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|
{-# LANGUAGE CPP #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Word64Set
-- Copyright : (c) Daan Leijen 2002
-- (c) Joachim Breitner 2011
-- License : BSD-style
-- Maintainer : libraries@haskell.org
-- Portability : portable
--
--
-- = Finite Int Sets
--
-- The @'Word64Set'@ type represents a set of elements of type @Int@.
--
-- For a walkthrough of the most commonly used functions see their
-- <https://haskell-containers.readthedocs.io/en/latest/set.html sets introduction>.
--
-- These modules are intended to be imported qualified, to avoid name
-- clashes with Prelude functions, e.g.
--
-- > import Data.Word64Set (Word64Set)
-- > import qualified Data.Word64Set as Word64Set
--
--
-- == Performance information
--
-- Many operations have a worst-case complexity of \(O(\min(n,W))\).
-- This means that the operation can become linear in the number of
-- elements with a maximum of \(W\) -- the number of bits in an 'Int'
-- (32 or 64).
--
--
-- == Implementation
--
-- The implementation is based on /big-endian patricia trees/. This data
-- structure performs especially well on binary operations like 'union'
-- and 'intersection'. However, my benchmarks show that it is also
-- (much) faster on insertions and deletions when compared to a generic
-- size-balanced set implementation (see "Data.Set").
--
-- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
-- Workshop on ML, September 1998, pages 77-86,
-- <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.5452>
--
-- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve Information Coded In Alphanumeric/\",
-- Journal of the ACM, 15(4), October 1968, pages 514-534.
--
-- Additionally, this implementation places bitmaps in the leaves of the tree.
-- Their size is the natural size of a machine word (32 or 64 bits) and greatly
-- reduces the memory footprint and execution times for dense sets, e.g. sets
-- where it is likely that many values lie close to each other. The asymptotics
-- are not affected by this optimization.
--
-----------------------------------------------------------------------------
module GHC.Data.Word64Set (
-- * Strictness properties
-- $strictness
-- * Set type
#if !defined(TESTING)
Word64Set -- instance Eq,Show
#else
Word64Set(..) -- instance Eq,Show
#endif
, Key
-- * Construction
, empty
, singleton
, fromList
, fromAscList
, fromDistinctAscList
-- * Insertion
, insert
-- * Deletion
, delete
-- * Generalized insertion/deletion
, alterF
-- * Query
, member
, notMember
, lookupLT
, lookupGT
, lookupLE
, lookupGE
, WS.null
, size
, isSubsetOf
, isProperSubsetOf
, disjoint
-- * Combine
, union
, unions
, difference
, (\\)
, intersection
-- * Filter
, WS.filter
, partition
, takeWhileAntitone
, dropWhileAntitone
, spanAntitone
, split
, splitMember
, splitRoot
-- * Map
, WS.map
, mapMonotonic
-- * Folds
, WS.foldr
, WS.foldl
-- ** Strict folds
, foldr'
, foldl'
-- ** Legacy folds
, fold
-- * Min\/Max
, findMin
, findMax
, deleteMin
, deleteMax
, deleteFindMin
, deleteFindMax
, maxView
, minView
-- * Conversion
-- ** List
, elems
, toList
, toAscList
, toDescList
-- * Debugging
, showTree
, showTreeWith
#if defined(TESTING)
-- * Internals
, match
#endif
) where
import GHC.Data.Word64Set.Internal as WS
-- $strictness
--
-- This module satisfies the following strictness property:
--
-- * Key arguments are evaluated to WHNF
--
-- Here are some examples that illustrate the property:
--
-- > delete undefined s == undefined
|
