622082796a9eb459df059b02503b7c0677286d66
[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.Typeable
98
99 {-
100 -- just for testing
101 import QuickCheck
102 import List (nub,sort)
103 import qualified List
104 -}
105
106 #if __GLASGOW_HASKELL__
107 import Text.Read
108 import Data.Generics.Basics
109 import Data.Generics.Instances
110 #endif
111
112 #if __GLASGOW_HASKELL__ >= 503
113 import GHC.Word
114 import GHC.Exts ( Word(..), Int(..), shiftRL# )
115 #elif __GLASGOW_HASKELL__
116 import Word
117 import GlaExts ( Word(..), Int(..), shiftRL# )
118 #else
119 import Data.Word
120 #endif
121
122 infixl 9 \\{-This comment teaches CPP correct behaviour -}
123
124 -- A "Nat" is a natural machine word (an unsigned Int)
125 type Nat = Word
126
127 natFromInt :: Int -> Nat
128 natFromInt i = fromIntegral i
129
130 intFromNat :: Nat -> Int
131 intFromNat w = fromIntegral w
132
133 shiftRL :: Nat -> Int -> Nat
134 #if __GLASGOW_HASKELL__
135 {--------------------------------------------------------------------
136 GHC: use unboxing to get @shiftRL@ inlined.
137 --------------------------------------------------------------------}
138 shiftRL (W# x) (I# i)
139 = W# (shiftRL# x i)
140 #else
141 shiftRL x i = shiftR x i
142 #endif
143
144 {--------------------------------------------------------------------
145 Operators
146 --------------------------------------------------------------------}
147 -- | /O(n+m)/. See 'difference'.
148 (\\) :: IntSet -> IntSet -> IntSet
149 m1 \\ m2 = difference m1 m2
150
151 {--------------------------------------------------------------------
152 Types
153 --------------------------------------------------------------------}
154 -- | A set of integers.
155 data IntSet = Nil
156 | Tip {-# UNPACK #-} !Int
157 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !IntSet !IntSet
158
159 type Prefix = Int
160 type Mask = Int
161
162 #if __GLASGOW_HASKELL__
163
164 {--------------------------------------------------------------------
165 A Data instance
166 --------------------------------------------------------------------}
167
168 -- This instance preserves data abstraction at the cost of inefficiency.
169 -- We omit reflection services for the sake of data abstraction.
170
171 instance Data IntSet where
172 gfoldl f z is = z fromList `f` (toList is)
173 toConstr _ = error "toConstr"
174 gunfold _ _ = error "gunfold"
175 dataTypeOf _ = mkNorepType "Data.IntSet.IntSet"
176
177 #endif
178
179 {--------------------------------------------------------------------
180 Query
181 --------------------------------------------------------------------}
182 -- | /O(1)/. Is the set empty?
183 null :: IntSet -> Bool
184 null Nil = True
185 null other = False
186
187 -- | /O(n)/. Cardinality of the set.
188 size :: IntSet -> Int
189 size t
190 = case t of
191 Bin p m l r -> size l + size r
192 Tip y -> 1
193 Nil -> 0
194
195 -- | /O(min(n,W))/. Is the value a member of the set?
196 member :: Int -> IntSet -> Bool
197 member x t
198 = case t of
199 Bin p m l r
200 | nomatch x p m -> False
201 | zero x m -> member x l
202 | otherwise -> member x r
203 Tip y -> (x==y)
204 Nil -> False
205
206 -- 'lookup' is used by 'intersection' for left-biasing
207 lookup :: Int -> IntSet -> Maybe Int
208 lookup k t
209 = let nk = natFromInt k in seq nk (lookupN nk t)
210
211 lookupN :: Nat -> IntSet -> Maybe Int
212 lookupN k t
213 = case t of
214 Bin p m l r
215 | zeroN k (natFromInt m) -> lookupN k l
216 | otherwise -> lookupN k r
217 Tip kx
218 | (k == natFromInt kx) -> Just kx
219 | otherwise -> Nothing
220 Nil -> Nothing
221
222 {--------------------------------------------------------------------
223 Construction
224 --------------------------------------------------------------------}
225 -- | /O(1)/. The empty set.
226 empty :: IntSet
227 empty
228 = Nil
229
230 -- | /O(1)/. A set of one element.
231 singleton :: Int -> IntSet
232 singleton x
233 = Tip x
234
235 {--------------------------------------------------------------------
236 Insert
237 --------------------------------------------------------------------}
238 -- | /O(min(n,W))/. Add a value to the set. When the value is already
239 -- an element of the set, it is replaced by the new one, ie. 'insert'
240 -- is left-biased.
241 insert :: Int -> IntSet -> IntSet
242 insert x t
243 = case t of
244 Bin p m l r
245 | nomatch x p m -> join x (Tip x) p t
246 | zero x m -> Bin p m (insert x l) r
247 | otherwise -> Bin p m l (insert x r)
248 Tip y
249 | x==y -> Tip x
250 | otherwise -> join x (Tip x) y t
251 Nil -> Tip x
252
253 -- right-biased insertion, used by 'union'
254 insertR :: Int -> IntSet -> IntSet
255 insertR x t
256 = case t of
257 Bin p m l r
258 | nomatch x p m -> join x (Tip x) p t
259 | zero x m -> Bin p m (insert x l) r
260 | otherwise -> Bin p m l (insert x r)
261 Tip y
262 | x==y -> t
263 | otherwise -> join x (Tip x) y t
264 Nil -> Tip x
265
266 -- | /O(min(n,W))/. Delete a value in the set. Returns the
267 -- original set when the value was not present.
268 delete :: Int -> IntSet -> IntSet
269 delete x t
270 = case t of
271 Bin p m l r
272 | nomatch x p m -> t
273 | zero x m -> bin p m (delete x l) r
274 | otherwise -> bin p m l (delete x r)
275 Tip y
276 | x==y -> Nil
277 | otherwise -> t
278 Nil -> Nil
279
280
281 {--------------------------------------------------------------------
282 Union
283 --------------------------------------------------------------------}
284 -- | The union of a list of sets.
285 unions :: [IntSet] -> IntSet
286 unions xs
287 = foldlStrict union empty xs
288
289
290 -- | /O(n+m)/. The union of two sets.
291 union :: IntSet -> IntSet -> IntSet
292 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
293 | shorter m1 m2 = union1
294 | shorter m2 m1 = union2
295 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
296 | otherwise = join p1 t1 p2 t2
297 where
298 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
299 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
300 | otherwise = Bin p1 m1 l1 (union r1 t2)
301
302 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
303 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
304 | otherwise = Bin p2 m2 l2 (union t1 r2)
305
306 union (Tip x) t = insert x t
307 union t (Tip x) = insertR x t -- right bias
308 union Nil t = t
309 union t Nil = t
310
311
312 {--------------------------------------------------------------------
313 Difference
314 --------------------------------------------------------------------}
315 -- | /O(n+m)/. Difference between two sets.
316 difference :: IntSet -> IntSet -> IntSet
317 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
318 | shorter m1 m2 = difference1
319 | shorter m2 m1 = difference2
320 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
321 | otherwise = t1
322 where
323 difference1 | nomatch p2 p1 m1 = t1
324 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
325 | otherwise = bin p1 m1 l1 (difference r1 t2)
326
327 difference2 | nomatch p1 p2 m2 = t1
328 | zero p1 m2 = difference t1 l2
329 | otherwise = difference t1 r2
330
331 difference t1@(Tip x) t2
332 | member x t2 = Nil
333 | otherwise = t1
334
335 difference Nil t = Nil
336 difference t (Tip x) = delete x t
337 difference t Nil = t
338
339
340
341 {--------------------------------------------------------------------
342 Intersection
343 --------------------------------------------------------------------}
344 -- | /O(n+m)/. The intersection of two sets.
345 intersection :: IntSet -> IntSet -> IntSet
346 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
347 | shorter m1 m2 = intersection1
348 | shorter m2 m1 = intersection2
349 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
350 | otherwise = Nil
351 where
352 intersection1 | nomatch p2 p1 m1 = Nil
353 | zero p2 m1 = intersection l1 t2
354 | otherwise = intersection r1 t2
355
356 intersection2 | nomatch p1 p2 m2 = Nil
357 | zero p1 m2 = intersection t1 l2
358 | otherwise = intersection t1 r2
359
360 intersection t1@(Tip x) t2
361 | member x t2 = t1
362 | otherwise = Nil
363 intersection t (Tip x)
364 = case lookup x t of
365 Just y -> Tip y
366 Nothing -> Nil
367 intersection Nil t = Nil
368 intersection t Nil = Nil
369
370
371
372 {--------------------------------------------------------------------
373 Subset
374 --------------------------------------------------------------------}
375 -- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
376 isProperSubsetOf :: IntSet -> IntSet -> Bool
377 isProperSubsetOf t1 t2
378 = case subsetCmp t1 t2 of
379 LT -> True
380 ge -> False
381
382 subsetCmp t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
383 | shorter m1 m2 = GT
384 | shorter m2 m1 = subsetCmpLt
385 | p1 == p2 = subsetCmpEq
386 | otherwise = GT -- disjoint
387 where
388 subsetCmpLt | nomatch p1 p2 m2 = GT
389 | zero p1 m2 = subsetCmp t1 l2
390 | otherwise = subsetCmp t1 r2
391 subsetCmpEq = case (subsetCmp l1 l2, subsetCmp r1 r2) of
392 (GT,_ ) -> GT
393 (_ ,GT) -> GT
394 (EQ,EQ) -> EQ
395 other -> LT
396
397 subsetCmp (Bin p m l r) t = GT
398 subsetCmp (Tip x) (Tip y)
399 | x==y = EQ
400 | otherwise = GT -- disjoint
401 subsetCmp (Tip x) t
402 | member x t = LT
403 | otherwise = GT -- disjoint
404 subsetCmp Nil Nil = EQ
405 subsetCmp Nil t = LT
406
407 -- | /O(n+m)/. Is this a subset?
408 -- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@.
409
410 isSubsetOf :: IntSet -> IntSet -> Bool
411 isSubsetOf t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
412 | shorter m1 m2 = False
413 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubsetOf t1 l2
414 else isSubsetOf t1 r2)
415 | otherwise = (p1==p2) && isSubsetOf l1 l2 && isSubsetOf r1 r2
416 isSubsetOf (Bin p m l r) t = False
417 isSubsetOf (Tip x) t = member x t
418 isSubsetOf Nil t = True
419
420
421 {--------------------------------------------------------------------
422 Filter
423 --------------------------------------------------------------------}
424 -- | /O(n)/. Filter all elements that satisfy some predicate.
425 filter :: (Int -> Bool) -> IntSet -> IntSet
426 filter pred t
427 = case t of
428 Bin p m l r
429 -> bin p m (filter pred l) (filter pred r)
430 Tip x
431 | pred x -> t
432 | otherwise -> Nil
433 Nil -> Nil
434
435 -- | /O(n)/. partition the set according to some predicate.
436 partition :: (Int -> Bool) -> IntSet -> (IntSet,IntSet)
437 partition pred t
438 = case t of
439 Bin p m l r
440 -> let (l1,l2) = partition pred l
441 (r1,r2) = partition pred r
442 in (bin p m l1 r1, bin p m l2 r2)
443 Tip x
444 | pred x -> (t,Nil)
445 | otherwise -> (Nil,t)
446 Nil -> (Nil,Nil)
447
448
449 -- | /O(log n)/. The expression (@'split' x set@) is a pair @(set1,set2)@
450 -- where all elements in @set1@ are lower than @x@ and all elements in
451 -- @set2@ larger than @x@.
452 --
453 -- > split 3 (fromList [1..5]) == (fromList [1,2], fromList [3,4])
454 split :: Int -> IntSet -> (IntSet,IntSet)
455 split x t
456 = case t of
457 Bin p m l r
458 | zero x m -> let (lt,gt) = split x l in (lt,union gt r)
459 | otherwise -> let (lt,gt) = split x r in (union l lt,gt)
460 Tip y
461 | x>y -> (t,Nil)
462 | x<y -> (Nil,t)
463 | otherwise -> (Nil,Nil)
464 Nil -> (Nil,Nil)
465
466 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
467 -- element was found in the original set.
468 splitMember :: Int -> IntSet -> (IntSet,Bool,IntSet)
469 splitMember x t
470 = case t of
471 Bin p m l r
472 | zero x m -> let (lt,found,gt) = splitMember x l in (lt,found,union gt r)
473 | otherwise -> let (lt,found,gt) = splitMember x r in (union l lt,found,gt)
474 Tip y
475 | x>y -> (t,False,Nil)
476 | x<y -> (Nil,False,t)
477 | otherwise -> (Nil,True,Nil)
478 Nil -> (Nil,False,Nil)
479
480 {----------------------------------------------------------------------
481 Map
482 ----------------------------------------------------------------------}
483
484 -- | /O(n*min(n,W))/.
485 -- @'map' f s@ is the set obtained by applying @f@ to each element of @s@.
486 --
487 -- It's worth noting that the size of the result may be smaller if,
488 -- for some @(x,y)@, @x \/= y && f x == f y@
489
490 map :: (Int->Int) -> IntSet -> IntSet
491 map f = fromList . List.map f . toList
492
493 {--------------------------------------------------------------------
494 Fold
495 --------------------------------------------------------------------}
496 -- | /O(n)/. Fold over the elements of a set in an unspecified order.
497 --
498 -- > sum set == fold (+) 0 set
499 -- > elems set == fold (:) [] set
500 fold :: (Int -> b -> b) -> b -> IntSet -> b
501 fold f z t
502 = foldr f z t
503
504 foldr :: (Int -> b -> b) -> b -> IntSet -> b
505 foldr f z t
506 = case t of
507 Bin p m l r -> foldr f (foldr f z r) l
508 Tip x -> f x z
509 Nil -> z
510
511 {--------------------------------------------------------------------
512 List variations
513 --------------------------------------------------------------------}
514 -- | /O(n)/. The elements of a set. (For sets, this is equivalent to toList)
515 elems :: IntSet -> [Int]
516 elems s
517 = toList s
518
519 {--------------------------------------------------------------------
520 Lists
521 --------------------------------------------------------------------}
522 -- | /O(n)/. Convert the set to a list of elements.
523 toList :: IntSet -> [Int]
524 toList t
525 = fold (:) [] t
526
527 -- | /O(n)/. Convert the set to an ascending list of elements.
528 toAscList :: IntSet -> [Int]
529 toAscList t
530 = -- NOTE: the following algorithm only works for big-endian trees
531 let (pos,neg) = span (>=0) (foldr (:) [] t) in neg ++ pos
532
533 -- | /O(n*min(n,W))/. Create a set from a list of integers.
534 fromList :: [Int] -> IntSet
535 fromList xs
536 = foldlStrict ins empty xs
537 where
538 ins t x = insert x t
539
540 -- | /O(n*min(n,W))/. Build a set from an ascending list of elements.
541 fromAscList :: [Int] -> IntSet
542 fromAscList xs
543 = fromList xs
544
545 -- | /O(n*min(n,W))/. Build a set from an ascending list of distinct elements.
546 fromDistinctAscList :: [Int] -> IntSet
547 fromDistinctAscList xs
548 = fromList xs
549
550
551 {--------------------------------------------------------------------
552 Eq
553 --------------------------------------------------------------------}
554 instance Eq IntSet where
555 t1 == t2 = equal t1 t2
556 t1 /= t2 = nequal t1 t2
557
558 equal :: IntSet -> IntSet -> Bool
559 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
560 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
561 equal (Tip x) (Tip y)
562 = (x==y)
563 equal Nil Nil = True
564 equal t1 t2 = False
565
566 nequal :: IntSet -> IntSet -> Bool
567 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
568 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
569 nequal (Tip x) (Tip y)
570 = (x/=y)
571 nequal Nil Nil = False
572 nequal t1 t2 = True
573
574 {--------------------------------------------------------------------
575 Ord
576 --------------------------------------------------------------------}
577
578 instance Ord IntSet where
579 compare s1 s2 = compare (toAscList s1) (toAscList s2)
580 -- tentative implementation. See if more efficient exists.
581
582 {--------------------------------------------------------------------
583 Show
584 --------------------------------------------------------------------}
585 instance Show IntSet where
586 showsPrec p xs = showParen (p > 10) $
587 showString "fromList " . shows (toList xs)
588
589 showSet :: [Int] -> ShowS
590 showSet []
591 = showString "{}"
592 showSet (x:xs)
593 = showChar '{' . shows x . showTail xs
594 where
595 showTail [] = showChar '}'
596 showTail (x:xs) = showChar ',' . shows x . showTail xs
597
598 {--------------------------------------------------------------------
599 Read
600 --------------------------------------------------------------------}
601 instance Read IntSet where
602 #ifdef __GLASGOW_HASKELL__
603 readPrec = parens $ prec 10 $ do
604 Ident "fromList" <- lexP
605 xs <- readPrec
606 return (fromList xs)
607
608 readListPrec = readListPrecDefault
609 #else
610 readsPrec p = readParen (p > 10) $ \ r -> do
611 ("fromList",s) <- lex r
612 (xs,t) <- reads s
613 return (fromList xs,t)
614 #endif
615
616 {--------------------------------------------------------------------
617 Typeable
618 --------------------------------------------------------------------}
619
620 #include "Typeable.h"
621 INSTANCE_TYPEABLE0(IntSet,intSetTc,"IntSet")
622
623 {--------------------------------------------------------------------
624 Debugging
625 --------------------------------------------------------------------}
626 -- | /O(n)/. Show the tree that implements the set. The tree is shown
627 -- in a compressed, hanging format.
628 showTree :: IntSet -> String
629 showTree s
630 = showTreeWith True False s
631
632
633 {- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
634 the tree that implements the set. If @hang@ is
635 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
636 @wide@ is 'True', an extra wide version is shown.
637 -}
638 showTreeWith :: Bool -> Bool -> IntSet -> String
639 showTreeWith hang wide t
640 | hang = (showsTreeHang wide [] t) ""
641 | otherwise = (showsTree wide [] [] t) ""
642
643 showsTree :: Bool -> [String] -> [String] -> IntSet -> ShowS
644 showsTree wide lbars rbars t
645 = case t of
646 Bin p m l r
647 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
648 showWide wide rbars .
649 showsBars lbars . showString (showBin p m) . showString "\n" .
650 showWide wide lbars .
651 showsTree wide (withEmpty lbars) (withBar lbars) l
652 Tip x
653 -> showsBars lbars . showString " " . shows x . showString "\n"
654 Nil -> showsBars lbars . showString "|\n"
655
656 showsTreeHang :: Bool -> [String] -> IntSet -> ShowS
657 showsTreeHang wide bars t
658 = case t of
659 Bin p m l r
660 -> showsBars bars . showString (showBin p m) . showString "\n" .
661 showWide wide bars .
662 showsTreeHang wide (withBar bars) l .
663 showWide wide bars .
664 showsTreeHang wide (withEmpty bars) r
665 Tip x
666 -> showsBars bars . showString " " . shows x . showString "\n"
667 Nil -> showsBars bars . showString "|\n"
668
669 showBin p m
670 = "*" -- ++ show (p,m)
671
672 showWide wide bars
673 | wide = showString (concat (reverse bars)) . showString "|\n"
674 | otherwise = id
675
676 showsBars :: [String] -> ShowS
677 showsBars bars
678 = case bars of
679 [] -> id
680 _ -> showString (concat (reverse (tail bars))) . showString node
681
682 node = "+--"
683 withBar bars = "| ":bars
684 withEmpty bars = " ":bars
685
686
687 {--------------------------------------------------------------------
688 Helpers
689 --------------------------------------------------------------------}
690 {--------------------------------------------------------------------
691 Join
692 --------------------------------------------------------------------}
693 join :: Prefix -> IntSet -> Prefix -> IntSet -> IntSet
694 join p1 t1 p2 t2
695 | zero p1 m = Bin p m t1 t2
696 | otherwise = Bin p m t2 t1
697 where
698 m = branchMask p1 p2
699 p = mask p1 m
700
701 {--------------------------------------------------------------------
702 @bin@ assures that we never have empty trees within a tree.
703 --------------------------------------------------------------------}
704 bin :: Prefix -> Mask -> IntSet -> IntSet -> IntSet
705 bin p m l Nil = l
706 bin p m Nil r = r
707 bin p m l r = Bin p m l r
708
709
710 {--------------------------------------------------------------------
711 Endian independent bit twiddling
712 --------------------------------------------------------------------}
713 zero :: Int -> Mask -> Bool
714 zero i m
715 = (natFromInt i) .&. (natFromInt m) == 0
716
717 nomatch,match :: Int -> Prefix -> Mask -> Bool
718 nomatch i p m
719 = (mask i m) /= p
720
721 match i p m
722 = (mask i m) == p
723
724 mask :: Int -> Mask -> Prefix
725 mask i m
726 = maskW (natFromInt i) (natFromInt m)
727
728 zeroN :: Nat -> Nat -> Bool
729 zeroN i m = (i .&. m) == 0
730
731 {--------------------------------------------------------------------
732 Big endian operations
733 --------------------------------------------------------------------}
734 maskW :: Nat -> Nat -> Prefix
735 maskW i m
736 = intFromNat (i .&. (complement (m-1) `xor` m))
737
738 shorter :: Mask -> Mask -> Bool
739 shorter m1 m2
740 = (natFromInt m1) > (natFromInt m2)
741
742 branchMask :: Prefix -> Prefix -> Mask
743 branchMask p1 p2
744 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
745
746 {----------------------------------------------------------------------
747 Finding the highest bit (mask) in a word [x] can be done efficiently in
748 three ways:
749 * convert to a floating point value and the mantissa tells us the
750 [log2(x)] that corresponds with the highest bit position. The mantissa
751 is retrieved either via the standard C function [frexp] or by some bit
752 twiddling on IEEE compatible numbers (float). Note that one needs to
753 use at least [double] precision for an accurate mantissa of 32 bit
754 numbers.
755 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
756 * use processor specific assembler instruction (asm).
757
758 The most portable way would be [bit], but is it efficient enough?
759 I have measured the cycle counts of the different methods on an AMD
760 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
761
762 highestBitMask: method cycles
763 --------------
764 frexp 200
765 float 33
766 bit 11
767 asm 12
768
769 highestBit: method cycles
770 --------------
771 frexp 195
772 float 33
773 bit 11
774 asm 11
775
776 Wow, the bit twiddling is on today's RISC like machines even faster
777 than a single CISC instruction (BSR)!
778 ----------------------------------------------------------------------}
779
780 {----------------------------------------------------------------------
781 [highestBitMask] returns a word where only the highest bit is set.
782 It is found by first setting all bits in lower positions than the
783 highest bit and than taking an exclusive or with the original value.
784 Allthough the function may look expensive, GHC compiles this into
785 excellent C code that subsequently compiled into highly efficient
786 machine code. The algorithm is derived from Jorg Arndt's FXT library.
787 ----------------------------------------------------------------------}
788 highestBitMask :: Nat -> Nat
789 highestBitMask x
790 = case (x .|. shiftRL x 1) of
791 x -> case (x .|. shiftRL x 2) of
792 x -> case (x .|. shiftRL x 4) of
793 x -> case (x .|. shiftRL x 8) of
794 x -> case (x .|. shiftRL x 16) of
795 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
796 x -> (x `xor` (shiftRL x 1))
797
798
799 {--------------------------------------------------------------------
800 Utilities
801 --------------------------------------------------------------------}
802 foldlStrict f z xs
803 = case xs of
804 [] -> z
805 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
806
807
808 {-
809 {--------------------------------------------------------------------
810 Testing
811 --------------------------------------------------------------------}
812 testTree :: [Int] -> IntSet
813 testTree xs = fromList xs
814 test1 = testTree [1..20]
815 test2 = testTree [30,29..10]
816 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
817
818 {--------------------------------------------------------------------
819 QuickCheck
820 --------------------------------------------------------------------}
821 qcheck prop
822 = check config prop
823 where
824 config = Config
825 { configMaxTest = 500
826 , configMaxFail = 5000
827 , configSize = \n -> (div n 2 + 3)
828 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
829 }
830
831
832 {--------------------------------------------------------------------
833 Arbitrary, reasonably balanced trees
834 --------------------------------------------------------------------}
835 instance Arbitrary IntSet where
836 arbitrary = do{ xs <- arbitrary
837 ; return (fromList xs)
838 }
839
840
841 {--------------------------------------------------------------------
842 Single, Insert, Delete
843 --------------------------------------------------------------------}
844 prop_Single :: Int -> Bool
845 prop_Single x
846 = (insert x empty == singleton x)
847
848 prop_InsertDelete :: Int -> IntSet -> Property
849 prop_InsertDelete k t
850 = not (member k t) ==> delete k (insert k t) == t
851
852
853 {--------------------------------------------------------------------
854 Union
855 --------------------------------------------------------------------}
856 prop_UnionInsert :: Int -> IntSet -> Bool
857 prop_UnionInsert x t
858 = union t (singleton x) == insert x t
859
860 prop_UnionAssoc :: IntSet -> IntSet -> IntSet -> Bool
861 prop_UnionAssoc t1 t2 t3
862 = union t1 (union t2 t3) == union (union t1 t2) t3
863
864 prop_UnionComm :: IntSet -> IntSet -> Bool
865 prop_UnionComm t1 t2
866 = (union t1 t2 == union t2 t1)
867
868 prop_Diff :: [Int] -> [Int] -> Bool
869 prop_Diff xs ys
870 = toAscList (difference (fromList xs) (fromList ys))
871 == List.sort ((List.\\) (nub xs) (nub ys))
872
873 prop_Int :: [Int] -> [Int] -> Bool
874 prop_Int xs ys
875 = toAscList (intersection (fromList xs) (fromList ys))
876 == List.sort (nub ((List.intersect) (xs) (ys)))
877
878 {--------------------------------------------------------------------
879 Lists
880 --------------------------------------------------------------------}
881 prop_Ordered
882 = forAll (choose (5,100)) $ \n ->
883 let xs = [0..n::Int]
884 in fromAscList xs == fromList xs
885
886 prop_List :: [Int] -> Bool
887 prop_List xs
888 = (sort (nub xs) == toAscList (fromList xs))
889 -}