//===- 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/Support/Allocator.h"
#include "llvm/Support/RecyclingAllocator.h"
#include <algorithm>
#include <cassert>
#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.
union {
RootLeaf leaf;
RootBranchData branchData;
};
// 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;
const RootLeaf &rootLeaf() const {
assert(!branched() && "Cannot acces leaf data in branched root");
return leaf;
}
RootLeaf &rootLeaf() {
assert(!branched() && "Cannot acces leaf data in branched root");
return leaf;
}
const RootBranchData &rootBranchData() const {
assert(branched() && "Cannot access branch data in non-branched root");
return branchData;
}
RootBranchData &rootBranchData() {
assert(branched() && "Cannot access branch data in non-branched root");
return branchData;
}
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) {
new(&rootLeaf()) RootLeaf();
}
// The default copy/move constructors and assignment operators would perform
// a shallow copy, leading to an incorrect internal state. To prevent
// accidental use, explicitly delete these operators.
// If necessary, implement them to perform a deep copy.
IntervalMap(const IntervalMap &Other) = delete;
IntervalMap(IntervalMap &&Other) = delete;
// Note: these are already implicitly deleted, because RootLeaf (union
// member) has a non-trivial assignment operator (because of std::pair).
IntervalMap &operator=(const IntervalMap &Other) = delete;
IntervalMap &operator=(IntervalMap &&Other) = delete;
~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