQB hi' lo') where - zeros = countTrailingZeros lo - lo1 = (lo `shiftRL` 1) .|. (hi `shiftLL` (wordSize - 1)) - hi1 = (hi `shiftRL` 1) .|. (1 `shiftLL` (wordSize - 1)) - lo' = (lo1 `shiftRL` zeros) .|. (hi1 `shiftLL` (wordSize - zeros)) - hi' = hi1 `shiftRL` zeros - --- Test if the queue is empty, which occurs when theres --- nothing left but a guard bit in the least significant --- place. -nullQ :: BitQueue -> Bool -nullQ (BQ (BQB 0 1)) = True -nullQ _ = False -{-# INLINE nullQ #-} - --- | Dequeue an element, or discover the queue is empty. -unconsQ :: BitQueue -> Maybe (Bool, BitQueue) -unconsQ q | nullQ q = Nothing -unconsQ (BQ bq@(BQB _ lo)) = Just (hd, BQ tl) - where - !hd = (lo .&. 1) /= 0 - !tl = shiftQBR1 bq -{-# INLINE unconsQ #-} - --- | Convert a bit queue to a list of bits by unconsing. --- This is used to test that the queue functions properly. -toListQ :: BitQueue -> [Bool] -toListQ bq = case unconsQ bq of - Nothing -> [] - Just (hd, tl) -> hd : toListQ tl diff --git a/Data/Utils/BitUtil.hs b/Data/Utils/BitUtil.hs deleted file mode 100644 --- a/Data/Utils/BitUtil.hs +++ /dev/null @@ -1,99 +0,0 @@ -{-# LANGUAGE CPP #-} -#if __GLASGOW_HASKELL__ -{-# LANGUAGE MagicHash #-} -#endif -#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Trustworthy #-} -#endif - -#include "containers.h" - -{-# OPTIONS_HADDOCK hide #-} ------------------------------------------------------------------------------ --- | --- Module : Data.Utils.BitUtil --- Copyright : (c) Clark Gaebel 2012 --- (c) Johan Tibel 2012 --- License : BSD-style --- Maintainer : libraries@haskell.org --- Stability : provisional --- Portability : portable ------------------------------------------------------------------------------ --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. - -module Data.Utils.BitUtil - ( highestBitMask - , shiftLL - , shiftRL - , wordSize - ) where - -import Data.Bits ((.|.), xor) -#if MIN_VERSION_base(4,7,0) -import Data.Bits (finiteBitSize) -#else -import Data.Bits (bitSize) -#endif - - -#if __GLASGOW_HASKELL__ -import GHC.Exts (Word(..), Int(..)) -import GHC.Prim (uncheckedShiftL#, uncheckedShiftRL#) -#else -import Data.Word (shiftL, shiftR) -#endif - --- The highestBitMask implementation is based on --- http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2 --- which has been put in the public domain. - --- | Return a word where only the highest bit is set. -highestBitMask :: Word -> Word -highestBitMask x1 = let x2 = x1 .|. x1 `shiftRL` 1 - x3 = x2 .|. x2 `shiftRL` 2 - x4 = x3 .|. x3 `shiftRL` 4 - x5 = x4 .|. x4 `shiftRL` 8 - x6 = x5 .|. x5 `shiftRL` 16 -#if !(defined(__GLASGOW_HASKELL__) && WORD_SIZE_IN_BITS==32) - x7 = x6 .|. x6 `shiftRL` 32 - in x7 `xor` (x7 `shiftRL` 1) -#else - in x6 `xor` (x6 `shiftRL` 1) -#endif -{-# INLINE highestBitMask #-} - --- Right and left logical shifts. -shiftRL, shiftLL :: Word -> Int -> Word -#if __GLASGOW_HASKELL__ -{-------------------------------------------------------------------- - GHC: use unboxing to get @shiftRL@ inlined. ---------------------------------------------------------------------} -shiftRL (W# x) (I# i) = W# (uncheckedShiftRL# x i) -shiftLL (W# x) (I# i) = W# (uncheckedShiftL# x i) -{-# INLINE CONLIKE shiftRL #-} -{-# INLINE CONLIKE shiftLL #-} -#else -shiftRL x i = shiftR x i -shiftLL x i = shiftL x i -{-# INLINE shiftRL #-} -{-# INLINE shiftLL #-} -#endif - -{-# INLINE wordSize #-} -wordSize :: Int -#if MIN_VERSION_base(4,7,0) -wordSize = finiteBitSize (0 :: Word) -#else -wordSize = bitSize (0 :: Word) -#endif diff --git a/Data/Utils/PtrEquality.hs b/Data/Utils/PtrEquality.hs deleted file mode 100644 --- a/Data/Utils/PtrEquality.hs +++ /dev/null @@ -1,64 +0,0 @@ -{-# LANGUAGE CPP #-} -#ifdef __GLASGOW_HASKELL__ -{-# LANGUAGE MagicHash #-} -#endif - -{-# OPTIONS_HADDOCK hide #-} - --- | Really unsafe pointer equality --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. - -module Data.Utils.PtrEquality (ptrEq, hetPtrEq) where - -#ifdef __GLASGOW_HASKELL__ -import GHC.Exts ( reallyUnsafePtrEquality# ) -import Unsafe.Coerce ( unsafeCoerce ) -#if __GLASGOW_HASKELL__ < 707 -import GHC.Exts ( (==#) ) -#else -import GHC.Exts ( isTrue# ) -#endif -#endif - --- | Checks if two pointers are equal. Yes means yes; --- no means maybe. The values should be forced to at least --- WHNF before comparison to get moderately reliable results. -ptrEq :: a -> a -> Bool - --- | Checks if two pointers are equal, without requiring --- them to have the same type. The values should be forced --- to at least WHNF before comparison to get moderately --- reliable results. -hetPtrEq :: a -> b -> Bool - -#ifdef __GLASGOW_HASKELL__ -#if __GLASGOW_HASKELL__ < 707 -ptrEq x y = reallyUnsafePtrEquality# x y ==# 1# -hetPtrEq x y = unsafeCoerce reallyUnsafePtrEquality# x y ==# 1# -#else -ptrEq x y = isTrue# (reallyUnsafePtrEquality# x y) -hetPtrEq x y = isTrue# (unsafeCoerce reallyUnsafePtrEquality# x y) -#endif - -#else --- Not GHC -ptrEq _ _ = False -hetPtrEq _ _ = False -#endif - -{-# INLINE ptrEq #-} -{-# INLINE hetPtrEq #-} - -infix 4 `ptrEq` -infix 4 `hetPtrEq` diff --git a/Data/Utils/StrictFold.hs b/Data/Utils/StrictFold.hs deleted file mode 100644 --- a/Data/Utils/StrictFold.hs +++ /dev/null @@ -1,32 +0,0 @@ -{-# LANGUAGE CPP #-} -#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Safe #-} -#endif - -#include "containers.h" -{-# OPTIONS_HADDOCK hide #-} - --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. - -module Data.Utils.StrictFold (foldlStrict) where - --- | Same as regular 'Data.List.foldl'', but marked INLINE so that it is always --- inlined. This allows further optimization of the call to f, which can be --- optimized/specialised/inlined. - -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 #-} diff --git a/Data/Utils/StrictMaybe.hs b/Data/Utils/StrictMaybe.hs deleted file mode 100644 --- a/Data/Utils/StrictMaybe.hs +++ /dev/null @@ -1,43 +0,0 @@ -{-# LANGUAGE CPP #-} - -#include "containers.h" - -{-# OPTIONS_HADDOCK hide #-} --- | Strict 'Maybe' --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. - -module Data.Utils.StrictMaybe (MaybeS (..), maybeS, toMaybe, toMaybeS) where - -#if !MIN_VERSION_base(4,8,0) -import Data.Foldable (Foldable (..)) -import Data.Monoid (Monoid (..)) -#endif - -data MaybeS a = NothingS | JustS !a - -instance Foldable MaybeS where - foldMap _ NothingS = mempty - foldMap f (JustS a) = f a - -maybeS :: r -> (a -> r) -> MaybeS a -> r -maybeS n _ NothingS = n -maybeS _ j (JustS a) = j a - -toMaybe :: MaybeS a -> Maybe a -toMaybe NothingS = Nothing -toMaybe (JustS a) = Just a - -toMaybeS :: Maybe a -> MaybeS a -toMaybeS Nothing = NothingS -toMaybeS (Just a) = JustS a diff --git a/Data/Utils/StrictPair.hs b/Data/Utils/StrictPair.hs deleted file mode 100644 --- a/Data/Utils/StrictPair.hs +++ /dev/null @@ -1,32 +0,0 @@ -{-# LANGUAGE CPP #-} -#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 -{-# LANGUAGE Safe #-} -#endif - -#include "containers.h" - -{-# OPTIONS_HADDOCK hide #-} - --- | A strict pair --- --- = WARNING --- --- This module is considered __internal__. --- --- The Package Versioning Policy __does not apply__. --- --- This contents of this module may change __in any way whatsoever__ --- and __without any warning__ between minor versions of this package. --- --- Authors importing this module are expected to track development --- closely. - -module Data.Utils.StrictPair (StrictPair(..), toPair) where - --- | Same as regular Haskell pairs, but (x :*: _|_) = (_|_ :*: y) = --- _|_ -data StrictPair a b = !a :*: !b - -toPair :: StrictPair a b -> (a, b) -toPair (x :*: y) = (x, y) -{-# INLINE toPair #-} diff --git a/Utils/Containers/Internal/BitQueue.hs b/Utils/Containers/Internal/BitQueue.hs new file mode 100644 --- /dev/null +++ b/Utils/Containers/Internal/BitQueue.hs @@ -0,0 +1,146 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE BangPatterns #-} + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Utils.Containers.Internal.BitQueue +-- Copyright : (c) David Feuer 2016 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. +-- +-- = Description +-- +-- An extremely light-weight, fast, and limited representation of a string of +-- up to (2*WORDSIZE - 2) bits. In fact, there are two representations, +-- misleadingly named bit queue builder and bit queue. The builder supports +-- only `emptyQB`, creating an empty builder, and `snocQB`, enqueueing a bit. +-- The bit queue builder is then turned into a bit queue using `buildQ`, after +-- which bits can be removed one by one using `unconsQ`. If the size limit is +-- exceeded, further operations will silently produce nonsense. +----------------------------------------------------------------------------- + +module Utils.Containers.Internal.BitQueue + ( BitQueue + , BitQueueB + , emptyQB + , snocQB + , buildQ + , unconsQ + , toListQ + ) where + +#if !MIN_VERSION_base(4,8,0) +import Data.Word (Word) +#endif +import Utils.Containers.Internal.BitUtil (shiftLL, shiftRL, wordSize) +import Data.Bits ((.|.), (.&.), testBit) +#if MIN_VERSION_base(4,8,0) +import Data.Bits (countTrailingZeros) +#elif MIN_VERSION_base(4,5,0) +import Data.Bits (popCount) +#endif + +#if !MIN_VERSION_base(4,5,0) +-- We could almost certainly improve this fall-back (copied straight from the +-- default definition in Data.Bits), but it hardly seems worth the trouble +-- to speed things up on GHC 7.4 and below. +countTrailingZeros :: Word -> Int +countTrailingZeros x = go 0 + where + go i | i >= wordSize = i + | testBit x i = i + | otherwise = go (i+1) + +#elif !MIN_VERSION_base(4,8,0) +countTrailingZeros :: Word -> Int +countTrailingZeros x = popCount ((x .&. (-x)) - 1) +{-# INLINE countTrailingZeros #-} +#endif + +-- A bit queue builder. We represent a double word using two words +-- because we don't currently have access to proper double words. +data BitQueueB = BQB {-# UNPACK #-} !Word + {-# UNPACK #-} !Word + +newtype BitQueue = BQ BitQueueB deriving Show + +-- Intended for debugging. +instance Show BitQueueB where + show (BQB hi lo) = "BQ"++ + show (map (testBit hi) [(wordSize - 1),(wordSize - 2)..0] + ++ map (testBit lo) [(wordSize - 1),(wordSize - 2)..0]) + +-- | Create an empty bit queue builder. This is represented as a single guard +-- bit in the most significant position. +emptyQB :: BitQueueB +emptyQB = BQB (1 `shiftLL` (wordSize - 1)) 0 +{-# INLINE emptyQB #-} + +-- Shift the double word to the right by one bit. +shiftQBR1 :: BitQueueB -> BitQueueB +shiftQBR1 (BQB hi lo) = BQB hi' lo' where + lo' = (lo `shiftRL` 1) .|. (hi `shiftLL` (wordSize - 1)) + hi' = hi `shiftRL` 1 +{-# INLINE shiftQBR1 #-} + +-- | Enqueue a bit. This works by shifting the queue right one bit, +-- then setting the most significant bit as requested. +{-# INLINE snocQB #-} +snocQB :: BitQueueB -> Bool -> BitQueueB +snocQB bq b = case shiftQBR1 bq of + BQB hi lo -> BQB (hi .|. (fromIntegral (fromEnum b) `shiftLL` (wordSize - 1))) lo + +-- | Convert a bit queue builder to a bit queue. This shifts in a new +-- guard bit on the left, and shifts right until the old guard bit falls +-- off. +{-# INLINE buildQ #-} +buildQ :: BitQueueB -> BitQueue +buildQ (BQB hi 0) = BQ (BQB 0 lo') where + zeros = countTrailingZeros hi + lo' = ((hi `shiftRL` 1) .|. (1 `shiftLL` (wordSize - 1))) `shiftRL` zeros +buildQ (BQB hi lo) = BQ (BQB hi' lo') where + zeros = countTrailingZeros lo + lo1 = (lo `shiftRL` 1) .|. (hi `shiftLL` (wordSize - 1)) + hi1 = (hi `shiftRL` 1) .|. (1 `shiftLL` (wordSize - 1)) + lo' = (lo1 `shiftRL` zeros) .|. (hi1 `shiftLL` (wordSize - zeros)) + hi' = hi1 `shiftRL` zeros + +-- Test if the queue is empty, which occurs when theres +-- nothing left but a guard bit in the least significant +-- place. +nullQ :: BitQueue -> Bool +nullQ (BQ (BQB 0 1)) = True +nullQ _ = False +{-# INLINE nullQ #-} + +-- | Dequeue an element, or discover the queue is empty. +unconsQ :: BitQueue -> Maybe (Bool, BitQueue) +unconsQ q | nullQ q = Nothing +unconsQ (BQ bq@(BQB _ lo)) = Just (hd, BQ tl) + where + !hd = (lo .&. 1) /= 0 + !tl = shiftQBR1 bq +{-# INLINE unconsQ #-} + +-- | Convert a bit queue to a list of bits by unconsing. +-- This is used to test that the queue functions properly. +toListQ :: BitQueue -> [Bool] +toListQ bq = case unconsQ bq of + Nothing -> [] + Just (hd, tl) -> hd : toListQ tl diff --git a/Utils/Containers/Internal/BitUtil.hs b/Utils/Containers/Internal/BitUtil.hs new file mode 100644 --- /dev/null +++ b/Utils/Containers/Internal/BitUtil.hs @@ -0,0 +1,98 @@ +{-# LANGUAGE CPP #-} +#if __GLASGOW_HASKELL__ +{-# LANGUAGE MagicHash #-} +#endif +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Trustworthy #-} +#endif + +#include "containers.h" + +----------------------------------------------------------------------------- +-- | +-- Module : Utils.Containers.Internal.BitUtil +-- Copyright : (c) Clark Gaebel 2012 +-- (c) Johan Tibel 2012 +-- License : BSD-style +-- Maintainer : libraries@haskell.org +-- Stability : provisional +-- Portability : portable +----------------------------------------------------------------------------- +-- +-- = WARNING +-- +-- This module is considered __internal__. +-- +-- The Package Versioning Policy __does not apply__. +-- +-- This contents of this module may change __in any way whatsoever__ +-- and __without any warning__ between minor versions of this package. +-- +-- Authors importing this module are expected to track development +-- closely. + +module Utils.Containers.Internal.BitUtil + ( highestBitMask + , shiftLL + , shiftRL + , wordSize + ) where + +import Data.Bits ((.|.), xor) +#if MIN_VERSION_base(4,7,0) +import Data.Bits (finiteBitSize) +#else +import Data.Bits (bitSize) +#endif + + +#if __GLASGOW_HASKELL__ +import GHC.Exts (Word(..), Int(..)) +import GHC.Prim (uncheckedShiftL#, uncheckedShiftRL#) +#else +import Data.Word (shiftL, shiftR) +#endif + +-- The highestBitMask implementation is based on +-- http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2 +-- which has been put in the public domain. + +-- | Return a word where only the highest bit is set. +highestBitMask :: Word -> Word +highestBitMask x1 = let x2 = x1 .|. x1 `shiftRL` 1 + x3 = x2 .|. x2 `shiftRL` 2 + x4 = x3 .|. x3 `shiftRL` 4 + x5 = x4 .|. x4 `shiftRL` 8 + x6 = x5 .|. x5 `shiftRL` 16 +#if !(defined(__GLASGOW_HASKELL__) && WORD_SIZE_IN_BITS==32) + x7 = x6 .|. x6 `shiftRL` 32 + in x7 `xor` (x7 `shiftRL` 1) +#else + in x6 `xor` (x6 `shiftRL` 1) +#endif +{-# INLINE highestBitMask #-} + +-- Right and left logical shifts. +shiftRL, shiftLL :: Word -> Int -> Word +#if __GLASGOW_HASKELL__ +{-------------------------------------------------------------------- + GHC: use unboxing to get @shiftRL@ inlined. +--------------------------------------------------------------------} +shiftRL (W# x) (I# i) = W# (uncheckedShiftRL# x i) +shiftLL (W# x) (I# i) = W# (uncheckedShiftL# x i) +{-# INLINE CONLIKE shiftRL #-} +{-# INLINE CONLIKE shiftLL #-} +#else +shiftRL x i = shiftR x i +shiftLL x i = shiftL x i +{-# INLINE shiftRL #-} +{-# INLINE shiftLL #-} +#endif + +{-# INLINE wordSize #-} +wordSize :: Int +#if MIN_VERSION_base(4,7,0) +wordSize = finiteBitSize (0 :: Word) +#else +wordSize = bitSize (0 :: Word) +#endif diff --git a/Utils/Containers/Internal/PtrEquality.hs b/Utils/Containers/Internal/PtrEquality.hs new file mode 100644 --- /dev/null +++ b/Utils/Containers/Internal/PtrEquality.hs @@ -0,0 +1,51 @@ +{-# LANGUAGE CPP #-} +#ifdef __GLASGOW_HASKELL__ +{-# LANGUAGE MagicHash #-} +#endif + +{-# OPTIONS_HADDOCK hide #-} + +-- | Really unsafe pointer equality +module Utils.Containers.Internal.PtrEquality (ptrEq, hetPtrEq) where + +#ifdef __GLASGOW_HASKELL__ +import GHC.Exts ( reallyUnsafePtrEquality# ) +import Unsafe.Coerce ( unsafeCoerce ) +#if __GLASGOW_HASKELL__ < 707 +import GHC.Exts ( (==#) ) +#else +import GHC.Exts ( isTrue# ) +#endif +#endif + +-- | Checks if two pointers are equal. Yes means yes; +-- no means maybe. The values should be forced to at least +-- WHNF before comparison to get moderately reliable results. +ptrEq :: a -> a -> Bool + +-- | Checks if two pointers are equal, without requiring +-- them to have the same type. The values should be forced +-- to at least WHNF before comparison to get moderately +-- reliable results. +hetPtrEq :: a -> b -> Bool + +#ifdef __GLASGOW_HASKELL__ +#if __GLASGOW_HASKELL__ < 707 +ptrEq x y = reallyUnsafePtrEquality# x y ==# 1# +hetPtrEq x y = unsafeCoerce reallyUnsafePtrEquality# x y ==# 1# +#else +ptrEq x y = isTrue# (reallyUnsafePtrEquality# x y) +hetPtrEq x y = isTrue# (unsafeCoerce reallyUnsafePtrEquality# x y) +#endif + +#else +-- Not GHC +ptrEq _ _ = False +hetPtrEq _ _ = False +#endif + +{-# INLINE ptrEq #-} +{-# INLINE hetPtrEq #-} + +infix 4 `ptrEq` +infix 4 `hetPtrEq` diff --git a/Utils/Containers/Internal/StrictFold.hs b/Utils/Containers/Internal/StrictFold.hs new file mode 100644 --- /dev/null +++ b/Utils/Containers/Internal/StrictFold.hs @@ -0,0 +1,20 @@ +{-# LANGUAGE CPP #-} +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Safe #-} +#endif + +#include "containers.h" +{-# OPTIONS_HADDOCK hide #-} + +module Utils.Containers.Internal.StrictFold (foldlStrict) where + +-- | Same as regular 'Data.List.foldl'', but marked INLINE so that it is always +-- inlined. This allows further optimization of the call to f, which can be +-- optimized/specialised/inlined. + +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 #-} diff --git a/Utils/Containers/Internal/StrictMaybe.hs b/Utils/Containers/Internal/StrictMaybe.hs new file mode 100644 --- /dev/null +++ b/Utils/Containers/Internal/StrictMaybe.hs @@ -0,0 +1,31 @@ +{-# LANGUAGE CPP #-} + +#include "containers.h" + +{-# OPTIONS_HADDOCK hide #-} +-- | Strict 'Maybe' + +module Utils.Containers.Internal.StrictMaybe (MaybeS (..), maybeS, toMaybe, toMaybeS) where + +#if !MIN_VERSION_base(4,8,0) +import Data.Foldable (Foldable (..)) +import Data.Monoid (Monoid (..)) +#endif + +data MaybeS a = NothingS | JustS !a + +instance Foldable MaybeS where + foldMap _ NothingS = mempty + foldMap f (JustS a) = f a + +maybeS :: r -> (a -> r) -> MaybeS a -> r +maybeS n _ NothingS = n +maybeS _ j (JustS a) = j a + +toMaybe :: MaybeS a -> Maybe a +toMaybe NothingS = Nothing +toMaybe (JustS a) = Just a + +toMaybeS :: Maybe a -> MaybeS a +toMaybeS Nothing = NothingS +toMaybeS (Just a) = JustS a diff --git a/Utils/Containers/Internal/StrictPair.hs b/Utils/Containers/Internal/StrictPair.hs new file mode 100644 --- /dev/null +++ b/Utils/Containers/Internal/StrictPair.hs @@ -0,0 +1,24 @@ +{-# LANGUAGE CPP #-} +#if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703 +{-# LANGUAGE Safe #-} +#endif + +#include "containers.h" + +-- | A strict pair + +module Utils.Containers.Internal.StrictPair (StrictPair(..), toPair) where + +-- | The same as a regular Haskell pair, but +-- +-- @ +-- (x :*: _|_) = (_|_ :*: y) = _|_ +-- @ +data StrictPair a b = !a :*: !b + +infixr 1 :*: + +-- | Convert a strict pair to a standard pair. +toPair :: StrictPair a b -> (a, b) +toPair (x :*: y) = (x, y) +{-# INLINE toPair #-} diff --git a/benchmarks/IntMap.hs b/benchmarks/IntMap.hs --- a/benchmarks/IntMap.hs +++ b/benchmarks/IntMap.hs @@ -6,6 +6,7 @@ import Criterion.Main (bench, defaultMain, whnf) import Data.List (foldl') import qualified Data.IntMap as M +import qualified Data.IntMap.Strict as MS import Data.Maybe (fromMaybe) import Prelude hiding (lookup) @@ -64,10 +65,10 @@ insWithKey xs m = foldl' (\m (k, v) -> M.insertWithKey add3 k v m) m xs insWith' :: [(Int, Int)] -> M.IntMap Int -> M.IntMap Int -insWith' xs m = foldl' (\m (k, v) -> M.insertWith' (+) k v m) m xs +insWith' xs m = foldl' (\m (k, v) -> MS.insertWith (+) k v m) m xs insWithKey' :: [(Int, Int)] -> M.IntMap Int -> M.IntMap Int -insWithKey' xs m = foldl' (\m (k, v) -> M.insertWithKey' add3 k v m) m xs +insWithKey' xs m = foldl' (\m (k, v) -> MS.insertWithKey add3 k v m) m xs data PairS a b = PS !a !b diff --git a/benchmarks/LookupGE/LookupGE_IntMap.hs b/benchmarks/LookupGE/LookupGE_IntMap.hs --- a/benchmarks/LookupGE/LookupGE_IntMap.hs +++ b/benchmarks/LookupGE/LookupGE_IntMap.hs @@ -2,7 +2,7 @@ module LookupGE_IntMap where import Prelude hiding (null) -import Data.IntMap.Base +import Data.IntMap.Internal lookupGE1 :: Key -> IntMap a -> Maybe (Key,a) lookupGE1 k m = diff --git a/benchmarks/LookupGE/LookupGE_Map.hs b/benchmarks/LookupGE/LookupGE_Map.hs --- a/benchmarks/LookupGE/LookupGE_Map.hs +++ b/benchmarks/LookupGE/LookupGE_Map.hs @@ -1,7 +1,7 @@ {-# LANGUAGE BangPatterns, CPP #-} module LookupGE_Map where -import Data.Map.Base +import Data.Map.Internal lookupGE1 :: Ord k => k -> Map k a -> Maybe (k,a) lookupGE1 k m = diff --git a/benchmarks/Map.hs b/benchmarks/Map.hs --- a/benchmarks/Map.hs +++ b/benchmarks/Map.hs @@ -9,6 +9,7 @@ import Data.Functor.Identity (Identity(..)) import Data.List (foldl') import qualified Data.Map as M +import qualified Data.Map.Strict as MS import Data.Map (alterF) import Data.Maybe (fromMaybe) import Data.Functor ((<$)) @@ -147,10 +148,10 @@ insWithKey xs m = foldl' (\m (k, v) -> M.insertWithKey add3 k v m) m xs insWith' :: [(Int, Int)] -> M.Map Int Int -> M.Map Int Int -insWith' xs m = foldl' (\m (k, v) -> M.insertWith' (+) k v m) m xs +insWith' xs m = foldl' (\m (k, v) -> MS.insertWith (+) k v m) m xs insWithKey' :: [(Int, Int)] -> M.Map Int Int -> M.Map Int Int -insWithKey' xs m = foldl' (\m (k, v) -> M.insertWithKey' add3 k v m) m xs +insWithKey' xs m = foldl' (\m (k, v) -> MS.insertWithKey add3 k v m) m xs data PairS a b = PS !a !b @@ -163,7 +164,7 @@ insLookupWithKey' :: [(Int, Int)] -> M.Map Int Int -> (Int, M.Map Int Int) insLookupWithKey' xs m = let !(PS a b) = foldl' f (PS 0 m) xs in (a, b) where - f (PS n m) (k, v) = let !(n', m') = M.insertLookupWithKey' add3 k v m + f (PS n m) (k, v) = let !(n', m') = MS.insertLookupWithKey add3 k v m in PS (fromMaybe 0 n' + n) m' del :: [Int] -> M.Map Int Int -> M.Map Int Int diff --git a/changelog.md b/changelog.md --- a/changelog.md +++ b/changelog.md @@ -1,11 +1,39 @@ # Changelog for [`containers` package](http://github.com/haskell/containers) -## 0.5.8.2 +## 0.5.9.1 - * Fix completely incorrect implementations of `restrictKeys` and - `withoutKeys`. +* Planned for GHC 8.2. -## 0.5.8.1 +* Add `merge` and `mergeA` for `Data.IntMap`. + +* Add instances for `Data.Graph.SCC`: `Foldable`, `Traversable`, `Data`, + `Generic`, `Generic1`, `Eq`, `Eq1`, `Show`, `Show1`, `Read`, and `Read1`. + +* Add lifted instances (from `Data.Functor.Classes`) for `Data.Sequence`, + `Data.Map`, `Data.Set`, `Data.IntMap`, and `Data.Tree`. (Thanks to + Oleg Grenrus for doing a lot of this work.) + +* Properly deprecate functions in `Data.IntMap` long documented as deprecated. + +* Rename several internal modules for clarity. Thanks to esoeylemez for starting + this process. + +* Make `Data.Map.fromDistinctAscList` and `Data.Map.fromDistinctDescList` more + eager, improving performance. + +* Plug space leaks in `Data.Map.Lazy.fromAscList` and + `Data.Map.Lazy.fromDescList` by manually inlining constant functions. + +* Add `lookupMin` and `lookupMax` to `Data.Set` and `Data.Map` as total +alternatives to `findMin` and `findMax`. + +* Add `!?` to `Data.Map` as a total alternative to `!`. + +* Avoid using `deleteFindMin` and `deleteFindMax` internally, preferring +total functions instead. New implementations of said functions lead to slight +performance improvements overall. + +## 0.5.8.1 *Aug 2016* ### General package changes diff --git a/containers.cabal b/containers.cabal --- a/containers.cabal +++ b/containers.cabal @@ -1,5 +1,5 @@ name: containers -version: 0.5.8.2 +version: 0.5.9.1 license: BSD3 license-file: LICENSE maintainer: libraries@haskell.org @@ -44,29 +44,37 @@ Data.IntMap Data.IntMap.Lazy Data.IntMap.Strict - Data.IntMap.Base - Data.IntSet.Base + Data.IntMap.Internal + Data.IntMap.Merge.Lazy + Data.IntMap.Merge.Strict + Data.IntSet.Internal Data.IntSet Data.Map Data.Map.Lazy Data.Map.Lazy.Merge + Data.Map.Merge.Lazy Data.Map.Strict.Internal Data.Map.Strict Data.Map.Strict.Merge - Data.Map.Base - Data.Set.Base + Data.Map.Merge.Strict + Data.Map.Internal + Data.Map.Internal.Debug + Data.Set.Internal Data.Set Data.Graph Data.Sequence - Data.Sequence.Base + Data.Sequence.Internal Data.Tree - Data.Utils.BitUtil - Data.Utils.BitQueue - Data.Utils.StrictFold - Data.Utils.StrictPair - Data.Utils.StrictMaybe - Data.Utils.PtrEquality + Utils.Containers.Internal.BitUtil + Utils.Containers.Internal.BitQueue + Utils.Containers.Internal.StrictPair + other-modules: + Utils.Containers.Internal.StrictFold + Utils.Containers.Internal.StrictMaybe + Utils.Containers.Internal.PtrEquality + Data.Map.Internal.DeprecatedShowTree + include-dirs: include ----------------------------- @@ -104,7 +112,8 @@ base >= 4.2 && < 5, containers, criterion >= 0.4.0 && < 1.2, - deepseq >= 1.1.0.0 && < 1.5 + deepseq >= 1.1.0.0 && < 1.5, + transformers benchmark sequence-benchmarks type: exitcode-stdio-1.0 @@ -177,7 +186,7 @@ ghc-options: -O2 cpp-options: -DTESTING other-modules: - Data.IntMap.Base + Data.IntMap.Internal build-depends: base >= 4.2 && < 5, containers, @@ -192,7 +201,7 @@ ghc-options: -O2 cpp-options: -DTESTING other-modules: - Data.Map.Base + Data.Map.Internal build-depends: base >= 4.2 && < 5, containers, diff --git a/include/containers.h b/include/containers.h --- a/include/containers.h +++ b/include/containers.h @@ -29,6 +29,10 @@ #define INSTANCE_TYPEABLE2(tycon) #endif +#if __GLASGOW_HASKELL__ >= 800 +#define DEFINE_PATTERN_SYNONYMS 1 +#endif + /* * We use cabal-generated MIN_VERSION_base to adapt to changes of base. * Nevertheless, as a convenience, we also allow compiling without cabal by diff --git a/tests/bitqueue-properties.hs b/tests/bitqueue-properties.hs --- a/tests/bitqueue-properties.hs +++ b/tests/bitqueue-properties.hs @@ -8,8 +8,8 @@ import Test.Framework import Test.Framework.Providers.QuickCheck2 import Test.QuickCheck -import Data.Utils.BitUtil (wordSize) -import Data.Utils.BitQueue +import Utils.Containers.Internal.BitUtil (wordSize) +import Utils.Containers.Internal.BitQueue ( BitQueue , emptyQB , snocQB diff --git a/tests/deprecated-properties.hs b/tests/deprecated-properties.hs --- a/tests/deprecated-properties.hs +++ b/tests/deprecated-properties.hs @@ -1,4 +1,5 @@ {-# LANGUAGE CPP #-} +{-# OPTIONS_GHC -fno-warn-warnings-deprecations #-} -- This module tests the deprecated properties of Data.Map and Data.IntMap, -- because these cannot be tested in either map-properties or diff --git a/tests/intmap-properties.hs b/tests/intmap-properties.hs --- a/tests/intmap-properties.hs +++ b/tests/intmap-properties.hs @@ -167,8 +167,6 @@ , testProperty "foldl'" prop_foldl' , testProperty "keysSet" prop_keysSet , testProperty "fromSet" prop_fromSet - , testProperty "restrictKeys" prop_restrictKeys - , testProperty "withoutKeys" prop_withoutKeys ] apply2 :: Fun (a, b) c -> a -> b -> c diff --git a/tests/map-properties.hs b/tests/map-properties.hs --- a/tests/map-properties.hs +++ b/tests/map-properties.hs @@ -1,13 +1,14 @@ {-# LANGUAGE CPP #-} #ifdef STRICT -import Data.Map.Strict as Data.Map -import Data.Map.Strict.Merge +import Data.Map.Strict as Data.Map hiding (showTree, showTreeWith) +import Data.Map.Merge.Strict #else -import Data.Map.Lazy as Data.Map -import Data.Map.Lazy.Merge +import Data.Map.Lazy as Data.Map hiding (showTree, showTreeWith) +import Data.Map.Merge.Lazy #endif -import Data.Map.Base (Map (..), balanced, link2, link, bin) +import Data.Map.Internal (Map (..), link2, link, bin) +import Data.Map.Internal.Debug (showTree, showTreeWith, balanced) import Control.Applicative (Const(Const, getConst), pure, (<$>), (<*>)) import Data.Functor.Identity (Identity(runIdentity)) @@ -221,6 +222,8 @@ , testProperty "take" prop_take , testProperty "drop" prop_drop , testProperty "splitAt" prop_splitAt + , testProperty "lookupMin" prop_lookupMin + , testProperty "lookupMax" prop_lookupMax ] {-------------------------------------------------------------------- @@ -959,6 +962,12 @@ prop_deleteMax :: UMap -> Bool prop_deleteMax t = valid $ deleteMax $ deleteMax t + +prop_lookupMin :: IMap -> Property +prop_lookupMin m = lookupMin m === (fst <$> minViewWithKey m) + +prop_lookupMax :: IMap -> Property +prop_lookupMax m = lookupMax m === (fst <$> maxViewWithKey m) ---------------------------------------------------------------- diff --git a/tests/seq-properties.hs b/tests/seq-properties.hs --- a/tests/seq-properties.hs +++ b/tests/seq-properties.hs @@ -1,5 +1,19 @@ -import Data.Sequence.Base +{-# LANGUAGE CPP #-} +{-# LANGUAGE PatternGuards #-} +import Data.Sequence.Internal + ( Sized (..) + , Seq (Seq) + , FingerTree(..) + , Node(..) + , Elem(..) + , Digit (..) + , node2 + , node3 + , deep ) + +import Data.Sequence + import Control.Applicative (Applicative(..)) import Control.Arrow ((***)) import Control.Monad.Trans.State.Strict @@ -18,6 +32,9 @@ import qualified Data.List import Test.QuickCheck hiding ((><)) import Test.QuickCheck.Poly +#if __GLASGOW_HASKELL__ >= 800 +import Test.QuickCheck.Property +#endif import Test.QuickCheck.Function import Test.Framework import Test.Framework.Providers.QuickCheck2 @@ -109,6 +126,14 @@ , testProperty "cycleTaking" prop_cycleTaking , testProperty "intersperse" prop_intersperse , testProperty ">>=" prop_bind +#if __GLASGOW_HASKELL__ >= 800 + , testProperty "Empty pattern" prop_empty_pat + , testProperty "Empty constructor" prop_empty_con + , testProperty "Left view pattern" prop_viewl_pat + , testProperty "Left view constructor" prop_viewl_con + , testProperty "Right view pattern" prop_viewr_pat + , testProperty "Right view constructor" prop_viewr_con +#endif ] ------------------------------------------------------------------------ @@ -678,6 +703,33 @@ prop_cycleTaking :: Int -> Seq A -> Property prop_cycleTaking n xs = (n <= 0 || not (null xs)) ==> toList' (cycleTaking n xs) ~= Data.List.take n (Data.List.cycle (toList xs)) + +#if __GLASGOW_HASKELL__ >= 800 +prop_empty_pat :: Seq A -> Bool +prop_empty_pat xs@Empty = null xs +prop_empty_pat xs = not (null xs) + +prop_empty_con :: Bool +prop_empty_con = null Empty + +prop_viewl_pat :: Seq A -> Property +prop_viewl_pat xs@(y :<| ys) + | z :< zs <- viewl xs = y === z .&&. ys === zs + | otherwise = property failed +prop_viewl_pat xs = property . liftBool $ null xs + +prop_viewl_con :: A -> Seq A -> Property +prop_viewl_con x xs = x :<| xs === x <| xs + +prop_viewr_pat :: Seq A -> Property +prop_viewr_pat xs@(ys :|> y) + | zs :> z <- viewr xs = y === z .&&. ys === zs + | otherwise = property failed +prop_viewr_pat xs = property . liftBool $ null xs + +prop_viewr_con :: Seq A -> A -> Property +prop_viewr_con xs x = xs :|> x === xs |> x +#endif -- Monad operations diff --git a/tests/set-properties.hs b/tests/set-properties.hs --- a/tests/set-properties.hs +++ b/tests/set-properties.hs @@ -67,6 +67,8 @@ , testProperty "prop_isSubsetOf" prop_isSubsetOf , testProperty "prop_isSubsetOf2" prop_isSubsetOf2 , testProperty "prop_size" prop_size + , testProperty "prop_lookupMax" prop_lookupMax + , testProperty "prop_lookupMin" prop_lookupMin , testProperty "prop_findMax" prop_findMax , testProperty "prop_findMin" prop_findMin , testProperty "prop_ord" prop_ord @@ -492,6 +494,12 @@ prop_findMin :: Set Int -> Property prop_findMin s = not (null s) ==> findMin s == minimum (toList s) + +prop_lookupMin :: Set Int -> Property +prop_lookupMin m = lookupMin m === (fst <$> minView m) + +prop_lookupMax :: Set Int -> Property +prop_lookupMax m = lookupMax m === (fst <$> maxView m) prop_ord :: TwoSets -> Bool prop_ord (TwoSets s1 s2) = s1 `compare` s2 == toList s1 `compare` toList s2