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+//===- llvm/ADT/SparseMultiSet.h - Sparse multiset --------------*- C++ -*-===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// 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.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_ADT_SPARSEMULTISET_H
+#define LLVM_ADT_SPARSEMULTISET_H
+
+#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 &&
+                !std::numeric_limits<SparseT>::is_signed,
+                "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;
+    --NumFree;
+    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;
+    ++NumFree;
+  }
+
+public:
+  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)
+      return;
+    free(Sparse);
+    // 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;
+
+    SMSPtrTy SMS;
+    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; }
+
+  public:
+    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();
+      else
+        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);
+      --*this;
+      return I;
+    }
+    iterator_base operator++(int) { // postincrement
+      iterator_base I(*this);
+      ++*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().
+    Dense.clear();
+    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)
+        break;
+    }
+    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)
+      ++Ret;
+
+    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.
+    makeTombstone(I.Idx);
+
+    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);
+  }
+
+private:
+  /// 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.
+      findIndex(sparseIndex(N)).setPrev(N.Prev);
+      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
+
+#endif // LLVM_ADT_SPARSEMULTISET_H