@@ -1,10 +1,11 @@
1+{-# OPTIONS_GHC -Wno-missing-export-lists #-}
2+
13{-# LANGUAGE AllowAmbiguousTypes #-}
24{-# LANGUAGE BangPatterns #-}
35{-# LANGUAGE CPP #-}
46{-# LANGUAGE DataKinds #-}
57{-# LANGUAGE GADTs #-}
68{-# LANGUAGE InstanceSigs #-}
7−{-# LANGUAGE KindSignatures #-}
89{-# LANGUAGE MagicHash #-}
910{-# LANGUAGE PolyKinds #-}
1011{-# LANGUAGE Rank2Types #-}
@@ -18,7 +19,12 @@
1819
1920-- {-# OPTIONS_GHC -ddump-simpl -dsuppress-idinfo -dsuppress-coercions -dsuppress-type-applications -dsuppress-uniques -dsuppress-module-prefixes #-}
2021
21−{- | Internal API for 'TypeRepMap' and operations on it. The functions here do
22+{- |
23+Copyright: (c) 2017-2020 Kowainik
24+SPDX-License-Identifier: MPL-2.0
25+Maintainer: Kowainik <xrom.xkov@gmail.com>
26+
27+Internal API for 'TypeRepMap' and operations on it. The functions here do
2228not have any stability guarantees and can change between minor versions.
2329
2430If you need to use this module for purposes other than tests,
@@ -39,9 +45,9 @@ import Data.Kind (Type)
3945import Data.Type.Equality ((:~:) (..), TestEquality (..))
4046import Data.List (intercalate, nubBy)
4147import Data.Maybe (fromMaybe)
42−import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', readArray, sizeofArray,
48+import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', sizeofArray,
4349 thawArray, unsafeFreezeArray, writeArray)
44−import Data.Primitive.PrimArray (PrimArray, indexPrimArray, sizeofPrimArray)
50+import Data.Primitive.PrimArray (writePrimArray, newPrimArray, unsafeFreezePrimArray, primArrayToList, MutablePrimArray, primArrayFromListN, PrimArray, indexPrimArray, sizeofPrimArray)
4551import Data.Semigroup (Semigroup (..), All(..))
4652import GHC.Base (Any, Int (..), Int#, (*#), (+#), (<#))
4753import GHC.Exts (IsList (..), inline, sortWith)
@@ -58,7 +64,6 @@ import Type.Reflection (SomeTypeRep (..), TypeRep, Typeable, typeRep, withTypeab
5864import Type.Reflection.Unsafe (typeRepFingerprint)
5965import Unsafe.Coerce (unsafeCoerce)
6066
61−import qualified Data.Map.Strict as Map
6267import qualified GHC.Exts as GHC (fromList, toList)
6368
6469{- |
@@ -164,33 +169,49 @@ prop> member @a (one (x :: f a)) == True
164169
165170-}
166171one :: forall a f . Typeable a => f a -> TypeRepMap f
167−one x = insert x empty
172+one x = TypeRepMap (primArrayFromListN 1 [fa])
173+ (primArrayFromListN 1 [fb])
174+ (pure @Array v)
175+ (pure @Array k)
176+ where
177+ (Fingerprint fa fb, v, k) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
168178{-# INLINE one #-}
169179
170180{- |
171181
172182Insert a value into a 'TypeRepMap'.
183+TypeRepMap optimizes for fast reads rather than inserts, as a trade-off inserts are @O(n)@.
173184
174185prop> size (insert v tm) >= size tm
175186prop> member @a (insert (x :: f a) tm) == True
176187
177188-}
178189insert :: forall a f . Typeable a => f a -> TypeRepMap f -> TypeRepMap f
179−insert x = fromTriples . addX . toTriples
190+insert x m
191+ | size m == 0 = one x
192+ | otherwise = case cachedBinarySearch (typeFp @a) (fingerprintAs m) (fingerprintBs m) of
193+ Nothing -> union m $ one x
194+ Just i -> m {trAnys = changeAnyArr i (trAnys m)}
180195 where
181− tripleX :: (Fingerprint, Any, Any)
182− tripleX@(fpX, _, _) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
183−
184− addX :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
185− addX l = tripleX : deleteByFst fpX l
196+ changeAnyArr :: Int -> Array Any -> Array Any
197+ changeAnyArr i trAs = runST $ do
198+ let n = sizeofArray trAs
199+ mutArr <- thawArray trAs 0 n
200+ writeArray mutArr i $ toAny x
201+ unsafeFreezeArray mutArr
186202{-# INLINE insert #-}
187203
188204-- Extract the kind of a type. We use it to work around lack of syntax for
189205-- inferred type variables (which are not subject to type applications).
190206type KindOf (a :: k) = k
191207
208+type ArgKindOf (f :: k -> l) = k
209+
192210{- | Delete a value from a 'TypeRepMap'.
193211
212+TypeRepMap optimizes for fast reads rather than modifications, as a trade-off deletes are
213+@O(n)@, with an @O(log(n))@ optimization for when the element is already missing.
214+
194215prop> size (delete @a tm) <= size tm
195216prop> member @a (delete @a tm) == False
196217
@@ -203,30 +224,60 @@ False
203224True
204225-}
205226delete :: forall a (f :: KindOf a -> Type) . Typeable a => TypeRepMap f -> TypeRepMap f
206−delete = fromTriples . deleteByFst (typeFp @a) . toTriples
227+delete m
228+ -- Lookups are fast, so check if we even have the element first.
229+ | not (member @a m) = m
230+ -- We know we have the element, If the map has exactly one element, we can return the empty map
231+ | size m == 1 = empty
232+ -- Otherwise, filter out the element in linear time.
233+ | otherwise = fromSortedTriples . deleteFirst ((== typeFp @a) . fst3) . toSortedTriples $ m
207234{-# INLINE delete #-}
208235
236+deleteFirst :: (a -> Bool) -> [a] -> [a]
237+deleteFirst _ [] = []
238+deleteFirst p (x : xs) = if p x then xs else x : deleteFirst p xs
239+
209240{- |
210−Update a value at a specific key with the result of the provided function. When
211−the key is not a member of the map, the original map is returned.
241+Update a value at a specific key with the result of the provided function.
242+When the key is not a member of the map, the original map is returned.
212243
213244>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "a"]
214245>>> lookup @String $ adjust (fmap (++ "ww")) trmap
215246Just (Identity "aww")
216247-}
217248adjust :: forall a f . Typeable a => (f a -> f a) -> TypeRepMap f -> TypeRepMap f
218−adjust fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
219− Nothing -> tr
220− Just i -> tr {trAnys = changeAnyArr i (trAnys tr)}
249+adjust fun = alter (fmap fun)
250+{-# INLINE adjust #-}
251+
252+{- |
253+Updates a value at a specific key, whether or not it exists.
254+This can be used to insert, delete, or update a value of a given type in the map.
255+
256+>>> func = (\case Nothing -> Just (Identity "new"); Just (Identity s) -> Just (Identity (reverse s)))
257+>>> lookup @String $ alter func empty
258+Just (Identity "new")
259+>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "helllo"]
260+>>> lookup @String $ alter func trmap
261+>>> Just (Identity "olleh")
262+-}
263+alter :: forall a f . Typeable a => (Maybe (f a) -> Maybe (f a)) -> TypeRepMap f -> TypeRepMap f
264+alter fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
265+ Nothing ->
266+ case (fun Nothing) of
267+ Nothing -> tr
268+ Just v -> insert v tr
269+ Just i ->
270+ case fun (Just . fromAny $ indexArray (trAnys tr) i) of
271+ Nothing -> delete @a tr
272+ Just v -> tr{trAnys = replaceAnyAt i (toAny v) (trAnys tr)}
221273 where
222− changeAnyArr :: Int -> Array Any -> Array Any
223− changeAnyArr i trAs = runST $ do
274+ replaceAnyAt :: Int -> Any -> Array Any -> Array Any
275+ replaceAnyAt i v trAs = runST $ do
224276 let n = sizeofArray trAs
225277 mutArr <- thawArray trAs 0 n
226− a <- toAny . fun . fromAny <$> readArray mutArr i
227− writeArray mutArr i a
278+ writeArray mutArr i v
228279 unsafeFreezeArray mutArr
229−{-# INLINE adjust #-}
280+{-# INLINE alter #-}
230281
231282{- | Map over the elements of a 'TypeRepMap'.
232283
@@ -260,33 +311,89 @@ hoistWithKey f (TypeRepMap as bs ans ks) = TypeRepMap as bs newAns ks
260311 withTr t = withTypeable t f
261312{-# INLINE hoistWithKey #-}
262313
263−-- | The union of two 'TypeRepMap's using a combining function.
314+-- | The union of two 'TypeRepMap's using a combining function for conflicting entries. @O(n + m)@
264315unionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
265−unionWith f m1 m2 = fromTriples
266− $ toTripleList
267− $ Map.unionWith combine
268− (fromTripleList $ toTriples m1)
269− (fromTripleList $ toTriples m2)
316+unionWith f ma mb = do
317+ fromSortedTriples $ mergeMaps (toSortedTriples ma) (toSortedTriples mb)
270318 where
271319 f' :: forall x. TypeRep x -> f x -> f x -> f x
272320 f' tr = withTypeable tr f
273321
274− combine :: (Any, Any) -> (Any, Any) -> (Any, Any)
275− combine (av, ak) (bv, _) = (toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
276−
277− fromTripleList :: Ord a => [(a, b, c)] -> Map.Map a (b, c)
278− fromTripleList = Map.fromList . map (\(a, b, c) -> (a, (b, c)))
279−
280− toTripleList :: Map.Map a (b, c) -> [(a, b, c)]
281− toTripleList = map (\(a, (b, c)) -> (a, b, c)) . Map.toList
322+ combine :: (Fingerprint, Any, Any) -> (Fingerprint, Any, Any) -> (Fingerprint, Any, Any)
323+ combine (fp, av, ak) (_, bv, _) = (fp, toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
324+
325+ -- Merges two typrepmaps into a sorted, dedup'd list of triples.
326+ -- Using 'toSortedTriples' allows us to assume the triples are sorted by fingerprint,
327+ -- Given O(n) performance from 'toSortedTriples', and given that we can merge-sort in
328+ -- O(n + m) time, then can '.fromSortedTriples' back into cachedBinarySearch order in O(n + m)
329+ -- that gives a total of O(n + m).
330+ mergeMaps :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
331+ -- We've addressed all elements from both maps
332+ mergeMaps as [] = as
333+ mergeMaps [] bs = bs
334+ -- Merge
335+ mergeMaps (a@(af, _, _) : as) (b@(bf, _, _) : bs) =
336+ case compare af bf of
337+ -- Fingerprints are equal, union the elements using our function
338+ -- If the incoming maps were de-duped, there shouldn't be any other equivalent
339+ -- fingerprints
340+ EQ -> combine a b : mergeMaps as bs
341+ -- First fingerprint must not be in the second map or we would have seen it by now
342+ -- Add it to the result as-is
343+ LT -> a : mergeMaps as (b : bs)
344+ -- Second fingerprint must not be in the first map or we would have seen it by now
345+ -- Add it to the result as-is
346+ GT -> b : mergeMaps (a:as) bs
282347{-# INLINE unionWith #-}
283348
284−-- | The (left-biased) union of two 'TypeRepMap's. It prefers the first map when
349+-- | The (left-biased) union of two 'TypeRepMap's in @O(n + m)@. It prefers the first map when
285350-- duplicate keys are encountered, i.e. @'union' == 'unionWith' const@.
286351union :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
287352union = unionWith const
288353{-# INLINE union #-}
289354
355+-- | The 'intersection' of two 'TypeRepMap's using a combining function
356+--
357+-- @O(n + m)@
358+intersectionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
359+intersectionWith f ma mb =
360+ fromSortedTriples $ mergeMaps (toSortedTriples ma) (toSortedTriples mb)
361+ where
362+ f' :: forall x. TypeRep x -> f x -> f x -> f x
363+ f' tr = withTypeable tr f
364+
365+ combine :: (Fingerprint, Any, Any) -> (Fingerprint, Any, Any) -> (Fingerprint, Any, Any)
366+ combine (fp, av, ak) (_, bv, _) = (fp, toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
367+
368+ -- Merges two typrepmaps into a sorted, dedup'd list of triples.
369+ mergeMaps :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
370+ -- If either list is empty, the intersection must be finished.
371+ mergeMaps _ [] = []
372+ mergeMaps [] _ = []
373+ -- Merge the two maps considering one element at a time.
374+ mergeMaps (a@(af, _, _) : as) (b@(bf, _, _) : bs) =
375+ case compare af bf of
376+ -- Fingerprints are equal, union the elements using our function
377+ -- If the incoming maps were de-duped, there shouldn't be any other equivalent
378+ -- fingerprints
379+ EQ -> combine a b : mergeMaps as bs
380+ -- First fingerprint must not be in the second map or we would have seen it by now
381+ -- Skip it an move on
382+ LT -> mergeMaps as (b : bs)
383+ -- Second fingerprint must not be in the first map or we would have seen it by now
384+ -- Skip it an move on
385+ GT -> mergeMaps (a:as) bs
386+{-# INLINE intersectionWith #-}
387+
388+-- | The intersection of two 'TypeRepMap's.
389+-- It keeps all values from the first map whose keys are present in the second.
390+--
391+-- @O(n + m)@
392+intersection :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
393+intersection = intersectionWith const
394+{-# INLINE intersection #-}
395+
396+
290397{- | Check if a value of the given type is present in a 'TypeRepMap'.
291398
292399>>> member @Char $ one (Identity 'a')
@@ -322,9 +429,22 @@ size = sizeofPrimArray . fingerprintAs
322429
323430-- | Return the list of 'SomeTypeRep' from the keys.
324431keys :: TypeRepMap f -> [SomeTypeRep]
325−keys TypeRepMap{..} = SomeTypeRep . anyToTypeRep <$> toList trKeys
432+keys = keysWith SomeTypeRep
326433{-# INLINE keys #-}
327434
435+-- | Return the list of keys by wrapping them with a user-provided function.
436+keysWith :: (forall (a :: ArgKindOf f). TypeRep a -> r) -> TypeRepMap f -> [r]
437+keysWith f TypeRepMap{..} = f . anyToTypeRep <$> toList trKeys
438+{-# INLINE keysWith #-}
439+
440+-- | Return the list of key-value pairs by wrapping them with a user-provided function.
441+toListWith :: forall f r. (forall (a :: ArgKindOf f). Typeable a => f a -> r) -> TypeRepMap f -> [r]
442+toListWith f = map toF . toTriples
443+ where
444+ withTypeRep :: TypeRep a -> f a -> r
445+ withTypeRep tr an = withTypeable tr $ f an
446+ toF (_, an, k) = withTypeRep (unsafeCoerce k) (fromAny an)
447+
328448-- | Binary searched based on this article
329449-- http://bannalia.blogspot.com/2015/06/cache-friendly-binary-search.html
330450-- with modification for our two-vector search case.
@@ -368,8 +488,20 @@ typeFp = typeRepFingerprint $ typeRep @a
368488toTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
369489toTriples tm = zip3 (toFingerprints tm) (GHC.toList $ trAnys tm) (GHC.toList $ trKeys tm)
370490
371−deleteByFst :: Eq a => a -> [(a, b, c)] -> [(a, b, c)]
372−deleteByFst x = filter ((/= x) . fst3)
491+-- | Efficiently get sorted triples from a map in O(n) time
492+--
493+-- We assume the incoming TypeRepMap is already sorted into 'cachedBinarySearch' order using fromSortedList.
494+-- Then we can construct the index mapping from the "cached" ordering into monotonically
495+-- increasing order using 'generateOrderMapping' with the length of the TRM. This takes @O(n).
496+-- We then pull those indexes from the source TRM to get the sorted triples in a total of @O(n).
497+toSortedTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
498+toSortedTriples tm = trip <$> ordering
499+ where
500+ trip i = ( Fingerprint (indexPrimArray (fingerprintAs tm) i) (indexPrimArray (fingerprintBs tm) i)
501+ , indexArray (trAnys tm) i
502+ , indexArray (trKeys tm) i)
503+ ordering :: [ Int ]
504+ ordering = generateOrderMapping (size tm)
373505
374506nubByFst :: (Eq a) => [(a, b, c)] -> [(a, b, c)]
375507nubByFst = nubBy ((==) `on` fst3)
@@ -389,9 +521,6 @@ data WrapTypeable f where
389521instance Show (WrapTypeable f) where
390522 show (WrapTypeable (_ :: f a)) = show $ calcFp @a
391523
392−wrapTypeable :: TypeRep a -> f a -> WrapTypeable f
393−wrapTypeable tr = withTypeable tr WrapTypeable
394−
395524{- |
396525
397526prop> fromList . toList == 'id'
@@ -419,19 +548,19 @@ instance IsList (TypeRepMap f) where
419548 k (WrapTypeable (_ :: f a)) = unsafeCoerce $ typeRep @a
420549
421550 toList :: TypeRepMap f -> [WrapTypeable f]
422− toList = map toWrapTypeable . toTriples
423− where
424− toWrapTypeable :: (Fingerprint, Any, Any) -> WrapTypeable f
425− toWrapTypeable (_, an, k) = wrapTypeable (unsafeCoerce k) (fromAny an)
551+ toList = toListWith WrapTypeable
426552
427553calcFp :: forall a . Typeable a => Fingerprint
428554calcFp = typeRepFingerprint $ typeRep @a
429555
430556fromTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
431−fromTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
557+fromTriples = fromSortedTriples . sortWith fst3 . nubByFst
558+
559+fromSortedTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
560+fromSortedTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
432561 where
433562 (fpAs, fpBs) = unzip $ map (\(Fingerprint a b) -> (a, b)) fps
434− (fps, ans, ks) = unzip3 $ fromSortedList $ sortWith fst3 $ nubByFst kvs
563+ (fps, ans, ks) = unzip3 $ fromSortedList kvs
435564
436565----------------------------------------------------------------------------
437566-- Tree-like conversion
@@ -458,18 +587,42 @@ fromSortedList l = runST $ do
458587 writeArray result i (indexArray origin newFirst)
459588 loop (2 * i + 2) (newFirst + 1)
460589
590+-- Returns a list of indexes which represents the "sorted" order of an array generated by
591+-- fromSortedList of the provided length.
592+-- I.e. fmap (fromSortedList [1, 2, 3, 4, 5, 6] !!) (generateOrderMapping 6) == [1, 2, 3, 4, 5, 6]
593+--
594+-- >>> generateOrderMapping 6
595+-- [3,1,4,0,5,2]
596+--
597+-- >>> generateOrderMapping 8
598+-- [7,3,1,4,0,5,2,6]
599+generateOrderMapping :: Int -> [Int]
600+generateOrderMapping len = runST $ do
601+ orderMappingArr <- newPrimArray len
602+ _ <- loop orderMappingArr 0 0
603+ primArrayToList <$> unsafeFreezePrimArray orderMappingArr
604+ where
605+ loop :: MutablePrimArray s Int -> Int -> Int -> ST s Int
606+ loop result i first =
607+ if i >= len
608+ then pure first
609+ else do
610+ newFirst <- loop result (2 * i + 1) first
611+ writePrimArray result newFirst i
612+ loop result (2 * i + 2) (newFirst + 1)
613+
461614----------------------------------------------------------------------------
462615-- Helper functions.
463616----------------------------------------------------------------------------
464617
465−-- | Check that invariant of the structure is hold.
618+-- | Check that invariant of the structure holds.
466619-- The structure maintains the following invariant.
467620-- For each element @A@ at index @i@:
468621--
469−-- 1. if there is an element @B@ at index @2*i+1@,
622+-- 1. if there is an element @B@ at index @2*i+1@,
470623-- then @B < A@.
471624--
472−-- 2. if there is an element @C@ at index @2*i+2@,
625+-- 2. if there is an element @C@ at index @2*i+2@,
473626-- then @A < C@.
474627--
475628invariantCheck :: TypeRepMap f -> Bool
@@ -515,4 +668,3 @@ invariantCheck TypeRepMap{..} = getAll (check 0)
515668 , All $ fromMaybe True $ (<=) <$> leftMax <*> rightMin
516669 , check (i+1)
517670 ]
518−