YQ Connector: support managed ClickHouse

Со стороны dqrun можно обратиться к инстансу коннектора, который работает на streaming стенде, и извлечь данные из облачного CH.

1 files changed, 2185 insertions, 0 deletions

diff --git a/contrib/libs/llvm14/include/llvm/ADT/IntervalMap.h b/contrib/libs/llvm14/include/llvm/ADT/IntervalMap.h
new file mode 100644
index 0000000000..d2493c266e
--- /dev/null
+++ b/contrib/libs/llvm14/include/llvm/ADT/IntervalMap.h
@@ -0,0 +1,2185 @@
+#pragma once
+
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-parameter"
+#endif
+
+//===- llvm/ADT/IntervalMap.h - A sorted interval map -----------*- 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
+/// This file implements a coalescing interval map for small objects.
+///
+/// KeyT objects are mapped to ValT objects. Intervals of keys that map to the
+/// same value are represented in a compressed form.
+///
+/// Iterators provide ordered access to the compressed intervals rather than the
+/// individual keys, and insert and erase operations use key intervals as well.
+///
+/// Like SmallVector, IntervalMap will store the first N intervals in the map
+/// object itself without any allocations. When space is exhausted it switches
+/// to a B+-tree representation with very small overhead for small key and
+/// value objects.
+///
+/// A Traits class specifies how keys are compared. It also allows IntervalMap
+/// to work with both closed and half-open intervals.
+///
+/// Keys and values are not stored next to each other in a std::pair, so we
+/// don't provide such a value_type. Dereferencing iterators only returns the
+/// mapped value. The interval bounds are accessible through the start() and
+/// stop() iterator methods.
+///
+/// IntervalMap is optimized for small key and value objects, 4 or 8 bytes
+/// each is the optimal size. For large objects use std::map instead.
+//
+//===----------------------------------------------------------------------===//
+//
+// Synopsis:
+//
+// template <typename KeyT, typename ValT, unsigned N, typename Traits>
+// class IntervalMap {
+// public:
+//   typedef KeyT key_type;
+//   typedef ValT mapped_type;
+//   typedef RecyclingAllocator<...> Allocator;
+//   class iterator;
+//   class const_iterator;
+//
+//   explicit IntervalMap(Allocator&);
+//   ~IntervalMap():
+//
+//   bool empty() const;
+//   KeyT start() const;
+//   KeyT stop() const;
+//   ValT lookup(KeyT x, Value NotFound = Value()) const;
+//
+//   const_iterator begin() const;
+//   const_iterator end() const;
+//   iterator begin();
+//   iterator end();
+//   const_iterator find(KeyT x) const;
+//   iterator find(KeyT x);
+//
+//   void insert(KeyT a, KeyT b, ValT y);
+//   void clear();
+// };
+//
+// template <typename KeyT, typename ValT, unsigned N, typename Traits>
+// class IntervalMap::const_iterator {
+// public:
+//   using iterator_category = std::bidirectional_iterator_tag;
+//   using value_type = ValT;
+//   using difference_type = std::ptrdiff_t;
+//   using pointer = value_type *;
+//   using reference = value_type &;
+//
+//   bool operator==(const const_iterator &) const;
+//   bool operator!=(const const_iterator &) const;
+//   bool valid() const;
+//
+//   const KeyT &start() const;
+//   const KeyT &stop() const;
+//   const ValT &value() const;
+//   const ValT &operator*() const;
+//   const ValT *operator->() const;
+//
+//   const_iterator &operator++();
+//   const_iterator &operator++(int);
+//   const_iterator &operator--();
+//   const_iterator &operator--(int);
+//   void goToBegin();
+//   void goToEnd();
+//   void find(KeyT x);
+//   void advanceTo(KeyT x);
+// };
+//
+// template <typename KeyT, typename ValT, unsigned N, typename Traits>
+// class IntervalMap::iterator : public const_iterator {
+// public:
+//   void insert(KeyT a, KeyT b, Value y);
+//   void erase();
+// };
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_ADT_INTERVALMAP_H
+#define LLVM_ADT_INTERVALMAP_H
+
+#include "llvm/ADT/PointerIntPair.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/ADT/bit.h"
+#include "llvm/Support/AlignOf.h"
+#include "llvm/Support/Allocator.h"
+#include "llvm/Support/RecyclingAllocator.h"
+#include <algorithm>
+#include <cassert>
+#include <cstdint>
+#include <iterator>
+#include <new>
+#include <utility>
+
+namespace llvm {
+
+//===----------------------------------------------------------------------===//
+//---                              Key traits                              ---//
+//===----------------------------------------------------------------------===//
+//
+// The IntervalMap works with closed or half-open intervals.
+// Adjacent intervals that map to the same value are coalesced.
+//
+// The IntervalMapInfo traits class is used to determine if a key is contained
+// in an interval, and if two intervals are adjacent so they can be coalesced.
+// The provided implementation works for closed integer intervals, other keys
+// probably need a specialized version.
+//
+// The point x is contained in [a;b] when !startLess(x, a) && !stopLess(b, x).
+//
+// It is assumed that (a;b] half-open intervals are not used, only [a;b) is
+// allowed. This is so that stopLess(a, b) can be used to determine if two
+// intervals overlap.
+//
+//===----------------------------------------------------------------------===//
+
+template <typename T>
+struct IntervalMapInfo {
+  /// startLess - Return true if x is not in [a;b].
+  /// This is x < a both for closed intervals and for [a;b) half-open intervals.
+  static inline bool startLess(const T &x, const T &a) {
+    return x < a;
+  }
+
+  /// stopLess - Return true if x is not in [a;b].
+  /// This is b < x for a closed interval, b <= x for [a;b) half-open intervals.
+  static inline bool stopLess(const T &b, const T &x) {
+    return b < x;
+  }
+
+  /// adjacent - Return true when the intervals [x;a] and [b;y] can coalesce.
+  /// This is a+1 == b for closed intervals, a == b for half-open intervals.
+  static inline bool adjacent(const T &a, const T &b) {
+    return a+1 == b;
+  }
+
+  /// nonEmpty - Return true if [a;b] is non-empty.
+  /// This is a <= b for a closed interval, a < b for [a;b) half-open intervals.
+  static inline bool nonEmpty(const T &a, const T &b) {
+    return a <= b;
+  }
+};
+
+template <typename T>
+struct IntervalMapHalfOpenInfo {
+  /// startLess - Return true if x is not in [a;b).
+  static inline bool startLess(const T &x, const T &a) {
+    return x < a;
+  }
+
+  /// stopLess - Return true if x is not in [a;b).
+  static inline bool stopLess(const T &b, const T &x) {
+    return b <= x;
+  }
+
+  /// adjacent - Return true when the intervals [x;a) and [b;y) can coalesce.
+  static inline bool adjacent(const T &a, const T &b) {
+    return a == b;
+  }
+
+  /// nonEmpty - Return true if [a;b) is non-empty.
+  static inline bool nonEmpty(const T &a, const T &b) {
+    return a < b;
+  }
+};
+
+/// IntervalMapImpl - Namespace used for IntervalMap implementation details.
+/// It should be considered private to the implementation.
+namespace IntervalMapImpl {
+
+using IdxPair = std::pair<unsigned,unsigned>;
+
+//===----------------------------------------------------------------------===//
+//---                    IntervalMapImpl::NodeBase                         ---//
+//===----------------------------------------------------------------------===//
+//
+// Both leaf and branch nodes store vectors of pairs.
+// Leaves store ((KeyT, KeyT), ValT) pairs, branches use (NodeRef, KeyT).
+//
+// Keys and values are stored in separate arrays to avoid padding caused by
+// different object alignments. This also helps improve locality of reference
+// when searching the keys.
+//
+// The nodes don't know how many elements they contain - that information is
+// stored elsewhere. Omitting the size field prevents padding and allows a node
+// to fill the allocated cache lines completely.
+//
+// These are typical key and value sizes, the node branching factor (N), and
+// wasted space when nodes are sized to fit in three cache lines (192 bytes):
+//
+//   T1  T2   N Waste  Used by
+//    4   4  24   0    Branch<4> (32-bit pointers)
+//    8   4  16   0    Leaf<4,4>, Branch<4>
+//    8   8  12   0    Leaf<4,8>, Branch<8>
+//   16   4   9  12    Leaf<8,4>
+//   16   8   8   0    Leaf<8,8>
+//
+//===----------------------------------------------------------------------===//
+
+template <typename T1, typename T2, unsigned N>
+class NodeBase {
+public:
+  enum { Capacity = N };
+
+  T1 first[N];
+  T2 second[N];
+
+  /// copy - Copy elements from another node.
+  /// @param Other Node elements are copied from.
+  /// @param i     Beginning of the source range in other.
+  /// @param j     Beginning of the destination range in this.
+  /// @param Count Number of elements to copy.
+  template <unsigned M>
+  void copy(const NodeBase<T1, T2, M> &Other, unsigned i,
+            unsigned j, unsigned Count) {
+    assert(i + Count <= M && "Invalid source range");
+    assert(j + Count <= N && "Invalid dest range");
+    for (unsigned e = i + Count; i != e; ++i, ++j) {
+      first[j]  = Other.first[i];
+      second[j] = Other.second[i];
+    }
+  }
+
+  /// moveLeft - Move elements to the left.
+  /// @param i     Beginning of the source range.
+  /// @param j     Beginning of the destination range.
+  /// @param Count Number of elements to copy.
+  void moveLeft(unsigned i, unsigned j, unsigned Count) {
+    assert(j <= i && "Use moveRight shift elements right");
+    copy(*this, i, j, Count);
+  }
+
+  /// moveRight - Move elements to the right.
+  /// @param i     Beginning of the source range.
+  /// @param j     Beginning of the destination range.
+  /// @param Count Number of elements to copy.
+  void moveRight(unsigned i, unsigned j, unsigned Count) {
+    assert(i <= j && "Use moveLeft shift elements left");
+    assert(j + Count <= N && "Invalid range");
+    while (Count--) {
+      first[j + Count]  = first[i + Count];
+      second[j + Count] = second[i + Count];
+    }
+  }
+
+  /// erase - Erase elements [i;j).
+  /// @param i    Beginning of the range to erase.
+  /// @param j    End of the range. (Exclusive).
+  /// @param Size Number of elements in node.
+  void erase(unsigned i, unsigned j, unsigned Size) {
+    moveLeft(j, i, Size - j);
+  }
+
+  /// erase - Erase element at i.
+  /// @param i    Index of element to erase.
+  /// @param Size Number of elements in node.
+  void erase(unsigned i, unsigned Size) {
+    erase(i, i+1, Size);
+  }
+
+  /// shift - Shift elements [i;size) 1 position to the right.
+  /// @param i    Beginning of the range to move.
+  /// @param Size Number of elements in node.
+  void shift(unsigned i, unsigned Size) {
+    moveRight(i, i + 1, Size - i);
+  }
+
+  /// transferToLeftSib - Transfer elements to a left sibling node.
+  /// @param Size  Number of elements in this.
+  /// @param Sib   Left sibling node.
+  /// @param SSize Number of elements in sib.
+  /// @param Count Number of elements to transfer.
+  void transferToLeftSib(unsigned Size, NodeBase &Sib, unsigned SSize,
+                         unsigned Count) {
+    Sib.copy(*this, 0, SSize, Count);
+    erase(0, Count, Size);
+  }
+
+  /// transferToRightSib - Transfer elements to a right sibling node.
+  /// @param Size  Number of elements in this.
+  /// @param Sib   Right sibling node.
+  /// @param SSize Number of elements in sib.
+  /// @param Count Number of elements to transfer.
+  void transferToRightSib(unsigned Size, NodeBase &Sib, unsigned SSize,
+                          unsigned Count) {
+    Sib.moveRight(0, Count, SSize);
+    Sib.copy(*this, Size-Count, 0, Count);
+  }
+
+  /// adjustFromLeftSib - Adjust the number if elements in this node by moving
+  /// elements to or from a left sibling node.
+  /// @param Size  Number of elements in this.
+  /// @param Sib   Right sibling node.
+  /// @param SSize Number of elements in sib.
+  /// @param Add   The number of elements to add to this node, possibly < 0.
+  /// @return      Number of elements added to this node, possibly negative.
+  int adjustFromLeftSib(unsigned Size, NodeBase &Sib, unsigned SSize, int Add) {
+    if (Add > 0) {
+      // We want to grow, copy from sib.
+      unsigned Count = std::min(std::min(unsigned(Add), SSize), N - Size);
+      Sib.transferToRightSib(SSize, *this, Size, Count);
+      return Count;
+    } else {
+      // We want to shrink, copy to sib.
+      unsigned Count = std::min(std::min(unsigned(-Add), Size), N - SSize);
+      transferToLeftSib(Size, Sib, SSize, Count);
+      return -Count;
+    }
+  }
+};
+
+/// IntervalMapImpl::adjustSiblingSizes - Move elements between sibling nodes.
+/// @param Node  Array of pointers to sibling nodes.
+/// @param Nodes Number of nodes.
+/// @param CurSize Array of current node sizes, will be overwritten.
+/// @param NewSize Array of desired node sizes.
+template <typename NodeT>
+void adjustSiblingSizes(NodeT *Node[], unsigned Nodes,
+                        unsigned CurSize[], const unsigned NewSize[]) {
+  // Move elements right.
+  for (int n = Nodes - 1; n; --n) {
+    if (CurSize[n] == NewSize[n])
+      continue;
+    for (int m = n - 1; m != -1; --m) {
+      int d = Node[n]->adjustFromLeftSib(CurSize[n], *Node[m], CurSize[m],
+                                         NewSize[n] - CurSize[n]);
+      CurSize[m] -= d;
+      CurSize[n] += d;
+      // Keep going if the current node was exhausted.
+      if (CurSize[n] >= NewSize[n])
+          break;
+    }
+  }
+
+  if (Nodes == 0)
+    return;
+
+  // Move elements left.
+  for (unsigned n = 0; n != Nodes - 1; ++n) {
+    if (CurSize[n] == NewSize[n])
+      continue;
+    for (unsigned m = n + 1; m != Nodes; ++m) {
+      int d = Node[m]->adjustFromLeftSib(CurSize[m], *Node[n], CurSize[n],
+                                        CurSize[n] -  NewSize[n]);
+      CurSize[m] += d;
+      CurSize[n] -= d;
+      // Keep going if the current node was exhausted.
+      if (CurSize[n] >= NewSize[n])
+          break;
+    }
+  }
+
+#ifndef NDEBUG
+  for (unsigned n = 0; n != Nodes; n++)
+    assert(CurSize[n] == NewSize[n] && "Insufficient element shuffle");
+#endif
+}
+
+/// IntervalMapImpl::distribute - Compute a new distribution of node elements
+/// after an overflow or underflow. Reserve space for a new element at Position,
+/// and compute the node that will hold Position after redistributing node
+/// elements.
+///
+/// It is required that
+///
+///   Elements == sum(CurSize), and
+///   Elements + Grow <= Nodes * Capacity.
+///
+/// NewSize[] will be filled in such that:
+///
+///   sum(NewSize) == Elements, and
+///   NewSize[i] <= Capacity.
+///
+/// The returned index is the node where Position will go, so:
+///
+///   sum(NewSize[0..idx-1]) <= Position
+///   sum(NewSize[0..idx])   >= Position
+///
+/// The last equality, sum(NewSize[0..idx]) == Position, can only happen when
+/// Grow is set and NewSize[idx] == Capacity-1. The index points to the node
+/// before the one holding the Position'th element where there is room for an
+/// insertion.
+///
+/// @param Nodes    The number of nodes.
+/// @param Elements Total elements in all nodes.
+/// @param Capacity The capacity of each node.
+/// @param CurSize  Array[Nodes] of current node sizes, or NULL.
+/// @param NewSize  Array[Nodes] to receive the new node sizes.
+/// @param Position Insert position.
+/// @param Grow     Reserve space for a new element at Position.
+/// @return         (node, offset) for Position.
+IdxPair distribute(unsigned Nodes, unsigned Elements, unsigned Capacity,
+                   const unsigned *CurSize, unsigned NewSize[],
+                   unsigned Position, bool Grow);
+
+//===----------------------------------------------------------------------===//
+//---                   IntervalMapImpl::NodeSizer                         ---//
+//===----------------------------------------------------------------------===//
+//
+// Compute node sizes from key and value types.
+//
+// The branching factors are chosen to make nodes fit in three cache lines.
+// This may not be possible if keys or values are very large. Such large objects
+// are handled correctly, but a std::map would probably give better performance.
+//
+//===----------------------------------------------------------------------===//
+
+enum {
+  // Cache line size. Most architectures have 32 or 64 byte cache lines.
+  // We use 64 bytes here because it provides good branching factors.
+  Log2CacheLine = 6,
+  CacheLineBytes = 1 << Log2CacheLine,
+  DesiredNodeBytes = 3 * CacheLineBytes
+};
+
+template <typename KeyT, typename ValT>
+struct NodeSizer {
+  enum {
+    // Compute the leaf node branching factor that makes a node fit in three
+    // cache lines. The branching factor must be at least 3, or some B+-tree
+    // balancing algorithms won't work.
+    // LeafSize can't be larger than CacheLineBytes. This is required by the
+    // PointerIntPair used by NodeRef.
+    DesiredLeafSize = DesiredNodeBytes /
+      static_cast<unsigned>(2*sizeof(KeyT)+sizeof(ValT)),
+    MinLeafSize = 3,
+    LeafSize = DesiredLeafSize > MinLeafSize ? DesiredLeafSize : MinLeafSize
+  };
+
+  using LeafBase = NodeBase<std::pair<KeyT, KeyT>, ValT, LeafSize>;
+
+  enum {
+    // Now that we have the leaf branching factor, compute the actual allocation
+    // unit size by rounding up to a whole number of cache lines.
+    AllocBytes = (sizeof(LeafBase) + CacheLineBytes-1) & ~(CacheLineBytes-1),
+
+    // Determine the branching factor for branch nodes.
+    BranchSize = AllocBytes /
+      static_cast<unsigned>(sizeof(KeyT) + sizeof(void*))
+  };
+
+  /// Allocator - The recycling allocator used for both branch and leaf nodes.
+  /// This typedef is very likely to be identical for all IntervalMaps with
+  /// reasonably sized entries, so the same allocator can be shared among
+  /// different kinds of maps.
+  using Allocator =
+      RecyclingAllocator<BumpPtrAllocator, char, AllocBytes, CacheLineBytes>;
+};
+
+//===----------------------------------------------------------------------===//
+//---                     IntervalMapImpl::NodeRef                         ---//
+//===----------------------------------------------------------------------===//
+//
+// B+-tree nodes can be leaves or branches, so we need a polymorphic node
+// pointer that can point to both kinds.
+//
+// All nodes are cache line aligned and the low 6 bits of a node pointer are
+// always 0. These bits are used to store the number of elements in the
+// referenced node. Besides saving space, placing node sizes in the parents
+// allow tree balancing algorithms to run without faulting cache lines for nodes
+// that may not need to be modified.
+//
+// A NodeRef doesn't know whether it references a leaf node or a branch node.
+// It is the responsibility of the caller to use the correct types.
+//
+// Nodes are never supposed to be empty, and it is invalid to store a node size
+// of 0 in a NodeRef. The valid range of sizes is 1-64.
+//
+//===----------------------------------------------------------------------===//
+
+class NodeRef {
+  struct CacheAlignedPointerTraits {
+    static inline void *getAsVoidPointer(void *P) { return P; }
+    static inline void *getFromVoidPointer(void *P) { return P; }
+    static constexpr int NumLowBitsAvailable = Log2CacheLine;
+  };
+  PointerIntPair<void*, Log2CacheLine, unsigned, CacheAlignedPointerTraits> pip;
+
+public:
+  /// NodeRef - Create a null ref.
+  NodeRef() = default;
+
+  /// operator bool - Detect a null ref.
+  explicit operator bool() const { return pip.getOpaqueValue(); }
+
+  /// NodeRef - Create a reference to the node p with n elements.
+  template <typename NodeT>
+  NodeRef(NodeT *p, unsigned n) : pip(p, n - 1) {
+    assert(n <= NodeT::Capacity && "Size too big for node");
+  }
+
+  /// size - Return the number of elements in the referenced node.
+  unsigned size() const { return pip.getInt() + 1; }
+
+  /// setSize - Update the node size.
+  void setSize(unsigned n) { pip.setInt(n - 1); }
+
+  /// subtree - Access the i'th subtree reference in a branch node.
+  /// This depends on branch nodes storing the NodeRef array as their first
+  /// member.
+  NodeRef &subtree(unsigned i) const {
+    return reinterpret_cast<NodeRef*>(pip.getPointer())[i];
+  }
+
+  /// get - Dereference as a NodeT reference.
+  template <typename NodeT>
+  NodeT &get() const {
+    return *reinterpret_cast<NodeT*>(pip.getPointer());
+  }
+
+  bool operator==(const NodeRef &RHS) const {
+    if (pip == RHS.pip)
+      return true;
+    assert(pip.getPointer() != RHS.pip.getPointer() && "Inconsistent NodeRefs");
+    return false;
+  }
+
+  bool operator!=(const NodeRef &RHS) const {
+    return !operator==(RHS);
+  }
+};
+
+//===----------------------------------------------------------------------===//
+//---                      IntervalMapImpl::LeafNode                       ---//
+//===----------------------------------------------------------------------===//
+//
+// Leaf nodes store up to N disjoint intervals with corresponding values.
+//
+// The intervals are kept sorted and fully coalesced so there are no adjacent
+// intervals mapping to the same value.
+//
+// These constraints are always satisfied:
+//
+// - Traits::stopLess(start(i), stop(i))    - Non-empty, sane intervals.
+//
+// - Traits::stopLess(stop(i), start(i + 1) - Sorted.
+//
+// - value(i) != value(i + 1) || !Traits::adjacent(stop(i), start(i + 1))
+//                                          - Fully coalesced.
+//
+//===----------------------------------------------------------------------===//
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+class LeafNode : public NodeBase<std::pair<KeyT, KeyT>, ValT, N> {
+public:
+  const KeyT &start(unsigned i) const { return this->first[i].first; }
+  const KeyT &stop(unsigned i) const { return this->first[i].second; }
+  const ValT &value(unsigned i) const { return this->second[i]; }
+
+  KeyT &start(unsigned i) { return this->first[i].first; }
+  KeyT &stop(unsigned i) { return this->first[i].second; }
+  ValT &value(unsigned i) { return this->second[i]; }
+
+  /// findFrom - Find the first interval after i that may contain x.
+  /// @param i    Starting index for the search.
+  /// @param Size Number of elements in node.
+  /// @param x    Key to search for.
+  /// @return     First index with !stopLess(key[i].stop, x), or size.
+  ///             This is the first interval that can possibly contain x.
+  unsigned findFrom(unsigned i, unsigned Size, KeyT x) const {
+    assert(i <= Size && Size <= N && "Bad indices");
+    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
+           "Index is past the needed point");
+    while (i != Size && Traits::stopLess(stop(i), x)) ++i;
+    return i;
+  }
+
+  /// safeFind - Find an interval that is known to exist. This is the same as
+  /// findFrom except is it assumed that x is at least within range of the last
+  /// interval.
+  /// @param i Starting index for the search.
+  /// @param x Key to search for.
+  /// @return  First index with !stopLess(key[i].stop, x), never size.
+  ///          This is the first interval that can possibly contain x.
+  unsigned safeFind(unsigned i, KeyT x) const {
+    assert(i < N && "Bad index");
+    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
+           "Index is past the needed point");
+    while (Traits::stopLess(stop(i), x)) ++i;
+    assert(i < N && "Unsafe intervals");
+    return i;
+  }
+
+  /// safeLookup - Lookup mapped value for a safe key.
+  /// It is assumed that x is within range of the last entry.
+  /// @param x        Key to search for.
+  /// @param NotFound Value to return if x is not in any interval.
+  /// @return         The mapped value at x or NotFound.
+  ValT safeLookup(KeyT x, ValT NotFound) const {
+    unsigned i = safeFind(0, x);
+    return Traits::startLess(x, start(i)) ? NotFound : value(i);
+  }
+
+  unsigned insertFrom(unsigned &Pos, unsigned Size, KeyT a, KeyT b, ValT y);
+};
+
+/// insertFrom - Add mapping of [a;b] to y if possible, coalescing as much as
+/// possible. This may cause the node to grow by 1, or it may cause the node
+/// to shrink because of coalescing.
+/// @param Pos  Starting index = insertFrom(0, size, a)
+/// @param Size Number of elements in node.
+/// @param a    Interval start.
+/// @param b    Interval stop.
+/// @param y    Value be mapped.
+/// @return     (insert position, new size), or (i, Capacity+1) on overflow.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+unsigned LeafNode<KeyT, ValT, N, Traits>::
+insertFrom(unsigned &Pos, unsigned Size, KeyT a, KeyT b, ValT y) {
+  unsigned i = Pos;
+  assert(i <= Size && Size <= N && "Invalid index");
+  assert(!Traits::stopLess(b, a) && "Invalid interval");
+
+  // Verify the findFrom invariant.
+  assert((i == 0 || Traits::stopLess(stop(i - 1), a)));
+  assert((i == Size || !Traits::stopLess(stop(i), a)));
+  assert((i == Size || Traits::stopLess(b, start(i))) && "Overlapping insert");
+
+  // Coalesce with previous interval.
+  if (i && value(i - 1) == y && Traits::adjacent(stop(i - 1), a)) {
+    Pos = i - 1;
+    // Also coalesce with next interval?
+    if (i != Size && value(i) == y && Traits::adjacent(b, start(i))) {
+      stop(i - 1) = stop(i);
+      this->erase(i, Size);
+      return Size - 1;
+    }
+    stop(i - 1) = b;
+    return Size;
+  }
+
+  // Detect overflow.
+  if (i == N)
+    return N + 1;
+
+  // Add new interval at end.
+  if (i == Size) {
+    start(i) = a;
+    stop(i) = b;
+    value(i) = y;
+    return Size + 1;
+  }
+
+  // Try to coalesce with following interval.
+  if (value(i) == y && Traits::adjacent(b, start(i))) {
+    start(i) = a;
+    return Size;
+  }
+
+  // We must insert before i. Detect overflow.
+  if (Size == N)
+    return N + 1;
+
+  // Insert before i.
+  this->shift(i, Size);
+  start(i) = a;
+  stop(i) = b;
+  value(i) = y;
+  return Size + 1;
+}
+
+//===----------------------------------------------------------------------===//
+//---                   IntervalMapImpl::BranchNode                        ---//
+//===----------------------------------------------------------------------===//
+//
+// A branch node stores references to 1--N subtrees all of the same height.
+//
+// The key array in a branch node holds the rightmost stop key of each subtree.
+// It is redundant to store the last stop key since it can be found in the
+// parent node, but doing so makes tree balancing a lot simpler.
+//
+// It is unusual for a branch node to only have one subtree, but it can happen
+// in the root node if it is smaller than the normal nodes.
+//
+// When all of the leaf nodes from all the subtrees are concatenated, they must
+// satisfy the same constraints as a single leaf node. They must be sorted,
+// sane, and fully coalesced.
+//
+//===----------------------------------------------------------------------===//
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+class BranchNode : public NodeBase<NodeRef, KeyT, N> {
+public:
+  const KeyT &stop(unsigned i) const { return this->second[i]; }
+  const NodeRef &subtree(unsigned i) const { return this->first[i]; }
+
+  KeyT &stop(unsigned i) { return this->second[i]; }
+  NodeRef &subtree(unsigned i) { return this->first[i]; }
+
+  /// findFrom - Find the first subtree after i that may contain x.
+  /// @param i    Starting index for the search.
+  /// @param Size Number of elements in node.
+  /// @param x    Key to search for.
+  /// @return     First index with !stopLess(key[i], x), or size.
+  ///             This is the first subtree that can possibly contain x.
+  unsigned findFrom(unsigned i, unsigned Size, KeyT x) const {
+    assert(i <= Size && Size <= N && "Bad indices");
+    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
+           "Index to findFrom is past the needed point");
+    while (i != Size && Traits::stopLess(stop(i), x)) ++i;
+    return i;
+  }
+
+  /// safeFind - Find a subtree that is known to exist. This is the same as
+  /// findFrom except is it assumed that x is in range.
+  /// @param i Starting index for the search.
+  /// @param x Key to search for.
+  /// @return  First index with !stopLess(key[i], x), never size.
+  ///          This is the first subtree that can possibly contain x.
+  unsigned safeFind(unsigned i, KeyT x) const {
+    assert(i < N && "Bad index");
+    assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
+           "Index is past the needed point");
+    while (Traits::stopLess(stop(i), x)) ++i;
+    assert(i < N && "Unsafe intervals");
+    return i;
+  }
+
+  /// safeLookup - Get the subtree containing x, Assuming that x is in range.
+  /// @param x Key to search for.
+  /// @return  Subtree containing x
+  NodeRef safeLookup(KeyT x) const {
+    return subtree(safeFind(0, x));
+  }
+
+  /// insert - Insert a new (subtree, stop) pair.
+  /// @param i    Insert position, following entries will be shifted.
+  /// @param Size Number of elements in node.
+  /// @param Node Subtree to insert.
+  /// @param Stop Last key in subtree.
+  void insert(unsigned i, unsigned Size, NodeRef Node, KeyT Stop) {
+    assert(Size < N && "branch node overflow");
+    assert(i <= Size && "Bad insert position");
+    this->shift(i, Size);
+    subtree(i) = Node;
+    stop(i) = Stop;
+  }
+};
+
+//===----------------------------------------------------------------------===//
+//---                         IntervalMapImpl::Path                        ---//
+//===----------------------------------------------------------------------===//
+//
+// A Path is used by iterators to represent a position in a B+-tree, and the
+// path to get there from the root.
+//
+// The Path class also contains the tree navigation code that doesn't have to
+// be templatized.
+//
+//===----------------------------------------------------------------------===//
+
+class Path {
+  /// Entry - Each step in the path is a node pointer and an offset into that
+  /// node.
+  struct Entry {
+    void *node;
+    unsigned size;
+    unsigned offset;
+
+    Entry(void *Node, unsigned Size, unsigned Offset)
+      : node(Node), size(Size), offset(Offset) {}
+
+    Entry(NodeRef Node, unsigned Offset)
+      : node(&Node.subtree(0)), size(Node.size()), offset(Offset) {}
+
+    NodeRef &subtree(unsigned i) const {
+      return reinterpret_cast<NodeRef*>(node)[i];
+    }
+  };
+
+  /// path - The path entries, path[0] is the root node, path.back() is a leaf.
+  SmallVector<Entry, 4> path;
+
+public:
+  // Node accessors.
+  template <typename NodeT> NodeT &node(unsigned Level) const {
+    return *reinterpret_cast<NodeT*>(path[Level].node);
+  }
+  unsigned size(unsigned Level) const { return path[Level].size; }
+  unsigned offset(unsigned Level) const { return path[Level].offset; }
+  unsigned &offset(unsigned Level) { return path[Level].offset; }
+
+  // Leaf accessors.
+  template <typename NodeT> NodeT &leaf() const {
+    return *reinterpret_cast<NodeT*>(path.back().node);
+  }
+  unsigned leafSize() const { return path.back().size; }
+  unsigned leafOffset() const { return path.back().offset; }
+  unsigned &leafOffset() { return path.back().offset; }
+
+  /// valid - Return true if path is at a valid node, not at end().
+  bool valid() const {
+    return !path.empty() && path.front().offset < path.front().size;
+  }
+
+  /// height - Return the height of the tree corresponding to this path.
+  /// This matches map->height in a full path.
+  unsigned height() const { return path.size() - 1; }
+
+  /// subtree - Get the subtree referenced from Level. When the path is
+  /// consistent, node(Level + 1) == subtree(Level).
+  /// @param Level 0..height-1. The leaves have no subtrees.
+  NodeRef &subtree(unsigned Level) const {
+    return path[Level].subtree(path[Level].offset);
+  }
+
+  /// reset - Reset cached information about node(Level) from subtree(Level -1).
+  /// @param Level 1..height. The node to update after parent node changed.
+  void reset(unsigned Level) {
+    path[Level] = Entry(subtree(Level - 1), offset(Level));
+  }
+
+  /// push - Add entry to path.
+  /// @param Node Node to add, should be subtree(path.size()-1).
+  /// @param Offset Offset into Node.
+  void push(NodeRef Node, unsigned Offset) {
+    path.push_back(Entry(Node, Offset));
+  }
+
+  /// pop - Remove the last path entry.
+  void pop() {
+    path.pop_back();
+  }
+
+  /// setSize - Set the size of a node both in the path and in the tree.
+  /// @param Level 0..height. Note that setting the root size won't change
+  ///              map->rootSize.
+  /// @param Size New node size.
+  void setSize(unsigned Level, unsigned Size) {
+    path[Level].size = Size;
+    if (Level)
+      subtree(Level - 1).setSize(Size);
+  }
+
+  /// setRoot - Clear the path and set a new root node.
+  /// @param Node New root node.
+  /// @param Size New root size.
+  /// @param Offset Offset into root node.
+  void setRoot(void *Node, unsigned Size, unsigned Offset) {
+    path.clear();
+    path.push_back(Entry(Node, Size, Offset));
+  }
+
+  /// replaceRoot - Replace the current root node with two new entries after the
+  /// tree height has increased.
+  /// @param Root The new root node.
+  /// @param Size Number of entries in the new root.
+  /// @param Offsets Offsets into the root and first branch nodes.
+  void replaceRoot(void *Root, unsigned Size, IdxPair Offsets);
+
+  /// getLeftSibling - Get the left sibling node at Level, or a null NodeRef.
+  /// @param Level Get the sibling to node(Level).
+  /// @return Left sibling, or NodeRef().
+  NodeRef getLeftSibling(unsigned Level) const;
+
+  /// moveLeft - Move path to the left sibling at Level. Leave nodes below Level
+  /// unaltered.
+  /// @param Level Move node(Level).
+  void moveLeft(unsigned Level);
+
+  /// fillLeft - Grow path to Height by taking leftmost branches.
+  /// @param Height The target height.
+  void fillLeft(unsigned Height) {
+    while (height() < Height)
+      push(subtree(height()), 0);
+  }
+
+  /// getLeftSibling - Get the left sibling node at Level, or a null NodeRef.
+  /// @param Level Get the sibling to node(Level).
+  /// @return Left sibling, or NodeRef().
+  NodeRef getRightSibling(unsigned Level) const;
+
+  /// moveRight - Move path to the left sibling at Level. Leave nodes below
+  /// Level unaltered.
+  /// @param Level Move node(Level).
+  void moveRight(unsigned Level);
+
+  /// atBegin - Return true if path is at begin().
+  bool atBegin() const {
+    for (unsigned i = 0, e = path.size(); i != e; ++i)
+      if (path[i].offset != 0)
+        return false;
+    return true;
+  }
+
+  /// atLastEntry - Return true if the path is at the last entry of the node at
+  /// Level.
+  /// @param Level Node to examine.
+  bool atLastEntry(unsigned Level) const {
+    return path[Level].offset == path[Level].size - 1;
+  }
+
+  /// legalizeForInsert - Prepare the path for an insertion at Level. When the
+  /// path is at end(), node(Level) may not be a legal node. legalizeForInsert
+  /// ensures that node(Level) is real by moving back to the last node at Level,
+  /// and setting offset(Level) to size(Level) if required.
+  /// @param Level The level where an insertion is about to take place.
+  void legalizeForInsert(unsigned Level) {
+    if (valid())
+      return;
+    moveLeft(Level);
+    ++path[Level].offset;
+  }
+};
+
+} // end namespace IntervalMapImpl
+
+//===----------------------------------------------------------------------===//
+//---                          IntervalMap                                ----//
+//===----------------------------------------------------------------------===//
+
+template <typename KeyT, typename ValT,
+          unsigned N = IntervalMapImpl::NodeSizer<KeyT, ValT>::LeafSize,
+          typename Traits = IntervalMapInfo<KeyT>>
+class IntervalMap {
+  using Sizer = IntervalMapImpl::NodeSizer<KeyT, ValT>;
+  using Leaf = IntervalMapImpl::LeafNode<KeyT, ValT, Sizer::LeafSize, Traits>;
+  using Branch =
+      IntervalMapImpl::BranchNode<KeyT, ValT, Sizer::BranchSize, Traits>;
+  using RootLeaf = IntervalMapImpl::LeafNode<KeyT, ValT, N, Traits>;
+  using IdxPair = IntervalMapImpl::IdxPair;
+
+  // The RootLeaf capacity is given as a template parameter. We must compute the
+  // corresponding RootBranch capacity.
+  enum {
+    DesiredRootBranchCap = (sizeof(RootLeaf) - sizeof(KeyT)) /
+      (sizeof(KeyT) + sizeof(IntervalMapImpl::NodeRef)),
+    RootBranchCap = DesiredRootBranchCap ? DesiredRootBranchCap : 1
+  };
+
+  using RootBranch =
+      IntervalMapImpl::BranchNode<KeyT, ValT, RootBranchCap, Traits>;
+
+  // When branched, we store a global start key as well as the branch node.
+  struct RootBranchData {
+    KeyT start;
+    RootBranch node;
+  };
+
+public:
+  using Allocator = typename Sizer::Allocator;
+  using KeyType = KeyT;
+  using ValueType = ValT;
+  using KeyTraits = Traits;
+
+private:
+  // The root data is either a RootLeaf or a RootBranchData instance.
+  AlignedCharArrayUnion<RootLeaf, RootBranchData> data;
+
+  // Tree height.
+  // 0: Leaves in root.
+  // 1: Root points to leaf.
+  // 2: root->branch->leaf ...
+  unsigned height;
+
+  // Number of entries in the root node.
+  unsigned rootSize;
+
+  // Allocator used for creating external nodes.
+  Allocator &allocator;
+
+  /// Represent data as a node type without breaking aliasing rules.
+  template <typename T> T &dataAs() const { return *llvm::bit_cast<T *>(&data); }
+
+  const RootLeaf &rootLeaf() const {
+    assert(!branched() && "Cannot acces leaf data in branched root");
+    return dataAs<RootLeaf>();
+  }
+  RootLeaf &rootLeaf() {
+    assert(!branched() && "Cannot acces leaf data in branched root");
+    return dataAs<RootLeaf>();
+  }
+
+  RootBranchData &rootBranchData() const {
+    assert(branched() && "Cannot access branch data in non-branched root");
+    return dataAs<RootBranchData>();
+  }
+  RootBranchData &rootBranchData() {
+    assert(branched() && "Cannot access branch data in non-branched root");
+    return dataAs<RootBranchData>();
+  }
+
+  const RootBranch &rootBranch() const { return rootBranchData().node; }
+  RootBranch &rootBranch()             { return rootBranchData().node; }
+  KeyT rootBranchStart() const { return rootBranchData().start; }
+  KeyT &rootBranchStart()      { return rootBranchData().start; }
+
+  template <typename NodeT> NodeT *newNode() {
+    return new(allocator.template Allocate<NodeT>()) NodeT();
+  }
+
+  template <typename NodeT> void deleteNode(NodeT *P) {
+    P->~NodeT();
+    allocator.Deallocate(P);
+  }
+
+  IdxPair branchRoot(unsigned Position);
+  IdxPair splitRoot(unsigned Position);
+
+  void switchRootToBranch() {
+    rootLeaf().~RootLeaf();
+    height = 1;
+    new (&rootBranchData()) RootBranchData();
+  }
+
+  void switchRootToLeaf() {
+    rootBranchData().~RootBranchData();
+    height = 0;
+    new(&rootLeaf()) RootLeaf();
+  }
+
+  bool branched() const { return height > 0; }
+
+  ValT treeSafeLookup(KeyT x, ValT NotFound) const;
+  void visitNodes(void (IntervalMap::*f)(IntervalMapImpl::NodeRef,
+                  unsigned Level));
+  void deleteNode(IntervalMapImpl::NodeRef Node, unsigned Level);
+
+public:
+  explicit IntervalMap(Allocator &a) : height(0), rootSize(0), allocator(a) {
+    assert((uintptr_t(&data) & (alignof(RootLeaf) - 1)) == 0 &&
+           "Insufficient alignment");
+    new(&rootLeaf()) RootLeaf();
+  }
+
+  ~IntervalMap() {
+    clear();
+    rootLeaf().~RootLeaf();
+  }
+
+  /// empty -  Return true when no intervals are mapped.
+  bool empty() const {
+    return rootSize == 0;
+  }
+
+  /// start - Return the smallest mapped key in a non-empty map.
+  KeyT start() const {
+    assert(!empty() && "Empty IntervalMap has no start");
+    return !branched() ? rootLeaf().start(0) : rootBranchStart();
+  }
+
+  /// stop - Return the largest mapped key in a non-empty map.
+  KeyT stop() const {
+    assert(!empty() && "Empty IntervalMap has no stop");
+    return !branched() ? rootLeaf().stop(rootSize - 1) :
+                         rootBranch().stop(rootSize - 1);
+  }
+
+  /// lookup - Return the mapped value at x or NotFound.
+  ValT lookup(KeyT x, ValT NotFound = ValT()) const {
+    if (empty() || Traits::startLess(x, start()) || Traits::stopLess(stop(), x))
+      return NotFound;
+    return branched() ? treeSafeLookup(x, NotFound) :
+                        rootLeaf().safeLookup(x, NotFound);
+  }
+
+  /// insert - Add a mapping of [a;b] to y, coalesce with adjacent intervals.
+  /// It is assumed that no key in the interval is mapped to another value, but
+  /// overlapping intervals already mapped to y will be coalesced.
+  void insert(KeyT a, KeyT b, ValT y) {
+    if (branched() || rootSize == RootLeaf::Capacity)
+      return find(a).insert(a, b, y);
+
+    // Easy insert into root leaf.
+    unsigned p = rootLeaf().findFrom(0, rootSize, a);
+    rootSize = rootLeaf().insertFrom(p, rootSize, a, b, y);
+  }
+
+  /// clear - Remove all entries.
+  void clear();
+
+  class const_iterator;
+  class iterator;
+  friend class const_iterator;
+  friend class iterator;
+
+  const_iterator begin() const {
+    const_iterator I(*this);
+    I.goToBegin();
+    return I;
+  }
+
+  iterator begin() {
+    iterator I(*this);
+    I.goToBegin();
+    return I;
+  }
+
+  const_iterator end() const {
+    const_iterator I(*this);
+    I.goToEnd();
+    return I;
+  }
+
+  iterator end() {
+    iterator I(*this);
+    I.goToEnd();
+    return I;
+  }
+
+  /// find - Return an iterator pointing to the first interval ending at or
+  /// after x, or end().
+  const_iterator find(KeyT x) const {
+    const_iterator I(*this);
+    I.find(x);
+    return I;
+  }
+
+  iterator find(KeyT x) {
+    iterator I(*this);
+    I.find(x);
+    return I;
+  }
+
+  /// overlaps(a, b) - Return true if the intervals in this map overlap with the
+  /// interval [a;b].
+  bool overlaps(KeyT a, KeyT b) const {
+    assert(Traits::nonEmpty(a, b));
+    const_iterator I = find(a);
+    if (!I.valid())
+      return false;
+    // [a;b] and [x;y] overlap iff x<=b and a<=y. The find() call guarantees the
+    // second part (y = find(a).stop()), so it is sufficient to check the first
+    // one.
+    return !Traits::stopLess(b, I.start());
+  }
+};
+
+/// treeSafeLookup - Return the mapped value at x or NotFound, assuming a
+/// branched root.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+ValT IntervalMap<KeyT, ValT, N, Traits>::
+treeSafeLookup(KeyT x, ValT NotFound) const {
+  assert(branched() && "treeLookup assumes a branched root");
+
+  IntervalMapImpl::NodeRef NR = rootBranch().safeLookup(x);
+  for (unsigned h = height-1; h; --h)
+    NR = NR.get<Branch>().safeLookup(x);
+  return NR.get<Leaf>().safeLookup(x, NotFound);
+}
+
+// branchRoot - Switch from a leaf root to a branched root.
+// Return the new (root offset, node offset) corresponding to Position.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+IntervalMapImpl::IdxPair IntervalMap<KeyT, ValT, N, Traits>::
+branchRoot(unsigned Position) {
+  using namespace IntervalMapImpl;
+  // How many external leaf nodes to hold RootLeaf+1?
+  const unsigned Nodes = RootLeaf::Capacity / Leaf::Capacity + 1;
+
+  // Compute element distribution among new nodes.
+  unsigned size[Nodes];
+  IdxPair NewOffset(0, Position);
+
+  // Is is very common for the root node to be smaller than external nodes.
+  if (Nodes == 1)
+    size[0] = rootSize;
+  else
+    NewOffset = distribute(Nodes, rootSize, Leaf::Capacity,  nullptr, size,
+                           Position, true);
+
+  // Allocate new nodes.
+  unsigned pos = 0;
+  NodeRef node[Nodes];
+  for (unsigned n = 0; n != Nodes; ++n) {
+    Leaf *L = newNode<Leaf>();
+    L->copy(rootLeaf(), pos, 0, size[n]);
+    node[n] = NodeRef(L, size[n]);
+    pos += size[n];
+  }
+
+  // Destroy the old leaf node, construct branch node instead.
+  switchRootToBranch();
+  for (unsigned n = 0; n != Nodes; ++n) {
+    rootBranch().stop(n) = node[n].template get<Leaf>().stop(size[n]-1);
+    rootBranch().subtree(n) = node[n];
+  }
+  rootBranchStart() = node[0].template get<Leaf>().start(0);
+  rootSize = Nodes;
+  return NewOffset;
+}
+
+// splitRoot - Split the current BranchRoot into multiple Branch nodes.
+// Return the new (root offset, node offset) corresponding to Position.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+IntervalMapImpl::IdxPair IntervalMap<KeyT, ValT, N, Traits>::
+splitRoot(unsigned Position) {
+  using namespace IntervalMapImpl;
+  // How many external leaf nodes to hold RootBranch+1?
+  const unsigned Nodes = RootBranch::Capacity / Branch::Capacity + 1;
+
+  // Compute element distribution among new nodes.
+  unsigned Size[Nodes];
+  IdxPair NewOffset(0, Position);
+
+  // Is is very common for the root node to be smaller than external nodes.
+  if (Nodes == 1)
+    Size[0] = rootSize;
+  else
+    NewOffset = distribute(Nodes, rootSize, Leaf::Capacity,  nullptr, Size,
+                           Position, true);
+
+  // Allocate new nodes.
+  unsigned Pos = 0;
+  NodeRef Node[Nodes];
+  for (unsigned n = 0; n != Nodes; ++n) {
+    Branch *B = newNode<Branch>();
+    B->copy(rootBranch(), Pos, 0, Size[n]);
+    Node[n] = NodeRef(B, Size[n]);
+    Pos += Size[n];
+  }
+
+  for (unsigned n = 0; n != Nodes; ++n) {
+    rootBranch().stop(n) = Node[n].template get<Branch>().stop(Size[n]-1);
+    rootBranch().subtree(n) = Node[n];
+  }
+  rootSize = Nodes;
+  ++height;
+  return NewOffset;
+}
+
+/// visitNodes - Visit each external node.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+visitNodes(void (IntervalMap::*f)(IntervalMapImpl::NodeRef, unsigned Height)) {
+  if (!branched())
+    return;
+  SmallVector<IntervalMapImpl::NodeRef, 4> Refs, NextRefs;
+
+  // Collect level 0 nodes from the root.
+  for (unsigned i = 0; i != rootSize; ++i)
+    Refs.push_back(rootBranch().subtree(i));
+
+  // Visit all branch nodes.
+  for (unsigned h = height - 1; h; --h) {
+    for (unsigned i = 0, e = Refs.size(); i != e; ++i) {
+      for (unsigned j = 0, s = Refs[i].size(); j != s; ++j)
+        NextRefs.push_back(Refs[i].subtree(j));
+      (this->*f)(Refs[i], h);
+    }
+    Refs.clear();
+    Refs.swap(NextRefs);
+  }
+
+  // Visit all leaf nodes.
+  for (unsigned i = 0, e = Refs.size(); i != e; ++i)
+    (this->*f)(Refs[i], 0);
+}
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+deleteNode(IntervalMapImpl::NodeRef Node, unsigned Level) {
+  if (Level)
+    deleteNode(&Node.get<Branch>());
+  else
+    deleteNode(&Node.get<Leaf>());
+}
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+clear() {
+  if (branched()) {
+    visitNodes(&IntervalMap::deleteNode);
+    switchRootToLeaf();
+  }
+  rootSize = 0;
+}
+
+//===----------------------------------------------------------------------===//
+//---                   IntervalMap::const_iterator                       ----//
+//===----------------------------------------------------------------------===//
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+class IntervalMap<KeyT, ValT, N, Traits>::const_iterator {
+  friend class IntervalMap;
+
+public:
+  using iterator_category = std::bidirectional_iterator_tag;
+  using value_type = ValT;
+  using difference_type = std::ptrdiff_t;
+  using pointer = value_type *;
+  using reference = value_type &;
+
+protected:
+  // The map referred to.
+  IntervalMap *map = nullptr;
+
+  // We store a full path from the root to the current position.
+  // The path may be partially filled, but never between iterator calls.
+  IntervalMapImpl::Path path;
+
+  explicit const_iterator(const IntervalMap &map) :
+    map(const_cast<IntervalMap*>(&map)) {}
+
+  bool branched() const {
+    assert(map && "Invalid iterator");
+    return map->branched();
+  }
+
+  void setRoot(unsigned Offset) {
+    if (branched())
+      path.setRoot(&map->rootBranch(), map->rootSize, Offset);
+    else
+      path.setRoot(&map->rootLeaf(), map->rootSize, Offset);
+  }
+
+  void pathFillFind(KeyT x);
+  void treeFind(KeyT x);
+  void treeAdvanceTo(KeyT x);
+
+  /// unsafeStart - Writable access to start() for iterator.
+  KeyT &unsafeStart() const {
+    assert(valid() && "Cannot access invalid iterator");
+    return branched() ? path.leaf<Leaf>().start(path.leafOffset()) :
+                        path.leaf<RootLeaf>().start(path.leafOffset());
+  }
+
+  /// unsafeStop - Writable access to stop() for iterator.
+  KeyT &unsafeStop() const {
+    assert(valid() && "Cannot access invalid iterator");
+    return branched() ? path.leaf<Leaf>().stop(path.leafOffset()) :
+                        path.leaf<RootLeaf>().stop(path.leafOffset());
+  }
+
+  /// unsafeValue - Writable access to value() for iterator.
+  ValT &unsafeValue() const {
+    assert(valid() && "Cannot access invalid iterator");
+    return branched() ? path.leaf<Leaf>().value(path.leafOffset()) :
+                        path.leaf<RootLeaf>().value(path.leafOffset());
+  }
+
+public:
+  /// const_iterator - Create an iterator that isn't pointing anywhere.
+  const_iterator() = default;
+
+  /// setMap - Change the map iterated over. This call must be followed by a
+  /// call to goToBegin(), goToEnd(), or find()
+  void setMap(const IntervalMap &m) { map = const_cast<IntervalMap*>(&m); }
+
+  /// valid - Return true if the current position is valid, false for end().
+  bool valid() const { return path.valid(); }
+
+  /// atBegin - Return true if the current position is the first map entry.
+  bool atBegin() const { return path.atBegin(); }
+
+  /// start - Return the beginning of the current interval.
+  const KeyT &start() const { return unsafeStart(); }
+
+  /// stop - Return the end of the current interval.
+  const KeyT &stop() const { return unsafeStop(); }
+
+  /// value - Return the mapped value at the current interval.
+  const ValT &value() const { return unsafeValue(); }
+
+  const ValT &operator*() const { return value(); }
+
+  bool operator==(const const_iterator &RHS) const {
+    assert(map == RHS.map && "Cannot compare iterators from different maps");
+    if (!valid())
+      return !RHS.valid();
+    if (path.leafOffset() != RHS.path.leafOffset())
+      return false;
+    return &path.template leaf<Leaf>() == &RHS.path.template leaf<Leaf>();
+  }
+
+  bool operator!=(const const_iterator &RHS) const {
+    return !operator==(RHS);
+  }
+
+  /// goToBegin - Move to the first interval in map.
+  void goToBegin() {
+    setRoot(0);
+    if (branched())
+      path.fillLeft(map->height);
+  }
+
+  /// goToEnd - Move beyond the last interval in map.
+  void goToEnd() {
+    setRoot(map->rootSize);
+  }
+
+  /// preincrement - Move to the next interval.
+  const_iterator &operator++() {
+    assert(valid() && "Cannot increment end()");
+    if (++path.leafOffset() == path.leafSize() && branched())
+      path.moveRight(map->height);
+    return *this;
+  }
+
+  /// postincrement - Don't do that!
+  const_iterator operator++(int) {
+    const_iterator tmp = *this;
+    operator++();
+    return tmp;
+  }
+
+  /// predecrement - Move to the previous interval.
+  const_iterator &operator--() {
+    if (path.leafOffset() && (valid() || !branched()))
+      --path.leafOffset();
+    else
+      path.moveLeft(map->height);
+    return *this;
+  }
+
+  /// postdecrement - Don't do that!
+  const_iterator operator--(int) {
+    const_iterator tmp = *this;
+    operator--();
+    return tmp;
+  }
+
+  /// find - Move to the first interval with stop >= x, or end().
+  /// This is a full search from the root, the current position is ignored.
+  void find(KeyT x) {
+    if (branched())
+      treeFind(x);
+    else
+      setRoot(map->rootLeaf().findFrom(0, map->rootSize, x));
+  }
+
+  /// advanceTo - Move to the first interval with stop >= x, or end().
+  /// The search is started from the current position, and no earlier positions
+  /// can be found. This is much faster than find() for small moves.
+  void advanceTo(KeyT x) {
+    if (!valid())
+      return;
+    if (branched())
+      treeAdvanceTo(x);
+    else
+      path.leafOffset() =
+        map->rootLeaf().findFrom(path.leafOffset(), map->rootSize, x);
+  }
+};
+
+/// pathFillFind - Complete path by searching for x.
+/// @param x Key to search for.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+const_iterator::pathFillFind(KeyT x) {
+  IntervalMapImpl::NodeRef NR = path.subtree(path.height());
+  for (unsigned i = map->height - path.height() - 1; i; --i) {
+    unsigned p = NR.get<Branch>().safeFind(0, x);
+    path.push(NR, p);
+    NR = NR.subtree(p);
+  }
+  path.push(NR, NR.get<Leaf>().safeFind(0, x));
+}
+
+/// treeFind - Find in a branched tree.
+/// @param x Key to search for.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+const_iterator::treeFind(KeyT x) {
+  setRoot(map->rootBranch().findFrom(0, map->rootSize, x));
+  if (valid())
+    pathFillFind(x);
+}
+
+/// treeAdvanceTo - Find position after the current one.
+/// @param x Key to search for.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+const_iterator::treeAdvanceTo(KeyT x) {
+  // Can we stay on the same leaf node?
+  if (!Traits::stopLess(path.leaf<Leaf>().stop(path.leafSize() - 1), x)) {
+    path.leafOffset() = path.leaf<Leaf>().safeFind(path.leafOffset(), x);
+    return;
+  }
+
+  // Drop the current leaf.
+  path.pop();
+
+  // Search towards the root for a usable subtree.
+  if (path.height()) {
+    for (unsigned l = path.height() - 1; l; --l) {
+      if (!Traits::stopLess(path.node<Branch>(l).stop(path.offset(l)), x)) {
+        // The branch node at l+1 is usable
+        path.offset(l + 1) =
+          path.node<Branch>(l + 1).safeFind(path.offset(l + 1), x);
+        return pathFillFind(x);
+      }
+      path.pop();
+    }
+    // Is the level-1 Branch usable?
+    if (!Traits::stopLess(map->rootBranch().stop(path.offset(0)), x)) {
+      path.offset(1) = path.node<Branch>(1).safeFind(path.offset(1), x);
+      return pathFillFind(x);
+    }
+  }
+
+  // We reached the root.
+  setRoot(map->rootBranch().findFrom(path.offset(0), map->rootSize, x));
+  if (valid())
+    pathFillFind(x);
+}
+
+//===----------------------------------------------------------------------===//
+//---                       IntervalMap::iterator                         ----//
+//===----------------------------------------------------------------------===//
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+class IntervalMap<KeyT, ValT, N, Traits>::iterator : public const_iterator {
+  friend class IntervalMap;
+
+  using IdxPair = IntervalMapImpl::IdxPair;
+
+  explicit iterator(IntervalMap &map) : const_iterator(map) {}
+
+  void setNodeStop(unsigned Level, KeyT Stop);
+  bool insertNode(unsigned Level, IntervalMapImpl::NodeRef Node, KeyT Stop);
+  template <typename NodeT> bool overflow(unsigned Level);
+  void treeInsert(KeyT a, KeyT b, ValT y);
+  void eraseNode(unsigned Level);
+  void treeErase(bool UpdateRoot = true);
+  bool canCoalesceLeft(KeyT Start, ValT x);
+  bool canCoalesceRight(KeyT Stop, ValT x);
+
+public:
+  /// iterator - Create null iterator.
+  iterator() = default;
+
+  /// setStart - Move the start of the current interval.
+  /// This may cause coalescing with the previous interval.
+  /// @param a New start key, must not overlap the previous interval.
+  void setStart(KeyT a);
+
+  /// setStop - Move the end of the current interval.
+  /// This may cause coalescing with the following interval.
+  /// @param b New stop key, must not overlap the following interval.
+  void setStop(KeyT b);
+
+  /// setValue - Change the mapped value of the current interval.
+  /// This may cause coalescing with the previous and following intervals.
+  /// @param x New value.
+  void setValue(ValT x);
+
+  /// setStartUnchecked - Move the start of the current interval without
+  /// checking for coalescing or overlaps.
+  /// This should only be used when it is known that coalescing is not required.
+  /// @param a New start key.
+  void setStartUnchecked(KeyT a) { this->unsafeStart() = a; }
+
+  /// setStopUnchecked - Move the end of the current interval without checking
+  /// for coalescing or overlaps.
+  /// This should only be used when it is known that coalescing is not required.
+  /// @param b New stop key.
+  void setStopUnchecked(KeyT b) {
+    this->unsafeStop() = b;
+    // Update keys in branch nodes as well.
+    if (this->path.atLastEntry(this->path.height()))
+      setNodeStop(this->path.height(), b);
+  }
+
+  /// setValueUnchecked - Change the mapped value of the current interval
+  /// without checking for coalescing.
+  /// @param x New value.
+  void setValueUnchecked(ValT x) { this->unsafeValue() = x; }
+
+  /// insert - Insert mapping [a;b] -> y before the current position.
+  void insert(KeyT a, KeyT b, ValT y);
+
+  /// erase - Erase the current interval.
+  void erase();
+
+  iterator &operator++() {
+    const_iterator::operator++();
+    return *this;
+  }
+
+  iterator operator++(int) {
+    iterator tmp = *this;
+    operator++();
+    return tmp;
+  }
+
+  iterator &operator--() {
+    const_iterator::operator--();
+    return *this;
+  }
+
+  iterator operator--(int) {
+    iterator tmp = *this;
+    operator--();
+    return tmp;
+  }
+};
+
+/// canCoalesceLeft - Can the current interval coalesce to the left after
+/// changing start or value?
+/// @param Start New start of current interval.
+/// @param Value New value for current interval.
+/// @return True when updating the current interval would enable coalescing.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+bool IntervalMap<KeyT, ValT, N, Traits>::
+iterator::canCoalesceLeft(KeyT Start, ValT Value) {
+  using namespace IntervalMapImpl;
+  Path &P = this->path;
+  if (!this->branched()) {
+    unsigned i = P.leafOffset();
+    RootLeaf &Node = P.leaf<RootLeaf>();
+    return i && Node.value(i-1) == Value &&
+                Traits::adjacent(Node.stop(i-1), Start);
+  }
+  // Branched.
+  if (unsigned i = P.leafOffset()) {
+    Leaf &Node = P.leaf<Leaf>();
+    return Node.value(i-1) == Value && Traits::adjacent(Node.stop(i-1), Start);
+  } else if (NodeRef NR = P.getLeftSibling(P.height())) {
+    unsigned i = NR.size() - 1;
+    Leaf &Node = NR.get<Leaf>();
+    return Node.value(i) == Value && Traits::adjacent(Node.stop(i), Start);
+  }
+  return false;
+}
+
+/// canCoalesceRight - Can the current interval coalesce to the right after
+/// changing stop or value?
+/// @param Stop New stop of current interval.
+/// @param Value New value for current interval.
+/// @return True when updating the current interval would enable coalescing.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+bool IntervalMap<KeyT, ValT, N, Traits>::
+iterator::canCoalesceRight(KeyT Stop, ValT Value) {
+  using namespace IntervalMapImpl;
+  Path &P = this->path;
+  unsigned i = P.leafOffset() + 1;
+  if (!this->branched()) {
+    if (i >= P.leafSize())
+      return false;
+    RootLeaf &Node = P.leaf<RootLeaf>();
+    return Node.value(i) == Value && Traits::adjacent(Stop, Node.start(i));
+  }
+  // Branched.
+  if (i < P.leafSize()) {
+    Leaf &Node = P.leaf<Leaf>();
+    return Node.value(i) == Value && Traits::adjacent(Stop, Node.start(i));
+  } else if (NodeRef NR = P.getRightSibling(P.height())) {
+    Leaf &Node = NR.get<Leaf>();
+    return Node.value(0) == Value && Traits::adjacent(Stop, Node.start(0));
+  }
+  return false;
+}
+
+/// setNodeStop - Update the stop key of the current node at level and above.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::setNodeStop(unsigned Level, KeyT Stop) {
+  // There are no references to the root node, so nothing to update.
+  if (!Level)
+    return;
+  IntervalMapImpl::Path &P = this->path;
+  // Update nodes pointing to the current node.
+  while (--Level) {
+    P.node<Branch>(Level).stop(P.offset(Level)) = Stop;
+    if (!P.atLastEntry(Level))
+      return;
+  }
+  // Update root separately since it has a different layout.
+  P.node<RootBranch>(Level).stop(P.offset(Level)) = Stop;
+}
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::setStart(KeyT a) {
+  assert(Traits::nonEmpty(a, this->stop()) && "Cannot move start beyond stop");
+  KeyT &CurStart = this->unsafeStart();
+  if (!Traits::startLess(a, CurStart) || !canCoalesceLeft(a, this->value())) {
+    CurStart = a;
+    return;
+  }
+  // Coalesce with the interval to the left.
+  --*this;
+  a = this->start();
+  erase();
+  setStartUnchecked(a);
+}
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::setStop(KeyT b) {
+  assert(Traits::nonEmpty(this->start(), b) && "Cannot move stop beyond start");
+  if (Traits::startLess(b, this->stop()) ||
+      !canCoalesceRight(b, this->value())) {
+    setStopUnchecked(b);
+    return;
+  }
+  // Coalesce with interval to the right.
+  KeyT a = this->start();
+  erase();
+  setStartUnchecked(a);
+}
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::setValue(ValT x) {
+  setValueUnchecked(x);
+  if (canCoalesceRight(this->stop(), x)) {
+    KeyT a = this->start();
+    erase();
+    setStartUnchecked(a);
+  }
+  if (canCoalesceLeft(this->start(), x)) {
+    --*this;
+    KeyT a = this->start();
+    erase();
+    setStartUnchecked(a);
+  }
+}
+
+/// insertNode - insert a node before the current path at level.
+/// Leave the current path pointing at the new node.
+/// @param Level path index of the node to be inserted.
+/// @param Node The node to be inserted.
+/// @param Stop The last index in the new node.
+/// @return True if the tree height was increased.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+bool IntervalMap<KeyT, ValT, N, Traits>::
+iterator::insertNode(unsigned Level, IntervalMapImpl::NodeRef Node, KeyT Stop) {
+  assert(Level && "Cannot insert next to the root");
+  bool SplitRoot = false;
+  IntervalMap &IM = *this->map;
+  IntervalMapImpl::Path &P = this->path;
+
+  if (Level == 1) {
+    // Insert into the root branch node.
+    if (IM.rootSize < RootBranch::Capacity) {
+      IM.rootBranch().insert(P.offset(0), IM.rootSize, Node, Stop);
+      P.setSize(0, ++IM.rootSize);
+      P.reset(Level);
+      return SplitRoot;
+    }
+
+    // We need to split the root while keeping our position.
+    SplitRoot = true;
+    IdxPair Offset = IM.splitRoot(P.offset(0));
+    P.replaceRoot(&IM.rootBranch(), IM.rootSize, Offset);
+
+    // Fall through to insert at the new higher level.
+    ++Level;
+  }
+
+  // When inserting before end(), make sure we have a valid path.
+  P.legalizeForInsert(--Level);
+
+  // Insert into the branch node at Level-1.
+  if (P.size(Level) == Branch::Capacity) {
+    // Branch node is full, handle handle the overflow.
+    assert(!SplitRoot && "Cannot overflow after splitting the root");
+    SplitRoot = overflow<Branch>(Level);
+    Level += SplitRoot;
+  }
+  P.node<Branch>(Level).insert(P.offset(Level), P.size(Level), Node, Stop);
+  P.setSize(Level, P.size(Level) + 1);
+  if (P.atLastEntry(Level))
+    setNodeStop(Level, Stop);
+  P.reset(Level + 1);
+  return SplitRoot;
+}
+
+// insert
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::insert(KeyT a, KeyT b, ValT y) {
+  if (this->branched())
+    return treeInsert(a, b, y);
+  IntervalMap &IM = *this->map;
+  IntervalMapImpl::Path &P = this->path;
+
+  // Try simple root leaf insert.
+  unsigned Size = IM.rootLeaf().insertFrom(P.leafOffset(), IM.rootSize, a, b, y);
+
+  // Was the root node insert successful?
+  if (Size <= RootLeaf::Capacity) {
+    P.setSize(0, IM.rootSize = Size);
+    return;
+  }
+
+  // Root leaf node is full, we must branch.
+  IdxPair Offset = IM.branchRoot(P.leafOffset());
+  P.replaceRoot(&IM.rootBranch(), IM.rootSize, Offset);
+
+  // Now it fits in the new leaf.
+  treeInsert(a, b, y);
+}
+
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::treeInsert(KeyT a, KeyT b, ValT y) {
+  using namespace IntervalMapImpl;
+  Path &P = this->path;
+
+  if (!P.valid())
+    P.legalizeForInsert(this->map->height);
+
+  // Check if this insertion will extend the node to the left.
+  if (P.leafOffset() == 0 && Traits::startLess(a, P.leaf<Leaf>().start(0))) {
+    // Node is growing to the left, will it affect a left sibling node?
+    if (NodeRef Sib = P.getLeftSibling(P.height())) {
+      Leaf &SibLeaf = Sib.get<Leaf>();
+      unsigned SibOfs = Sib.size() - 1;
+      if (SibLeaf.value(SibOfs) == y &&
+          Traits::adjacent(SibLeaf.stop(SibOfs), a)) {
+        // This insertion will coalesce with the last entry in SibLeaf. We can
+        // handle it in two ways:
+        //  1. Extend SibLeaf.stop to b and be done, or
+        //  2. Extend a to SibLeaf, erase the SibLeaf entry and continue.
+        // We prefer 1., but need 2 when coalescing to the right as well.
+        Leaf &CurLeaf = P.leaf<Leaf>();
+        P.moveLeft(P.height());
+        if (Traits::stopLess(b, CurLeaf.start(0)) &&
+            (y != CurLeaf.value(0) || !Traits::adjacent(b, CurLeaf.start(0)))) {
+          // Easy, just extend SibLeaf and we're done.
+          setNodeStop(P.height(), SibLeaf.stop(SibOfs) = b);
+          return;
+        } else {
+          // We have both left and right coalescing. Erase the old SibLeaf entry
+          // and continue inserting the larger interval.
+          a = SibLeaf.start(SibOfs);
+          treeErase(/* UpdateRoot= */false);
+        }
+      }
+    } else {
+      // No left sibling means we are at begin(). Update cached bound.
+      this->map->rootBranchStart() = a;
+    }
+  }
+
+  // When we are inserting at the end of a leaf node, we must update stops.
+  unsigned Size = P.leafSize();
+  bool Grow = P.leafOffset() == Size;
+  Size = P.leaf<Leaf>().insertFrom(P.leafOffset(), Size, a, b, y);
+
+  // Leaf insertion unsuccessful? Overflow and try again.
+  if (Size > Leaf::Capacity) {
+    overflow<Leaf>(P.height());
+    Grow = P.leafOffset() == P.leafSize();
+    Size = P.leaf<Leaf>().insertFrom(P.leafOffset(), P.leafSize(), a, b, y);
+    assert(Size <= Leaf::Capacity && "overflow() didn't make room");
+  }
+
+  // Inserted, update offset and leaf size.
+  P.setSize(P.height(), Size);
+
+  // Insert was the last node entry, update stops.
+  if (Grow)
+    setNodeStop(P.height(), b);
+}
+
+/// erase - erase the current interval and move to the next position.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::erase() {
+  IntervalMap &IM = *this->map;
+  IntervalMapImpl::Path &P = this->path;
+  assert(P.valid() && "Cannot erase end()");
+  if (this->branched())
+    return treeErase();
+  IM.rootLeaf().erase(P.leafOffset(), IM.rootSize);
+  P.setSize(0, --IM.rootSize);
+}
+
+/// treeErase - erase() for a branched tree.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::treeErase(bool UpdateRoot) {
+  IntervalMap &IM = *this->map;
+  IntervalMapImpl::Path &P = this->path;
+  Leaf &Node = P.leaf<Leaf>();
+
+  // Nodes are not allowed to become empty.
+  if (P.leafSize() == 1) {
+    IM.deleteNode(&Node);
+    eraseNode(IM.height);
+    // Update rootBranchStart if we erased begin().
+    if (UpdateRoot && IM.branched() && P.valid() && P.atBegin())
+      IM.rootBranchStart() = P.leaf<Leaf>().start(0);
+    return;
+  }
+
+  // Erase current entry.
+  Node.erase(P.leafOffset(), P.leafSize());
+  unsigned NewSize = P.leafSize() - 1;
+  P.setSize(IM.height, NewSize);
+  // When we erase the last entry, update stop and move to a legal position.
+  if (P.leafOffset() == NewSize) {
+    setNodeStop(IM.height, Node.stop(NewSize - 1));
+    P.moveRight(IM.height);
+  } else if (UpdateRoot && P.atBegin())
+    IM.rootBranchStart() = P.leaf<Leaf>().start(0);
+}
+
+/// eraseNode - Erase the current node at Level from its parent and move path to
+/// the first entry of the next sibling node.
+/// The node must be deallocated by the caller.
+/// @param Level 1..height, the root node cannot be erased.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+void IntervalMap<KeyT, ValT, N, Traits>::
+iterator::eraseNode(unsigned Level) {
+  assert(Level && "Cannot erase root node");
+  IntervalMap &IM = *this->map;
+  IntervalMapImpl::Path &P = this->path;
+
+  if (--Level == 0) {
+    IM.rootBranch().erase(P.offset(0), IM.rootSize);
+    P.setSize(0, --IM.rootSize);
+    // If this cleared the root, switch to height=0.
+    if (IM.empty()) {
+      IM.switchRootToLeaf();
+      this->setRoot(0);
+      return;
+    }
+  } else {
+    // Remove node ref from branch node at Level.
+    Branch &Parent = P.node<Branch>(Level);
+    if (P.size(Level) == 1) {
+      // Branch node became empty, remove it recursively.
+      IM.deleteNode(&Parent);
+      eraseNode(Level);
+    } else {
+      // Branch node won't become empty.
+      Parent.erase(P.offset(Level), P.size(Level));
+      unsigned NewSize = P.size(Level) - 1;
+      P.setSize(Level, NewSize);
+      // If we removed the last branch, update stop and move to a legal pos.
+      if (P.offset(Level) == NewSize) {
+        setNodeStop(Level, Parent.stop(NewSize - 1));
+        P.moveRight(Level);
+      }
+    }
+  }
+  // Update path cache for the new right sibling position.
+  if (P.valid()) {
+    P.reset(Level + 1);
+    P.offset(Level + 1) = 0;
+  }
+}
+
+/// overflow - Distribute entries of the current node evenly among
+/// its siblings and ensure that the current node is not full.
+/// This may require allocating a new node.
+/// @tparam NodeT The type of node at Level (Leaf or Branch).
+/// @param Level path index of the overflowing node.
+/// @return True when the tree height was changed.
+template <typename KeyT, typename ValT, unsigned N, typename Traits>
+template <typename NodeT>
+bool IntervalMap<KeyT, ValT, N, Traits>::
+iterator::overflow(unsigned Level) {
+  using namespace IntervalMapImpl;
+  Path &P = this->path;
+  unsigned CurSize[4];
+  NodeT *Node[4];
+  unsigned Nodes = 0;
+  unsigned Elements = 0;
+  unsigned Offset = P.offset(Level);
+
+  // Do we have a left sibling?
+  NodeRef LeftSib = P.getLeftSibling(Level);
+  if (LeftSib) {
+    Offset += Elements = CurSize[Nodes] = LeftSib.size();
+    Node[Nodes++] = &LeftSib.get<NodeT>();
+  }
+
+  // Current node.
+  Elements += CurSize[Nodes] = P.size(Level);
+  Node[Nodes++] = &P.node<NodeT>(Level);
+
+  // Do we have a right sibling?
+  NodeRef RightSib = P.getRightSibling(Level);
+  if (RightSib) {
+    Elements += CurSize[Nodes] = RightSib.size();
+    Node[Nodes++] = &RightSib.get<NodeT>();
+  }
+
+  // Do we need to allocate a new node?
+  unsigned NewNode = 0;
+  if (Elements + 1 > Nodes * NodeT::Capacity) {
+    // Insert NewNode at the penultimate position, or after a single node.
+    NewNode = Nodes == 1 ? 1 : Nodes - 1;
+    CurSize[Nodes] = CurSize[NewNode];
+    Node[Nodes] = Node[NewNode];
+    CurSize[NewNode] = 0;
+    Node[NewNode] = this->map->template newNode<NodeT>();
+    ++Nodes;
+  }
+
+  // Compute the new element distribution.
+  unsigned NewSize[4];
+  IdxPair NewOffset = distribute(Nodes, Elements, NodeT::Capacity,
+                                 CurSize, NewSize, Offset, true);
+  adjustSiblingSizes(Node, Nodes, CurSize, NewSize);
+
+  // Move current location to the leftmost node.
+  if (LeftSib)
+    P.moveLeft(Level);
+
+  // Elements have been rearranged, now update node sizes and stops.
+  bool SplitRoot = false;
+  unsigned Pos = 0;
+  while (true) {
+    KeyT Stop = Node[Pos]->stop(NewSize[Pos]-1);
+    if (NewNode && Pos == NewNode) {
+      SplitRoot = insertNode(Level, NodeRef(Node[Pos], NewSize[Pos]), Stop);
+      Level += SplitRoot;
+    } else {
+      P.setSize(Level, NewSize[Pos]);
+      setNodeStop(Level, Stop);
+    }
+    if (Pos + 1 == Nodes)
+      break;
+    P.moveRight(Level);
+    ++Pos;
+  }
+
+  // Where was I? Find NewOffset.
+  while(Pos != NewOffset.first) {
+    P.moveLeft(Level);
+    --Pos;
+  }
+  P.offset(Level) = NewOffset.second;
+  return SplitRoot;
+}
+
+//===----------------------------------------------------------------------===//
+//---                       IntervalMapOverlaps                           ----//
+//===----------------------------------------------------------------------===//
+
+/// IntervalMapOverlaps - Iterate over the overlaps of mapped intervals in two
+/// IntervalMaps. The maps may be different, but the KeyT and Traits types
+/// should be the same.
+///
+/// Typical uses:
+///
+/// 1. Test for overlap:
+///    bool overlap = IntervalMapOverlaps(a, b).valid();
+///
+/// 2. Enumerate overlaps:
+///    for (IntervalMapOverlaps I(a, b); I.valid() ; ++I) { ... }
+///
+template <typename MapA, typename MapB>
+class IntervalMapOverlaps {
+  using KeyType = typename MapA::KeyType;
+  using Traits = typename MapA::KeyTraits;
+
+  typename MapA::const_iterator posA;
+  typename MapB::const_iterator posB;
+
+  /// advance - Move posA and posB forward until reaching an overlap, or until
+  /// either meets end.
+  /// Don't move the iterators if they are already overlapping.
+  void advance() {
+    if (!valid())
+      return;
+
+    if (Traits::stopLess(posA.stop(), posB.start())) {
+      // A ends before B begins. Catch up.
+      posA.advanceTo(posB.start());
+      if (!posA.valid() || !Traits::stopLess(posB.stop(), posA.start()))
+        return;
+    } else if (Traits::stopLess(posB.stop(), posA.start())) {
+      // B ends before A begins. Catch up.
+      posB.advanceTo(posA.start());
+      if (!posB.valid() || !Traits::stopLess(posA.stop(), posB.start()))
+        return;
+    } else
+      // Already overlapping.
+      return;
+
+    while (true) {
+      // Make a.end > b.start.
+      posA.advanceTo(posB.start());
+      if (!posA.valid() || !Traits::stopLess(posB.stop(), posA.start()))
+        return;
+      // Make b.end > a.start.
+      posB.advanceTo(posA.start());
+      if (!posB.valid() || !Traits::stopLess(posA.stop(), posB.start()))
+        return;
+    }
+  }
+
+public:
+  /// IntervalMapOverlaps - Create an iterator for the overlaps of a and b.
+  IntervalMapOverlaps(const MapA &a, const MapB &b)
+    : posA(b.empty() ? a.end() : a.find(b.start())),
+      posB(posA.valid() ? b.find(posA.start()) : b.end()) { advance(); }
+
+  /// valid - Return true if iterator is at an overlap.
+  bool valid() const {
+    return posA.valid() && posB.valid();
+  }
+
+  /// a - access the left hand side in the overlap.
+  const typename MapA::const_iterator &a() const { return posA; }
+
+  /// b - access the right hand side in the overlap.
+  const typename MapB::const_iterator &b() const { return posB; }
+
+  /// start - Beginning of the overlapping interval.
+  KeyType start() const {
+    KeyType ak = a().start();
+    KeyType bk = b().start();
+    return Traits::startLess(ak, bk) ? bk : ak;
+  }
+
+  /// stop - End of the overlapping interval.
+  KeyType stop() const {
+    KeyType ak = a().stop();
+    KeyType bk = b().stop();
+    return Traits::startLess(ak, bk) ? ak : bk;
+  }
+
+  /// skipA - Move to the next overlap that doesn't involve a().
+  void skipA() {
+    ++posA;
+    advance();
+  }
+
+  /// skipB - Move to the next overlap that doesn't involve b().
+  void skipB() {
+    ++posB;
+    advance();
+  }
+
+  /// Preincrement - Move to the next overlap.
+  IntervalMapOverlaps &operator++() {
+    // Bump the iterator that ends first. The other one may have more overlaps.
+    if (Traits::startLess(posB.stop(), posA.stop()))
+      skipB();
+    else
+      skipA();
+    return *this;
+  }
+
+  /// advanceTo - Move to the first overlapping interval with
+  /// stopLess(x, stop()).
+  void advanceTo(KeyType x) {
+    if (!valid())
+      return;
+    // Make sure advanceTo sees monotonic keys.
+    if (Traits::stopLess(posA.stop(), x))
+      posA.advanceTo(x);
+    if (Traits::stopLess(posB.stop(), x))
+      posB.advanceTo(x);
+    advance();
+  }
+};
+
+} // end namespace llvm
+
+#endif // LLVM_ADT_INTERVALMAP_H
+
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif