e210442707c8bc98951e6f02e4bbf77f9ec8ea43
[packages/random.git] / 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.Monoid (Monoid(..))
140 import Data.Typeable
141
142 {-
143 -- just for testing
144 import qualified Prelude
145 import Debug.QuickCheck
146 import List (nub,sort)
147 import qualified List
148 -}
149
150 #if __GLASGOW_HASKELL__
151 import Text.Read
152 import Data.Generics.Basics
153 import Data.Generics.Instances
154 #endif
155
156 #if __GLASGOW_HASKELL__ >= 503
157 import GHC.Word
158 import GHC.Exts ( Word(..), Int(..), shiftRL# )
159 #elif __GLASGOW_HASKELL__
160 import Word
161 import GlaExts ( Word(..), Int(..), shiftRL# )
162 #else
163 import Data.Word
164 #endif
165
166 infixl 9 \\{-This comment teaches CPP correct behaviour -}
167
168 -- A "Nat" is a natural machine word (an unsigned Int)
169 type Nat = Word
170
171 natFromInt :: Key -> Nat
172 natFromInt i = fromIntegral i
173
174 intFromNat :: Nat -> Key
175 intFromNat w = fromIntegral w
176
177 shiftRL :: Nat -> Key -> Nat
178 #if __GLASGOW_HASKELL__
179 {--------------------------------------------------------------------
180 GHC: use unboxing to get @shiftRL@ inlined.
181 --------------------------------------------------------------------}
182 shiftRL (W# x) (I# i)
183 = W# (shiftRL# x i)
184 #else
185 shiftRL x i = shiftR x i
186 #endif
187
188 {--------------------------------------------------------------------
189 Operators
190 --------------------------------------------------------------------}
191
192 -- | /O(min(n,W))/. Find the value at a key.
193 -- Calls 'error' when the element can not be found.
194
195 (!) :: IntMap a -> Key -> a
196 m ! k = find' k m
197
198 -- | /O(n+m)/. See 'difference'.
199 (\\) :: IntMap a -> IntMap b -> IntMap a
200 m1 \\ m2 = difference m1 m2
201
202 {--------------------------------------------------------------------
203 Types
204 --------------------------------------------------------------------}
205 -- | A map of integers to values @a@.
206 data IntMap a = Nil
207 | Tip {-# UNPACK #-} !Key a
208 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
209
210 type Prefix = Int
211 type Mask = Int
212 type Key = Int
213
214 instance Ord a => Monoid (IntMap a) where
215 mempty = empty
216 mappend = union
217 mconcat = unions
218
219 #if __GLASGOW_HASKELL__
220
221 {--------------------------------------------------------------------
222 A Data instance
223 --------------------------------------------------------------------}
224
225 -- This instance preserves data abstraction at the cost of inefficiency.
226 -- We omit reflection services for the sake of data abstraction.
227
228 instance Data a => Data (IntMap a) where
229 gfoldl f z im = z fromList `f` (toList im)
230 toConstr _ = error "toConstr"
231 gunfold _ _ = error "gunfold"
232 dataTypeOf _ = mkNorepType "Data.IntMap.IntMap"
233
234 #endif
235
236 {--------------------------------------------------------------------
237 Query
238 --------------------------------------------------------------------}
239 -- | /O(1)/. Is the map empty?
240 null :: IntMap a -> Bool
241 null Nil = True
242 null other = False
243
244 -- | /O(n)/. Number of elements in the map.
245 size :: IntMap a -> Int
246 size t
247 = case t of
248 Bin p m l r -> size l + size r
249 Tip k x -> 1
250 Nil -> 0
251
252 -- | /O(min(n,W))/. Is the key a member of the map?
253 member :: Key -> IntMap a -> Bool
254 member k m
255 = case lookup k m of
256 Nothing -> False
257 Just x -> True
258
259 -- | /O(min(n,W))/. Lookup the value at a key in the map.
260 lookup :: Key -> IntMap a -> Maybe a
261 lookup k t
262 = let nk = natFromInt k in seq nk (lookupN nk t)
263
264 lookupN :: Nat -> IntMap a -> Maybe a
265 lookupN k t
266 = case t of
267 Bin p m l r
268 | zeroN k (natFromInt m) -> lookupN k l
269 | otherwise -> lookupN k r
270 Tip kx x
271 | (k == natFromInt kx) -> Just x
272 | otherwise -> Nothing
273 Nil -> Nothing
274
275 find' :: Key -> IntMap a -> a
276 find' k m
277 = case lookup k m of
278 Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
279 Just x -> x
280
281
282 -- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
283 -- returns the value at key @k@ or returns @def@ when the key is not an
284 -- element of the map.
285 findWithDefault :: a -> Key -> IntMap a -> a
286 findWithDefault def k m
287 = case lookup k m of
288 Nothing -> def
289 Just x -> x
290
291 {--------------------------------------------------------------------
292 Construction
293 --------------------------------------------------------------------}
294 -- | /O(1)/. The empty map.
295 empty :: IntMap a
296 empty
297 = Nil
298
299 -- | /O(1)/. A map of one element.
300 singleton :: Key -> a -> IntMap a
301 singleton k x
302 = Tip k x
303
304 {--------------------------------------------------------------------
305 Insert
306 --------------------------------------------------------------------}
307 -- | /O(min(n,W))/. Insert a new key\/value pair in the map.
308 -- If the key is already present in the map, the associated value is
309 -- replaced with the supplied value, i.e. 'insert' is equivalent to
310 -- @'insertWith' 'const'@.
311 insert :: Key -> a -> IntMap a -> IntMap a
312 insert k x t
313 = case t of
314 Bin p m l r
315 | nomatch k p m -> join k (Tip k x) p t
316 | zero k m -> Bin p m (insert k x l) r
317 | otherwise -> Bin p m l (insert k x r)
318 Tip ky y
319 | k==ky -> Tip k x
320 | otherwise -> join k (Tip k x) ky t
321 Nil -> Tip k x
322
323 -- right-biased insertion, used by 'union'
324 -- | /O(min(n,W))/. Insert with a combining function.
325 -- @'insertWith' f key value mp@
326 -- will insert the pair (key, value) into @mp@ if key does
327 -- not exist in the map. If the key does exist, the function will
328 -- insert @f new_value old_value@.
329 insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
330 insertWith f k x t
331 = insertWithKey (\k x y -> f x y) k x t
332
333 -- | /O(min(n,W))/. Insert with a combining function.
334 -- @'insertWithKey' f key value mp@
335 -- will insert the pair (key, value) into @mp@ if key does
336 -- not exist in the map. If the key does exist, the function will
337 -- insert @f key new_value old_value@.
338 insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
339 insertWithKey f k x t
340 = case t of
341 Bin p m l r
342 | nomatch k p m -> join k (Tip k x) p t
343 | zero k m -> Bin p m (insertWithKey f k x l) r
344 | otherwise -> Bin p m l (insertWithKey f k x r)
345 Tip ky y
346 | k==ky -> Tip k (f k x y)
347 | otherwise -> join k (Tip k x) ky t
348 Nil -> Tip k x
349
350
351 -- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
352 -- is a pair where the first element is equal to (@'lookup' k map@)
353 -- and the second element equal to (@'insertWithKey' f k x map@).
354 insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
355 insertLookupWithKey f k x t
356 = case t of
357 Bin p m l r
358 | nomatch k p m -> (Nothing,join k (Tip k x) p t)
359 | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
360 | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
361 Tip ky y
362 | k==ky -> (Just y,Tip k (f k x y))
363 | otherwise -> (Nothing,join k (Tip k x) ky t)
364 Nil -> (Nothing,Tip k x)
365
366
367 {--------------------------------------------------------------------
368 Deletion
369 [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
370 --------------------------------------------------------------------}
371 -- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
372 -- a member of the map, the original map is returned.
373 delete :: Key -> IntMap a -> IntMap a
374 delete k t
375 = case t of
376 Bin p m l r
377 | nomatch k p m -> t
378 | zero k m -> bin p m (delete k l) r
379 | otherwise -> bin p m l (delete k r)
380 Tip ky y
381 | k==ky -> Nil
382 | otherwise -> t
383 Nil -> Nil
384
385 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
386 -- a member of the map, the original map is returned.
387 adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
388 adjust f k m
389 = adjustWithKey (\k x -> f x) k m
390
391 -- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
392 -- a member of the map, the original map is returned.
393 adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
394 adjustWithKey f k m
395 = updateWithKey (\k x -> Just (f k x)) k m
396
397 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
398 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
399 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
400 update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
401 update f k m
402 = updateWithKey (\k x -> f x) k m
403
404 -- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
405 -- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
406 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
407 updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
408 updateWithKey f k t
409 = case t of
410 Bin p m l r
411 | nomatch k p m -> t
412 | zero k m -> bin p m (updateWithKey f k l) r
413 | otherwise -> bin p m l (updateWithKey f k r)
414 Tip ky y
415 | k==ky -> case (f k y) of
416 Just y' -> Tip ky y'
417 Nothing -> Nil
418 | otherwise -> t
419 Nil -> Nil
420
421 -- | /O(min(n,W))/. Lookup and update.
422 updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
423 updateLookupWithKey f k t
424 = case t of
425 Bin p m l r
426 | nomatch k p m -> (Nothing,t)
427 | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
428 | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
429 Tip ky y
430 | k==ky -> case (f k y) of
431 Just y' -> (Just y,Tip ky y')
432 Nothing -> (Just y,Nil)
433 | otherwise -> (Nothing,t)
434 Nil -> (Nothing,Nil)
435
436
437 {--------------------------------------------------------------------
438 Union
439 --------------------------------------------------------------------}
440 -- | The union of a list of maps.
441 unions :: [IntMap a] -> IntMap a
442 unions xs
443 = foldlStrict union empty xs
444
445 -- | The union of a list of maps, with a combining operation
446 unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
447 unionsWith f ts
448 = foldlStrict (unionWith f) empty ts
449
450 -- | /O(n+m)/. The (left-biased) union of two maps.
451 -- It prefers the first map when duplicate keys are encountered,
452 -- i.e. (@'union' == 'unionWith' 'const'@).
453 union :: IntMap a -> IntMap a -> IntMap a
454 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
455 | shorter m1 m2 = union1
456 | shorter m2 m1 = union2
457 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
458 | otherwise = join p1 t1 p2 t2
459 where
460 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
461 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
462 | otherwise = Bin p1 m1 l1 (union r1 t2)
463
464 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
465 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
466 | otherwise = Bin p2 m2 l2 (union t1 r2)
467
468 union (Tip k x) t = insert k x t
469 union t (Tip k x) = insertWith (\x y -> y) k x t -- right bias
470 union Nil t = t
471 union t Nil = t
472
473 -- | /O(n+m)/. The union with a combining function.
474 unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
475 unionWith f m1 m2
476 = unionWithKey (\k x y -> f x y) m1 m2
477
478 -- | /O(n+m)/. The union with a combining function.
479 unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
480 unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
481 | shorter m1 m2 = union1
482 | shorter m2 m1 = union2
483 | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
484 | otherwise = join p1 t1 p2 t2
485 where
486 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
487 | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
488 | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
489
490 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
491 | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
492 | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
493
494 unionWithKey f (Tip k x) t = insertWithKey f k x t
495 unionWithKey f t (Tip k x) = insertWithKey (\k x y -> f k y x) k x t -- right bias
496 unionWithKey f Nil t = t
497 unionWithKey f t Nil = t
498
499 {--------------------------------------------------------------------
500 Difference
501 --------------------------------------------------------------------}
502 -- | /O(n+m)/. Difference between two maps (based on keys).
503 difference :: IntMap a -> IntMap b -> IntMap a
504 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
505 | shorter m1 m2 = difference1
506 | shorter m2 m1 = difference2
507 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
508 | otherwise = t1
509 where
510 difference1 | nomatch p2 p1 m1 = t1
511 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
512 | otherwise = bin p1 m1 l1 (difference r1 t2)
513
514 difference2 | nomatch p1 p2 m2 = t1
515 | zero p1 m2 = difference t1 l2
516 | otherwise = difference t1 r2
517
518 difference t1@(Tip k x) t2
519 | member k t2 = Nil
520 | otherwise = t1
521
522 difference Nil t = Nil
523 difference t (Tip k x) = delete k t
524 difference t Nil = t
525
526 -- | /O(n+m)/. Difference with a combining function.
527 differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
528 differenceWith f m1 m2
529 = differenceWithKey (\k x y -> f x y) m1 m2
530
531 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
532 -- encountered, the combining function is applied to the key and both values.
533 -- If it returns 'Nothing', the element is discarded (proper set difference).
534 -- If it returns (@'Just' y@), the element is updated with a new value @y@.
535 differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
536 differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
537 | shorter m1 m2 = difference1
538 | shorter m2 m1 = difference2
539 | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
540 | otherwise = t1
541 where
542 difference1 | nomatch p2 p1 m1 = t1
543 | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
544 | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
545
546 difference2 | nomatch p1 p2 m2 = t1
547 | zero p1 m2 = differenceWithKey f t1 l2
548 | otherwise = differenceWithKey f t1 r2
549
550 differenceWithKey f t1@(Tip k x) t2
551 = case lookup k t2 of
552 Just y -> case f k x y of
553 Just y' -> Tip k y'
554 Nothing -> Nil
555 Nothing -> t1
556
557 differenceWithKey f Nil t = Nil
558 differenceWithKey f t (Tip k y) = updateWithKey (\k x -> f k x y) k t
559 differenceWithKey f t Nil = t
560
561
562 {--------------------------------------------------------------------
563 Intersection
564 --------------------------------------------------------------------}
565 -- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
566 intersection :: IntMap a -> IntMap b -> IntMap a
567 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
568 | shorter m1 m2 = intersection1
569 | shorter m2 m1 = intersection2
570 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
571 | otherwise = Nil
572 where
573 intersection1 | nomatch p2 p1 m1 = Nil
574 | zero p2 m1 = intersection l1 t2
575 | otherwise = intersection r1 t2
576
577 intersection2 | nomatch p1 p2 m2 = Nil
578 | zero p1 m2 = intersection t1 l2
579 | otherwise = intersection t1 r2
580
581 intersection t1@(Tip k x) t2
582 | member k t2 = t1
583 | otherwise = Nil
584 intersection t (Tip k x)
585 = case lookup k t of
586 Just y -> Tip k y
587 Nothing -> Nil
588 intersection Nil t = Nil
589 intersection t Nil = Nil
590
591 -- | /O(n+m)/. The intersection with a combining function.
592 intersectionWith :: (a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
593 intersectionWith f m1 m2
594 = intersectionWithKey (\k x y -> f x y) m1 m2
595
596 -- | /O(n+m)/. The intersection with a combining function.
597 intersectionWithKey :: (Key -> a -> b -> a) -> IntMap a -> IntMap b -> IntMap a
598 intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
599 | shorter m1 m2 = intersection1
600 | shorter m2 m1 = intersection2
601 | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
602 | otherwise = Nil
603 where
604 intersection1 | nomatch p2 p1 m1 = Nil
605 | zero p2 m1 = intersectionWithKey f l1 t2
606 | otherwise = intersectionWithKey f r1 t2
607
608 intersection2 | nomatch p1 p2 m2 = Nil
609 | zero p1 m2 = intersectionWithKey f t1 l2
610 | otherwise = intersectionWithKey f t1 r2
611
612 intersectionWithKey f t1@(Tip k x) t2
613 = case lookup k t2 of
614 Just y -> Tip k (f k x y)
615 Nothing -> Nil
616 intersectionWithKey f t1 (Tip k y)
617 = case lookup k t1 of
618 Just x -> Tip k (f k x y)
619 Nothing -> Nil
620 intersectionWithKey f Nil t = Nil
621 intersectionWithKey f t Nil = Nil
622
623
624 {--------------------------------------------------------------------
625 Submap
626 --------------------------------------------------------------------}
627 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
628 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
629 isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
630 isProperSubmapOf m1 m2
631 = isProperSubmapOfBy (==) m1 m2
632
633 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
634 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
635 @m1@ and @m2@ are not equal,
636 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
637 applied to their respective values. For example, the following
638 expressions are all 'True':
639
640 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
641 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
642
643 But the following are all 'False':
644
645 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
646 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
647 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
648 -}
649 isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
650 isProperSubmapOfBy pred t1 t2
651 = case submapCmp pred t1 t2 of
652 LT -> True
653 ge -> False
654
655 submapCmp pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
656 | shorter m1 m2 = GT
657 | shorter m2 m1 = submapCmpLt
658 | p1 == p2 = submapCmpEq
659 | otherwise = GT -- disjoint
660 where
661 submapCmpLt | nomatch p1 p2 m2 = GT
662 | zero p1 m2 = submapCmp pred t1 l2
663 | otherwise = submapCmp pred t1 r2
664 submapCmpEq = case (submapCmp pred l1 l2, submapCmp pred r1 r2) of
665 (GT,_ ) -> GT
666 (_ ,GT) -> GT
667 (EQ,EQ) -> EQ
668 other -> LT
669
670 submapCmp pred (Bin p m l r) t = GT
671 submapCmp pred (Tip kx x) (Tip ky y)
672 | (kx == ky) && pred x y = EQ
673 | otherwise = GT -- disjoint
674 submapCmp pred (Tip k x) t
675 = case lookup k t of
676 Just y | pred x y -> LT
677 other -> GT -- disjoint
678 submapCmp pred Nil Nil = EQ
679 submapCmp pred Nil t = LT
680
681 -- | /O(n+m)/. Is this a submap?
682 -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
683 isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
684 isSubmapOf m1 m2
685 = isSubmapOfBy (==) m1 m2
686
687 {- | /O(n+m)/.
688 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
689 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
690 applied to their respective values. For example, the following
691 expressions are all 'True':
692
693 > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
694 > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
695 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
696
697 But the following are all 'False':
698
699 > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
700 > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
701 > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
702 -}
703
704 isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
705 isSubmapOfBy pred t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
706 | shorter m1 m2 = False
707 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy pred t1 l2
708 else isSubmapOfBy pred t1 r2)
709 | otherwise = (p1==p2) && isSubmapOfBy pred l1 l2 && isSubmapOfBy pred r1 r2
710 isSubmapOfBy pred (Bin p m l r) t = False
711 isSubmapOfBy pred (Tip k x) t = case lookup k t of
712 Just y -> pred x y
713 Nothing -> False
714 isSubmapOfBy pred Nil t = True
715
716 {--------------------------------------------------------------------
717 Mapping
718 --------------------------------------------------------------------}
719 -- | /O(n)/. Map a function over all values in the map.
720 map :: (a -> b) -> IntMap a -> IntMap b
721 map f m
722 = mapWithKey (\k x -> f x) m
723
724 -- | /O(n)/. Map a function over all values in the map.
725 mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
726 mapWithKey f t
727 = case t of
728 Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
729 Tip k x -> Tip k (f k x)
730 Nil -> Nil
731
732 -- | /O(n)/. The function @'mapAccum'@ threads an accumulating
733 -- argument through the map in ascending order of keys.
734 mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
735 mapAccum f a m
736 = mapAccumWithKey (\a k x -> f a x) a m
737
738 -- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
739 -- argument through the map in ascending order of keys.
740 mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
741 mapAccumWithKey f a t
742 = mapAccumL f a t
743
744 -- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
745 -- argument through the map in ascending order of keys.
746 mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
747 mapAccumL f a t
748 = case t of
749 Bin p m l r -> let (a1,l') = mapAccumL f a l
750 (a2,r') = mapAccumL f a1 r
751 in (a2,Bin p m l' r')
752 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
753 Nil -> (a,Nil)
754
755
756 -- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
757 -- argument throught the map in descending order of keys.
758 mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
759 mapAccumR f a t
760 = case t of
761 Bin p m l r -> let (a1,r') = mapAccumR f a r
762 (a2,l') = mapAccumR f a1 l
763 in (a2,Bin p m l' r')
764 Tip k x -> let (a',x') = f a k x in (a',Tip k x')
765 Nil -> (a,Nil)
766
767 {--------------------------------------------------------------------
768 Filter
769 --------------------------------------------------------------------}
770 -- | /O(n)/. Filter all values that satisfy some predicate.
771 filter :: (a -> Bool) -> IntMap a -> IntMap a
772 filter p m
773 = filterWithKey (\k x -> p x) m
774
775 -- | /O(n)/. Filter all keys\/values that satisfy some predicate.
776 filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
777 filterWithKey pred t
778 = case t of
779 Bin p m l r
780 -> bin p m (filterWithKey pred l) (filterWithKey pred r)
781 Tip k x
782 | pred k x -> t
783 | otherwise -> Nil
784 Nil -> Nil
785
786 -- | /O(n)/. partition the map according to some predicate. The first
787 -- map contains all elements that satisfy the predicate, the second all
788 -- elements that fail the predicate. See also 'split'.
789 partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
790 partition p m
791 = partitionWithKey (\k x -> p x) m
792
793 -- | /O(n)/. partition the map according to some predicate. The first
794 -- map contains all elements that satisfy the predicate, the second all
795 -- elements that fail the predicate. See also 'split'.
796 partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
797 partitionWithKey pred t
798 = case t of
799 Bin p m l r
800 -> let (l1,l2) = partitionWithKey pred l
801 (r1,r2) = partitionWithKey pred r
802 in (bin p m l1 r1, bin p m l2 r2)
803 Tip k x
804 | pred k x -> (t,Nil)
805 | otherwise -> (Nil,t)
806 Nil -> (Nil,Nil)
807
808
809 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
810 -- where all keys in @map1@ are lower than @k@ and all keys in
811 -- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
812 split :: Key -> IntMap a -> (IntMap a,IntMap a)
813 split k t
814 = case t of
815 Bin p m l r
816 | m < 0 -> (if k >= 0 -- handle negative numbers.
817 then let (lt,gt) = split' k l in (union r lt, gt)
818 else let (lt,gt) = split' k r in (lt, union gt l))
819 | otherwise -> split' k t
820 Tip ky y
821 | k>ky -> (t,Nil)
822 | k<ky -> (Nil,t)
823 | otherwise -> (Nil,Nil)
824 Nil -> (Nil,Nil)
825
826 split' :: Key -> IntMap a -> (IntMap a,IntMap a)
827 split' k t
828 = case t of
829 Bin p m l r
830 | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
831 | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
832 | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
833 Tip ky y
834 | k>ky -> (t,Nil)
835 | k<ky -> (Nil,t)
836 | otherwise -> (Nil,Nil)
837 Nil -> (Nil,Nil)
838
839 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
840 -- key was found in the original map.
841 splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
842 splitLookup k t
843 = case t of
844 Bin p m l r
845 | m < 0 -> (if k >= 0 -- handle negative numbers.
846 then let (lt,found,gt) = splitLookup' k l in (union r lt,found, gt)
847 else let (lt,found,gt) = splitLookup' k r in (lt,found, union gt l))
848 | otherwise -> splitLookup' k t
849 Tip ky y
850 | k>ky -> (t,Nothing,Nil)
851 | k<ky -> (Nil,Nothing,t)
852 | otherwise -> (Nil,Just y,Nil)
853 Nil -> (Nil,Nothing,Nil)
854
855 splitLookup' :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
856 splitLookup' k t
857 = case t of
858 Bin p m l r
859 | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
860 | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
861 | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
862 Tip ky y
863 | k>ky -> (t,Nothing,Nil)
864 | k<ky -> (Nil,Nothing,t)
865 | otherwise -> (Nil,Just y,Nil)
866 Nil -> (Nil,Nothing,Nil)
867
868 {--------------------------------------------------------------------
869 Fold
870 --------------------------------------------------------------------}
871 -- | /O(n)/. Fold the values in the map, such that
872 -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
873 -- For example,
874 --
875 -- > elems map = fold (:) [] map
876 --
877 fold :: (a -> b -> b) -> b -> IntMap a -> b
878 fold f z t
879 = foldWithKey (\k x y -> f x y) z t
880
881 -- | /O(n)/. Fold the keys and values in the map, such that
882 -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
883 -- For example,
884 --
885 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
886 --
887 foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
888 foldWithKey f z t
889 = foldr f z t
890
891 foldr :: (Key -> a -> b -> b) -> b -> IntMap a -> b
892 foldr f z t
893 = case t of
894 Bin 0 m l r | m < 0 -> foldr' f (foldr' f z l) r -- put negative numbers before.
895 Bin _ _ _ _ -> foldr' f z t
896 Tip k x -> f k x z
897 Nil -> z
898
899 foldr' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
900 foldr' f z t
901 = case t of
902 Bin p m l r -> foldr' f (foldr' f z r) l
903 Tip k x -> f k x z
904 Nil -> z
905
906
907
908 {--------------------------------------------------------------------
909 List variations
910 --------------------------------------------------------------------}
911 -- | /O(n)/.
912 -- Return all elements of the map in the ascending order of their keys.
913 elems :: IntMap a -> [a]
914 elems m
915 = foldWithKey (\k x xs -> x:xs) [] m
916
917 -- | /O(n)/. Return all keys of the map in ascending order.
918 keys :: IntMap a -> [Key]
919 keys m
920 = foldWithKey (\k x ks -> k:ks) [] m
921
922 -- | /O(n*min(n,W))/. The set of all keys of the map.
923 keysSet :: IntMap a -> IntSet.IntSet
924 keysSet m = IntSet.fromDistinctAscList (keys m)
925
926
927 -- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
928 assocs :: IntMap a -> [(Key,a)]
929 assocs m
930 = toList m
931
932
933 {--------------------------------------------------------------------
934 Lists
935 --------------------------------------------------------------------}
936 -- | /O(n)/. Convert the map to a list of key\/value pairs.
937 toList :: IntMap a -> [(Key,a)]
938 toList t
939 = foldWithKey (\k x xs -> (k,x):xs) [] t
940
941 -- | /O(n)/. Convert the map to a list of key\/value pairs where the
942 -- keys are in ascending order.
943 toAscList :: IntMap a -> [(Key,a)]
944 toAscList t
945 = -- NOTE: the following algorithm only works for big-endian trees
946 let (pos,neg) = span (\(k,x) -> k >=0) (foldr (\k x xs -> (k,x):xs) [] t) in neg ++ pos
947
948 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
949 fromList :: [(Key,a)] -> IntMap a
950 fromList xs
951 = foldlStrict ins empty xs
952 where
953 ins t (k,x) = insert k x t
954
955 -- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
956 fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
957 fromListWith f xs
958 = fromListWithKey (\k x y -> f x y) xs
959
960 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
961 fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
962 fromListWithKey f xs
963 = foldlStrict ins empty xs
964 where
965 ins t (k,x) = insertWithKey f k x t
966
967 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
968 -- the keys are in ascending order.
969 fromAscList :: [(Key,a)] -> IntMap a
970 fromAscList xs
971 = fromList xs
972
973 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
974 -- the keys are in ascending order, with a combining function on equal keys.
975 fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
976 fromAscListWith f xs
977 = fromListWith f xs
978
979 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
980 -- the keys are in ascending order, with a combining function on equal keys.
981 fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
982 fromAscListWithKey f xs
983 = fromListWithKey f xs
984
985 -- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs where
986 -- the keys are in ascending order and all distinct.
987 fromDistinctAscList :: [(Key,a)] -> IntMap a
988 fromDistinctAscList xs
989 = fromList xs
990
991
992 {--------------------------------------------------------------------
993 Eq
994 --------------------------------------------------------------------}
995 instance Eq a => Eq (IntMap a) where
996 t1 == t2 = equal t1 t2
997 t1 /= t2 = nequal t1 t2
998
999 equal :: Eq a => IntMap a -> IntMap a -> Bool
1000 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
1001 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
1002 equal (Tip kx x) (Tip ky y)
1003 = (kx == ky) && (x==y)
1004 equal Nil Nil = True
1005 equal t1 t2 = False
1006
1007 nequal :: Eq a => IntMap a -> IntMap a -> Bool
1008 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
1009 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
1010 nequal (Tip kx x) (Tip ky y)
1011 = (kx /= ky) || (x/=y)
1012 nequal Nil Nil = False
1013 nequal t1 t2 = True
1014
1015 {--------------------------------------------------------------------
1016 Ord
1017 --------------------------------------------------------------------}
1018
1019 instance Ord a => Ord (IntMap a) where
1020 compare m1 m2 = compare (toList m1) (toList m2)
1021
1022 {--------------------------------------------------------------------
1023 Functor
1024 --------------------------------------------------------------------}
1025
1026 instance Functor IntMap where
1027 fmap = map
1028
1029 {--------------------------------------------------------------------
1030 Show
1031 --------------------------------------------------------------------}
1032
1033 instance Show a => Show (IntMap a) where
1034 showsPrec d m = showParen (d > 10) $
1035 showString "fromList " . shows (toList m)
1036
1037 showMap :: (Show a) => [(Key,a)] -> ShowS
1038 showMap []
1039 = showString "{}"
1040 showMap (x:xs)
1041 = showChar '{' . showElem x . showTail xs
1042 where
1043 showTail [] = showChar '}'
1044 showTail (x:xs) = showChar ',' . showElem x . showTail xs
1045
1046 showElem (k,x) = shows k . showString ":=" . shows x
1047
1048 {--------------------------------------------------------------------
1049 Read
1050 --------------------------------------------------------------------}
1051 instance (Read e) => Read (IntMap e) where
1052 #ifdef __GLASGOW_HASKELL__
1053 readPrec = parens $ prec 10 $ do
1054 Ident "fromList" <- lexP
1055 xs <- readPrec
1056 return (fromList xs)
1057
1058 readListPrec = readListPrecDefault
1059 #else
1060 readsPrec p = readParen (p > 10) $ \ r -> do
1061 ("fromList",s) <- lex r
1062 (xs,t) <- reads s
1063 return (fromList xs,t)
1064 #endif
1065
1066 {--------------------------------------------------------------------
1067 Typeable
1068 --------------------------------------------------------------------}
1069
1070 #include "Typeable.h"
1071 INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
1072
1073 {--------------------------------------------------------------------
1074 Debugging
1075 --------------------------------------------------------------------}
1076 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1077 -- in a compressed, hanging format.
1078 showTree :: Show a => IntMap a -> String
1079 showTree s
1080 = showTreeWith True False s
1081
1082
1083 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
1084 the tree that implements the map. If @hang@ is
1085 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1086 @wide@ is 'True', an extra wide version is shown.
1087 -}
1088 showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
1089 showTreeWith hang wide t
1090 | hang = (showsTreeHang wide [] t) ""
1091 | otherwise = (showsTree wide [] [] t) ""
1092
1093 showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
1094 showsTree wide lbars rbars t
1095 = case t of
1096 Bin p m l r
1097 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
1098 showWide wide rbars .
1099 showsBars lbars . showString (showBin p m) . showString "\n" .
1100 showWide wide lbars .
1101 showsTree wide (withEmpty lbars) (withBar lbars) l
1102 Tip k x
1103 -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1104 Nil -> showsBars lbars . showString "|\n"
1105
1106 showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
1107 showsTreeHang wide bars t
1108 = case t of
1109 Bin p m l r
1110 -> showsBars bars . showString (showBin p m) . showString "\n" .
1111 showWide wide bars .
1112 showsTreeHang wide (withBar bars) l .
1113 showWide wide bars .
1114 showsTreeHang wide (withEmpty bars) r
1115 Tip k x
1116 -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
1117 Nil -> showsBars bars . showString "|\n"
1118
1119 showBin p m
1120 = "*" -- ++ show (p,m)
1121
1122 showWide wide bars
1123 | wide = showString (concat (reverse bars)) . showString "|\n"
1124 | otherwise = id
1125
1126 showsBars :: [String] -> ShowS
1127 showsBars bars
1128 = case bars of
1129 [] -> id
1130 _ -> showString (concat (reverse (tail bars))) . showString node
1131
1132 node = "+--"
1133 withBar bars = "| ":bars
1134 withEmpty bars = " ":bars
1135
1136
1137 {--------------------------------------------------------------------
1138 Helpers
1139 --------------------------------------------------------------------}
1140 {--------------------------------------------------------------------
1141 Join
1142 --------------------------------------------------------------------}
1143 join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
1144 join p1 t1 p2 t2
1145 | zero p1 m = Bin p m t1 t2
1146 | otherwise = Bin p m t2 t1
1147 where
1148 m = branchMask p1 p2
1149 p = mask p1 m
1150
1151 {--------------------------------------------------------------------
1152 @bin@ assures that we never have empty trees within a tree.
1153 --------------------------------------------------------------------}
1154 bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
1155 bin p m l Nil = l
1156 bin p m Nil r = r
1157 bin p m l r = Bin p m l r
1158
1159
1160 {--------------------------------------------------------------------
1161 Endian independent bit twiddling
1162 --------------------------------------------------------------------}
1163 zero :: Key -> Mask -> Bool
1164 zero i m
1165 = (natFromInt i) .&. (natFromInt m) == 0
1166
1167 nomatch,match :: Key -> Prefix -> Mask -> Bool
1168 nomatch i p m
1169 = (mask i m) /= p
1170
1171 match i p m
1172 = (mask i m) == p
1173
1174 mask :: Key -> Mask -> Prefix
1175 mask i m
1176 = maskW (natFromInt i) (natFromInt m)
1177
1178
1179 zeroN :: Nat -> Nat -> Bool
1180 zeroN i m = (i .&. m) == 0
1181
1182 {--------------------------------------------------------------------
1183 Big endian operations
1184 --------------------------------------------------------------------}
1185 maskW :: Nat -> Nat -> Prefix
1186 maskW i m
1187 = intFromNat (i .&. (complement (m-1) `xor` m))
1188
1189 shorter :: Mask -> Mask -> Bool
1190 shorter m1 m2
1191 = (natFromInt m1) > (natFromInt m2)
1192
1193 branchMask :: Prefix -> Prefix -> Mask
1194 branchMask p1 p2
1195 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
1196
1197 {----------------------------------------------------------------------
1198 Finding the highest bit (mask) in a word [x] can be done efficiently in
1199 three ways:
1200 * convert to a floating point value and the mantissa tells us the
1201 [log2(x)] that corresponds with the highest bit position. The mantissa
1202 is retrieved either via the standard C function [frexp] or by some bit
1203 twiddling on IEEE compatible numbers (float). Note that one needs to
1204 use at least [double] precision for an accurate mantissa of 32 bit
1205 numbers.
1206 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
1207 * use processor specific assembler instruction (asm).
1208
1209 The most portable way would be [bit], but is it efficient enough?
1210 I have measured the cycle counts of the different methods on an AMD
1211 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
1212
1213 highestBitMask: method cycles
1214 --------------
1215 frexp 200
1216 float 33
1217 bit 11
1218 asm 12
1219
1220 highestBit: method cycles
1221 --------------
1222 frexp 195
1223 float 33
1224 bit 11
1225 asm 11
1226
1227 Wow, the bit twiddling is on today's RISC like machines even faster
1228 than a single CISC instruction (BSR)!
1229 ----------------------------------------------------------------------}
1230
1231 {----------------------------------------------------------------------
1232 [highestBitMask] returns a word where only the highest bit is set.
1233 It is found by first setting all bits in lower positions than the
1234 highest bit and than taking an exclusive or with the original value.
1235 Allthough the function may look expensive, GHC compiles this into
1236 excellent C code that subsequently compiled into highly efficient
1237 machine code. The algorithm is derived from Jorg Arndt's FXT library.
1238 ----------------------------------------------------------------------}
1239 highestBitMask :: Nat -> Nat
1240 highestBitMask x
1241 = case (x .|. shiftRL x 1) of
1242 x -> case (x .|. shiftRL x 2) of
1243 x -> case (x .|. shiftRL x 4) of
1244 x -> case (x .|. shiftRL x 8) of
1245 x -> case (x .|. shiftRL x 16) of
1246 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
1247 x -> (x `xor` (shiftRL x 1))
1248
1249
1250 {--------------------------------------------------------------------
1251 Utilities
1252 --------------------------------------------------------------------}
1253 foldlStrict f z xs
1254 = case xs of
1255 [] -> z
1256 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1257
1258 {-
1259 {--------------------------------------------------------------------
1260 Testing
1261 --------------------------------------------------------------------}
1262 testTree :: [Int] -> IntMap Int
1263 testTree xs = fromList [(x,x*x*30696 `mod` 65521) | x <- xs]
1264 test1 = testTree [1..20]
1265 test2 = testTree [30,29..10]
1266 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1267
1268 {--------------------------------------------------------------------
1269 QuickCheck
1270 --------------------------------------------------------------------}
1271 qcheck prop
1272 = check config prop
1273 where
1274 config = Config
1275 { configMaxTest = 500
1276 , configMaxFail = 5000
1277 , configSize = \n -> (div n 2 + 3)
1278 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1279 }
1280
1281
1282 {--------------------------------------------------------------------
1283 Arbitrary, reasonably balanced trees
1284 --------------------------------------------------------------------}
1285 instance Arbitrary a => Arbitrary (IntMap a) where
1286 arbitrary = do{ ks <- arbitrary
1287 ; xs <- mapM (\k -> do{ x <- arbitrary; return (k,x)}) ks
1288 ; return (fromList xs)
1289 }
1290
1291
1292 {--------------------------------------------------------------------
1293 Single, Insert, Delete
1294 --------------------------------------------------------------------}
1295 prop_Single :: Key -> Int -> Bool
1296 prop_Single k x
1297 = (insert k x empty == singleton k x)
1298
1299 prop_InsertDelete :: Key -> Int -> IntMap Int -> Property
1300 prop_InsertDelete k x t
1301 = not (member k t) ==> delete k (insert k x t) == t
1302
1303 prop_UpdateDelete :: Key -> IntMap Int -> Bool
1304 prop_UpdateDelete k t
1305 = update (const Nothing) k t == delete k t
1306
1307
1308 {--------------------------------------------------------------------
1309 Union
1310 --------------------------------------------------------------------}
1311 prop_UnionInsert :: Key -> Int -> IntMap Int -> Bool
1312 prop_UnionInsert k x t
1313 = union (singleton k x) t == insert k x t
1314
1315 prop_UnionAssoc :: IntMap Int -> IntMap Int -> IntMap Int -> Bool
1316 prop_UnionAssoc t1 t2 t3
1317 = union t1 (union t2 t3) == union (union t1 t2) t3
1318
1319 prop_UnionComm :: IntMap Int -> IntMap Int -> Bool
1320 prop_UnionComm t1 t2
1321 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1322
1323
1324 prop_Diff :: [(Key,Int)] -> [(Key,Int)] -> Bool
1325 prop_Diff xs ys
1326 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1327 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1328
1329 prop_Int :: [(Key,Int)] -> [(Key,Int)] -> Bool
1330 prop_Int xs ys
1331 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1332 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1333
1334 {--------------------------------------------------------------------
1335 Lists
1336 --------------------------------------------------------------------}
1337 prop_Ordered
1338 = forAll (choose (5,100)) $ \n ->
1339 let xs = [(x,()) | x <- [0..n::Int]]
1340 in fromAscList xs == fromList xs
1341
1342 prop_List :: [Key] -> Bool
1343 prop_List xs
1344 = (sort (nub xs) == [x | (x,()) <- toAscList (fromList [(x,()) | x <- xs])])
1345 -}