[project @ 2005-01-14 00:00:22 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
98
99 {-
100 -- just for testing
101 import QuickCheck
102 import List (nub,sort)
103 import qualified List
104 -}
105
106 #if __GLASGOW_HASKELL__ >= 503
107 import GHC.Word
108 import GHC.Exts ( Word(..), Int(..), shiftRL# )
109 #elif __GLASGOW_HASKELL__
110 import Word
111 import GlaExts ( Word(..), Int(..), shiftRL# )
112 #else
113 import Data.Word
114 #endif
115
116 infixl 9 \\{-This comment teaches CPP correct behaviour -}
117
118 #if __HUGS__
119 {--------------------------------------------------------------------
120 Hugs:
121 * Older Hugs doesn't define 'Word'.
122 * Newer Hugs defines 'Word' in the Prelude but no operations.
123 --------------------------------------------------------------------}
124 type Nat = Word32 -- illegal on 64-bit platforms!
125 #else
126 {--------------------------------------------------------------------
127 'Standard' Haskell
128 * A "Nat" is a natural machine word (an unsigned Int)
129 --------------------------------------------------------------------}
130 type Nat = Word
131 #endif
132
133 natFromInt :: Int -> Nat
134 natFromInt i = fromIntegral i
135
136 intFromNat :: Nat -> Int
137 intFromNat w = fromIntegral w
138
139 shiftRL :: Nat -> Int -> Nat
140 #if __GLASGOW_HASKELL__
141 {--------------------------------------------------------------------
142 GHC: use unboxing to get @shiftRL@ inlined.
143 --------------------------------------------------------------------}
144 shiftRL (W# x) (I# i)
145 = W# (shiftRL# x i)
146 #else
147 shiftRL x i = shiftR x i
148 #endif
149
150 {--------------------------------------------------------------------
151 Operators
152 --------------------------------------------------------------------}
153 -- | /O(n+m)/. See 'difference'.
154 (\\) :: IntSet -> IntSet -> IntSet
155 m1 \\ m2 = difference m1 m2
156
157 {--------------------------------------------------------------------
158 Types
159 --------------------------------------------------------------------}
160 -- | A set of integers.
161 data IntSet = Nil
162 | Tip {-# UNPACK #-} !Int
163 | Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !IntSet !IntSet
164
165 type Prefix = Int
166 type Mask = Int
167
168 {--------------------------------------------------------------------
169 Query
170 --------------------------------------------------------------------}
171 -- | /O(1)/. Is the set empty?
172 null :: IntSet -> Bool
173 null Nil = True
174 null other = False
175
176 -- | /O(n)/. Cardinality of the set.
177 size :: IntSet -> Int
178 size t
179 = case t of
180 Bin p m l r -> size l + size r
181 Tip y -> 1
182 Nil -> 0
183
184 -- | /O(min(n,W))/. Is the value a member of the set?
185 member :: Int -> IntSet -> Bool
186 member x t
187 = case t of
188 Bin p m l r
189 | nomatch x p m -> False
190 | zero x m -> member x l
191 | otherwise -> member x r
192 Tip y -> (x==y)
193 Nil -> False
194
195 -- 'lookup' is used by 'intersection' for left-biasing
196 lookup :: Int -> IntSet -> Maybe Int
197 lookup k t
198 = let nk = natFromInt k in seq nk (lookupN nk t)
199
200 lookupN :: Nat -> IntSet -> Maybe Int
201 lookupN k t
202 = case t of
203 Bin p m l r
204 | zeroN k (natFromInt m) -> lookupN k l
205 | otherwise -> lookupN k r
206 Tip kx
207 | (k == natFromInt kx) -> Just kx
208 | otherwise -> Nothing
209 Nil -> Nothing
210
211 {--------------------------------------------------------------------
212 Construction
213 --------------------------------------------------------------------}
214 -- | /O(1)/. The empty set.
215 empty :: IntSet
216 empty
217 = Nil
218
219 -- | /O(1)/. A set of one element.
220 singleton :: Int -> IntSet
221 singleton x
222 = Tip x
223
224 {--------------------------------------------------------------------
225 Insert
226 --------------------------------------------------------------------}
227 -- | /O(min(n,W))/. Add a value to the set. When the value is already
228 -- an element of the set, it is replaced by the new one, ie. 'insert'
229 -- is left-biased.
230 insert :: Int -> IntSet -> IntSet
231 insert x t
232 = case t of
233 Bin p m l r
234 | nomatch x p m -> join x (Tip x) p t
235 | zero x m -> Bin p m (insert x l) r
236 | otherwise -> Bin p m l (insert x r)
237 Tip y
238 | x==y -> Tip x
239 | otherwise -> join x (Tip x) y t
240 Nil -> Tip x
241
242 -- right-biased insertion, used by 'union'
243 insertR :: Int -> IntSet -> IntSet
244 insertR x t
245 = case t of
246 Bin p m l r
247 | nomatch x p m -> join x (Tip x) p t
248 | zero x m -> Bin p m (insert x l) r
249 | otherwise -> Bin p m l (insert x r)
250 Tip y
251 | x==y -> t
252 | otherwise -> join x (Tip x) y t
253 Nil -> Tip x
254
255 -- | /O(min(n,W))/. Delete a value in the set. Returns the
256 -- original set when the value was not present.
257 delete :: Int -> IntSet -> IntSet
258 delete x t
259 = case t of
260 Bin p m l r
261 | nomatch x p m -> t
262 | zero x m -> bin p m (delete x l) r
263 | otherwise -> bin p m l (delete x r)
264 Tip y
265 | x==y -> Nil
266 | otherwise -> t
267 Nil -> Nil
268
269
270 {--------------------------------------------------------------------
271 Union
272 --------------------------------------------------------------------}
273 -- | The union of a list of sets.
274 unions :: [IntSet] -> IntSet
275 unions xs
276 = foldlStrict union empty xs
277
278
279 -- | /O(n+m)/. The union of two sets.
280 union :: IntSet -> IntSet -> IntSet
281 union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
282 | shorter m1 m2 = union1
283 | shorter m2 m1 = union2
284 | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
285 | otherwise = join p1 t1 p2 t2
286 where
287 union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
288 | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
289 | otherwise = Bin p1 m1 l1 (union r1 t2)
290
291 union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
292 | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
293 | otherwise = Bin p2 m2 l2 (union t1 r2)
294
295 union (Tip x) t = insert x t
296 union t (Tip x) = insertR x t -- right bias
297 union Nil t = t
298 union t Nil = t
299
300
301 {--------------------------------------------------------------------
302 Difference
303 --------------------------------------------------------------------}
304 -- | /O(n+m)/. Difference between two sets.
305 difference :: IntSet -> IntSet -> IntSet
306 difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
307 | shorter m1 m2 = difference1
308 | shorter m2 m1 = difference2
309 | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
310 | otherwise = t1
311 where
312 difference1 | nomatch p2 p1 m1 = t1
313 | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
314 | otherwise = bin p1 m1 l1 (difference r1 t2)
315
316 difference2 | nomatch p1 p2 m2 = t1
317 | zero p1 m2 = difference t1 l2
318 | otherwise = difference t1 r2
319
320 difference t1@(Tip x) t2
321 | member x t2 = Nil
322 | otherwise = t1
323
324 difference Nil t = Nil
325 difference t (Tip x) = delete x t
326 difference t Nil = t
327
328
329
330 {--------------------------------------------------------------------
331 Intersection
332 --------------------------------------------------------------------}
333 -- | /O(n+m)/. The intersection of two sets.
334 intersection :: IntSet -> IntSet -> IntSet
335 intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
336 | shorter m1 m2 = intersection1
337 | shorter m2 m1 = intersection2
338 | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
339 | otherwise = Nil
340 where
341 intersection1 | nomatch p2 p1 m1 = Nil
342 | zero p2 m1 = intersection l1 t2
343 | otherwise = intersection r1 t2
344
345 intersection2 | nomatch p1 p2 m2 = Nil
346 | zero p1 m2 = intersection t1 l2
347 | otherwise = intersection t1 r2
348
349 intersection t1@(Tip x) t2
350 | member x t2 = t1
351 | otherwise = Nil
352 intersection t (Tip x)
353 = case lookup x t of
354 Just y -> Tip y
355 Nothing -> Nil
356 intersection Nil t = Nil
357 intersection t Nil = Nil
358
359
360
361 {--------------------------------------------------------------------
362 Subset
363 --------------------------------------------------------------------}
364 -- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
365 isProperSubsetOf :: IntSet -> IntSet -> Bool
366 isProperSubsetOf t1 t2
367 = case subsetCmp t1 t2 of
368 LT -> True
369 ge -> False
370
371 subsetCmp t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
372 | shorter m1 m2 = GT
373 | shorter m2 m1 = subsetCmpLt
374 | p1 == p2 = subsetCmpEq
375 | otherwise = GT -- disjoint
376 where
377 subsetCmpLt | nomatch p1 p2 m2 = GT
378 | zero p1 m2 = subsetCmp t1 l2
379 | otherwise = subsetCmp t1 r2
380 subsetCmpEq = case (subsetCmp l1 l2, subsetCmp r1 r2) of
381 (GT,_ ) -> GT
382 (_ ,GT) -> GT
383 (EQ,EQ) -> EQ
384 other -> LT
385
386 subsetCmp (Bin p m l r) t = GT
387 subsetCmp (Tip x) (Tip y)
388 | x==y = EQ
389 | otherwise = GT -- disjoint
390 subsetCmp (Tip x) t
391 | member x t = LT
392 | otherwise = GT -- disjoint
393 subsetCmp Nil Nil = EQ
394 subsetCmp Nil t = LT
395
396 -- | /O(n+m)/. Is this a subset?
397 -- @(s1 `isSubsetOf` s2)@ tells whether s1 is a subset of s2.
398
399 isSubsetOf :: IntSet -> IntSet -> Bool
400 isSubsetOf t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
401 | shorter m1 m2 = False
402 | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubsetOf t1 l2
403 else isSubsetOf t1 r2)
404 | otherwise = (p1==p2) && isSubsetOf l1 l2 && isSubsetOf r1 r2
405 isSubsetOf (Bin p m l r) t = False
406 isSubsetOf (Tip x) t = member x t
407 isSubsetOf Nil t = True
408
409
410 {--------------------------------------------------------------------
411 Filter
412 --------------------------------------------------------------------}
413 -- | /O(n)/. Filter all elements that satisfy some predicate.
414 filter :: (Int -> Bool) -> IntSet -> IntSet
415 filter pred t
416 = case t of
417 Bin p m l r
418 -> bin p m (filter pred l) (filter pred r)
419 Tip x
420 | pred x -> t
421 | otherwise -> Nil
422 Nil -> Nil
423
424 -- | /O(n)/. partition the set according to some predicate.
425 partition :: (Int -> Bool) -> IntSet -> (IntSet,IntSet)
426 partition pred t
427 = case t of
428 Bin p m l r
429 -> let (l1,l2) = partition pred l
430 (r1,r2) = partition pred r
431 in (bin p m l1 r1, bin p m l2 r2)
432 Tip x
433 | pred x -> (t,Nil)
434 | otherwise -> (Nil,t)
435 Nil -> (Nil,Nil)
436
437
438 -- | /O(log n)/. The expression (@split x set@) is a pair @(set1,set2)@
439 -- where all elements in @set1@ are lower than @x@ and all elements in
440 -- @set2@ larger than @x@.
441 --
442 -- > split 3 (fromList [1..5]) == (fromList [1,2], fromList [3,4])
443 split :: Int -> IntSet -> (IntSet,IntSet)
444 split x t
445 = case t of
446 Bin p m l r
447 | zero x m -> let (lt,gt) = split x l in (lt,union gt r)
448 | otherwise -> let (lt,gt) = split x r in (union l lt,gt)
449 Tip y
450 | x>y -> (t,Nil)
451 | x<y -> (Nil,t)
452 | otherwise -> (Nil,Nil)
453 Nil -> (Nil,Nil)
454
455 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
456 -- element was found in the original set.
457 splitMember :: Int -> IntSet -> (Bool,IntSet,IntSet)
458 splitMember x t
459 = case t of
460 Bin p m l r
461 | zero x m -> let (found,lt,gt) = splitMember x l in (found,lt,union gt r)
462 | otherwise -> let (found,lt,gt) = splitMember x r in (found,union l lt,gt)
463 Tip y
464 | x>y -> (False,t,Nil)
465 | x<y -> (False,Nil,t)
466 | otherwise -> (True,Nil,Nil)
467 Nil -> (False,Nil,Nil)
468
469 {----------------------------------------------------------------------
470 Map
471 ----------------------------------------------------------------------}
472
473 -- | /O(n*min(n,W))/.
474 -- @map f s@ is the set obtained by applying @f@ to each element of @s@.
475 --
476 -- It's worth noting that the size of the result may be smaller if,
477 -- for some @(x,y)@, @x \/= y && f x == f y@
478
479 map :: (Int->Int) -> IntSet -> IntSet
480 map f = fromList . List.map f . toList
481
482 {--------------------------------------------------------------------
483 Fold
484 --------------------------------------------------------------------}
485 -- | /O(n)/. Fold over the elements of a set in an unspecified order.
486 --
487 -- > sum set == fold (+) 0 set
488 -- > elems set == fold (:) [] set
489 fold :: (Int -> b -> b) -> b -> IntSet -> b
490 fold f z t
491 = foldr f z t
492
493 foldr :: (Int -> b -> b) -> b -> IntSet -> b
494 foldr f z t
495 = case t of
496 Bin p m l r -> foldr f (foldr f z r) l
497 Tip x -> f x z
498 Nil -> z
499
500 {--------------------------------------------------------------------
501 List variations
502 --------------------------------------------------------------------}
503 -- | /O(n)/. The elements of a set. (For sets, this is equivalent to toList)
504 elems :: IntSet -> [Int]
505 elems s
506 = toList s
507
508 {--------------------------------------------------------------------
509 Lists
510 --------------------------------------------------------------------}
511 -- | /O(n)/. Convert the set to a list of elements.
512 toList :: IntSet -> [Int]
513 toList t
514 = fold (:) [] t
515
516 -- | /O(n)/. Convert the set to an ascending list of elements.
517 toAscList :: IntSet -> [Int]
518 toAscList t
519 = -- NOTE: the following algorithm only works for big-endian trees
520 let (pos,neg) = span (>=0) (foldr (:) [] t) in neg ++ pos
521
522 -- | /O(n*min(n,W))/. Create a set from a list of integers.
523 fromList :: [Int] -> IntSet
524 fromList xs
525 = foldlStrict ins empty xs
526 where
527 ins t x = insert x t
528
529 -- | /O(n*min(n,W))/. Build a set from an ascending list of elements.
530 fromAscList :: [Int] -> IntSet
531 fromAscList xs
532 = fromList xs
533
534 -- | /O(n*min(n,W))/. Build a set from an ascending list of distinct elements.
535 fromDistinctAscList :: [Int] -> IntSet
536 fromDistinctAscList xs
537 = fromList xs
538
539
540 {--------------------------------------------------------------------
541 Eq
542 --------------------------------------------------------------------}
543 instance Eq IntSet where
544 t1 == t2 = equal t1 t2
545 t1 /= t2 = nequal t1 t2
546
547 equal :: IntSet -> IntSet -> Bool
548 equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
549 = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
550 equal (Tip x) (Tip y)
551 = (x==y)
552 equal Nil Nil = True
553 equal t1 t2 = False
554
555 nequal :: IntSet -> IntSet -> Bool
556 nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
557 = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
558 nequal (Tip x) (Tip y)
559 = (x/=y)
560 nequal Nil Nil = False
561 nequal t1 t2 = True
562
563 {--------------------------------------------------------------------
564 Ord
565 --------------------------------------------------------------------}
566
567 instance Ord IntSet where
568 compare s1 s2 = compare (toAscList s1) (toAscList s2)
569 -- tentative implementation. See if more efficient exists.
570
571 {--------------------------------------------------------------------
572 Monoid
573 --------------------------------------------------------------------}
574
575 instance Monoid IntSet where
576 mempty = empty
577 mappend = union
578 mconcat = unions
579
580 {--------------------------------------------------------------------
581 Show
582 --------------------------------------------------------------------}
583 instance Show IntSet where
584 showsPrec d s = showSet (toList s)
585
586 showSet :: [Int] -> ShowS
587 showSet []
588 = showString "{}"
589 showSet (x:xs)
590 = showChar '{' . shows x . showTail xs
591 where
592 showTail [] = showChar '}'
593 showTail (x:xs) = showChar ',' . shows x . showTail xs
594
595 {--------------------------------------------------------------------
596 Debugging
597 --------------------------------------------------------------------}
598 -- | /O(n)/. Show the tree that implements the set. The tree is shown
599 -- in a compressed, hanging format.
600 showTree :: IntSet -> String
601 showTree s
602 = showTreeWith True False s
603
604
605 {- | /O(n)/. The expression (@showTreeWith hang wide map@) shows
606 the tree that implements the set. If @hang@ is
607 @True@, a /hanging/ tree is shown otherwise a rotated tree is shown. If
608 @wide@ is true, an extra wide version is shown.
609 -}
610 showTreeWith :: Bool -> Bool -> IntSet -> String
611 showTreeWith hang wide t
612 | hang = (showsTreeHang wide [] t) ""
613 | otherwise = (showsTree wide [] [] t) ""
614
615 showsTree :: Bool -> [String] -> [String] -> IntSet -> ShowS
616 showsTree wide lbars rbars t
617 = case t of
618 Bin p m l r
619 -> showsTree wide (withBar rbars) (withEmpty rbars) r .
620 showWide wide rbars .
621 showsBars lbars . showString (showBin p m) . showString "\n" .
622 showWide wide lbars .
623 showsTree wide (withEmpty lbars) (withBar lbars) l
624 Tip x
625 -> showsBars lbars . showString " " . shows x . showString "\n"
626 Nil -> showsBars lbars . showString "|\n"
627
628 showsTreeHang :: Bool -> [String] -> IntSet -> ShowS
629 showsTreeHang wide bars t
630 = case t of
631 Bin p m l r
632 -> showsBars bars . showString (showBin p m) . showString "\n" .
633 showWide wide bars .
634 showsTreeHang wide (withBar bars) l .
635 showWide wide bars .
636 showsTreeHang wide (withEmpty bars) r
637 Tip x
638 -> showsBars bars . showString " " . shows x . showString "\n"
639 Nil -> showsBars bars . showString "|\n"
640
641 showBin p m
642 = "*" -- ++ show (p,m)
643
644 showWide wide bars
645 | wide = showString (concat (reverse bars)) . showString "|\n"
646 | otherwise = id
647
648 showsBars :: [String] -> ShowS
649 showsBars bars
650 = case bars of
651 [] -> id
652 _ -> showString (concat (reverse (tail bars))) . showString node
653
654 node = "+--"
655 withBar bars = "| ":bars
656 withEmpty bars = " ":bars
657
658
659 {--------------------------------------------------------------------
660 Helpers
661 --------------------------------------------------------------------}
662 {--------------------------------------------------------------------
663 Join
664 --------------------------------------------------------------------}
665 join :: Prefix -> IntSet -> Prefix -> IntSet -> IntSet
666 join p1 t1 p2 t2
667 | zero p1 m = Bin p m t1 t2
668 | otherwise = Bin p m t2 t1
669 where
670 m = branchMask p1 p2
671 p = mask p1 m
672
673 {--------------------------------------------------------------------
674 @bin@ assures that we never have empty trees within a tree.
675 --------------------------------------------------------------------}
676 bin :: Prefix -> Mask -> IntSet -> IntSet -> IntSet
677 bin p m l Nil = l
678 bin p m Nil r = r
679 bin p m l r = Bin p m l r
680
681
682 {--------------------------------------------------------------------
683 Endian independent bit twiddling
684 --------------------------------------------------------------------}
685 zero :: Int -> Mask -> Bool
686 zero i m
687 = (natFromInt i) .&. (natFromInt m) == 0
688
689 nomatch,match :: Int -> Prefix -> Mask -> Bool
690 nomatch i p m
691 = (mask i m) /= p
692
693 match i p m
694 = (mask i m) == p
695
696 mask :: Int -> Mask -> Prefix
697 mask i m
698 = maskW (natFromInt i) (natFromInt m)
699
700 zeroN :: Nat -> Nat -> Bool
701 zeroN i m = (i .&. m) == 0
702
703 {--------------------------------------------------------------------
704 Big endian operations
705 --------------------------------------------------------------------}
706 maskW :: Nat -> Nat -> Prefix
707 maskW i m
708 = intFromNat (i .&. (complement (m-1) `xor` m))
709
710 shorter :: Mask -> Mask -> Bool
711 shorter m1 m2
712 = (natFromInt m1) > (natFromInt m2)
713
714 branchMask :: Prefix -> Prefix -> Mask
715 branchMask p1 p2
716 = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
717
718 {----------------------------------------------------------------------
719 Finding the highest bit (mask) in a word [x] can be done efficiently in
720 three ways:
721 * convert to a floating point value and the mantissa tells us the
722 [log2(x)] that corresponds with the highest bit position. The mantissa
723 is retrieved either via the standard C function [frexp] or by some bit
724 twiddling on IEEE compatible numbers (float). Note that one needs to
725 use at least [double] precision for an accurate mantissa of 32 bit
726 numbers.
727 * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
728 * use processor specific assembler instruction (asm).
729
730 The most portable way would be [bit], but is it efficient enough?
731 I have measured the cycle counts of the different methods on an AMD
732 Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
733
734 highestBitMask: method cycles
735 --------------
736 frexp 200
737 float 33
738 bit 11
739 asm 12
740
741 highestBit: method cycles
742 --------------
743 frexp 195
744 float 33
745 bit 11
746 asm 11
747
748 Wow, the bit twiddling is on today's RISC like machines even faster
749 than a single CISC instruction (BSR)!
750 ----------------------------------------------------------------------}
751
752 {----------------------------------------------------------------------
753 [highestBitMask] returns a word where only the highest bit is set.
754 It is found by first setting all bits in lower positions than the
755 highest bit and than taking an exclusive or with the original value.
756 Allthough the function may look expensive, GHC compiles this into
757 excellent C code that subsequently compiled into highly efficient
758 machine code. The algorithm is derived from Jorg Arndt's FXT library.
759 ----------------------------------------------------------------------}
760 highestBitMask :: Nat -> Nat
761 highestBitMask x
762 = case (x .|. shiftRL x 1) of
763 x -> case (x .|. shiftRL x 2) of
764 x -> case (x .|. shiftRL x 4) of
765 x -> case (x .|. shiftRL x 8) of
766 x -> case (x .|. shiftRL x 16) of
767 x -> case (x .|. shiftRL x 32) of -- for 64 bit platforms
768 x -> (x `xor` (shiftRL x 1))
769
770
771 {--------------------------------------------------------------------
772 Utilities
773 --------------------------------------------------------------------}
774 foldlStrict f z xs
775 = case xs of
776 [] -> z
777 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
778
779
780 {-
781 {--------------------------------------------------------------------
782 Testing
783 --------------------------------------------------------------------}
784 testTree :: [Int] -> IntSet
785 testTree xs = fromList xs
786 test1 = testTree [1..20]
787 test2 = testTree [30,29..10]
788 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
789
790 {--------------------------------------------------------------------
791 QuickCheck
792 --------------------------------------------------------------------}
793 qcheck prop
794 = check config prop
795 where
796 config = Config
797 { configMaxTest = 500
798 , configMaxFail = 5000
799 , configSize = \n -> (div n 2 + 3)
800 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
801 }
802
803
804 {--------------------------------------------------------------------
805 Arbitrary, reasonably balanced trees
806 --------------------------------------------------------------------}
807 instance Arbitrary IntSet where
808 arbitrary = do{ xs <- arbitrary
809 ; return (fromList xs)
810 }
811
812
813 {--------------------------------------------------------------------
814 Single, Insert, Delete
815 --------------------------------------------------------------------}
816 prop_Single :: Int -> Bool
817 prop_Single x
818 = (insert x empty == singleton x)
819
820 prop_InsertDelete :: Int -> IntSet -> Property
821 prop_InsertDelete k t
822 = not (member k t) ==> delete k (insert k t) == t
823
824
825 {--------------------------------------------------------------------
826 Union
827 --------------------------------------------------------------------}
828 prop_UnionInsert :: Int -> IntSet -> Bool
829 prop_UnionInsert x t
830 = union t (singleton x) == insert x t
831
832 prop_UnionAssoc :: IntSet -> IntSet -> IntSet -> Bool
833 prop_UnionAssoc t1 t2 t3
834 = union t1 (union t2 t3) == union (union t1 t2) t3
835
836 prop_UnionComm :: IntSet -> IntSet -> Bool
837 prop_UnionComm t1 t2
838 = (union t1 t2 == union t2 t1)
839
840 prop_Diff :: [Int] -> [Int] -> Bool
841 prop_Diff xs ys
842 = toAscList (difference (fromList xs) (fromList ys))
843 == List.sort ((List.\\) (nub xs) (nub ys))
844
845 prop_Int :: [Int] -> [Int] -> Bool
846 prop_Int xs ys
847 = toAscList (intersection (fromList xs) (fromList ys))
848 == List.sort (nub ((List.intersect) (xs) (ys)))
849
850 {--------------------------------------------------------------------
851 Lists
852 --------------------------------------------------------------------}
853 prop_Ordered
854 = forAll (choose (5,100)) $ \n ->
855 let xs = [0..n::Int]
856 in fromAscList xs == fromList xs
857
858 prop_List :: [Int] -> Bool
859 prop_List xs
860 = (sort (nub xs) == toAscList (fromList xs))
861 -}