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//===- llvm/ADT/SparseMultiSet.h - Sparse multiset --------------*- C++ -*-===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// This file defines the SparseMultiSet class, which adds multiset behavior to
// the SparseSet.
// A sparse multiset holds a small number of objects identified by integer keys
// from a moderately sized universe. The sparse multiset uses more memory than
// other containers in order to provide faster operations. Any key can map to
// multiple values. A SparseMultiSetNode class is provided, which serves as a
// convenient base class for the contents of a SparseMultiSet.
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/SparseSet.h"
#include <cassert>
#include <cstdint>
#include <cstdlib>
#include <iterator>
#include <limits>
#include <utility>
namespace llvm {
/// Fast multiset implementation for objects that can be identified by small
/// unsigned keys.
/// SparseMultiSet allocates memory proportional to the size of the key
/// universe, so it is not recommended for building composite data structures.
/// It is useful for algorithms that require a single set with fast operations.
/// Compared to DenseSet and DenseMap, SparseMultiSet provides constant-time
/// fast clear() as fast as a vector. The find(), insert(), and erase()
/// operations are all constant time, and typically faster than a hash table.
/// The iteration order doesn't depend on numerical key values, it only depends
/// on the order of insert() and erase() operations. Iteration order is the
/// insertion order. Iteration is only provided over elements of equivalent
/// keys, but iterators are bidirectional.
/// Compared to BitVector, SparseMultiSet<unsigned> uses 8x-40x more memory, but
/// offers constant-time clear() and size() operations as well as fast iteration
/// independent on the size of the universe.
/// SparseMultiSet contains a dense vector holding all the objects and a sparse
/// array holding indexes into the dense vector. Most of the memory is used by
/// the sparse array which is the size of the key universe. The SparseT template
/// parameter provides a space/speed tradeoff for sets holding many elements.
/// When SparseT is uint32_t, find() only touches up to 3 cache lines, but the
/// sparse array uses 4 x Universe bytes.
/// When SparseT is uint8_t (the default), find() touches up to 3+[N/256] cache
/// lines, but the sparse array is 4x smaller. N is the number of elements in
/// the set.
/// For sets that may grow to thousands of elements, SparseT should be set to
/// uint16_t or uint32_t.
/// Multiset behavior is provided by providing doubly linked lists for values
/// that are inlined in the dense vector. SparseMultiSet is a good choice when
/// one desires a growable number of entries per key, as it will retain the
/// SparseSet algorithmic properties despite being growable. Thus, it is often a
/// better choice than a SparseSet of growable containers or a vector of
/// vectors. SparseMultiSet also keeps iterators valid after erasure (provided
/// the iterators don't point to the element erased), allowing for more
/// intuitive and fast removal.
/// @tparam ValueT The type of objects in the set.
/// @tparam KeyFunctorT A functor that computes an unsigned index from KeyT.
/// @tparam SparseT An unsigned integer type. See above.
template<typename ValueT,
typename KeyFunctorT = identity<unsigned>,
typename SparseT = uint8_t>
class SparseMultiSet {
static_assert(std::numeric_limits<SparseT>::is_integer &&
"SparseT must be an unsigned integer type");
/// The actual data that's stored, as a doubly-linked list implemented via
/// indices into the DenseVector. The doubly linked list is implemented
/// circular in Prev indices, and INVALID-terminated in Next indices. This
/// provides efficient access to list tails. These nodes can also be
/// tombstones, in which case they are actually nodes in a single-linked
/// freelist of recyclable slots.
struct SMSNode {
static const unsigned INVALID = ~0U;
ValueT Data;
unsigned Prev;
unsigned Next;
SMSNode(ValueT D, unsigned P, unsigned N) : Data(D), Prev(P), Next(N) {}
/// List tails have invalid Nexts.
bool isTail() const {
return Next == INVALID;
/// Whether this node is a tombstone node, and thus is in our freelist.
bool isTombstone() const {
return Prev == INVALID;
/// Since the list is circular in Prev, all non-tombstone nodes have a valid
/// Prev.
bool isValid() const { return Prev != INVALID; }
using KeyT = typename KeyFunctorT::argument_type;
using DenseT = SmallVector<SMSNode, 8>;
DenseT Dense;
SparseT *Sparse = nullptr;
unsigned Universe = 0;
KeyFunctorT KeyIndexOf;
SparseSetValFunctor<KeyT, ValueT, KeyFunctorT> ValIndexOf;
/// We have a built-in recycler for reusing tombstone slots. This recycler
/// puts a singly-linked free list into tombstone slots, allowing us quick
/// erasure, iterator preservation, and dense size.
unsigned FreelistIdx = SMSNode::INVALID;
unsigned NumFree = 0;
unsigned sparseIndex(const ValueT &Val) const {
assert(ValIndexOf(Val) < Universe &&
"Invalid key in set. Did object mutate?");
return ValIndexOf(Val);
unsigned sparseIndex(const SMSNode &N) const { return sparseIndex(N.Data); }
/// Whether the given entry is the head of the list. List heads's previous
/// pointers are to the tail of the list, allowing for efficient access to the
/// list tail. D must be a valid entry node.
bool isHead(const SMSNode &D) const {
assert(D.isValid() && "Invalid node for head");
return Dense[D.Prev].isTail();
/// Whether the given entry is a singleton entry, i.e. the only entry with
/// that key.
bool isSingleton(const SMSNode &N) const {
assert(N.isValid() && "Invalid node for singleton");
// Is N its own predecessor?
return &Dense[N.Prev] == &N;
/// Add in the given SMSNode. Uses a free entry in our freelist if
/// available. Returns the index of the added node.
unsigned addValue(const ValueT& V, unsigned Prev, unsigned Next) {
if (NumFree == 0) {
Dense.push_back(SMSNode(V, Prev, Next));
return Dense.size() - 1;
// Peel off a free slot
unsigned Idx = FreelistIdx;
unsigned NextFree = Dense[Idx].Next;
assert(Dense[Idx].isTombstone() && "Non-tombstone free?");
Dense[Idx] = SMSNode(V, Prev, Next);
FreelistIdx = NextFree;
return Idx;
/// Make the current index a new tombstone. Pushes it onto the freelist.
void makeTombstone(unsigned Idx) {
Dense[Idx].Prev = SMSNode::INVALID;
Dense[Idx].Next = FreelistIdx;
FreelistIdx = Idx;
using value_type = ValueT;
using reference = ValueT &;
using const_reference = const ValueT &;
using pointer = ValueT *;
using const_pointer = const ValueT *;
using size_type = unsigned;
SparseMultiSet() = default;
SparseMultiSet(const SparseMultiSet &) = delete;
SparseMultiSet &operator=(const SparseMultiSet &) = delete;
~SparseMultiSet() { free(Sparse); }
/// Set the universe size which determines the largest key the set can hold.
/// The universe must be sized before any elements can be added.
/// @param U Universe size. All object keys must be less than U.
void setUniverse(unsigned U) {
// It's not hard to resize the universe on a non-empty set, but it doesn't
// seem like a likely use case, so we can add that code when we need it.
assert(empty() && "Can only resize universe on an empty map");
// Hysteresis prevents needless reallocations.
if (U >= Universe/4 && U <= Universe)
// The Sparse array doesn't actually need to be initialized, so malloc
// would be enough here, but that will cause tools like valgrind to
// complain about branching on uninitialized data.
Sparse = static_cast<SparseT*>(safe_calloc(U, sizeof(SparseT)));
Universe = U;
/// Our iterators are iterators over the collection of objects that share a
/// key.
template<typename SMSPtrTy>
class iterator_base : public std::iterator<std::bidirectional_iterator_tag,
ValueT> {
friend class SparseMultiSet;
unsigned Idx;
unsigned SparseIdx;
iterator_base(SMSPtrTy P, unsigned I, unsigned SI)
: SMS(P), Idx(I), SparseIdx(SI) {}
/// Whether our iterator has fallen outside our dense vector.
bool isEnd() const {
if (Idx == SMSNode::INVALID)
return true;
assert(Idx < SMS->Dense.size() && "Out of range, non-INVALID Idx?");
return false;
/// Whether our iterator is properly keyed, i.e. the SparseIdx is valid
bool isKeyed() const { return SparseIdx < SMS->Universe; }
unsigned Prev() const { return SMS->Dense[Idx].Prev; }
unsigned Next() const { return SMS->Dense[Idx].Next; }
void setPrev(unsigned P) { SMS->Dense[Idx].Prev = P; }
void setNext(unsigned N) { SMS->Dense[Idx].Next = N; }
using super = std::iterator<std::bidirectional_iterator_tag, ValueT>;
using value_type = typename super::value_type;
using difference_type = typename super::difference_type;
using pointer = typename super::pointer;
using reference = typename super::reference;
reference operator*() const {
assert(isKeyed() && SMS->sparseIndex(SMS->Dense[Idx].Data) == SparseIdx &&
"Dereferencing iterator of invalid key or index");
return SMS->Dense[Idx].Data;
pointer operator->() const { return &operator*(); }
/// Comparison operators
bool operator==(const iterator_base &RHS) const {
// end compares equal
if (SMS == RHS.SMS && Idx == RHS.Idx) {
assert((isEnd() || SparseIdx == RHS.SparseIdx) &&
"Same dense entry, but different keys?");
return true;
return false;
bool operator!=(const iterator_base &RHS) const {
return !operator==(RHS);
/// Increment and decrement operators
iterator_base &operator--() { // predecrement - Back up
assert(isKeyed() && "Decrementing an invalid iterator");
assert((isEnd() || !SMS->isHead(SMS->Dense[Idx])) &&
"Decrementing head of list");
// If we're at the end, then issue a new find()
if (isEnd())
Idx = SMS->findIndex(SparseIdx).Prev();
Idx = Prev();
return *this;
iterator_base &operator++() { // preincrement - Advance
assert(!isEnd() && isKeyed() && "Incrementing an invalid/end iterator");
Idx = Next();
return *this;
iterator_base operator--(int) { // postdecrement
iterator_base I(*this);
return I;
iterator_base operator++(int) { // postincrement
iterator_base I(*this);
return I;
using iterator = iterator_base<SparseMultiSet *>;
using const_iterator = iterator_base<const SparseMultiSet *>;
// Convenience types
using RangePair = std::pair<iterator, iterator>;
/// Returns an iterator past this container. Note that such an iterator cannot
/// be decremented, but will compare equal to other end iterators.
iterator end() { return iterator(this, SMSNode::INVALID, SMSNode::INVALID); }
const_iterator end() const {
return const_iterator(this, SMSNode::INVALID, SMSNode::INVALID);
/// Returns true if the set is empty.
/// This is not the same as BitVector::empty().
bool empty() const { return size() == 0; }
/// Returns the number of elements in the set.
/// This is not the same as BitVector::size() which returns the size of the
/// universe.
size_type size() const {
assert(NumFree <= Dense.size() && "Out-of-bounds free entries");
return Dense.size() - NumFree;
/// Clears the set. This is a very fast constant time operation.
void clear() {
// Sparse does not need to be cleared, see find().
NumFree = 0;
FreelistIdx = SMSNode::INVALID;
/// Find an element by its index.
/// @param Idx A valid index to find.
/// @returns An iterator to the element identified by key, or end().
iterator findIndex(unsigned Idx) {
assert(Idx < Universe && "Key out of range");
const unsigned Stride = std::numeric_limits<SparseT>::max() + 1u;
for (unsigned i = Sparse[Idx], e = Dense.size(); i < e; i += Stride) {
const unsigned FoundIdx = sparseIndex(Dense[i]);
// Check that we're pointing at the correct entry and that it is the head
// of a valid list.
if (Idx == FoundIdx && Dense[i].isValid() && isHead(Dense[i]))
return iterator(this, i, Idx);
// Stride is 0 when SparseT >= unsigned. We don't need to loop.
if (!Stride)
return end();
/// Find an element by its key.
/// @param Key A valid key to find.
/// @returns An iterator to the element identified by key, or end().
iterator find(const KeyT &Key) {
return findIndex(KeyIndexOf(Key));
const_iterator find(const KeyT &Key) const {
iterator I = const_cast<SparseMultiSet*>(this)->findIndex(KeyIndexOf(Key));
return const_iterator(I.SMS, I.Idx, KeyIndexOf(Key));
/// Returns the number of elements identified by Key. This will be linear in
/// the number of elements of that key.
size_type count(const KeyT &Key) const {
unsigned Ret = 0;
for (const_iterator It = find(Key); It != end(); ++It)
return Ret;
/// Returns true if this set contains an element identified by Key.
bool contains(const KeyT &Key) const {
return find(Key) != end();
/// Return the head and tail of the subset's list, otherwise returns end().
iterator getHead(const KeyT &Key) { return find(Key); }
iterator getTail(const KeyT &Key) {
iterator I = find(Key);
if (I != end())
I = iterator(this, I.Prev(), KeyIndexOf(Key));
return I;
/// The bounds of the range of items sharing Key K. First member is the head
/// of the list, and the second member is a decrementable end iterator for
/// that key.
RangePair equal_range(const KeyT &K) {
iterator B = find(K);
iterator E = iterator(this, SMSNode::INVALID, B.SparseIdx);
return make_pair(B, E);
/// Insert a new element at the tail of the subset list. Returns an iterator
/// to the newly added entry.
iterator insert(const ValueT &Val) {
unsigned Idx = sparseIndex(Val);
iterator I = findIndex(Idx);
unsigned NodeIdx = addValue(Val, SMSNode::INVALID, SMSNode::INVALID);
if (I == end()) {
// Make a singleton list
Sparse[Idx] = NodeIdx;
Dense[NodeIdx].Prev = NodeIdx;
return iterator(this, NodeIdx, Idx);
// Stick it at the end.
unsigned HeadIdx = I.Idx;
unsigned TailIdx = I.Prev();
Dense[TailIdx].Next = NodeIdx;
Dense[HeadIdx].Prev = NodeIdx;
Dense[NodeIdx].Prev = TailIdx;
return iterator(this, NodeIdx, Idx);
/// Erases an existing element identified by a valid iterator.
/// This invalidates iterators pointing at the same entry, but erase() returns
/// an iterator pointing to the next element in the subset's list. This makes
/// it possible to erase selected elements while iterating over the subset:
/// tie(I, E) = Set.equal_range(Key);
/// while (I != E)
/// if (test(*I))
/// I = Set.erase(I);
/// else
/// ++I;
/// Note that if the last element in the subset list is erased, this will
/// return an end iterator which can be decremented to get the new tail (if it
/// exists):
/// tie(B, I) = Set.equal_range(Key);
/// for (bool isBegin = B == I; !isBegin; /* empty */) {
/// isBegin = (--I) == B;
/// if (test(I))
/// break;
/// I = erase(I);
/// }
iterator erase(iterator I) {
assert(I.isKeyed() && !I.isEnd() && !Dense[I.Idx].isTombstone() &&
"erasing invalid/end/tombstone iterator");
// First, unlink the node from its list. Then swap the node out with the
// dense vector's last entry
iterator NextI = unlink(Dense[I.Idx]);
// Put in a tombstone.
return NextI;
/// Erase all elements with the given key. This invalidates all
/// iterators of that key.
void eraseAll(const KeyT &K) {
for (iterator I = find(K); I != end(); /* empty */)
I = erase(I);
/// Unlink the node from its list. Returns the next node in the list.
iterator unlink(const SMSNode &N) {
if (isSingleton(N)) {
// Singleton is already unlinked
assert(N.Next == SMSNode::INVALID && "Singleton has next?");
return iterator(this, SMSNode::INVALID, ValIndexOf(N.Data));
if (isHead(N)) {
// If we're the head, then update the sparse array and our next.
Sparse[sparseIndex(N)] = N.Next;
Dense[N.Next].Prev = N.Prev;
return iterator(this, N.Next, ValIndexOf(N.Data));
if (N.isTail()) {
// If we're the tail, then update our head and our previous.
Dense[N.Prev].Next = N.Next;
// Give back an end iterator that can be decremented
iterator I(this, N.Prev, ValIndexOf(N.Data));
return ++I;
// Otherwise, just drop us
Dense[N.Next].Prev = N.Prev;
Dense[N.Prev].Next = N.Next;
return iterator(this, N.Next, ValIndexOf(N.Data));
} // end namespace llvm