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EquivalenceClasses.h
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1 //===- llvm/ADT/EquivalenceClasses.h - Generic Equiv. Classes ---*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // Generic implementation of equivalence classes through the use Tarjan's
10 // efficient union-find algorithm.
11 //
12 //===----------------------------------------------------------------------===//
13 
14 #ifndef LLVM_ADT_EQUIVALENCECLASSES_H
15 #define LLVM_ADT_EQUIVALENCECLASSES_H
16 
17 #include <cassert>
18 #include <cstddef>
19 #include <cstdint>
20 #include <iterator>
21 #include <set>
22 
23 namespace llvm {
24 
25 /// EquivalenceClasses - This represents a collection of equivalence classes and
26 /// supports three efficient operations: insert an element into a class of its
27 /// own, union two classes, and find the class for a given element. In
28 /// addition to these modification methods, it is possible to iterate over all
29 /// of the equivalence classes and all of the elements in a class.
30 ///
31 /// This implementation is an efficient implementation that only stores one copy
32 /// of the element being indexed per entry in the set, and allows any arbitrary
33 /// type to be indexed (as long as it can be ordered with operator<).
34 ///
35 /// Here is a simple example using integers:
36 ///
37 /// \code
38 /// EquivalenceClasses<int> EC;
39 /// EC.unionSets(1, 2); // insert 1, 2 into the same set
40 /// EC.insert(4); EC.insert(5); // insert 4, 5 into own sets
41 /// EC.unionSets(5, 1); // merge the set for 1 with 5's set.
42 ///
43 /// for (EquivalenceClasses<int>::iterator I = EC.begin(), E = EC.end();
44 /// I != E; ++I) { // Iterate over all of the equivalence sets.
45 /// if (!I->isLeader()) continue; // Ignore non-leader sets.
46 /// for (EquivalenceClasses<int>::member_iterator MI = EC.member_begin(I);
47 /// MI != EC.member_end(); ++MI) // Loop over members in this set.
48 /// cerr << *MI << " "; // Print member.
49 /// cerr << "\n"; // Finish set.
50 /// }
51 /// \endcode
52 ///
53 /// This example prints:
54 /// 4
55 /// 5 1 2
56 ///
57 template <class ElemTy>
59  /// ECValue - The EquivalenceClasses data structure is just a set of these.
60  /// Each of these represents a relation for a value. First it stores the
61  /// value itself, which provides the ordering that the set queries. Next, it
62  /// provides a "next pointer", which is used to enumerate all of the elements
63  /// in the unioned set. Finally, it defines either a "end of list pointer" or
64  /// "leader pointer" depending on whether the value itself is a leader. A
65  /// "leader pointer" points to the node that is the leader for this element,
66  /// if the node is not a leader. A "end of list pointer" points to the last
67  /// node in the list of members of this list. Whether or not a node is a
68  /// leader is determined by a bit stolen from one of the pointers.
69  class ECValue {
70  friend class EquivalenceClasses;
71 
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;
124  operator=(RHS);
125  }
126 
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  using iterator = typename std::set<ECValue>::const_iterator;
145 
146  iterator begin() const { return TheMapping.begin(); }
147  iterator end() const { return TheMapping.end(); }
148 
149  bool empty() const { return TheMapping.empty(); }
150 
151  /// member_* Iterate over the members of an equivalence class.
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  member_iterator findLeader(iterator I) const {
208  if (I == TheMapping.end()) return member_end();
209  return member_iterator(I->getLeader());
210  }
211  member_iterator findLeader(const ElemTy &V) const {
212  return findLeader(TheMapping.find(V));
213  }
214 
215  /// union - Merge the two equivalence sets for the specified values, inserting
216  /// them if they do not already exist in the equivalence set.
217  member_iterator unionSets(const ElemTy &V1, const ElemTy &V2) {
218  iterator V1I = insert(V1), V2I = insert(V2);
219  return unionSets(findLeader(V1I), findLeader(V2I));
220  }
221  member_iterator unionSets(member_iterator L1, member_iterator L2) {
222  assert(L1 != member_end() && L2 != member_end() && "Illegal inputs!");
223  if (L1 == L2) return L1; // Unifying the same two sets, noop.
224 
225  // Otherwise, this is a real union operation. Set the end of the L1 list to
226  // point to the L2 leader node.
227  const ECValue &L1LV = *L1.Node, &L2LV = *L2.Node;
228  L1LV.getEndOfList()->setNext(&L2LV);
229 
230  // Update L1LV's end of list pointer.
231  L1LV.Leader = L2LV.getEndOfList();
232 
233  // Clear L2's leader flag:
234  L2LV.Next = L2LV.getNext();
235 
236  // L2's leader is now L1.
237  L2LV.Leader = &L1LV;
238  return L1;
239  }
240 
241  // isEquivalent - Return true if V1 is equivalent to V2. This can happen if
242  // V1 is equal to V2 or if they belong to one equivalence class.
243  bool isEquivalent(const ElemTy &V1, const ElemTy &V2) const {
244  // Fast path: any element is equivalent to itself.
245  if (V1 == V2)
246  return true;
247  auto It = findLeader(V1);
248  return It != member_end() && It == findLeader(V2);
249  }
250 
251  class member_iterator : public std::iterator<std::forward_iterator_tag,
252  const ElemTy, ptrdiff_t> {
253  friend class EquivalenceClasses;
254 
255  using super = std::iterator<std::forward_iterator_tag,
256  const ElemTy, ptrdiff_t>;
257 
258  const ECValue *Node;
259 
260  public:
261  using size_type = size_t;
262  using pointer = typename super::pointer;
263  using reference = typename super::reference;
264 
265  explicit member_iterator() = default;
266  explicit member_iterator(const ECValue *N) : Node(N) {}
267 
269  assert(Node != nullptr && "Dereferencing end()!");
270  return Node->getData();
271  }
272  pointer operator->() const { return &operator*(); }
273 
275  assert(Node != nullptr && "++'d off the end of the list!");
276  Node = Node->getNext();
277  return *this;
278  }
279 
280  member_iterator operator++(int) { // postincrement operators.
281  member_iterator tmp = *this;
282  ++*this;
283  return tmp;
284  }
285 
286  bool operator==(const member_iterator &RHS) const {
287  return Node == RHS.Node;
288  }
289  bool operator!=(const member_iterator &RHS) const {
290  return Node != RHS.Node;
291  }
292  };
293 };
294 
295 } // end namespace llvm
296 
297 #endif // LLVM_ADT_EQUIVALENCECLASSES_H
This class represents lattice values for constants.
Definition: AllocatorList.h:23
const ElemTy & getLeaderValue(const ElemTy &V) const
getLeaderValue - Return the leader for the specified value that is in the set.
member_iterator unionSets(const ElemTy &V1, const ElemTy &V2)
union - Merge the two equivalence sets for the specified values, inserting them if they do not alread...
APInt operator*(APInt a, uint64_t RHS)
Definition: APInt.h:2090
EquivalenceClasses(const EquivalenceClasses &RHS)
member_iterator member_begin(iterator I) const
iterator insert(const ElemTy &Data)
insert - Insert a new value into the union/find set, ignoring the request if the value already exists...
iterator findValue(const ElemTy &V) const
findValue - Return an iterator to the specified value.
member_iterator findLeader(iterator I) const
findLeader - Given a value in the set, return a member iterator for the equivalence class it is in...
static GCRegistry::Add< CoreCLRGC > E("coreclr", "CoreCLR-compatible GC")
EquivalenceClasses - This represents a collection of equivalence classes and supports three efficient...
member_iterator member_end() const
const EquivalenceClasses & operator=(const EquivalenceClasses &RHS)
const ElemTy & getOrInsertLeaderValue(const ElemTy &V)
getOrInsertLeaderValue - Return the leader for the specified value that is in the set...
#define NC
Definition: regutils.h:42
bool operator!=(const member_iterator &RHS) const
bool operator==(const member_iterator &RHS) const
member_iterator unionSets(member_iterator L1, member_iterator L2)
#define I(x, y, z)
Definition: MD5.cpp:58
#define N
typename std::set< ECValue >::const_iterator iterator
iterator* - Provides a way to iterate over all values in the set.
unsigned getNumClasses() const
getNumClasses - Return the number of equivalence classes in this set.
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
bool operator<(int64_t V1, const APSInt &V2)
Definition: APSInt.h:325
IRTranslator LLVM IR MI
bool isEquivalent(const ElemTy &V1, const ElemTy &V2) const
member_iterator findLeader(const ElemTy &V) const