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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 "llvm/Support/DataTypes.h"
19#include <cassert>
20#include <set>
21
22namespace llvm {
23
24/// EquivalenceClasses - This represents a collection of equivalence classes and
25/// supports three efficient operations: insert an element into a class of its
26/// own, union two classes, and find the class for a given element. In
27/// addition to these modification methods, it is possible to iterate over all
28/// of the equivalence classes and all of the elements in a class.
29///
30/// This implementation is an efficient implementation that only stores one copy
31/// of the element being indexed per entry in the set, and allows any arbitrary
32/// type to be indexed (as long as it can be ordered with operator<).
33///
34/// Here is a simple example using integers:
35///
36/// \code
37/// EquivalenceClasses<int> EC;
38/// EC.unionSets(1, 2); // insert 1, 2 into the same set
39/// EC.insert(4); EC.insert(5); // insert 4, 5 into own sets
40/// EC.unionSets(5, 1); // merge the set for 1 with 5's set.
41///
42/// for (EquivalenceClasses<int>::iterator I = EC.begin(), E = EC.end();
43/// I != E; ++I) { // Iterate over all of the equivalence sets.
44/// if (!I->isLeader()) continue; // Ignore non-leader sets.
45/// for (EquivalenceClasses<int>::member_iterator MI = EC.member_begin(I);
46/// MI != EC.member_end(); ++MI) // Loop over members in this set.
47/// cerr << *MI << " "; // Print member.
48/// cerr << "\n"; // Finish set.
49/// }
50/// \endcode
51///
52/// This example prints:
53/// 4
54/// 5 1 2
55///
56template <class ElemTy>
57class EquivalenceClasses {
58 /// ECValue - The EquivalenceClasses data structure is just a set of these.
59 /// Each of these represents a relation for a value. First it stores the
60 /// value itself, which provides the ordering that the set queries. Next, it
61 /// provides a "next pointer", which is used to enumerate all of the elements
62 /// in the unioned set. Finally, it defines either a "end of list pointer" or
63 /// "leader pointer" depending on whether the value itself is a leader. A
64 /// "leader pointer" points to the node that is the leader for this element,
65 /// if the node is not a leader. A "end of list pointer" points to the last
66 /// node in the list of members of this list. Whether or not a node is a
67 /// leader is determined by a bit stolen from one of the pointers.
68 class ECValue {
69 friend class EquivalenceClasses;
70 mutable const ECValue *Leader, *Next;
71 ElemTy Data;
72 // ECValue ctor - Start out with EndOfList pointing to this node, Next is
73 // Null, isLeader = true.
74 ECValue(const ElemTy &Elt)
75 : Leader(this), Next((ECValue*)(intptr_t)1), Data(Elt) {}
76
77 const ECValue *getLeader() const {
78 if (isLeader()) return this;
79 if (Leader->isLeader()) return Leader;
80 // Path compression.
81 return Leader = Leader->getLeader();
82 }
83 const ECValue *getEndOfList() const {
84 assert(isLeader() && "Cannot get the end of a list for a non-leader!");
85 return Leader;
86 }
87
88 void setNext(const ECValue *NewNext) const {
1a4d82fc 89 assert(getNext() == nullptr && "Already has a next pointer!");
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90 Next = (const ECValue*)((intptr_t)NewNext | (intptr_t)isLeader());
91 }
92 public:
93 ECValue(const ECValue &RHS) : Leader(this), Next((ECValue*)(intptr_t)1),
94 Data(RHS.Data) {
95 // Only support copying of singleton nodes.
1a4d82fc 96 assert(RHS.isLeader() && RHS.getNext() == nullptr && "Not a singleton!");
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97 }
98
99 bool operator<(const ECValue &UFN) const { return Data < UFN.Data; }
100
101 bool isLeader() const { return (intptr_t)Next & 1; }
102 const ElemTy &getData() const { return Data; }
103
104 const ECValue *getNext() const {
105 return (ECValue*)((intptr_t)Next & ~(intptr_t)1);
106 }
107
108 template<typename T>
109 bool operator<(const T &Val) const { return Data < Val; }
110 };
111
112 /// TheMapping - This implicitly provides a mapping from ElemTy values to the
113 /// ECValues, it just keeps the key as part of the value.
114 std::set<ECValue> TheMapping;
115
116public:
117 EquivalenceClasses() {}
118 EquivalenceClasses(const EquivalenceClasses &RHS) {
119 operator=(RHS);
120 }
121
122 const EquivalenceClasses &operator=(const EquivalenceClasses &RHS) {
123 TheMapping.clear();
124 for (iterator I = RHS.begin(), E = RHS.end(); I != E; ++I)
125 if (I->isLeader()) {
126 member_iterator MI = RHS.member_begin(I);
127 member_iterator LeaderIt = member_begin(insert(*MI));
128 for (++MI; MI != member_end(); ++MI)
129 unionSets(LeaderIt, member_begin(insert(*MI)));
130 }
131 return *this;
132 }
133
134 //===--------------------------------------------------------------------===//
135 // Inspection methods
136 //
137
138 /// iterator* - Provides a way to iterate over all values in the set.
139 typedef typename std::set<ECValue>::const_iterator iterator;
140 iterator begin() const { return TheMapping.begin(); }
141 iterator end() const { return TheMapping.end(); }
142
143 bool empty() const { return TheMapping.empty(); }
144
145 /// member_* Iterate over the members of an equivalence class.
146 ///
147 class member_iterator;
148 member_iterator member_begin(iterator I) const {
149 // Only leaders provide anything to iterate over.
1a4d82fc 150 return member_iterator(I->isLeader() ? &*I : nullptr);
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151 }
152 member_iterator member_end() const {
1a4d82fc 153 return member_iterator(nullptr);
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154 }
155
156 /// findValue - Return an iterator to the specified value. If it does not
157 /// exist, end() is returned.
158 iterator findValue(const ElemTy &V) const {
159 return TheMapping.find(V);
160 }
161
162 /// getLeaderValue - Return the leader for the specified value that is in the
163 /// set. It is an error to call this method for a value that is not yet in
164 /// the set. For that, call getOrInsertLeaderValue(V).
165 const ElemTy &getLeaderValue(const ElemTy &V) const {
166 member_iterator MI = findLeader(V);
167 assert(MI != member_end() && "Value is not in the set!");
168 return *MI;
169 }
170
171 /// getOrInsertLeaderValue - Return the leader for the specified value that is
172 /// in the set. If the member is not in the set, it is inserted, then
173 /// returned.
174 const ElemTy &getOrInsertLeaderValue(const ElemTy &V) {
175 member_iterator MI = findLeader(insert(V));
176 assert(MI != member_end() && "Value is not in the set!");
177 return *MI;
178 }
179
180 /// getNumClasses - Return the number of equivalence classes in this set.
181 /// Note that this is a linear time operation.
182 unsigned getNumClasses() const {
183 unsigned NC = 0;
184 for (iterator I = begin(), E = end(); I != E; ++I)
185 if (I->isLeader()) ++NC;
186 return NC;
187 }
188
189
190 //===--------------------------------------------------------------------===//
191 // Mutation methods
192
193 /// insert - Insert a new value into the union/find set, ignoring the request
194 /// if the value already exists.
195 iterator insert(const ElemTy &Data) {
196 return TheMapping.insert(ECValue(Data)).first;
197 }
198
199 /// findLeader - Given a value in the set, return a member iterator for the
200 /// equivalence class it is in. This does the path-compression part that
201 /// makes union-find "union findy". This returns an end iterator if the value
202 /// is not in the equivalence class.
203 ///
204 member_iterator findLeader(iterator I) const {
205 if (I == TheMapping.end()) return member_end();
206 return member_iterator(I->getLeader());
207 }
208 member_iterator findLeader(const ElemTy &V) const {
209 return findLeader(TheMapping.find(V));
210 }
211
212
213 /// union - Merge the two equivalence sets for the specified values, inserting
214 /// them if they do not already exist in the equivalence set.
215 member_iterator unionSets(const ElemTy &V1, const ElemTy &V2) {
216 iterator V1I = insert(V1), V2I = insert(V2);
217 return unionSets(findLeader(V1I), findLeader(V2I));
218 }
219 member_iterator unionSets(member_iterator L1, member_iterator L2) {
220 assert(L1 != member_end() && L2 != member_end() && "Illegal inputs!");
221 if (L1 == L2) return L1; // Unifying the same two sets, noop.
222
223 // Otherwise, this is a real union operation. Set the end of the L1 list to
224 // point to the L2 leader node.
225 const ECValue &L1LV = *L1.Node, &L2LV = *L2.Node;
226 L1LV.getEndOfList()->setNext(&L2LV);
227
228 // Update L1LV's end of list pointer.
229 L1LV.Leader = L2LV.getEndOfList();
230
231 // Clear L2's leader flag:
232 L2LV.Next = L2LV.getNext();
233
234 // L2's leader is now L1.
235 L2LV.Leader = &L1LV;
236 return L1;
237 }
238
239 class member_iterator : public std::iterator<std::forward_iterator_tag,
240 const ElemTy, ptrdiff_t> {
241 typedef std::iterator<std::forward_iterator_tag,
242 const ElemTy, ptrdiff_t> super;
243 const ECValue *Node;
244 friend class EquivalenceClasses;
245 public:
246 typedef size_t size_type;
247 typedef typename super::pointer pointer;
248 typedef typename super::reference reference;
249
250 explicit member_iterator() {}
251 explicit member_iterator(const ECValue *N) : Node(N) {}
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252
253 reference operator*() const {
1a4d82fc 254 assert(Node != nullptr && "Dereferencing end()!");
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255 return Node->getData();
256 }
257 reference operator->() const { return operator*(); }
258
259 member_iterator &operator++() {
1a4d82fc 260 assert(Node != nullptr && "++'d off the end of the list!");
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261 Node = Node->getNext();
262 return *this;
263 }
264
265 member_iterator operator++(int) { // postincrement operators.
266 member_iterator tmp = *this;
267 ++*this;
268 return tmp;
269 }
270
271 bool operator==(const member_iterator &RHS) const {
272 return Node == RHS.Node;
273 }
274 bool operator!=(const member_iterator &RHS) const {
275 return Node != RHS.Node;
276 }
277 };
278};
279
280} // End llvm namespace
281
282#endif