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Diffstat (limited to 'include/llvm/ADT/IntervalMap.h')
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diff --git a/include/llvm/ADT/IntervalMap.h b/include/llvm/ADT/IntervalMap.h new file mode 100644 index 000000000000..79f24d31c068 --- /dev/null +++ b/include/llvm/ADT/IntervalMap.h @@ -0,0 +1,2139 @@ +//===- llvm/ADT/IntervalMap.h - A sorted interval map -----------*- C++ -*-===// +// +// The LLVM Compiler Infrastructure +// +// This file is distributed under the University of Illinois Open Source +// License. See LICENSE.TXT for details. +// +//===----------------------------------------------------------------------===// +// +// 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 std::iterator<std::bidirectional_iterator_tag, ValT> { +// public: +// 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/SmallVector.h" +#include "llvm/ADT/PointerIntPair.h" +#include "llvm/Support/Allocator.h" +#include "llvm/Support/RecyclingAllocator.h" +#include <iterator> + +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; + } + +}; + +/// IntervalMapImpl - Namespace used for IntervalMap implementation details. +/// It should be considered private to the implementation. +namespace IntervalMapImpl { + +// Forward declarations. +template <typename, typename, unsigned, typename> class LeafNode; +template <typename, typename, unsigned, typename> class BranchNode; + +typedef std::pair<unsigned,unsigned> IdxPair; + + +//===----------------------------------------------------------------------===// +//--- 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 + }; + + typedef NodeBase<std::pair<KeyT, KeyT>, ValT, LeafSize> LeafBase; + + 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. + typedef RecyclingAllocator<BumpPtrAllocator, char, + AllocBytes, CacheLineBytes> Allocator; + +}; + + +//===----------------------------------------------------------------------===// +//--- 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; } + enum { NumLowBitsAvailable = Log2CacheLine }; + }; + PointerIntPair<void*, Log2CacheLine, unsigned, CacheAlignedPointerTraits> pip; + +public: + /// NodeRef - Create a null ref. + NodeRef() {} + + /// operator bool - Detect a null ref. + 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 i 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 constains 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 sinbling 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; + } +}; + +} // namespace IntervalMapImpl + + +//===----------------------------------------------------------------------===// +//--- IntervalMap ----// +//===----------------------------------------------------------------------===// + +template <typename KeyT, typename ValT, + unsigned N = IntervalMapImpl::NodeSizer<KeyT, ValT>::LeafSize, + typename Traits = IntervalMapInfo<KeyT> > +class IntervalMap { + typedef IntervalMapImpl::NodeSizer<KeyT, ValT> Sizer; + typedef IntervalMapImpl::LeafNode<KeyT, ValT, Sizer::LeafSize, Traits> Leaf; + typedef IntervalMapImpl::BranchNode<KeyT, ValT, Sizer::BranchSize, Traits> + Branch; + typedef IntervalMapImpl::LeafNode<KeyT, ValT, N, Traits> RootLeaf; + typedef IntervalMapImpl::IdxPair 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 + }; + + typedef IntervalMapImpl::BranchNode<KeyT, ValT, RootBranchCap, Traits> + RootBranch; + + // When branched, we store a global start key as well as the branch node. + struct RootBranchData { + KeyT start; + RootBranch node; + }; + + enum { + RootDataSize = sizeof(RootBranchData) > sizeof(RootLeaf) ? + sizeof(RootBranchData) : sizeof(RootLeaf) + }; + +public: + typedef typename Sizer::Allocator Allocator; + typedef KeyT KeyType; + typedef ValT ValueType; + typedef Traits KeyTraits; + +private: + // The root data is either a RootLeaf or a RootBranchData instance. + // We can't put them in a union since C++03 doesn't allow non-trivial + // constructors in unions. + // Instead, we use a char array with pointer alignment. The alignment is + // ensured by the allocator member in the class, but still verified in the + // constructor. We don't support keys or values that are more aligned than a + // pointer. + char data[RootDataSize]; + + // 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; + + /// dataAs - Represent data as a node type without breaking aliasing rules. + template <typename T> + T &dataAs() const { + union { + const char *d; + T *t; + } u; + u.d = data; + return *u.t; + } + + 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; + } +}; + +/// 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, NULL, 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, NULL, 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 : + public std::iterator<std::bidirectional_iterator_tag, ValT> { +protected: + friend class IntervalMap; + + // The map referred to. + IntervalMap *map; + + // 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() : map(0) {} + + /// valid - Return true if the current position is valid, false for end(). + bool valid() const { return path.valid(); } + + /// 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 - Dont 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 - Dont 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; + typedef IntervalMapImpl::IdxPair 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() {} + + /// 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::stopLess(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::stopLess(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. +/// @param 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->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; + for (;;) { + 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 { + typedef typename MapA::KeyType KeyType; + typedef typename MapA::KeyTraits Traits; + 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; + + for (;;) { + // 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(); + } +}; + +} // namespace llvm + +#endif |