//===- 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 #include <cassert> #include <cstddef> #include <cstdint> #include <iterator> #include <set> 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 { /// 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: EquivalenceClasses() = default; EquivalenceClasses(const EquivalenceClasses &RHS) { operator=(RHS); } 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; } //===--------------------------------------------------------------------===// // Inspection methods // /// iterator* - Provides a way to iterate over all values in the set. using iterator = typename std::set<ECValue>::const_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); } 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(); // Clear L2's leader flag: L2LV.Next = L2LV.getNext(); // L2's leader is now L1. L2LV.Leader = &L1LV; return L1; } // isEquivalent - Return true if V1 is equivalent to V2. This can happen if // V1 is equal to V2 or if they belong to one equivalence class. bool isEquivalent(const ElemTy &V1, const ElemTy &V2) const { // Fast path: any element is equivalent to itself. if (V1 == V2) return true; auto It = findLeader(V1); return It != member_end() && It == findLeader(V2); } class member_iterator : public std::iterator<std::forward_iterator_tag, const ElemTy, ptrdiff_t> { friend class EquivalenceClasses; using super = std::iterator<std::forward_iterator_tag, const ElemTy, ptrdiff_t>; const ECValue *Node; public: using size_type = size_t; using pointer = typename super::pointer; using reference = typename super::reference; explicit member_iterator() = default; 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 namespace llvm #endif // LLVM_ADT_EQUIVALENCECLASSES_H