f9ee03a21febb3957181df5d47942ce4f85ac087
[ghc.git] / libraries / base / Data / IntMap.hs
1 {-# OPTIONS -cpp -fglasgow-exts #-}
2 -----------------------------------------------------------------------------
3 -- Module : Data.IntMap
4 -- Copyright : (c) Daan Leijen 2002
5 -- License : BSD-style
6 -- Maintainer : libraries@haskell.org
7 -- Stability : provisional
8 -- Portability : portable
9 --
10 -- An efficient implementation of maps from integer keys to values.
11 --
12 -- This module is intended to be imported @qualified@, to avoid name
13 -- clashes with "Prelude" functions. eg.
14 --
15 -- > import Data.IntMap as Map
16 --
17 -- The implementation is based on /big-endian patricia trees/. This data
18 -- structure performs especially well on binary operations like 'union'
19 -- and 'intersection'. However, my benchmarks show that it is also
20 -- (much) faster on insertions and deletions when compared to a generic
21 -- size-balanced map implementation (see "Data.Map" and "Data.FiniteMap").
22 --
23 -- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
24 -- Workshop on ML, September 1998, pages 77-86,
25 -- <http://www.cse.ogi.edu/~andy/pub/finite.htm>
26 --
27 -- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
28 -- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
29 -- October 1968, pages 514-534.
30 --
31 -- Many operations have a worst-case complexity of /O(min(n,W))/.
32 -- This means that the operation can become linear in the number of
33 -- elements with a maximum of /W/ -- the number of bits in an 'Int'
34 -- (32 or 64).
35 -----------------------------------------------------------------------------
36
37 module Data.IntMap (
38 -- * Map type
39 IntMap, Key -- instance Eq,Show
40
41 -- * Operators
42 , (!), (\\)
43
44 -- * Query
45 , null
46 , size
47 , member
48 , lookup
49 , findWithDefault
50
51 -- * Construction
52 , empty
53 , singleton
54
55 -- ** Insertion
56 , insert
57 , insertWith, insertWithKey, insertLookupWithKey
58
59 -- ** Delete\/Update
60 , delete
61 , adjust
62 , adjustWithKey
63 , update
64 , updateWithKey
65 , updateLookupWithKey
66
67 -- * Combine
68
69 -- ** Union
70 , union
71 , unionWith
72 , unionWithKey
73 , unions
74 , unionsWith
75
76 -- ** Difference
77 , difference
78 , differenceWith
79 , differenceWithKey
80
81 -- ** Intersection
82 , intersection
83 , intersectionWith
84 , intersectionWithKey
85
86 -- * Traversal
87 -- ** Map
88 , map
89 , mapWithKey
90 , mapAccum
91 , mapAccumWithKey
92
93 -- ** Fold
94 , fold
95 , foldWithKey
96
97 -- * Conversion
98 , elems
99 , keys
100 , keysSet
101 , assocs
102
103 -- ** Lists
104 , toList
105 , fromList
106 , fromListWith
107 , fromListWithKey
108
109 -- ** Ordered lists
110 , toAscList
111 , fromAscList
112 , fromAscListWith
113 , fromAscListWithKey
114 , fromDistinctAscList
115
116 -- * Filter
117 , filter
118 , filterWithKey
119 , partition
120 , partitionWithKey
121
122 , split
123 , splitLookup
124
125 -- * Submap
126 , isSubmapOf, isSubmapOfBy
127 , isProperSubmapOf, isProperSubmapOfBy
128
129 -- * Debugging
130 , showTree
131 , showTreeWith
132 ) where
133
134
135 import Prelude hiding (lookup,map,filter,foldr,foldl,null)
136 import Data.Bits
137 import Data.Int
138 import qualified Data.IntSet as IntSet
139 import Data.Typeable
140
141 {-
142 -- just for testing
143 import qualified Prelude
144 import Debug.QuickCheck
145 import List (nub,sort)
146 import qualified List
147 -}
148
149 #if __GLASGOW_HASKELL__
150 import Text.Read
151 import Data.Generics.Basics
152 import Data.Generics.Instances
153 #endif
154
155 #if __GLASGOW_HASKELL__ >= 503
156 import GHC.Word
157 import GHC.Exts ( Word(..), Int(..), shiftRL# )
158 #elif __GLASGOW_HASKELL__
159 import Word
160 import GlaExts ( Word(..), Int(..), shiftRL# )
161 #else
162 import Data.Word
163 #endif
164
165 infixl 9 \\{-This comment teaches CPP correct behaviour -}
166
167 -- A "Nat" is a natural machine word (an unsigned Int)
168 type Nat = Word
169
170 natFromInt :: Key -> Nat
171 natFromInt i = fromIntegral i
172
173 intFromNat :: Nat -> Key
174 intFromNat w = fromIntegral w
175
176 shiftRL :: Nat -> Key -> Nat
177 #if __GLASGOW_HASKELL__
178 {--------------------------------------------------------------------
179 GHC: use unboxing to get @shiftRL@ inlined.
180 --------------------------------------------------------------------}
181 shiftRL (W# x) (I# i)
182 = W# (shiftRL# x i)
183 #else
184 shiftRL x i = shiftR x i
185 #endif
186
187 {--------------------------------------------------------------------
188 Operators
189 --------------------------------------------------------------------}
190
191 -- | /O(min(n,W))/. Find the value at a key.
192 -- Calls 'error' when the element can not be found.
193
194 (!) :: IntMap a -> Key -> a
195 m ! k = find' k m
196
197 -- | /O(n+m)/. See 'difference'.
198 (\\) :: IntMap a -> IntMap b -> IntMap a
199 m1 \\ m2 = difference m1 m2
200
201 {--------------------------------------------------------------------
202 Types
203 --------------------------------------------------------------------}
204 -- | A map of integers to values @a@.
205 data IntMap a = Nil
206 | Tip {-# UNPACK #-} !Key a
207 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
208
209 type Prefix = Int
210 type Mask = Int
211 type Key = Int
212
213 #if __GLASGOW_HASKELL__
214
215 {--------------------------------------------------------------------
216 A Data instance
217 --------------------------------------------------------------------}
218
219 -- This instance preserves data abstraction at the cost of inefficiency.
220 -- We omit reflection services for the sake of data abstraction.
221
222 instance Data a => Data (IntMap a) where
223 gfoldl f z im = z fromList `f` (toList im)
224 toConstr _ = error "toConstr"
225 gunfold _ _ = error "gunfold"
226 dataTypeOf _ = mkNorepType "Data.IntMap.IntMap"
227
228 #endif
229
230 {--------------------------------------------------------------------
231 Query
232 --------------------------------------------------------------------}
233 -- | /O(1)/. Is the map empty?
234 null :: IntMap a -> Bool
235 null Nil = True
236 null other = False
237
238 -- | /O(n)/. Number of elements in the map.
239 size :: IntMap a -> Int
240 size t
241 = case t of
242 Bin p m l r -> size l + size r
243 Tip k x -> 1
244 Nil -> 0
245
246 -- | /O(min(n,W))/. Is the key a member of the map?
247 member :: Key -> IntMap a -> Bool
248 member k m
249 = case lookup k m of
250 Nothing -> False
251 Just x -> True
252
253 -- | /O(min(n,W))/. Lookup the value at a key in the map.
254 lookup :: Key -> IntMap a -> Maybe a
255 lookup k t
256 = let nk = natFromInt k in seq nk (lookupN nk t)
257
258 lookupN :: Nat -> IntMap a -> Maybe a
259 lookupN k t
260 = case t of
261 Bin p m l r
262 | zeroN k (natFromInt m) -> lookupN k l
263 | otherwise -> lookupN k r
264 Tip kx x
265 | (k == natFromInt kx) -> Just x
266 | otherwise -> Nothing
267 Nil -> Nothing
268
269 find' :: Key -> IntMap a -> a
270 find' k m
271 = case lookup k m of
272 Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
273 Just x -> x
274
275
276 -- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
277 -- returns the value at key @k@ or returns @def@ when the key is not an
278 -- element of the map.
279 findWithDefault :: a -> Key -> IntMap a -> a
280 findWithDefault def k m
281 = case lookup k m of
282 Nothing -> def
283 Just x -> x
284
285 {--------------------------------------------------------------------
286 Construction
287 --------------------------------------------------------------------}
288 -- | /O(1)/. The empty map.
289 empty :: IntMap a
290 empty
291 = Nil
292
293 -- | /O(1)/. A map of one element.
294 singleton :: Key -> a -> IntMap a
295 singleton k x
296 = Tip k x
297
298 {--------------------------------------------------------------------
299 Insert
300 --------------------------------------------------------------------}
301 -- | /O(min(n,W))/. Insert a new key\/value pair in the map.
302 -- If the key is already present in the map, the associated value is
303 -- replaced with the supplied value, i.e. 'insert' is equivalent to
304 -- @'insertWith' 'const'@.
305 insert :: Key -> a -> IntMap a -> IntMap a
306 insert k x t
307 = case t of
308 Bin p m l r
309 | nomatch k p m -> join k (Tip k x) p t
310 | zero k m -> Bin p m (insert k x l) r
311 | otherwise -> Bin p m l (insert k x r)
312 Tip ky y
313 | k==ky -> Tip k x
314 | otherwise -> join k (Tip k x) ky t
315 Nil -> Tip k x
316
317 -- right-biased insertion, used by 'union'
318 -- | /O(min(n,W))/. Insert with a combining function.
319 insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
320 insertWith f k x t
321 = insertWithKey (\k x y -> f x y) k x t
322
323 -- | /O(min(n,W))/. Insert with a combining function.
324 insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
325 insertWithKey f k x t
326 = case t of
327 Bin p m l r
328 | nomatch k p m -> join k (Tip k x) p t
329 | zero k m -> Bin p m (insertWithKey f k x l) r
330 | otherwise -> Bin p m l (insertWithKey f k x r)
331 Tip ky y
332 | k==ky -> Tip k (f k x y)
333 | otherwise -> join k (Tip k x) ky t
334 Nil -> Tip k x
335
336
337 -- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
338 -- is a pair where the first element is equal to (@'lookup' k map@)
339 -- and the second element equal to (@'insertWithKey' f k x map@).
340 insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
341 insertLookupWithKey f k x t
342 = case t of
343 Bin p m l r
344 | nomatch k p m -> (Nothing,join k (Tip k x) p t)
345 | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
346 | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
347 Tip ky y
348 | k==ky -> (Just y,Tip k (f k x y))
349 | otherwise -> (Nothing,join k (Tip k x) ky t)
350 Nil -> (Nothing,Tip k x)
351
352
353 {--------------------------------------------------------------------
354 Deletion
355 [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
356 --------------------------------------------------------------------}
357 -- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
358 -- a member of the map, the original map is returned.
359 delete :: Key -> IntMap a -> IntMap a
360 delete k t
361 = case t of
362 Bin p m l r
363 | nomatch k p m -> t
364 | zero k m -> bin p m (delete k l) r
365 | otherwise -> bin p m l (delete k r)
366 Tip ky y
367 | k==ky -> Nil
368 | otherwise -> t
369 Nil -> Nil
370
371 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
372 -- a member of the map, the original map is returned.
373 adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
374 adjust f k m
375 = adjustWithKey (\k x -> f x) k m
376
377 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
378 -- a member of the map, the original map is returned.
379 adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
380 adjustWithKey f k m
381 = updateWithKey (\k x -> Just (f k x)) k m
382
383 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
384 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
385 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
386 update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
387 update f k m
388 = updateWithKey (\k x -> f x) k m
389
390 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
391 -- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
392 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
393 updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
394 updateWithKey f k t
395 = case t of
396 Bin p m l r
397 | nomatch k p m -> t
398 | zero k m -> bin p m (updateWithKey f k l) r
399 | otherwise -> bin p m l (updateWithKey f k r)
400 Tip ky y
401 | k==ky -> case (f k y) of
402 Just y' -> Tip ky y'
403 Nothing -> Nil
404 | otherwise -> t
405 Nil -> Nil
406
407 -- | /O(min(n,W))/. Lookup and update.
408 updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
409 updateLookupWithKey f k t
410 = case t of
411 Bin p m l r
412 | nomatch k p m -> (Nothing,t)
413 | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
414 | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
415 Tip ky y
416 | k==ky -> case (f k y) of
417 Just y' -> (Just y,Tip ky y')
418 Nothing -> (Just y,Nil)
419 | otherwise -> (Nothing,t)
420 Nil -> (Nothing,Nil)
421
422
423 {--------------------------------------------------------------------
424 Union
425 --------------------------------------------------------------------}
426 -- | The union of a list of maps.
427 unions :: [IntMap a] -> IntMap a
428 unions xs
429 = foldlStrict union empty xs
430
431 -- | The union of a list of maps, with a combining operation
432 unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
433 unionsWith f ts
434 = foldlStrict (unionWith f) empty ts
435
436 -- | /O(n+m)/. The (left-biased) union of two maps.
437 -- It prefers the first map when duplicate keys are encountered,
438 -- i.e. (@'union' == 'unionWith' 'const'@).
439 union :: IntMap a -> IntMap a -> IntMap a
440 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
441 | shorter m1 m2 = union1
442 | shorter m2 m1 = union2
443 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
444 | otherwise = join p1 t1 p2 t2
445 where
446 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
447 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
448 | otherwise = Bin p1 m1 l1 (union r1 t2)
449
450 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
451 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
452 | otherwise = Bin p2 m2 l2 (union t1 r2)
453
454 union (Tip k x) t = insert k x t
455 union t (Tip k x) = insertWith (\x y -> y) k x t -- right bias
456 union Nil t = t
457 union t Nil = t
458
459 -- | /O(n+m)/. The union with a combining function.
460 unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
461 unionWith f m1 m2
462 = unionWithKey (\k x y -> f x y) m1 m2
463
464 -- | /O(n+m)/. The union with a combining function.
465 unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
466 unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
467 | shorter m1 m2 = union1
468 | shorter m2 m1 = union2
469 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
470 | otherwise = join p1 t1 p2 t2
471 where
472 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
473 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
474 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
475
476 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
477 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
478 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
479
480 unionWithKey f (Tip k x) t = insertWithKey f k x t
481 unionWithKey f t (Tip k x) = insertWithKey (\k x y -> f k y x) k x t -- right bias
482 unionWithKey f Nil t = t
483 unionWithKey f t Nil = t
484
485 {--------------------------------------------------------------------
486 Difference
487 --------------------------------------------------------------------}
488 -- | /O(n+m)/. Difference between two maps (based on keys).
489 difference :: IntMap a -> IntMap b -> IntMap a
490 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
491 | shorter m1 m2 = difference1
492 | shorter m2 m1 = difference2
493 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
494 | otherwise = t1
495 where
496 difference1 | nomatch p2 p1 m1 = t1
497 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
498 | otherwise = bin p1 m1 l1 (difference r1 t2)
499
500 difference2 | nomatch p1 p2 m2 = t1
501 | zero p1 m2 = difference t1 l2
502 | otherwise = difference t1 r2
503
504 difference t1@(Tip k x) t2
505 | member k t2 = Nil
506 | otherwise = t1
507
508 difference Nil t = Nil
509 difference t (Tip k x) = delete k t
510 difference t Nil = t
511
512 -- | /O(n+m)/. Difference with a combining function.
513 differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
514 differenceWith f m1 m2
515 = differenceWithKey (\k x y -> f x y) m1 m2
516
517 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
518 -- encountered, the combining function is applied to the key and both values.
519 -- If it returns 'Nothing', the element is discarded (proper set difference).
520 -- If it returns (@'Just' y@), the element is updated with a new value @y@.
521 differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
522 differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
523 | shorter m1 m2 = difference1
524 | shorter m2 m1 = difference2
525 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
526 | otherwise = t1
527 where
528 difference1 | nomatch p2 p1 m1 = t1
529 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
530 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
531
532 difference2 | nomatch p1 p2 m2 = t1
533 | zero p1 m2 = differenceWithKey f t1 l2
534 | otherwise = differenceWithKey f t1 r2
535
536 differenceWithKey f t1@(Tip k x) t2
537 = case lookup k t2 of
538 Just y -> case f k x y of
539 Just y' -> Tip k y'
540 Nothing -> Nil
541 Nothing -> t1
542
543 differenceWithKey f Nil t = Nil
544 differenceWithKey f t (Tip k y) = updateWithKey (\k x -> f k x y) k t
545 differenceWithKey f t Nil = t
546
547
548 {--------------------------------------------------------------------
549 Intersection
550 --------------------------------------------------------------------}
551 -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
552 intersection :: IntMap a -> IntMap b -> IntMap a
553 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
554 | shorter m1 m2 = intersection1
555 | shorter m2 m1 = intersection2
556 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
557 | otherwise = Nil
558 where
559 intersection1 | nomatch p2 p1 m1 = Nil
560 | zero p2 m1 = intersection l1 t2
561 | otherwise = intersection r1 t2
562
563 intersection2 | nomatch p1 p2 m2 = Nil
564 | zero p1 m2 = intersection t1 l2
565 | otherwise = intersection t1 r2
566
567 intersection t1@(Tip k x) t2
568 | member k t2 = t1
569 | otherwise = Nil
570 intersection t (Tip k x)
571 = case lookup k t of
572 Just y -> Tip k y
573 Nothing -> Nil
574 intersection Nil t = Nil
575 intersection t Nil = Nil
576
577 -- | /O(n+m)/. The intersection with a combining function.
578 intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
579 intersectionWith f m1 m2
580 = intersectionWithKey (\k x y -> f x y) m1 m2
581
582 -- | /O(n+m)/. The intersection with a combining function.
583 intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
584 intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
585 | shorter m1 m2 = intersection1
586 | shorter m2 m1 = intersection2
587 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
588 | otherwise = Nil
589 where
590 intersection1 | nomatch p2 p1 m1 = Nil
591 | zero p2 m1 = intersectionWithKey f l1 t2
592 | otherwise = intersectionWithKey f r1 t2
593
594 intersection2 | nomatch p1 p2 m2 = Nil
595 | zero p1 m2 = intersectionWithKey f t1 l2
596 | otherwise = intersectionWithKey f t1 r2
597
598 intersectionWithKey f t1@(Tip k x) t2
599 = case lookup k t2 of
600 Just y -> Tip k (f k x y)
601 Nothing -> Nil
602 intersectionWithKey f t1 (Tip k y)
603 = case lookup k t1 of
604 Just x -> Tip k (f k x y)
605 Nothing -> Nil
606 intersectionWithKey f Nil t = Nil
607 intersectionWithKey f t Nil = Nil
608
609
610 {--------------------------------------------------------------------
611 Submap
612 --------------------------------------------------------------------}
613 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
614 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
615 isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
616 isProperSubmapOf m1 m2
617 = isProperSubmapOfBy (==) m1 m2
618
619 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
620 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
621 @m1@ and @m2@ are not equal,
622 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
623 applied to their respective values. For example, the following
624 expressions are all 'True':
625
626 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
627 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
628
629 But the following are all 'False':
630
631 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
632 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
633 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
634 -}
635 isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
636 isProperSubmapOfBy pred t1 t2
637 = case submapCmp pred t1 t2 of
638 LT -> True
639 ge -> False
640
641 submapCmp pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
642 | shorter m1 m2 = GT
643 | shorter m2 m1 = submapCmpLt
644 | p1 == p2 = submapCmpEq
645 | otherwise = GT -- disjoint
646 where
647 submapCmpLt | nomatch p1 p2 m2 = GT
648 | zero p1 m2 = submapCmp pred t1 l2
649 | otherwise = submapCmp pred t1 r2
650 submapCmpEq = case (submapCmp pred l1 l2, submapCmp pred r1 r2) of
651 (GT,_ ) -> GT
652 (_ ,GT) -> GT
653 (EQ,EQ) -> EQ
654 other -> LT
655
656 submapCmp pred (Bin p m l r) t = GT
657 submapCmp pred (Tip kx x) (Tip ky y)
658 | (kx == ky) && pred x y = EQ
659 | otherwise = GT -- disjoint
660 submapCmp pred (Tip k x) t
661 = case lookup k t of
662 Just y | pred x y -> LT
663 other -> GT -- disjoint
664 submapCmp pred Nil Nil = EQ
665 submapCmp pred Nil t = LT
666
667 -- | /O(n+m)/. Is this a submap?
668 -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
669 isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
670 isSubmapOf m1 m2
671 = isSubmapOfBy (==) m1 m2
672
673 {- | /O(n+m)/.
674 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
675 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
676 applied to their respective values. For example, the following
677 expressions are all 'True':
678
679 > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
680 > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
681 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
682
683 But the following are all 'False':
684
685 > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
686 > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
687 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
688 -}
689
690 isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
691 isSubmapOfBy pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
692 | shorter m1 m2 = False
693 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy pred t1 l2
694 else isSubmapOfBy pred t1 r2)
695 | otherwise = (p1==p2) && isSubmapOfBy pred l1 l2 && isSubmapOfBy pred r1 r2
696 isSubmapOfBy pred (Bin p m l r) t = False
697 isSubmapOfBy pred (Tip k x) t = case lookup k t of
698 Just y -> pred x y
699 Nothing -> False
700 isSubmapOfBy pred Nil t = True
701
702 {--------------------------------------------------------------------
703 Mapping
704 --------------------------------------------------------------------}
705 -- | /O(n)/. Map a function over all values in the map.
706 map :: (a -> b) -> IntMap a -> IntMap b
707 map f m
708 = mapWithKey (\k x -> f x) m
709
710 -- | /O(n)/. Map a function over all values in the map.
711 mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
712 mapWithKey f t
713 = case t of
714 Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
715 Tip k x -> Tip k (f k x)
716 Nil -> Nil
717
718 -- | /O(n)/. The function @'mapAccum'@ threads an accumulating
719 -- argument through the map in ascending order of keys.
720 mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
721 mapAccum f a m
722 = mapAccumWithKey (\a k x -> f a x) a m
723
724 -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
725 -- argument through the map in ascending order of keys.
726 mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
727 mapAccumWithKey f a t
728 = mapAccumL f a t
729
730 -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
731 -- argument through the map in ascending order of keys.
732 mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
733 mapAccumL f a t
734 = case t of
735 Bin p m l r -> let (a1,l') = mapAccumL f a l
736 (a2,r') = mapAccumL f a1 r
737 in (a2,Bin p m l' r')
738 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
739 Nil -> (a,Nil)
740
741
742 -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
743 -- argument throught the map in descending order of keys.
744 mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
745 mapAccumR f a t
746 = case t of
747 Bin p m l r -> let (a1,r') = mapAccumR f a r
748 (a2,l') = mapAccumR f a1 l
749 in (a2,Bin p m l' r')
750 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
751 Nil -> (a,Nil)
752
753 {--------------------------------------------------------------------
754 Filter
755 --------------------------------------------------------------------}
756 -- | /O(n)/. Filter all values that satisfy some predicate.
757 filter :: (a -> Bool) -> IntMap a -> IntMap a
758 filter p m
759 = filterWithKey (\k x -> p x) m
760
761 -- | /O(n)/. Filter all keys\/values that satisfy some predicate.
762 filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
763 filterWithKey pred t
764 = case t of
765 Bin p m l r
766 -> bin p m (filterWithKey pred l) (filterWithKey pred r)
767 Tip k x
768 | pred k x -> t
769 | otherwise -> Nil
770 Nil -> Nil
771
772 -- | /O(n)/. partition the map according to some predicate. The first
773 -- map contains all elements that satisfy the predicate, the second all
774 -- elements that fail the predicate. See also 'split'.
775 partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
776 partition p m
777 = partitionWithKey (\k x -> p x) m
778
779 -- | /O(n)/. partition the map according to some predicate. The first
780 -- map contains all elements that satisfy the predicate, the second all
781 -- elements that fail the predicate. See also 'split'.
782 partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
783 partitionWithKey pred t
784 = case t of
785 Bin p m l r
786 -> let (l1,l2) = partitionWithKey pred l
787 (r1,r2) = partitionWithKey pred r
788 in (bin p m l1 r1, bin p m l2 r2)
789 Tip k x
790 | pred k x -> (t,Nil)
791 | otherwise -> (Nil,t)
792 Nil -> (Nil,Nil)
793
794
795 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
796 -- where all keys in @map1@ are lower than @k@ and all keys in
797 -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
798 split :: Key -> IntMap a -> (IntMap a,IntMap a)
799 split k t
800 = case t of
801 Bin p m l r
802 | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
803 | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
804 | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
805 Tip ky y
806 | k>ky -> (t,Nil)
807 | k<ky -> (Nil,t)
808 | otherwise -> (Nil,Nil)
809 Nil -> (Nil,Nil)
810
811 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
812 -- key was found in the original map.
813 splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
814 splitLookup k t
815 = case t of
816 Bin p m l r
817 | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
818 | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
819 | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
820 Tip ky y
821 | k>ky -> (t,Nothing,Nil)
822 | k<ky -> (Nil,Nothing,t)
823 | otherwise -> (Nil,Just y,Nil)
824 Nil -> (Nil,Nothing,Nil)
825
826 {--------------------------------------------------------------------
827 Fold
828 --------------------------------------------------------------------}
829 -- | /O(n)/. Fold the values in the map, such that
830 -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
831 -- For example,
832 --
833 -- > elems map = fold (:) [] map
834 --
835 fold :: (a -> b -> b) -> b -> IntMap a -> b
836 fold f z t
837 = foldWithKey (\k x y -> f x y) z t
838
839 -- | /O(n)/. Fold the keys and values in the map, such that
840 -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
841 -- For example,
842 --
843 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
844 --
845 foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
846 foldWithKey f z t
847 = foldr f z t
848
849 foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
850 foldr f z t
851 = case t of
852 Bin p m l r -> foldr f (foldr f z r) l
853 Tip k x -> f k x z
854 Nil -> z
855
856 {--------------------------------------------------------------------
857 List variations
858 --------------------------------------------------------------------}
859 -- | /O(n)/.
860 -- Return all elements of the map in the ascending order of their keys.
861 elems :: IntMap a -> [a]
862 elems m
863 = foldWithKey (\k x xs -> x:xs) [] m
864
865 -- | /O(n)/. Return all keys of the map in ascending order.
866 keys :: IntMap a -> [Key]
867 keys m
868 = foldWithKey (\k x ks -> k:ks) [] m
869
870 -- | /O(n*min(n,W))/. The set of all keys of the map.
871 keysSet :: IntMap a -> IntSet.IntSet
872 keysSet m = IntSet.fromDistinctAscList (keys m)
873
874
875 -- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
876 assocs :: IntMap a -> [(Key,a)]
877 assocs m
878 = toList m
879
880
881 {--------------------------------------------------------------------
882 Lists
883 --------------------------------------------------------------------}
884 -- | /O(n)/. Convert the map to a list of key\/value pairs.
885 toList :: IntMap a -> [(Key,a)]
886 toList t
887 = foldWithKey (\k x xs -> (k,x):xs) [] t
888
889 -- | /O(n)/. Convert the map to a list of key\/value pairs where the
890 -- keys are in ascending order.
891 toAscList :: IntMap a -> [(Key,a)]
892 toAscList t
893 = -- NOTE: the following algorithm only works for big-endian trees
894 let (pos,neg) = span (\(k,x) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos
895
896 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
897 fromList :: [(Key,a)] -> IntMap a
898 fromList xs
899 = foldlStrict ins empty xs
900 where
901 ins t (k,x) = insert k x t
902
903 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
904 fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
905 fromListWith f xs
906 = fromListWithKey (\k x y -> f x y) xs
907
908 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
909 fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
910 fromListWithKey f xs
911 = foldlStrict ins empty xs
912 where
913 ins t (k,x) = insertWithKey f k x t
914
915 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
916 -- the keys are in ascending order.
917 fromAscList :: [(Key,a)] -> IntMap a
918 fromAscList xs
919 = fromList xs
920
921 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
922 -- the keys are in ascending order, with a combining function on equal keys.
923 fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
924 fromAscListWith f xs
925 = fromListWith f xs
926
927 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
928 -- the keys are in ascending order, with a combining function on equal keys.
929 fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
930 fromAscListWithKey f xs
931 = fromListWithKey f xs
932
933 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
934 -- the keys are in ascending order and all distinct.
935 fromDistinctAscList :: [(Key,a)] -> IntMap a
936 fromDistinctAscList xs
937 = fromList xs
938
939
940 {--------------------------------------------------------------------
941 Eq
942 --------------------------------------------------------------------}
943 instance Eq a => Eq (IntMap a) where
944 t1 == t2 = equal t1 t2
945 t1 /= t2 = nequal t1 t2
946
947 equal :: Eq a => IntMap a -> IntMap a -> Bool
948 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
949 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
950 equal (Tip kx x) (Tip ky y)
951 = (kx == ky) && (x==y)
952 equal Nil Nil = True
953 equal t1 t2 = False
954
955 nequal :: Eq a => IntMap a -> IntMap a -> Bool
956 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
957 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
958 nequal (Tip kx x) (Tip ky y)
959 = (kx /= ky) || (x/=y)
960 nequal Nil Nil = False
961 nequal t1 t2 = True
962
963 {--------------------------------------------------------------------
964 Ord
965 --------------------------------------------------------------------}
966
967 instance Ord a => Ord (IntMap a) where
968 compare m1 m2 = compare (toList m1) (toList m2)
969
970 {--------------------------------------------------------------------
971 Functor
972 --------------------------------------------------------------------}
973
974 instance Functor IntMap where
975 fmap = map
976
977 {--------------------------------------------------------------------
978 Show
979 --------------------------------------------------------------------}
980
981 instance Show a => Show (IntMap a) where
982 showsPrec d m = showParen (d > 10) $
983 showString "fromList " . shows (toList m)
984
985 showMap :: (Show a) => [(Key,a)] -> ShowS
986 showMap []
987 = showString "{}"
988 showMap (x:xs)
989 = showChar '{' . showElem x . showTail xs
990 where
991 showTail [] = showChar '}'
992 showTail (x:xs) = showChar ',' . showElem x . showTail xs
993
994 showElem (k,x) = shows k . showString ":=" . shows x
995
996 {--------------------------------------------------------------------
997 Read
998 --------------------------------------------------------------------}
999 instance (Read e) => Read (IntMap e) where
1000 #ifdef __GLASGOW_HASKELL__
1001 readPrec = parens $ prec 10 $ do
1002 Ident "fromList" <- lexP
1003 xs <- readPrec
1004 return (fromList xs)
1005
1006 readListPrec = readListPrecDefault
1007 #else
1008 readsPrec p = readParen (p > 10) $ \ r -> do
1009 ("fromList",s) <- lex r
1010 (xs,t) <- reads s
1011 return (fromList xs,t)
1012 #endif
1013
1014 {--------------------------------------------------------------------
1015 Typeable
1016 --------------------------------------------------------------------}
1017
1018 #include "Typeable.h"
1019 INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
1020
1021 {--------------------------------------------------------------------
1022 Debugging
1023 --------------------------------------------------------------------}
1024 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1025 -- in a compressed, hanging format.
1026 showTree :: Show a => IntMap a -> String
1027 showTree s
1028 = showTreeWith True False s
1029
1030
1031 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
1032 the tree that implements the map. If @hang@ is
1033 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1034 @wide@ is 'True', an extra wide version is shown.
1035 -}
1036 showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
1037 showTreeWith hang wide t
1038 | hang = (showsTreeHang wide [] t) ""
1039 | otherwise = (showsTree wide [] [] t) ""
1040
1041 showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
1042 showsTree wide lbars rbars t
1043 = case t of
1044 Bin p m l r
1045 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
1046 showWide wide rbars .
1047 showsBars lbars . showString (showBin p m) . showString "\n" .
1048 showWide wide lbars .
1049 showsTree wide (withEmpty lbars) (withBar lbars) l
1050 Tip k x
1051 -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1052 Nil -> showsBars lbars . showString "|\n"
1053
1054 showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
1055 showsTreeHang wide bars t
1056 = case t of
1057 Bin p m l r
1058 -> showsBars bars . showString (showBin p m) . showString "\n" .
1059 showWide wide bars .
1060 showsTreeHang wide (withBar bars) l .
1061 showWide wide bars .
1062 showsTreeHang wide (withEmpty bars) r
1063 Tip k x
1064 -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1065 Nil -> showsBars bars . showString "|\n"
1066
1067 showBin p m
1068 = "*" -- ++ show (p,m)
1069
1070 showWide wide bars
1071 | wide = showString (concat (reverse bars)) . showString "|\n"
1072 | otherwise = id
1073
1074 showsBars :: [String] -> ShowS
1075 showsBars bars
1076 = case bars of
1077 [] -> id
1078 _ -> showString (concat (reverse (tail bars))) . showString node
1079
1080 node = "+--"
1081 withBar bars = "| ":bars
1082 withEmpty bars = " ":bars
1083
1084
1085 {--------------------------------------------------------------------
1086 Helpers
1087 --------------------------------------------------------------------}
1088 {--------------------------------------------------------------------
1089 Join
1090 --------------------------------------------------------------------}
1091 join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
1092 join p1 t1 p2 t2
1093 | zero p1 m = Bin p m t1 t2
1094 | otherwise = Bin p m t2 t1
1095 where
1096 m = branchMask p1 p2
1097 p = mask p1 m
1098
1099 {--------------------------------------------------------------------
1100 @bin@ assures that we never have empty trees within a tree.
1101 --------------------------------------------------------------------}
1102 bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
1103 bin p m l Nil = l
1104 bin p m Nil r = r
1105 bin p m l r = Bin p m l r
1106
1107
1108 {--------------------------------------------------------------------
1109 Endian independent bit twiddling
1110 --------------------------------------------------------------------}
1111 zero :: Key -> Mask -> Bool
1112 zero i m
1113 = (natFromInt i) .&. (natFromInt m) == 0
1114
1115 nomatch,match :: Key -> Prefix -> Mask -> Bool
1116 nomatch i p m
1117 = (mask i m) /= p
1118
1119 match i p m
1120 = (mask i m) == p
1121
1122 mask :: Key -> Mask -> Prefix
1123 mask i m
1124 = maskW (natFromInt i) (natFromInt m)
1125
1126
1127 zeroN :: Nat -> Nat -> Bool
1128 zeroN i m = (i .&. m) == 0
1129
1130 {--------------------------------------------------------------------
1131 Big endian operations
1132 --------------------------------------------------------------------}
1133 maskW :: Nat -> Nat -> Prefix
1134 maskW i m
1135 = intFromNat (i .&. (complement (m-1) `xor` m))
1136
1137 shorter :: Mask -> Mask -> Bool
1138 shorter m1 m2
1139 = (natFromInt m1) > (natFromInt m2)
1140
1141 branchMask :: Prefix -> Prefix -> Mask
1142 branchMask p1 p2
1143 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
1144
1145 {----------------------------------------------------------------------
1146 Finding the highest bit (mask) in a word [x] can be done efficiently in
1147 three ways:
1148 * convert to a floating point value and the mantissa tells us the
1149 [log2(x)] that corresponds with the highest bit position. The mantissa
1150 is retrieved either via the standard C function [frexp] or by some bit
1151 twiddling on IEEE compatible numbers (float). Note that one needs to
1152 use at least [double] precision for an accurate mantissa of 32 bit
1153 numbers.
1154 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
1155 * use processor specific assembler instruction (asm).
1156
1157 The most portable way would be [bit], but is it efficient enough?
1158 I have measured the cycle counts of the different methods on an AMD
1159 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
1160
1161 highestBitMask: method cycles
1162 --------------
1163 frexp 200
1164 float 33
1165 bit 11
1166 asm 12
1167
1168 highestBit: method cycles
1169 --------------
1170 frexp 195
1171 float 33
1172 bit 11
1173 asm 11
1174
1175 Wow, the bit twiddling is on today's RISC like machines even faster
1176 than a single CISC instruction (BSR)!
1177 ----------------------------------------------------------------------}
1178
1179 {----------------------------------------------------------------------
1180 [highestBitMask] returns a word where only the highest bit is set.
1181 It is found by first setting all bits in lower positions than the
1182 highest bit and than taking an exclusive or with the original value.
1183 Allthough the function may look expensive, GHC compiles this into
1184 excellent C code that subsequently compiled into highly efficient
1185 machine code. The algorithm is derived from Jorg Arndt's FXT library.
1186 ----------------------------------------------------------------------}
1187 highestBitMask :: Nat -> Nat
1188 highestBitMask x
1189 = case (x .|. shiftRL x 1) of
1190 x -> case (x .|. shiftRL x 2) of
1191 x -> case (x .|. shiftRL x 4) of
1192 x -> case (x .|. shiftRL x 8) of
1193 x -> case (x .|. shiftRL x 16) of
1194 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
1195 x -> (x `xor` (shiftRL x 1))
1196
1197
1198 {--------------------------------------------------------------------
1199 Utilities
1200 --------------------------------------------------------------------}
1201 foldlStrict f z xs
1202 = case xs of
1203 [] -> z
1204 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1205
1206 {-
1207 {--------------------------------------------------------------------
1208 Testing
1209 --------------------------------------------------------------------}
1210 testTree :: [Int] -> IntMap Int
1211 testTree xs = fromList [(x,x*x*30696 `mod` 65521) | x <- xs]
1212 test1 = testTree [1..20]
1213 test2 = testTree [30,29..10]
1214 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1215
1216 {--------------------------------------------------------------------
1217 QuickCheck
1218 --------------------------------------------------------------------}
1219 qcheck prop
1220 = check config prop
1221 where
1222 config = Config
1223 { configMaxTest = 500
1224 , configMaxFail = 5000
1225 , configSize = \n -> (div n 2 + 3)
1226 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1227 }
1228
1229
1230 {--------------------------------------------------------------------
1231 Arbitrary, reasonably balanced trees
1232 --------------------------------------------------------------------}
1233 instance Arbitrary a => Arbitrary (IntMap a) where
1234 arbitrary = do{ ks <- arbitrary
1235 ; xs <- mapM (\k -> do{ x <- arbitrary; return (k,x)}) ks
1236 ; return (fromList xs)
1237 }
1238
1239
1240 {--------------------------------------------------------------------
1241 Single, Insert, Delete
1242 --------------------------------------------------------------------}
1243 prop_Single :: Key -> Int -> Bool
1244 prop_Single k x
1245 = (insert k x empty == singleton k x)
1246
1247 prop_InsertDelete :: Key -> Int -> IntMap Int -> Property
1248 prop_InsertDelete k x t
1249 = not (member k t) ==> delete k (insert k x t) == t
1250
1251 prop_UpdateDelete :: Key -> IntMap Int -> Bool
1252 prop_UpdateDelete k t
1253 = update (const Nothing) k t == delete k t
1254
1255
1256 {--------------------------------------------------------------------
1257 Union
1258 --------------------------------------------------------------------}
1259 prop_UnionInsert :: Key -> Int -> IntMap Int -> Bool
1260 prop_UnionInsert k x t
1261 = union (singleton k x) t == insert k x t
1262
1263 prop_UnionAssoc :: IntMap Int -> IntMap Int -> IntMap Int -> Bool
1264 prop_UnionAssoc t1 t2 t3
1265 = union t1 (union t2 t3) == union (union t1 t2) t3
1266
1267 prop_UnionComm :: IntMap Int -> IntMap Int -> Bool
1268 prop_UnionComm t1 t2
1269 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1270
1271
1272 prop_Diff :: [(Key,Int)] -> [(Key,Int)] -> Bool
1273 prop_Diff xs ys
1274 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1275 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1276
1277 prop_Int :: [(Key,Int)] -> [(Key,Int)] -> Bool
1278 prop_Int xs ys
1279 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1280 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1281
1282 {--------------------------------------------------------------------
1283 Lists
1284 --------------------------------------------------------------------}
1285 prop_Ordered
1286 = forAll (choose (5,100)) $ \n ->
1287 let xs = [(x,()) | x <- [0..n::Int]]
1288 in fromAscList xs == fromList xs
1289
1290 prop_List :: [Key] -> Bool
1291 prop_List xs
1292 = (sort (nub xs) == [x | (x,()) <- toAscList (fromList [(x,()) | x <- xs])])
1293 -}