-//===-- Support/EquivalenceClasses.h ----------------------------*- C++ -*-===//
-//
-// Generic implementation of equivalence classes and implementation of
-// union-find algorithms A not-so-fancy implementation: 2 level tree i.e root
-// and one more level Overhead of a union = size of the equivalence class being
-// attached Overhead of a find = 1.
-//
+//===-- llvm/ADT/EquivalenceClasses.h - Generic Equiv. Classes --*- C++ -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
//===----------------------------------------------------------------------===//
+//
+// Generic implementation of equivalence classes through the use Tarjan's
+// efficient union-find algorithm.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_ADT_EQUIVALENCECLASSES_H
+#define LLVM_ADT_EQUIVALENCECLASSES_H
-#ifndef SUPPORT_EQUIVALENCECLASSES_H
-#define SUPPORT_EQUIVALENCECLASSES_H
+#include "llvm/Support/DataTypes.h"
+#include <cassert>
+#include <cstddef>
+#include <set>
-#include <map>
-#include <vector>
+namespace llvm {
+/// EquivalenceClasses - This represents a collection of equivalence classes and
+/// supports three efficient operations: insert an element into a class of its
+/// own, union two classes, and find the class for a given element. In
+/// addition to these modification methods, it is possible to iterate over all
+/// of the equivalence classes and all of the elements in a class.
+///
+/// This implementation is an efficient implementation that only stores one copy
+/// of the element being indexed per entry in the set, and allows any arbitrary
+/// type to be indexed (as long as it can be ordered with operator<).
+///
+/// Here is a simple example using integers:
+///
+/// \code
+/// EquivalenceClasses<int> EC;
+/// EC.unionSets(1, 2); // insert 1, 2 into the same set
+/// EC.insert(4); EC.insert(5); // insert 4, 5 into own sets
+/// EC.unionSets(5, 1); // merge the set for 1 with 5's set.
+///
+/// for (EquivalenceClasses<int>::iterator I = EC.begin(), E = EC.end();
+/// I != E; ++I) { // Iterate over all of the equivalence sets.
+/// if (!I->isLeader()) continue; // Ignore non-leader sets.
+/// for (EquivalenceClasses<int>::member_iterator MI = EC.member_begin(I);
+/// MI != EC.member_end(); ++MI) // Loop over members in this set.
+/// cerr << *MI << " "; // Print member.
+/// cerr << "\n"; // Finish set.
+/// }
+/// \endcode
+///
+/// This example prints:
+/// 4
+/// 5 1 2
+///
template <class ElemTy>
class EquivalenceClasses {
- // Maps each element to the element that is the leader of its
- // equivalence class.
- std::map<ElemTy, ElemTy> Elem2ECLeaderMap;
-
- // Make Element2 the leader of the union of classes Element1 and Element2
- // Element1 and Element2 are presumed to be leaders of their respective
- // equivalence classes.
- void attach(ElemTy Element1, ElemTy Element2) {
- for (typename std::map<ElemTy, ElemTy>::iterator ElemI =
- Elem2ECLeaderMap.begin(), ElemE = Elem2ECLeaderMap.end();
- ElemI != ElemE; ++ElemI) {
- if (ElemI->second == Element1)
- Elem2ECLeaderMap[ElemI->first] = Element2;
+ /// ECValue - The EquivalenceClasses data structure is just a set of these.
+ /// Each of these represents a relation for a value. First it stores the
+ /// value itself, which provides the ordering that the set queries. Next, it
+ /// provides a "next pointer", which is used to enumerate all of the elements
+ /// in the unioned set. Finally, it defines either a "end of list pointer" or
+ /// "leader pointer" depending on whether the value itself is a leader. A
+ /// "leader pointer" points to the node that is the leader for this element,
+ /// if the node is not a leader. A "end of list pointer" points to the last
+ /// node in the list of members of this list. Whether or not a node is a
+ /// leader is determined by a bit stolen from one of the pointers.
+ class ECValue {
+ friend class EquivalenceClasses;
+ mutable const ECValue *Leader, *Next;
+ ElemTy Data;
+ // ECValue ctor - Start out with EndOfList pointing to this node, Next is
+ // Null, isLeader = true.
+ ECValue(const ElemTy &Elt)
+ : Leader(this), Next((ECValue*)(intptr_t)1), Data(Elt) {}
+
+ const ECValue *getLeader() const {
+ if (isLeader()) return this;
+ if (Leader->isLeader()) return Leader;
+ // Path compression.
+ return Leader = Leader->getLeader();
}
- }
+ const ECValue *getEndOfList() const {
+ assert(isLeader() && "Cannot get the end of a list for a non-leader!");
+ return Leader;
+ }
+
+ void setNext(const ECValue *NewNext) const {
+ assert(getNext() == nullptr && "Already has a next pointer!");
+ Next = (const ECValue*)((intptr_t)NewNext | (intptr_t)isLeader());
+ }
+ public:
+ ECValue(const ECValue &RHS) : Leader(this), Next((ECValue*)(intptr_t)1),
+ Data(RHS.Data) {
+ // Only support copying of singleton nodes.
+ assert(RHS.isLeader() && RHS.getNext() == nullptr && "Not a singleton!");
+ }
+
+ bool operator<(const ECValue &UFN) const { return Data < UFN.Data; }
+
+ bool isLeader() const { return (intptr_t)Next & 1; }
+ const ElemTy &getData() const { return Data; }
+
+ const ECValue *getNext() const {
+ return (ECValue*)((intptr_t)Next & ~(intptr_t)1);
+ }
+
+ template<typename T>
+ bool operator<(const T &Val) const { return Data < Val; }
+ };
+
+ /// TheMapping - This implicitly provides a mapping from ElemTy values to the
+ /// ECValues, it just keeps the key as part of the value.
+ std::set<ECValue> TheMapping;
public:
-
- void addElement (ElemTy NewElement) {
- if (Elem2ECLeaderMap.find(NewElement) == Elem2ECLeaderMap.end())
- Elem2ECLeaderMap[NewElement] = NewElement;
+ EquivalenceClasses() {}
+ EquivalenceClasses(const EquivalenceClasses &RHS) {
+ operator=(RHS);
}
-
- ElemTy findClass(ElemTy Element) {
- if (Elem2ECLeaderMap.find(Element) == Elem2ECLeaderMap.end())
- return 0;
- else
- return Elem2ECLeaderMap[Element];
+
+ const EquivalenceClasses &operator=(const EquivalenceClasses &RHS) {
+ TheMapping.clear();
+ for (iterator I = RHS.begin(), E = RHS.end(); I != E; ++I)
+ if (I->isLeader()) {
+ member_iterator MI = RHS.member_begin(I);
+ member_iterator LeaderIt = member_begin(insert(*MI));
+ for (++MI; MI != member_end(); ++MI)
+ unionSets(LeaderIt, member_begin(insert(*MI)));
+ }
+ return *this;
}
- /// Attach the set with Element1 to the set with Element2 adding Element1 and
- /// Element2 to the set of equivalence classes if they are not there already.
- /// Implication: Make Element1 the element in the smaller set.
- void unionSetsWith(ElemTy Element1, ElemTy Element2) {
- // If either Element1 or Element2 does not already exist, include it
- if (Elem2ECLeaderMap.find(Element1) == Elem2ECLeaderMap.end())
- Elem2ECLeaderMap[Element1] = Element1;
- if (Elem2ECLeaderMap.find(Element2) == Elem2ECLeaderMap.end())
- Elem2ECLeaderMap[Element2] = Element2;
-
- attach(Elem2ECLeaderMap[Element1], Elem2ECLeaderMap[Element2]);
+ //===--------------------------------------------------------------------===//
+ // Inspection methods
+ //
+
+ /// iterator* - Provides a way to iterate over all values in the set.
+ typedef typename std::set<ECValue>::const_iterator iterator;
+ iterator begin() const { return TheMapping.begin(); }
+ iterator end() const { return TheMapping.end(); }
+
+ bool empty() const { return TheMapping.empty(); }
+
+ /// member_* Iterate over the members of an equivalence class.
+ ///
+ class member_iterator;
+ member_iterator member_begin(iterator I) const {
+ // Only leaders provide anything to iterate over.
+ return member_iterator(I->isLeader() ? &*I : nullptr);
}
-
- // Returns a vector containing all the elements in the equivalent class
- // including Element1
- std::vector<ElemTy> getEqClass(ElemTy Element1) {
- std::vector<ElemTy> EqClass;
-
- if (Elem2ECLeaderMap.find(EqClass) == Elem2ECLeaderMap.end())
- return EqClass;
-
- ElemTy classLeader = Elem2ECLeaderMap[Element1];
- for (typename std::map<ElemTy, ElemTy>::iterator ElemI =
- Elem2ECLeaderMap.begin(), ElemE = Elem2ECLeaderMap.end();
- ElemI != ElemE; ++ElemI) {
- if (ElemI->second == classLeader)
- EqClass.push_back(ElemI->first);
- }
-
- return EqClass;
+ member_iterator member_end() const {
+ return member_iterator(nullptr);
+ }
+
+ /// findValue - Return an iterator to the specified value. If it does not
+ /// exist, end() is returned.
+ iterator findValue(const ElemTy &V) const {
+ return TheMapping.find(V);
+ }
+
+ /// getLeaderValue - Return the leader for the specified value that is in the
+ /// set. It is an error to call this method for a value that is not yet in
+ /// the set. For that, call getOrInsertLeaderValue(V).
+ const ElemTy &getLeaderValue(const ElemTy &V) const {
+ member_iterator MI = findLeader(V);
+ assert(MI != member_end() && "Value is not in the set!");
+ return *MI;
+ }
+
+ /// getOrInsertLeaderValue - Return the leader for the specified value that is
+ /// in the set. If the member is not in the set, it is inserted, then
+ /// returned.
+ const ElemTy &getOrInsertLeaderValue(const ElemTy &V) {
+ member_iterator MI = findLeader(insert(V));
+ assert(MI != member_end() && "Value is not in the set!");
+ return *MI;
+ }
+
+ /// getNumClasses - Return the number of equivalence classes in this set.
+ /// Note that this is a linear time operation.
+ unsigned getNumClasses() const {
+ unsigned NC = 0;
+ for (iterator I = begin(), E = end(); I != E; ++I)
+ if (I->isLeader()) ++NC;
+ return NC;
+ }
+
+
+ //===--------------------------------------------------------------------===//
+ // Mutation methods
+
+ /// insert - Insert a new value into the union/find set, ignoring the request
+ /// if the value already exists.
+ iterator insert(const ElemTy &Data) {
+ return TheMapping.insert(ECValue(Data)).first;
+ }
+
+ /// findLeader - Given a value in the set, return a member iterator for the
+ /// equivalence class it is in. This does the path-compression part that
+ /// makes union-find "union findy". This returns an end iterator if the value
+ /// is not in the equivalence class.
+ ///
+ member_iterator findLeader(iterator I) const {
+ if (I == TheMapping.end()) return member_end();
+ return member_iterator(I->getLeader());
}
+ member_iterator findLeader(const ElemTy &V) const {
+ return findLeader(TheMapping.find(V));
+ }
+
+
+ /// union - Merge the two equivalence sets for the specified values, inserting
+ /// them if they do not already exist in the equivalence set.
+ member_iterator unionSets(const ElemTy &V1, const ElemTy &V2) {
+ iterator V1I = insert(V1), V2I = insert(V2);
+ return unionSets(findLeader(V1I), findLeader(V2I));
+ }
+ member_iterator unionSets(member_iterator L1, member_iterator L2) {
+ assert(L1 != member_end() && L2 != member_end() && "Illegal inputs!");
+ if (L1 == L2) return L1; // Unifying the same two sets, noop.
+
+ // Otherwise, this is a real union operation. Set the end of the L1 list to
+ // point to the L2 leader node.
+ const ECValue &L1LV = *L1.Node, &L2LV = *L2.Node;
+ L1LV.getEndOfList()->setNext(&L2LV);
+
+ // Update L1LV's end of list pointer.
+ L1LV.Leader = L2LV.getEndOfList();
- std::map<ElemTy, ElemTy>& getLeaderMap() {
- return Elem2ECLeaderMap ;
+ // Clear L2's leader flag:
+ L2LV.Next = L2LV.getNext();
+
+ // L2's leader is now L1.
+ L2LV.Leader = &L1LV;
+ return L1;
}
+
+ class member_iterator : public std::iterator<std::forward_iterator_tag,
+ const ElemTy, ptrdiff_t> {
+ typedef std::iterator<std::forward_iterator_tag,
+ const ElemTy, ptrdiff_t> super;
+ const ECValue *Node;
+ friend class EquivalenceClasses;
+ public:
+ typedef size_t size_type;
+ typedef typename super::pointer pointer;
+ typedef typename super::reference reference;
+
+ explicit member_iterator() {}
+ explicit member_iterator(const ECValue *N) : Node(N) {}
+
+ reference operator*() const {
+ assert(Node != nullptr && "Dereferencing end()!");
+ return Node->getData();
+ }
+ pointer operator->() const { return &operator*(); }
+
+ member_iterator &operator++() {
+ assert(Node != nullptr && "++'d off the end of the list!");
+ Node = Node->getNext();
+ return *this;
+ }
+
+ member_iterator operator++(int) { // postincrement operators.
+ member_iterator tmp = *this;
+ ++*this;
+ return tmp;
+ }
+
+ bool operator==(const member_iterator &RHS) const {
+ return Node == RHS.Node;
+ }
+ bool operator!=(const member_iterator &RHS) const {
+ return Node != RHS.Node;
+ }
+ };
};
+} // End llvm namespace
+
#endif
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