1 //===-- llvm/ADT/EquivalenceClasses.h - Generic Equiv. Classes --*- C++ -*-===// 2 // 3 // The LLVM Compiler Infrastructure 4 // 5 // This file is distributed under the University of Illinois Open Source 6 // License. See LICENSE.TXT for details. 7 // 8 //===----------------------------------------------------------------------===// 9 // 10 // Generic implementation of equivalence classes through the use Tarjan's 11 // efficient union-find algorithm. 12 // 13 //===----------------------------------------------------------------------===// 14 15 #ifndef LLVM_ADT_EQUIVALENCECLASSES_H 16 #define LLVM_ADT_EQUIVALENCECLASSES_H 17 18 #include <cassert> 19 #include <cstddef> 20 #include <cstdint> 21 #include <iterator> 22 #include <set> 23 24 namespace llvm { 25 26 /// EquivalenceClasses - This represents a collection of equivalence classes and 27 /// supports three efficient operations: insert an element into a class of its 28 /// own, union two classes, and find the class for a given element. In 29 /// addition to these modification methods, it is possible to iterate over all 30 /// of the equivalence classes and all of the elements in a class. 31 /// 32 /// This implementation is an efficient implementation that only stores one copy 33 /// of the element being indexed per entry in the set, and allows any arbitrary 34 /// type to be indexed (as long as it can be ordered with operator<). 35 /// 36 /// Here is a simple example using integers: 37 /// 38 /// \code 39 /// EquivalenceClasses<int> EC; 40 /// EC.unionSets(1, 2); // insert 1, 2 into the same set 41 /// EC.insert(4); EC.insert(5); // insert 4, 5 into own sets 42 /// EC.unionSets(5, 1); // merge the set for 1 with 5's set. 43 /// 44 /// for (EquivalenceClasses<int>::iterator I = EC.begin(), E = EC.end(); 45 /// I != E; ++I) { // Iterate over all of the equivalence sets. 46 /// if (!I->isLeader()) continue; // Ignore non-leader sets. 47 /// for (EquivalenceClasses<int>::member_iterator MI = EC.member_begin(I); 48 /// MI != EC.member_end(); ++MI) // Loop over members in this set. 49 /// cerr << *MI << " "; // Print member. 50 /// cerr << "\n"; // Finish set. 51 /// } 52 /// \endcode 53 /// 54 /// This example prints: 55 /// 4 56 /// 5 1 2 57 /// 58 template <class ElemTy> 59 class EquivalenceClasses { 60 /// ECValue - The EquivalenceClasses data structure is just a set of these. 61 /// Each of these represents a relation for a value. First it stores the 62 /// value itself, which provides the ordering that the set queries. Next, it 63 /// provides a "next pointer", which is used to enumerate all of the elements 64 /// in the unioned set. Finally, it defines either a "end of list pointer" or 65 /// "leader pointer" depending on whether the value itself is a leader. A 66 /// "leader pointer" points to the node that is the leader for this element, 67 /// if the node is not a leader. A "end of list pointer" points to the last 68 /// node in the list of members of this list. Whether or not a node is a 69 /// leader is determined by a bit stolen from one of the pointers. 70 class ECValue { 71 friend class EquivalenceClasses; 72 mutable const ECValue *Leader, *Next; 73 ElemTy Data; 74 75 // ECValue ctor - Start out with EndOfList pointing to this node, Next is 76 // Null, isLeader = true. 77 ECValue(const ElemTy &Elt) 78 : Leader(this), Next((ECValue*)(intptr_t)1), Data(Elt) {} 79 80 const ECValue *getLeader() const { 81 if (isLeader()) return this; 82 if (Leader->isLeader()) return Leader; 83 // Path compression. 84 return Leader = Leader->getLeader(); 85 } 86 87 const ECValue *getEndOfList() const { 88 assert(isLeader() && "Cannot get the end of a list for a non-leader!"); 89 return Leader; 90 } 91 92 void setNext(const ECValue *NewNext) const { 93 assert(getNext() == nullptr && "Already has a next pointer!"); 94 Next = (const ECValue*)((intptr_t)NewNext | (intptr_t)isLeader()); 95 } 96 97 public: 98 ECValue(const ECValue &RHS) : Leader(this), Next((ECValue*)(intptr_t)1), 99 Data(RHS.Data) { 100 // Only support copying of singleton nodes. 101 assert(RHS.isLeader() && RHS.getNext() == nullptr && "Not a singleton!"); 102 } 103 104 bool operator<(const ECValue &UFN) const { return Data < UFN.Data; } 105 106 bool isLeader() const { return (intptr_t)Next & 1; } 107 const ElemTy &getData() const { return Data; } 108 109 const ECValue *getNext() const { 110 return (ECValue*)((intptr_t)Next & ~(intptr_t)1); 111 } 112 113 template<typename T> 114 bool operator<(const T &Val) const { return Data < Val; } 115 }; 116 117 /// TheMapping - This implicitly provides a mapping from ElemTy values to the 118 /// ECValues, it just keeps the key as part of the value. 119 std::set<ECValue> TheMapping; 120 121 public: 122 EquivalenceClasses() = default; 123 EquivalenceClasses(const EquivalenceClasses &RHS) { 124 operator=(RHS); 125 } 126 127 const EquivalenceClasses &operator=(const EquivalenceClasses &RHS) { 128 TheMapping.clear(); 129 for (iterator I = RHS.begin(), E = RHS.end(); I != E; ++I) 130 if (I->isLeader()) { 131 member_iterator MI = RHS.member_begin(I); 132 member_iterator LeaderIt = member_begin(insert(*MI)); 133 for (++MI; MI != member_end(); ++MI) 134 unionSets(LeaderIt, member_begin(insert(*MI))); 135 } 136 return *this; 137 } 138 139 //===--------------------------------------------------------------------===// 140 // Inspection methods 141 // 142 143 /// iterator* - Provides a way to iterate over all values in the set. 144 typedef typename std::set<ECValue>::const_iterator iterator; 145 iterator begin() const { return TheMapping.begin(); } 146 iterator end() const { return TheMapping.end(); } 147 148 bool empty() const { return TheMapping.empty(); } 149 150 /// member_* Iterate over the members of an equivalence class. 151 /// 152 class member_iterator; 153 member_iterator member_begin(iterator I) const { 154 // Only leaders provide anything to iterate over. 155 return member_iterator(I->isLeader() ? &*I : nullptr); 156 } 157 member_iterator member_end() const { 158 return member_iterator(nullptr); 159 } 160 161 /// findValue - Return an iterator to the specified value. If it does not 162 /// exist, end() is returned. 163 iterator findValue(const ElemTy &V) const { 164 return TheMapping.find(V); 165 } 166 167 /// getLeaderValue - Return the leader for the specified value that is in the 168 /// set. It is an error to call this method for a value that is not yet in 169 /// the set. For that, call getOrInsertLeaderValue(V). 170 const ElemTy &getLeaderValue(const ElemTy &V) const { 171 member_iterator MI = findLeader(V); 172 assert(MI != member_end() && "Value is not in the set!"); 173 return *MI; 174 } 175 176 /// getOrInsertLeaderValue - Return the leader for the specified value that is 177 /// in the set. If the member is not in the set, it is inserted, then 178 /// returned. 179 const ElemTy &getOrInsertLeaderValue(const ElemTy &V) { 180 member_iterator MI = findLeader(insert(V)); 181 assert(MI != member_end() && "Value is not in the set!"); 182 return *MI; 183 } 184 185 /// getNumClasses - Return the number of equivalence classes in this set. 186 /// Note that this is a linear time operation. 187 unsigned getNumClasses() const { 188 unsigned NC = 0; 189 for (iterator I = begin(), E = end(); I != E; ++I) 190 if (I->isLeader()) ++NC; 191 return NC; 192 } 193 194 //===--------------------------------------------------------------------===// 195 // Mutation methods 196 197 /// insert - Insert a new value into the union/find set, ignoring the request 198 /// if the value already exists. 199 iterator insert(const ElemTy &Data) { 200 return TheMapping.insert(ECValue(Data)).first; 201 } 202 203 /// findLeader - Given a value in the set, return a member iterator for the 204 /// equivalence class it is in. This does the path-compression part that 205 /// makes union-find "union findy". This returns an end iterator if the value 206 /// is not in the equivalence class. 207 /// 208 member_iterator findLeader(iterator I) const { 209 if (I == TheMapping.end()) return member_end(); 210 return member_iterator(I->getLeader()); 211 } 212 member_iterator findLeader(const ElemTy &V) const { 213 return findLeader(TheMapping.find(V)); 214 } 215 216 /// union - Merge the two equivalence sets for the specified values, inserting 217 /// them if they do not already exist in the equivalence set. 218 member_iterator unionSets(const ElemTy &V1, const ElemTy &V2) { 219 iterator V1I = insert(V1), V2I = insert(V2); 220 return unionSets(findLeader(V1I), findLeader(V2I)); 221 } 222 member_iterator unionSets(member_iterator L1, member_iterator L2) { 223 assert(L1 != member_end() && L2 != member_end() && "Illegal inputs!"); 224 if (L1 == L2) return L1; // Unifying the same two sets, noop. 225 226 // Otherwise, this is a real union operation. Set the end of the L1 list to 227 // point to the L2 leader node. 228 const ECValue &L1LV = *L1.Node, &L2LV = *L2.Node; 229 L1LV.getEndOfList()->setNext(&L2LV); 230 231 // Update L1LV's end of list pointer. 232 L1LV.Leader = L2LV.getEndOfList(); 233 234 // Clear L2's leader flag: 235 L2LV.Next = L2LV.getNext(); 236 237 // L2's leader is now L1. 238 L2LV.Leader = &L1LV; 239 return L1; 240 } 241 242 class member_iterator : public std::iterator<std::forward_iterator_tag, 243 const ElemTy, ptrdiff_t> { 244 typedef std::iterator<std::forward_iterator_tag, 245 const ElemTy, ptrdiff_t> super; 246 const ECValue *Node; 247 friend class EquivalenceClasses; 248 249 public: 250 typedef size_t size_type; 251 typedef typename super::pointer pointer; 252 typedef typename super::reference reference; 253 254 explicit member_iterator() = default; 255 explicit member_iterator(const ECValue *N) : Node(N) {} 256 257 reference operator*() const { 258 assert(Node != nullptr && "Dereferencing end()!"); 259 return Node->getData(); 260 } 261 pointer operator->() const { return &operator*(); } 262 263 member_iterator &operator++() { 264 assert(Node != nullptr && "++'d off the end of the list!"); 265 Node = Node->getNext(); 266 return *this; 267 } 268 269 member_iterator operator++(int) { // postincrement operators. 270 member_iterator tmp = *this; 271 ++*this; 272 return tmp; 273 } 274 275 bool operator==(const member_iterator &RHS) const { 276 return Node == RHS.Node; 277 } 278 bool operator!=(const member_iterator &RHS) const { 279 return Node != RHS.Node; 280 } 281 }; 282 }; 283 284 } // end namespace llvm 285 286 #endif // LLVM_ADT_EQUIVALENCECLASSES_H 287