//===- llvm/ADT/EquivalenceClasses.h - Generic Equiv. Classes ---*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
///
/// \file
/// 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< or a
/// comparator is provided).
///
/// 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 Compare = std::less<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 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);
}
};
/// A wrapper of the comparator, to be passed to the set.
struct ECValueComparator {
using is_transparent = void;
ECValueComparator() : compare(Compare()) {}
bool operator()(const ECValue &lhs, const ECValue &rhs) const {
return compare(lhs.Data, rhs.Data);
}
template <typename T>
bool operator()(const T &lhs, const ECValue &rhs) const {
return compare(lhs, rhs.Data);
}
template <typename T>
bool operator()(const ECValue &lhs, const T &rhs) const {
return compare(lhs.Data, rhs);
}
const Compare compare;
};
/// 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, ECValueComparator> 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, ECValueComparator>::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 {
friend class EquivalenceClasses;
const ECValue *Node;
public:
using iterator_category = std::forward_iterator_tag;
using value_type = const ElemTy;
using size_type = std::size_t;
using difference_type = std::ptrdiff_t;
using pointer = value_type *;
using reference = value_type &;
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