[project @ 2005-10-25 09:29:16 by ross]
[packages/old-time.git] / Data / IntSet.hs
1 {-# OPTIONS -cpp -fglasgow-exts #-}
2 -----------------------------------------------------------------------------
3 -- |
4 -- Module : Data.IntSet
5 -- Copyright : (c) Daan Leijen 2002
6 -- License : BSD-style
7 -- Maintainer : libraries@haskell.org
8 -- Stability : provisional
9 -- Portability : portable
10 --
11 -- An efficient implementation of integer sets.
12 --
13 -- This module is intended to be imported @qualified@, to avoid name
14 -- clashes with "Prelude" functions. eg.
15 --
16 -- > import Data.IntSet as Set
17 --
18 -- The implementation is based on /big-endian patricia trees/. This data
19 -- structure performs especially well on binary operations like 'union'
20 -- and 'intersection'. However, my benchmarks show that it is also
21 -- (much) faster on insertions and deletions when compared to a generic
22 -- size-balanced set implementation (see "Data.Set").
23 --
24 -- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
25 -- Workshop on ML, September 1998, pages 77-86,
26 -- <http://www.cse.ogi.edu/~andy/pub/finite.htm>
27 --
28 -- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
29 -- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
30 -- October 1968, pages 514-534.
31 --
32 -- Many operations have a worst-case complexity of /O(min(n,W))/.
33 -- This means that the operation can become linear in the number of
34 -- elements with a maximum of /W/ -- the number of bits in an 'Int'
35 -- (32 or 64).
36 -----------------------------------------------------------------------------
37
38 module Data.IntSet (
39 -- * Set type
40 IntSet -- instance Eq,Show
41
42 -- * Operators
43 , (\\)
44
45 -- * Query
46 , null
47 , size
48 , member
49 , isSubsetOf
50 , isProperSubsetOf
51
52 -- * Construction
53 , empty
54 , singleton
55 , insert
56 , delete
57
58 -- * Combine
59 , union, unions
60 , difference
61 , intersection
62
63 -- * Filter
64 , filter
65 , partition
66 , split
67 , splitMember
68
69 -- * Map
70 , map
71
72 -- * Fold
73 , fold
74
75 -- * Conversion
76 -- ** List
77 , elems
78 , toList
79 , fromList
80
81 -- ** Ordered list
82 , toAscList
83 , fromAscList
84 , fromDistinctAscList
85
86 -- * Debugging
87 , showTree
88 , showTreeWith
89 ) where
90
91
92 import Prelude hiding (lookup,filter,foldr,foldl,null,map)
93 import Data.Bits
94 import Data.Int
95
96 import qualified Data.List as List
97 import Data.Monoid (Monoid(..))
98 import Data.Typeable
99
100 {-
101 -- just for testing
102 import QuickCheck
103 import List (nub,sort)
104 import qualified List
105 -}
106
107 #if __GLASGOW_HASKELL__
108 import Text.Read
109 import Data.Generics.Basics
110 import Data.Generics.Instances
111 #endif
112
113 #if __GLASGOW_HASKELL__ >= 503
114 import GHC.Word
115 import GHC.Exts ( Word(..), Int(..), shiftRL# )
116 #elif __GLASGOW_HASKELL__
117 import Word
118 import GlaExts ( Word(..), Int(..), shiftRL# )
119 #else
120 import Data.Word
121 #endif
122
123 infixl 9 \\{-This comment teaches CPP correct behaviour -}
124
125 -- A "Nat" is a natural machine word (an unsigned Int)
126 type Nat = Word
127
128 natFromInt :: Int -> Nat
129 natFromInt i = fromIntegral i
130
131 intFromNat :: Nat -> Int
132 intFromNat w = fromIntegral w
133
134 shiftRL :: Nat -> Int -> Nat
135 #if __GLASGOW_HASKELL__
136 {--------------------------------------------------------------------
137 GHC: use unboxing to get @shiftRL@ inlined.
138 --------------------------------------------------------------------}
139 shiftRL (W# x) (I# i)
140 = W# (shiftRL# x i)
141 #else
142 shiftRL x i = shiftR x i
143 #endif
144
145 {--------------------------------------------------------------------
146 Operators
147 --------------------------------------------------------------------}
148 -- | /O(n+m)/. See 'difference'.
149 (\\) :: IntSet -> IntSet -> IntSet
150 m1 \\ m2 = difference m1 m2
151
152 {--------------------------------------------------------------------
153 Types
154 --------------------------------------------------------------------}
155 -- | A set of integers.
156 data IntSet = Nil
157 | Tip {-# UNPACK #-} !Int
158 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !IntSet !IntSet
159
160 type Prefix = Int
161 type Mask = Int
162
163 instance Monoid IntSet where
164 mempty = empty
165 mappend = union
166 mconcat = unions
167
168 #if __GLASGOW_HASKELL__
169
170 {--------------------------------------------------------------------
171 A Data instance
172 --------------------------------------------------------------------}
173
174 -- This instance preserves data abstraction at the cost of inefficiency.
175 -- We omit reflection services for the sake of data abstraction.
176
177 instance Data IntSet where
178 gfoldl f z is = z fromList `f` (toList is)
179 toConstr _ = error "toConstr"
180 gunfold _ _ = error "gunfold"
181 dataTypeOf _ = mkNorepType "Data.IntSet.IntSet"
182
183 #endif
184
185 {--------------------------------------------------------------------
186 Query
187 --------------------------------------------------------------------}
188 -- | /O(1)/. Is the set empty?
189 null :: IntSet -> Bool
190 null Nil = True
191 null other = False
192
193 -- | /O(n)/. Cardinality of the set.
194 size :: IntSet -> Int
195 size t
196 = case t of
197 Bin p m l r -> size l + size r
198 Tip y -> 1
199 Nil -> 0
200
201 -- | /O(min(n,W))/. Is the value a member of the set?
202 member :: Int -> IntSet -> Bool
203 member x t
204 = case t of
205 Bin p m l r
206 | nomatch x p m -> False
207 | zero x m -> member x l
208 | otherwise -> member x r
209 Tip y -> (x==y)
210 Nil -> False
211
212 -- 'lookup' is used by 'intersection' for left-biasing
213 lookup :: Int -> IntSet -> Maybe Int
214 lookup k t
215 = let nk = natFromInt k in seq nk (lookupN nk t)
216
217 lookupN :: Nat -> IntSet -> Maybe Int
218 lookupN k t
219 = case t of
220 Bin p m l r
221 | zeroN k (natFromInt m) -> lookupN k l
222 | otherwise -> lookupN k r
223 Tip kx
224 | (k == natFromInt kx) -> Just kx
225 | otherwise -> Nothing
226 Nil -> Nothing
227
228 {--------------------------------------------------------------------
229 Construction
230 --------------------------------------------------------------------}
231 -- | /O(1)/. The empty set.
232 empty :: IntSet
233 empty
234 = Nil
235
236 -- | /O(1)/. A set of one element.
237 singleton :: Int -> IntSet
238 singleton x
239 = Tip x
240
241 {--------------------------------------------------------------------
242 Insert
243 --------------------------------------------------------------------}
244 -- | /O(min(n,W))/. Add a value to the set. When the value is already
245 -- an element of the set, it is replaced by the new one, ie. 'insert'
246 -- is left-biased.
247 insert :: Int -> IntSet -> IntSet
248 insert x t
249 = case t of
250 Bin p m l r
251 | nomatch x p m -> join x (Tip x) p t
252 | zero x m -> Bin p m (insert x l) r
253 | otherwise -> Bin p m l (insert x r)
254 Tip y
255 | x==y -> Tip x
256 | otherwise -> join x (Tip x) y t
257 Nil -> Tip x
258
259 -- right-biased insertion, used by 'union'
260 insertR :: Int -> IntSet -> IntSet
261 insertR x t
262 = case t of
263 Bin p m l r
264 | nomatch x p m -> join x (Tip x) p t
265 | zero x m -> Bin p m (insert x l) r
266 | otherwise -> Bin p m l (insert x r)
267 Tip y
268 | x==y -> t
269 | otherwise -> join x (Tip x) y t
270 Nil -> Tip x
271
272 -- | /O(min(n,W))/. Delete a value in the set. Returns the
273 -- original set when the value was not present.
274 delete :: Int -> IntSet -> IntSet
275 delete x t
276 = case t of
277 Bin p m l r
278 | nomatch x p m -> t
279 | zero x m -> bin p m (delete x l) r
280 | otherwise -> bin p m l (delete x r)
281 Tip y
282 | x==y -> Nil
283 | otherwise -> t
284 Nil -> Nil
285
286
287 {--------------------------------------------------------------------
288 Union
289 --------------------------------------------------------------------}
290 -- | The union of a list of sets.
291 unions :: [IntSet] -> IntSet
292 unions xs
293 = foldlStrict union empty xs
294
295
296 -- | /O(n+m)/. The union of two sets.
297 union :: IntSet -> IntSet -> IntSet
298 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
299 | shorter m1 m2 = union1
300 | shorter m2 m1 = union2
301 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
302 | otherwise = join p1 t1 p2 t2
303 where
304 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
305 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
306 | otherwise = Bin p1 m1 l1 (union r1 t2)
307
308 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
309 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
310 | otherwise = Bin p2 m2 l2 (union t1 r2)
311
312 union (Tip x) t = insert x t
313 union t (Tip x) = insertR x t -- right bias
314 union Nil t = t
315 union t Nil = t
316
317
318 {--------------------------------------------------------------------
319 Difference
320 --------------------------------------------------------------------}
321 -- | /O(n+m)/. Difference between two sets.
322 difference :: IntSet -> IntSet -> IntSet
323 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
324 | shorter m1 m2 = difference1
325 | shorter m2 m1 = difference2
326 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
327 | otherwise = t1
328 where
329 difference1 | nomatch p2 p1 m1 = t1
330 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
331 | otherwise = bin p1 m1 l1 (difference r1 t2)
332
333 difference2 | nomatch p1 p2 m2 = t1
334 | zero p1 m2 = difference t1 l2
335 | otherwise = difference t1 r2
336
337 difference t1@(Tip x) t2
338 | member x t2 = Nil
339 | otherwise = t1
340
341 difference Nil t = Nil
342 difference t (Tip x) = delete x t
343 difference t Nil = t
344
345
346
347 {--------------------------------------------------------------------
348 Intersection
349 --------------------------------------------------------------------}
350 -- | /O(n+m)/. The intersection of two sets.
351 intersection :: IntSet -> IntSet -> IntSet
352 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
353 | shorter m1 m2 = intersection1
354 | shorter m2 m1 = intersection2
355 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
356 | otherwise = Nil
357 where
358 intersection1 | nomatch p2 p1 m1 = Nil
359 | zero p2 m1 = intersection l1 t2
360 | otherwise = intersection r1 t2
361
362 intersection2 | nomatch p1 p2 m2 = Nil
363 | zero p1 m2 = intersection t1 l2
364 | otherwise = intersection t1 r2
365
366 intersection t1@(Tip x) t2
367 | member x t2 = t1
368 | otherwise = Nil
369 intersection t (Tip x)
370 = case lookup x t of
371 Just y -> Tip y
372 Nothing -> Nil
373 intersection Nil t = Nil
374 intersection t Nil = Nil
375
376
377
378 {--------------------------------------------------------------------
379 Subset
380 --------------------------------------------------------------------}
381 -- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
382 isProperSubsetOf :: IntSet -> IntSet -> Bool
383 isProperSubsetOf t1 t2
384 = case subsetCmp t1 t2 of
385 LT -> True
386 ge -> False
387
388 subsetCmp t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
389 | shorter m1 m2 = GT
390 | shorter m2 m1 = subsetCmpLt
391 | p1 == p2 = subsetCmpEq
392 | otherwise = GT -- disjoint
393 where
394 subsetCmpLt | nomatch p1 p2 m2 = GT
395 | zero p1 m2 = subsetCmp t1 l2
396 | otherwise = subsetCmp t1 r2
397 subsetCmpEq = case (subsetCmp l1 l2, subsetCmp r1 r2) of
398 (GT,_ ) -> GT
399 (_ ,GT) -> GT
400 (EQ,EQ) -> EQ
401 other -> LT
402
403 subsetCmp (Bin p m l r) t = GT
404 subsetCmp (Tip x) (Tip y)
405 | x==y = EQ
406 | otherwise = GT -- disjoint
407 subsetCmp (Tip x) t
408 | member x t = LT
409 | otherwise = GT -- disjoint
410 subsetCmp Nil Nil = EQ
411 subsetCmp Nil t = LT
412
413 -- | /O(n+m)/. Is this a subset?
414 -- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@.
415
416 isSubsetOf :: IntSet -> IntSet -> Bool
417 isSubsetOf t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
418 | shorter m1 m2 = False
419 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubsetOf t1 l2
420 else isSubsetOf t1 r2)
421 | otherwise = (p1==p2) && isSubsetOf l1 l2 && isSubsetOf r1 r2
422 isSubsetOf (Bin p m l r) t = False
423 isSubsetOf (Tip x) t = member x t
424 isSubsetOf Nil t = True
425
426
427 {--------------------------------------------------------------------
428 Filter
429 --------------------------------------------------------------------}
430 -- | /O(n)/. Filter all elements that satisfy some predicate.
431 filter :: (Int -> Bool) -> IntSet -> IntSet
432 filter pred t
433 = case t of
434 Bin p m l r
435 -> bin p m (filter pred l) (filter pred r)
436 Tip x
437 | pred x -> t
438 | otherwise -> Nil
439 Nil -> Nil
440
441 -- | /O(n)/. partition the set according to some predicate.
442 partition :: (Int -> Bool) -> IntSet -> (IntSet,IntSet)
443 partition pred t
444 = case t of
445 Bin p m l r
446 -> let (l1,l2) = partition pred l
447 (r1,r2) = partition pred r
448 in (bin p m l1 r1, bin p m l2 r2)
449 Tip x
450 | pred x -> (t,Nil)
451 | otherwise -> (Nil,t)
452 Nil -> (Nil,Nil)
453
454
455 -- | /O(log n)/. The expression (@'split' x set@) is a pair @(set1,set2)@
456 -- where all elements in @set1@ are lower than @x@ and all elements in
457 -- @set2@ larger than @x@.
458 --
459 -- > split 3 (fromList [1..5]) == (fromList [1,2], fromList [3,4])
460 split :: Int -> IntSet -> (IntSet,IntSet)
461 split x t
462 = case t of
463 Bin p m l r
464 | zero x m -> let (lt,gt) = split x l in (lt,union gt r)
465 | otherwise -> let (lt,gt) = split x r in (union l lt,gt)
466 Tip y
467 | x>y -> (t,Nil)
468 | x<y -> (Nil,t)
469 | otherwise -> (Nil,Nil)
470 Nil -> (Nil,Nil)
471
472 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
473 -- element was found in the original set.
474 splitMember :: Int -> IntSet -> (IntSet,Bool,IntSet)
475 splitMember x t
476 = case t of
477 Bin p m l r
478 | zero x m -> let (lt,found,gt) = splitMember x l in (lt,found,union gt r)
479 | otherwise -> let (lt,found,gt) = splitMember x r in (union l lt,found,gt)
480 Tip y
481 | x>y -> (t,False,Nil)
482 | x<y -> (Nil,False,t)
483 | otherwise -> (Nil,True,Nil)
484 Nil -> (Nil,False,Nil)
485
486 {----------------------------------------------------------------------
487 Map
488 ----------------------------------------------------------------------}
489
490 -- | /O(n*min(n,W))/.
491 -- @'map' f s@ is the set obtained by applying @f@ to each element of @s@.
492 --
493 -- It's worth noting that the size of the result may be smaller if,
494 -- for some @(x,y)@, @x \/= y && f x == f y@
495
496 map :: (Int->Int) -> IntSet -> IntSet
497 map f = fromList . List.map f . toList
498
499 {--------------------------------------------------------------------
500 Fold
501 --------------------------------------------------------------------}
502 -- | /O(n)/. Fold over the elements of a set in an unspecified order.
503 --
504 -- > sum set == fold (+) 0 set
505 -- > elems set == fold (:) [] set
506 fold :: (Int -> b -> b) -> b -> IntSet -> b
507 fold f z t
508 = foldr f z t
509
510 foldr :: (Int -> b -> b) -> b -> IntSet -> b
511 foldr f z t
512 = case t of
513 Bin p m l r -> foldr f (foldr f z r) l
514 Tip x -> f x z
515 Nil -> z
516
517 {--------------------------------------------------------------------
518 List variations
519 --------------------------------------------------------------------}
520 -- | /O(n)/. The elements of a set. (For sets, this is equivalent to toList)
521 elems :: IntSet -> [Int]
522 elems s
523 = toList s
524
525 {--------------------------------------------------------------------
526 Lists
527 --------------------------------------------------------------------}
528 -- | /O(n)/. Convert the set to a list of elements.
529 toList :: IntSet -> [Int]
530 toList t
531 = fold (:) [] t
532
533 -- | /O(n)/. Convert the set to an ascending list of elements.
534 toAscList :: IntSet -> [Int]
535 toAscList t
536 = -- NOTE: the following algorithm only works for big-endian trees
537 let (pos,neg) = span (>=0) (foldr (:) [] t) in neg ++ pos
538
539 -- | /O(n*min(n,W))/. Create a set from a list of integers.
540 fromList :: [Int] -> IntSet
541 fromList xs
542 = foldlStrict ins empty xs
543 where
544 ins t x = insert x t
545
546 -- | /O(n*min(n,W))/. Build a set from an ascending list of elements.
547 fromAscList :: [Int] -> IntSet
548 fromAscList xs
549 = fromList xs
550
551 -- | /O(n*min(n,W))/. Build a set from an ascending list of distinct elements.
552 fromDistinctAscList :: [Int] -> IntSet
553 fromDistinctAscList xs
554 = fromList xs
555
556
557 {--------------------------------------------------------------------
558 Eq
559 --------------------------------------------------------------------}
560 instance Eq IntSet where
561 t1 == t2 = equal t1 t2
562 t1 /= t2 = nequal t1 t2
563
564 equal :: IntSet -> IntSet -> Bool
565 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
566 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
567 equal (Tip x) (Tip y)
568 = (x==y)
569 equal Nil Nil = True
570 equal t1 t2 = False
571
572 nequal :: IntSet -> IntSet -> Bool
573 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
574 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
575 nequal (Tip x) (Tip y)
576 = (x/=y)
577 nequal Nil Nil = False
578 nequal t1 t2 = True
579
580 {--------------------------------------------------------------------
581 Ord
582 --------------------------------------------------------------------}
583
584 instance Ord IntSet where
585 compare s1 s2 = compare (toAscList s1) (toAscList s2)
586 -- tentative implementation. See if more efficient exists.
587
588 {--------------------------------------------------------------------
589 Show
590 --------------------------------------------------------------------}
591 instance Show IntSet where
592 showsPrec p xs = showParen (p > 10) $
593 showString "fromList " . shows (toList xs)
594
595 showSet :: [Int] -> ShowS
596 showSet []
597 = showString "{}"
598 showSet (x:xs)
599 = showChar '{' . shows x . showTail xs
600 where
601 showTail [] = showChar '}'
602 showTail (x:xs) = showChar ',' . shows x . showTail xs
603
604 {--------------------------------------------------------------------
605 Read
606 --------------------------------------------------------------------}
607 instance Read IntSet where
608 #ifdef __GLASGOW_HASKELL__
609 readPrec = parens $ prec 10 $ do
610 Ident "fromList" <- lexP
611 xs <- readPrec
612 return (fromList xs)
613
614 readListPrec = readListPrecDefault
615 #else
616 readsPrec p = readParen (p > 10) $ \ r -> do
617 ("fromList",s) <- lex r
618 (xs,t) <- reads s
619 return (fromList xs,t)
620 #endif
621
622 {--------------------------------------------------------------------
623 Typeable
624 --------------------------------------------------------------------}
625
626 #include "Typeable.h"
627 INSTANCE_TYPEABLE0(IntSet,intSetTc,"IntSet")
628
629 {--------------------------------------------------------------------
630 Debugging
631 --------------------------------------------------------------------}
632 -- | /O(n)/. Show the tree that implements the set. The tree is shown
633 -- in a compressed, hanging format.
634 showTree :: IntSet -> String
635 showTree s
636 = showTreeWith True False s
637
638
639 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
640 the tree that implements the set. If @hang@ is
641 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
642 @wide@ is 'True', an extra wide version is shown.
643 -}
644 showTreeWith :: Bool -> Bool -> IntSet -> String
645 showTreeWith hang wide t
646 | hang = (showsTreeHang wide [] t) ""
647 | otherwise = (showsTree wide [] [] t) ""
648
649 showsTree :: Bool -> [String] -> [String] -> IntSet -> ShowS
650 showsTree wide lbars rbars t
651 = case t of
652 Bin p m l r
653 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
654 showWide wide rbars .
655 showsBars lbars . showString (showBin p m) . showString "\n" .
656 showWide wide lbars .
657 showsTree wide (withEmpty lbars) (withBar lbars) l
658 Tip x
659 -> showsBars lbars . showString " " . shows x . showString "\n"
660 Nil -> showsBars lbars . showString "|\n"
661
662 showsTreeHang :: Bool -> [String] -> IntSet -> ShowS
663 showsTreeHang wide bars t
664 = case t of
665 Bin p m l r
666 -> showsBars bars . showString (showBin p m) . showString "\n" .
667 showWide wide bars .
668 showsTreeHang wide (withBar bars) l .
669 showWide wide bars .
670 showsTreeHang wide (withEmpty bars) r
671 Tip x
672 -> showsBars bars . showString " " . shows x . showString "\n"
673 Nil -> showsBars bars . showString "|\n"
674
675 showBin p m
676 = "*" -- ++ show (p,m)
677
678 showWide wide bars
679 | wide = showString (concat (reverse bars)) . showString "|\n"
680 | otherwise = id
681
682 showsBars :: [String] -> ShowS
683 showsBars bars
684 = case bars of
685 [] -> id
686 _ -> showString (concat (reverse (tail bars))) . showString node
687
688 node = "+--"
689 withBar bars = "| ":bars
690 withEmpty bars = " ":bars
691
692
693 {--------------------------------------------------------------------
694 Helpers
695 --------------------------------------------------------------------}
696 {--------------------------------------------------------------------
697 Join
698 --------------------------------------------------------------------}
699 join :: Prefix -> IntSet -> Prefix -> IntSet -> IntSet
700 join p1 t1 p2 t2
701 | zero p1 m = Bin p m t1 t2
702 | otherwise = Bin p m t2 t1
703 where
704 m = branchMask p1 p2
705 p = mask p1 m
706
707 {--------------------------------------------------------------------
708 @bin@ assures that we never have empty trees within a tree.
709 --------------------------------------------------------------------}
710 bin :: Prefix -> Mask -> IntSet -> IntSet -> IntSet
711 bin p m l Nil = l
712 bin p m Nil r = r
713 bin p m l r = Bin p m l r
714
715
716 {--------------------------------------------------------------------
717 Endian independent bit twiddling
718 --------------------------------------------------------------------}
719 zero :: Int -> Mask -> Bool
720 zero i m
721 = (natFromInt i) .&. (natFromInt m) == 0
722
723 nomatch,match :: Int -> Prefix -> Mask -> Bool
724 nomatch i p m
725 = (mask i m) /= p
726
727 match i p m
728 = (mask i m) == p
729
730 mask :: Int -> Mask -> Prefix
731 mask i m
732 = maskW (natFromInt i) (natFromInt m)
733
734 zeroN :: Nat -> Nat -> Bool
735 zeroN i m = (i .&. m) == 0
736
737 {--------------------------------------------------------------------
738 Big endian operations
739 --------------------------------------------------------------------}
740 maskW :: Nat -> Nat -> Prefix
741 maskW i m
742 = intFromNat (i .&. (complement (m-1) `xor` m))
743
744 shorter :: Mask -> Mask -> Bool
745 shorter m1 m2
746 = (natFromInt m1) > (natFromInt m2)
747
748 branchMask :: Prefix -> Prefix -> Mask
749 branchMask p1 p2
750 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
751
752 {----------------------------------------------------------------------
753 Finding the highest bit (mask) in a word [x] can be done efficiently in
754 three ways:
755 * convert to a floating point value and the mantissa tells us the
756 [log2(x)] that corresponds with the highest bit position. The mantissa
757 is retrieved either via the standard C function [frexp] or by some bit
758 twiddling on IEEE compatible numbers (float). Note that one needs to
759 use at least [double] precision for an accurate mantissa of 32 bit
760 numbers.
761 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
762 * use processor specific assembler instruction (asm).
763
764 The most portable way would be [bit], but is it efficient enough?
765 I have measured the cycle counts of the different methods on an AMD
766 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
767
768 highestBitMask: method cycles
769 --------------
770 frexp 200
771 float 33
772 bit 11
773 asm 12
774
775 highestBit: method cycles
776 --------------
777 frexp 195
778 float 33
779 bit 11
780 asm 11
781
782 Wow, the bit twiddling is on today's RISC like machines even faster
783 than a single CISC instruction (BSR)!
784 ----------------------------------------------------------------------}
785
786 {----------------------------------------------------------------------
787 [highestBitMask] returns a word where only the highest bit is set.
788 It is found by first setting all bits in lower positions than the
789 highest bit and than taking an exclusive or with the original value.
790 Allthough the function may look expensive, GHC compiles this into
791 excellent C code that subsequently compiled into highly efficient
792 machine code. The algorithm is derived from Jorg Arndt's FXT library.
793 ----------------------------------------------------------------------}
794 highestBitMask :: Nat -> Nat
795 highestBitMask x
796 = case (x .|. shiftRL x 1) of
797 x -> case (x .|. shiftRL x 2) of
798 x -> case (x .|. shiftRL x 4) of
799 x -> case (x .|. shiftRL x 8) of
800 x -> case (x .|. shiftRL x 16) of
801 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
802 x -> (x `xor` (shiftRL x 1))
803
804
805 {--------------------------------------------------------------------
806 Utilities
807 --------------------------------------------------------------------}
808 foldlStrict f z xs
809 = case xs of
810 [] -> z
811 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
812
813
814 {-
815 {--------------------------------------------------------------------
816 Testing
817 --------------------------------------------------------------------}
818 testTree :: [Int] -> IntSet
819 testTree xs = fromList xs
820 test1 = testTree [1..20]
821 test2 = testTree [30,29..10]
822 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
823
824 {--------------------------------------------------------------------
825 QuickCheck
826 --------------------------------------------------------------------}
827 qcheck prop
828 = check config prop
829 where
830 config = Config
831 { configMaxTest = 500
832 , configMaxFail = 5000
833 , configSize = \n -> (div n 2 + 3)
834 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
835 }
836
837
838 {--------------------------------------------------------------------
839 Arbitrary, reasonably balanced trees
840 --------------------------------------------------------------------}
841 instance Arbitrary IntSet where
842 arbitrary = do{ xs <- arbitrary
843 ; return (fromList xs)
844 }
845
846
847 {--------------------------------------------------------------------
848 Single, Insert, Delete
849 --------------------------------------------------------------------}
850 prop_Single :: Int -> Bool
851 prop_Single x
852 = (insert x empty == singleton x)
853
854 prop_InsertDelete :: Int -> IntSet -> Property
855 prop_InsertDelete k t
856 = not (member k t) ==> delete k (insert k t) == t
857
858
859 {--------------------------------------------------------------------
860 Union
861 --------------------------------------------------------------------}
862 prop_UnionInsert :: Int -> IntSet -> Bool
863 prop_UnionInsert x t
864 = union t (singleton x) == insert x t
865
866 prop_UnionAssoc :: IntSet -> IntSet -> IntSet -> Bool
867 prop_UnionAssoc t1 t2 t3
868 = union t1 (union t2 t3) == union (union t1 t2) t3
869
870 prop_UnionComm :: IntSet -> IntSet -> Bool
871 prop_UnionComm t1 t2
872 = (union t1 t2 == union t2 t1)
873
874 prop_Diff :: [Int] -> [Int] -> Bool
875 prop_Diff xs ys
876 = toAscList (difference (fromList xs) (fromList ys))
877 == List.sort ((List.\\) (nub xs) (nub ys))
878
879 prop_Int :: [Int] -> [Int] -> Bool
880 prop_Int xs ys
881 = toAscList (intersection (fromList xs) (fromList ys))
882 == List.sort (nub ((List.intersect) (xs) (ys)))
883
884 {--------------------------------------------------------------------
885 Lists
886 --------------------------------------------------------------------}
887 prop_Ordered
888 = forAll (choose (5,100)) $ \n ->
889 let xs = [0..n::Int]
890 in fromAscList xs == fromList xs
891
892 prop_List :: [Int] -> Bool
893 prop_List xs
894 = (sort (nub xs) == toAscList (fromList xs))
895 -}