@@ -1,69 +1,50 @@
1−{-# OPTIONS_GHC -Wno-missing-export-lists #-}
2−
3−{-# LANGUAGE AllowAmbiguousTypes #-}
4−{-# LANGUAGE BangPatterns #-}
5−{-# LANGUAGE CPP #-}
6−{-# LANGUAGE DataKinds #-}
7−{-# LANGUAGE GADTs #-}
8−{-# LANGUAGE InstanceSigs #-}
9−{-# LANGUAGE MagicHash #-}
10−{-# LANGUAGE PolyKinds #-}
11−{-# LANGUAGE Rank2Types #-}
12−{-# LANGUAGE TypeFamilies #-}
13−{-# LANGUAGE TypeInType #-}
14−{-# LANGUAGE ViewPatterns #-}
15−
16−#if __GLASGOW_HASKELL__ >= 806
17−{-# LANGUAGE QuantifiedConstraints #-}
18−#endif
1+{-# LANGUAGE AllowAmbiguousTypes #-}
2+{-# LANGUAGE BangPatterns #-}
3+{-# LANGUAGE DataKinds #-}
4+{-# LANGUAGE GADTs #-}
5+{-# LANGUAGE InstanceSigs #-}
6+{-# LANGUAGE KindSignatures #-}
7+{-# LANGUAGE MagicHash #-}
8+{-# LANGUAGE PolyKinds #-}
9+{-# LANGUAGE Rank2Types #-}
10+{-# LANGUAGE TypeFamilies #-}
11+{-# LANGUAGE TypeInType #-}
12+{-# LANGUAGE ViewPatterns #-}
1913
2014-- {-# OPTIONS_GHC -ddump-simpl -dsuppress-idinfo -dsuppress-coercions -dsuppress-type-applications -dsuppress-uniques -dsuppress-module-prefixes #-}
2115
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
28−not have any stability guarantees and can change between minor versions.
29−
30−If you need to use this module for purposes other than tests,
31−create an issue.
32−-}
33−
34−#include "MachDeps.h"
35−
16+-- | Internal API for 'TypeRepMap' and operations on it. The functions here do
17+-- not have any stability guarantees and can change between minor versions.
18+--
19+-- If you need to use this module for purposes other than tests,
20+-- create an issue.
21+--
3622module Data.TypeRepMap.Internal where
3723
3824import Prelude hiding (lookup)
3925
40−import Control.DeepSeq
41−import Control.Monad.ST (ST, runST)
26+import Control.Monad.ST (runST)
4227import Control.Monad.Zip (mzip)
4328import Data.Function (on)
29+import Data.IntMap.Strict (IntMap)
4430import Data.Kind (Type)
45−import Data.Type.Equality ((:~:) (..), TestEquality (..))
4631import Data.List (intercalate, nubBy)
47−import Data.Maybe (fromMaybe)
48−import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', sizeofArray,
49− thawArray, unsafeFreezeArray, writeArray)
50−import Data.Primitive.PrimArray (writePrimArray, newPrimArray, unsafeFreezePrimArray, primArrayToList, MutablePrimArray, primArrayFromListN, PrimArray, indexPrimArray, sizeofPrimArray)
51−import Data.Semigroup (Semigroup (..), All(..))
32+import Data.Maybe (fromJust)
33+import Data.Primitive.Array (Array, freezeArray, indexArray, mapArray', readArray, sizeofArray,
34+ thawArray, writeArray)
35+import Data.Primitive.PrimArray (PrimArray, indexPrimArray, sizeofPrimArray)
36+import Data.Semigroup (Semigroup (..))
5237import GHC.Base (Any, Int (..), Int#, (*#), (+#), (<#))
5338import GHC.Exts (IsList (..), inline, sortWith)
5439import GHC.Fingerprint (Fingerprint (..))
55−#if WORD_SIZE_IN_BITS >= 64
5640import GHC.Prim (eqWord#, ltWord#)
57−#else
58−import GHC.IntWord64 (eqWord64#, ltWord64#)
59−#define eqWord eqWord64
60−#define ltWord ltWord64
61−#endif
6241import GHC.Word (Word64 (..))
6342import Type.Reflection (SomeTypeRep (..), TypeRep, Typeable, typeRep, withTypeable)
6443import Type.Reflection.Unsafe (typeRepFingerprint)
6544import Unsafe.Coerce (unsafeCoerce)
6645
46+import qualified Data.IntMap.Strict as IM
47+import qualified Data.Map.Strict as Map
6748import qualified GHC.Exts as GHC (fromList, toList)
6849
6950{- |
@@ -96,9 +77,6 @@ data TypeRepMap (f :: k -> Type) =
9677 }
9778 -- ^ an unsafe constructor for 'TypeRepMap'
9879
99−instance NFData (TypeRepMap f) where
100− rnf x = rnf (keys x) `seq` ()
101−
10280-- | Shows only keys.
10381instance Show (TypeRepMap f) where
10482 show TypeRepMap{..} = "TypeRepMap [" ++ showKeys ++ "]"
@@ -118,31 +96,6 @@ instance Monoid (TypeRepMap f) where
11896 {-# INLINE mempty #-}
11997 {-# INLINE mappend #-}
12098
121−#if __GLASGOW_HASKELL__ >= 806
122−instance (forall a. Typeable a => Eq (f a)) => Eq (TypeRepMap f) where
123− tm1 == tm2 = size tm1 == size tm2 && go 0
124− where
125− go :: Int -> Bool
126− go i
127− | i == size tm1 = True
128− | otherwise = case testEquality tr1i tr2i of
129− Nothing -> False
130− Just Refl -> repEq tr1i (fromAny tv1i) (fromAny tv2i) && go (i + 1)
131− where
132− tr1i :: TypeRep x
133− tr1i = anyToTypeRep $ indexArray (trKeys tm1) i
134−
135− tr2i :: TypeRep y
136− tr2i = anyToTypeRep $ indexArray (trKeys tm2) i
137−
138− tv1i, tv2i :: Any
139− tv1i = indexArray (trAnys tm1) i
140− tv2i = indexArray (trAnys tm2) i
141−
142− repEq :: TypeRep x -> f x -> f x -> Bool
143− repEq tr = withTypeable tr (==)
144−#endif
145−
14699-- | Returns the list of 'Fingerprint's from 'TypeRepMap'.
147100toFingerprints :: TypeRepMap f -> [Fingerprint]
148101toFingerprints TypeRepMap{..} =
@@ -169,49 +122,33 @@ prop> member @a (one (x :: f a)) == True
169122
170123-}
171124one :: forall a f . Typeable a => f a -> TypeRepMap f
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)
125+one x = insert x empty
178126{-# INLINE one #-}
179127
180128{- |
181129
182130Insert a value into a 'TypeRepMap'.
183−TypeRepMap optimizes for fast reads rather than inserts, as a trade-off inserts are @O(n)@.
184131
185132prop> size (insert v tm) >= size tm
186133prop> member @a (insert (x :: f a) tm) == True
187134
188135-}
189136insert :: forall a f . Typeable a => f a -> TypeRepMap f -> TypeRepMap f
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)}
137+insert x = fromTriples . addX . toTriples
195138 where
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
139+ tripleX :: (Fingerprint, Any, Any)
140+ tripleX@(fpX, _, _) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
141+
142+ addX :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
143+ addX l = tripleX : deleteByFst fpX l
202144{-# INLINE insert #-}
203145
204146-- Extract the kind of a type. We use it to work around lack of syntax for
205147-- inferred type variables (which are not subject to type applications).
206148type KindOf (a :: k) = k
207149
208−type ArgKindOf (f :: k -> l) = k
209−
210150{- | Delete a value from a 'TypeRepMap'.
211151
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−
215152prop> size (delete @a tm) <= size tm
216153prop> member @a (delete @a tm) == False
217154
@@ -224,60 +161,30 @@ False
224161True
225162-}
226163delete :: forall a (f :: KindOf a -> Type) . Typeable a => TypeRepMap f -> TypeRepMap f
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
164+delete = fromTriples . deleteByFst (typeFp @a) . toTriples
234165{-# INLINE delete #-}
235166
236−deleteFirst :: (a -> Bool) -> [a] -> [a]
237−deleteFirst _ [] = []
238−deleteFirst p (x : xs) = if p x then xs else x : deleteFirst p xs
239−
240167{- |
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.
168+Update a value at a specific key with the result of the provided function. When
169+the key is not a member of the map, the original map is returned.
243170
244171>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "a"]
245172>>> lookup @String $ adjust (fmap (++ "ww")) trmap
246173Just (Identity "aww")
247174-}
248175adjust :: forall a f . Typeable a => (f a -> f a) -> TypeRepMap f -> TypeRepMap f
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)}
176+adjust fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
177+ Nothing -> tr
178+ Just i -> tr {trAnys = changeAnyArr i (trAnys tr)}
273179 where
274− replaceAnyAt :: Int -> Any -> Array Any -> Array Any
275− replaceAnyAt i v trAs = runST $ do
180+ changeAnyArr :: Int -> Array Any -> Array Any
181+ changeAnyArr i trAs = runST $ do
276182 let n = sizeofArray trAs
277183 mutArr <- thawArray trAs 0 n
278− writeArray mutArr i v
279− unsafeFreezeArray mutArr
280−{-# INLINE alter #-}
184+ a <- toAny . fun . fromAny <$> readArray mutArr i
185+ writeArray mutArr i a
186+ freezeArray mutArr 0 n
187+{-# INLINE adjust #-}
281188
282189{- | Map over the elements of a 'TypeRepMap'.
283190
@@ -311,89 +218,30 @@ hoistWithKey f (TypeRepMap as bs ans ks) = TypeRepMap as bs newAns ks
311218 withTr t = withTypeable t f
312219{-# INLINE hoistWithKey #-}
313220
314−-- | The union of two 'TypeRepMap's using a combining function for conflicting entries. @O(n + m)@
315−unionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
316−unionWith f ma mb = do
317− fromSortedTriples $ mergeMaps (toSortedTriples ma) (toSortedTriples mb)
221+-- | The union of two 'TypeRepMap's using a combining function.
222+unionWith :: (forall x. f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
223+unionWith f m1 m2 = fromTriples
224+ $ toTripleList
225+ $ Map.unionWith combine
226+ (fromTripleList $ toTriples m1)
227+ (fromTripleList $ toTriples m2)
318228 where
319− f' :: forall x. TypeRep x -> f x -> f x -> f x
320− f' tr = withTypeable tr f
321−
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
229+ combine :: (Any, Any) -> (Any, Any) -> (Any, Any)
230+ combine (av, ak) (bv, _) = (toAny $ f (fromAny av) (fromAny bv), ak)
231+
232+ fromTripleList :: Ord a => [(a, b, c)] -> Map.Map a (b, c)
233+ fromTripleList = Map.fromList . map (\(a, b, c) -> (a, (b, c)))
234+
235+ toTripleList :: Map.Map a (b, c) -> [(a, b, c)]
236+ toTripleList = map (\(a, (b, c)) -> (a, b, c)) . Map.toList
347237{-# INLINE unionWith #-}
348238
349−-- | The (left-biased) union of two 'TypeRepMap's in @O(n + m)@. It prefers the first map when
239+-- | The (left-biased) union of two 'TypeRepMap's. It prefers the first map when
350240-- duplicate keys are encountered, i.e. @'union' == 'unionWith' const@.
351241union :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
352242union = unionWith const
353243{-# INLINE union #-}
354244
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−
397245{- | Check if a value of the given type is present in a 'TypeRepMap'.
398246
399247>>> member @Char $ one (Identity 'a')
@@ -429,22 +277,9 @@ size = sizeofPrimArray . fingerprintAs
429277
430278-- | Return the list of 'SomeTypeRep' from the keys.
431279keys :: TypeRepMap f -> [SomeTypeRep]
432−keys = keysWith SomeTypeRep
280+keys TypeRepMap{..} = SomeTypeRep . anyToTypeRep <$> toList trKeys
433281{-# INLINE keys #-}
434282
435−-- | Return the list of keys by wrapping them with a user-provided function.
436−keysWith :: (forall (a :: ArgKindOf f). TypeRep a -> r) -> TypeRepMap f -> [r]
437−keysWith f TypeRepMap{..} = f . anyToTypeRep <$> 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−
448283-- | Binary searched based on this article
449284-- http://bannalia.blogspot.com/2015/06/cache-friendly-binary-search.html
450285-- with modification for our two-vector search case.
@@ -488,20 +323,8 @@ typeFp = typeRepFingerprint $ typeRep @a
488323toTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
489324toTriples tm = zip3 (toFingerprints tm) (GHC.toList $ trAnys tm) (GHC.toList $ trKeys tm)
490325
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)
326+deleteByFst :: Eq a => a -> [(a, b, c)] -> [(a, b, c)]
327+deleteByFst x = filter ((/= x) . fst3)
505328
506329nubByFst :: (Eq a) => [(a, b, c)] -> [(a, b, c)]
507330nubByFst = nubBy ((==) `on` fst3)
@@ -548,123 +371,33 @@ instance IsList (TypeRepMap f) where
548371 k (WrapTypeable (_ :: f a)) = unsafeCoerce $ typeRep @a
549372
550373 toList :: TypeRepMap f -> [WrapTypeable f]
551− toList = toListWith WrapTypeable
374+ toList = map toWrapTypeable . toTriples
375+ where
376+ toWrapTypeable :: (Fingerprint, Any, Any) -> WrapTypeable f
377+ toWrapTypeable (_, an, k) = withTypeable (unsafeCoerce k) $ fromAny an
552378
553379calcFp :: forall a . Typeable a => Fingerprint
554380calcFp = typeRepFingerprint $ typeRep @a
555381
556382fromTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
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)
383+fromTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
561384 where
562385 (fpAs, fpBs) = unzip $ map (\(Fingerprint a b) -> (a, b)) fps
563− (fps, ans, ks) = unzip3 $ fromSortedList kvs
386+ (fps, ans, ks) = unzip3 $ fromSortedList $ sortWith fst3 $ nubByFst kvs
564387
565388----------------------------------------------------------------------------
566389-- Tree-like conversion
567390----------------------------------------------------------------------------
568391
569392fromSortedList :: forall a . [a] -> [a]
570−fromSortedList l = runST $ do
571− let n = length l
572− let arrOrigin = fromListN n l
573− arrResult <- thawArray arrOrigin 0 n
574− go n arrResult arrOrigin
575− toList <$> unsafeFreezeArray arrResult
393+fromSortedList l = IM.elems $ fst $ go 0 0 mempty (IM.fromList $ zip [0..] l)
576394 where
577395 -- state monad could be used here, but it's another dependency
578− go :: forall s . Int -> MutableArray s a -> Array a -> ST s ()
579− go len result origin = () <$ loop 0 0
580− where
581− loop :: Int -> Int -> ST s Int
582− loop i first =
583− if i >= len
584− then pure first
585− else do
586− newFirst <- loop (2 * i + 1) first
587− writeArray result i (indexArray origin newFirst)
588− loop (2 * i + 2) (newFirst + 1)
589−
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−
614−----------------------------------------------------------------------------
615−-- Helper functions.
616−----------------------------------------------------------------------------
617−
618−-- | Check that invariant of the structure holds.
619−-- The structure maintains the following invariant.
620−-- For each element @A@ at index @i@:
621−--
622−-- 1. if there is an element @B@ at index @2*i+1@,
623−-- then @B < A@.
624−--
625−-- 2. if there is an element @C@ at index @2*i+2@,
626−-- then @A < C@.
627−--
628−invariantCheck :: TypeRepMap f -> Bool
629−invariantCheck TypeRepMap{..} = getAll (check 0)
630− where
631− lastMay [] = Nothing
632− lastMay [x] = Just x
633− lastMay (_:xs) = lastMay xs
634− sz = sizeofPrimArray fingerprintAs
635− check i | i >= sz = All True
636− | otherwise =
637− let left = i*2+1
638− right = i*2+2
639− -- maximum value in the left branch
640− leftMax =
641− fmap (\j -> (indexPrimArray fingerprintAs j, indexPrimArray fingerprintBs j))
642− $ lastMay
643− $ takeWhile (<sz)
644− $ iterate (\j -> j*2+2) left
645− -- minimum value in the right branch
646− rightMin =
647− fmap (\j -> (indexPrimArray fingerprintAs j, indexPrimArray fingerprintBs j))
648− $ lastMay
649− $ takeWhile (<sz)
650− $ iterate (\j -> j*2+1) right
651− in mconcat
652− [ All $
653− if left < sz
654− then
655− case indexPrimArray fingerprintAs i `compare` indexPrimArray fingerprintAs left of
656− LT -> False
657− EQ -> indexPrimArray fingerprintBs i >= indexPrimArray fingerprintBs left
658− GT -> True
659− else True
660− , All $
661− if right < sz
662− then
663− case indexPrimArray fingerprintAs i `compare` indexPrimArray fingerprintAs right of
664− LT -> True
665− EQ -> indexPrimArray fingerprintBs i <= indexPrimArray fingerprintBs right
666− GT -> False
667− else True
668− , All $ fromMaybe True $ (<=) <$> leftMax <*> rightMin
669− , check (i+1)
670− ]
396+ go :: Int -> Int -> IntMap a -> IntMap a -> (IntMap a, Int)
397+ go i first result vector =
398+ if i >= IM.size vector
399+ then (result, first)
400+ else do
401+ let (newResult, newFirst) = go (2 * i + 1) first result vector
402+ let withCur = IM.insert i (fromJust $ IM.lookup newFirst vector) newResult
403+ go (2 * i + 2) (newFirst + 1) withCur vector