1 //===- llvm/ADT/IntervalMap.h - A sorted interval map -----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements a coalescing interval map for small objects.
12 // KeyT objects are mapped to ValT objects. Intervals of keys that map to the
13 // same value are represented in a compressed form.
15 // Iterators provide ordered access to the compressed intervals rather than the
16 // individual keys, and insert and erase operations use key intervals as well.
18 // Like SmallVector, IntervalMap will store the first N intervals in the map
19 // object itself without any allocations. When space is exhausted it switches to
20 // a B+-tree representation with very small overhead for small key and value
23 // A Traits class specifies how keys are compared. It also allows IntervalMap to
24 // work with both closed and half-open intervals.
26 // Keys and values are not stored next to each other in a std::pair, so we don't
27 // provide such a value_type. Dereferencing iterators only returns the mapped
28 // value. The interval bounds are accessible through the start() and stop()
31 // IntervalMap is optimized for small key and value objects, 4 or 8 bytes each
32 // is the optimal size. For large objects use std::map instead.
34 //===----------------------------------------------------------------------===//
38 // template <typename KeyT, typename ValT, unsigned N, typename Traits>
39 // class IntervalMap {
41 // typedef KeyT key_type;
42 // typedef ValT mapped_type;
43 // typedef RecyclingAllocator<...> Allocator;
45 // class const_iterator;
47 // explicit IntervalMap(Allocator&);
50 // bool empty() const;
51 // KeyT start() const;
53 // ValT lookup(KeyT x, Value NotFound = Value()) const;
55 // const_iterator begin() const;
56 // const_iterator end() const;
59 // const_iterator find(KeyT x) const;
60 // iterator find(KeyT x);
62 // void insert(KeyT a, KeyT b, ValT y);
66 // template <typename KeyT, typename ValT, unsigned N, typename Traits>
67 // class IntervalMap::const_iterator :
68 // public std::iterator<std::bidirectional_iterator_tag, ValT> {
70 // bool operator==(const const_iterator &) const;
71 // bool operator!=(const const_iterator &) const;
72 // bool valid() const;
74 // const KeyT &start() const;
75 // const KeyT &stop() const;
76 // const ValT &value() const;
77 // const ValT &operator*() const;
78 // const ValT *operator->() const;
80 // const_iterator &operator++();
81 // const_iterator &operator++(int);
82 // const_iterator &operator--();
83 // const_iterator &operator--(int);
87 // void advanceTo(KeyT x);
90 // template <typename KeyT, typename ValT, unsigned N, typename Traits>
91 // class IntervalMap::iterator : public const_iterator {
93 // void insert(KeyT a, KeyT b, Value y);
97 //===----------------------------------------------------------------------===//
99 #ifndef LLVM_ADT_INTERVALMAP_H
100 #define LLVM_ADT_INTERVALMAP_H
102 #include "llvm/ADT/PointerIntPair.h"
103 #include "llvm/ADT/SmallVector.h"
104 #include "llvm/Support/Allocator.h"
105 #include "llvm/Support/RecyclingAllocator.h"
111 //===----------------------------------------------------------------------===//
112 //--- Key traits ---//
113 //===----------------------------------------------------------------------===//
115 // The IntervalMap works with closed or half-open intervals.
116 // Adjacent intervals that map to the same value are coalesced.
118 // The IntervalMapInfo traits class is used to determine if a key is contained
119 // in an interval, and if two intervals are adjacent so they can be coalesced.
120 // The provided implementation works for closed integer intervals, other keys
121 // probably need a specialized version.
123 // The point x is contained in [a;b] when !startLess(x, a) && !stopLess(b, x).
125 // It is assumed that (a;b] half-open intervals are not used, only [a;b) is
126 // allowed. This is so that stopLess(a, b) can be used to determine if two
127 // intervals overlap.
129 //===----------------------------------------------------------------------===//
131 template <typename T>
132 struct IntervalMapInfo {
134 /// startLess - Return true if x is not in [a;b].
135 /// This is x < a both for closed intervals and for [a;b) half-open intervals.
136 static inline bool startLess(const T &x, const T &a) {
140 /// stopLess - Return true if x is not in [a;b].
141 /// This is b < x for a closed interval, b <= x for [a;b) half-open intervals.
142 static inline bool stopLess(const T &b, const T &x) {
146 /// adjacent - Return true when the intervals [x;a] and [b;y] can coalesce.
147 /// This is a+1 == b for closed intervals, a == b for half-open intervals.
148 static inline bool adjacent(const T &a, const T &b) {
154 template <typename T>
155 struct IntervalMapHalfOpenInfo {
157 /// startLess - Return true if x is not in [a;b).
158 static inline bool startLess(const T &x, const T &a) {
162 /// stopLess - Return true if x is not in [a;b).
163 static inline bool stopLess(const T &b, const T &x) {
167 /// adjacent - Return true when the intervals [x;a) and [b;y) can coalesce.
168 static inline bool adjacent(const T &a, const T &b) {
174 /// IntervalMapImpl - Namespace used for IntervalMap implementation details.
175 /// It should be considered private to the implementation.
176 namespace IntervalMapImpl {
178 // Forward declarations.
179 template <typename, typename, unsigned, typename> class LeafNode;
180 template <typename, typename, unsigned, typename> class BranchNode;
182 typedef std::pair<unsigned,unsigned> IdxPair;
185 //===----------------------------------------------------------------------===//
186 //--- IntervalMapImpl::NodeBase ---//
187 //===----------------------------------------------------------------------===//
189 // Both leaf and branch nodes store vectors of pairs.
190 // Leaves store ((KeyT, KeyT), ValT) pairs, branches use (NodeRef, KeyT).
192 // Keys and values are stored in separate arrays to avoid padding caused by
193 // different object alignments. This also helps improve locality of reference
194 // when searching the keys.
196 // The nodes don't know how many elements they contain - that information is
197 // stored elsewhere. Omitting the size field prevents padding and allows a node
198 // to fill the allocated cache lines completely.
200 // These are typical key and value sizes, the node branching factor (N), and
201 // wasted space when nodes are sized to fit in three cache lines (192 bytes):
203 // T1 T2 N Waste Used by
204 // 4 4 24 0 Branch<4> (32-bit pointers)
205 // 8 4 16 0 Leaf<4,4>, Branch<4>
206 // 8 8 12 0 Leaf<4,8>, Branch<8>
207 // 16 4 9 12 Leaf<8,4>
208 // 16 8 8 0 Leaf<8,8>
210 //===----------------------------------------------------------------------===//
212 template <typename T1, typename T2, unsigned N>
215 enum { Capacity = N };
220 /// copy - Copy elements from another node.
221 /// @param Other Node elements are copied from.
222 /// @param i Beginning of the source range in other.
223 /// @param j Beginning of the destination range in this.
224 /// @param Count Number of elements to copy.
225 template <unsigned M>
226 void copy(const NodeBase<T1, T2, M> &Other, unsigned i,
227 unsigned j, unsigned Count) {
228 assert(i + Count <= M && "Invalid source range");
229 assert(j + Count <= N && "Invalid dest range");
230 for (unsigned e = i + Count; i != e; ++i, ++j) {
231 first[j] = Other.first[i];
232 second[j] = Other.second[i];
236 /// moveLeft - Move elements to the left.
237 /// @param i Beginning of the source range.
238 /// @param j Beginning of the destination range.
239 /// @param Count Number of elements to copy.
240 void moveLeft(unsigned i, unsigned j, unsigned Count) {
241 assert(j <= i && "Use moveRight shift elements right");
242 copy(*this, i, j, Count);
245 /// moveRight - Move elements to the right.
246 /// @param i Beginning of the source range.
247 /// @param j Beginning of the destination range.
248 /// @param Count Number of elements to copy.
249 void moveRight(unsigned i, unsigned j, unsigned Count) {
250 assert(i <= j && "Use moveLeft shift elements left");
251 assert(j + Count <= N && "Invalid range");
253 first[j + Count] = first[i + Count];
254 second[j + Count] = second[i + Count];
258 /// erase - Erase elements [i;j).
259 /// @param i Beginning of the range to erase.
260 /// @param j End of the range. (Exclusive).
261 /// @param Size Number of elements in node.
262 void erase(unsigned i, unsigned j, unsigned Size) {
263 moveLeft(j, i, Size - j);
266 /// erase - Erase element at i.
267 /// @param i Index of element to erase.
268 /// @param Size Number of elements in node.
269 void erase(unsigned i, unsigned Size) {
273 /// shift - Shift elements [i;size) 1 position to the right.
274 /// @param i Beginning of the range to move.
275 /// @param Size Number of elements in node.
276 void shift(unsigned i, unsigned Size) {
277 moveRight(i, i + 1, Size - i);
280 /// transferToLeftSib - Transfer elements to a left sibling node.
281 /// @param Size Number of elements in this.
282 /// @param Sib Left sibling node.
283 /// @param SSize Number of elements in sib.
284 /// @param Count Number of elements to transfer.
285 void transferToLeftSib(unsigned Size, NodeBase &Sib, unsigned SSize,
287 Sib.copy(*this, 0, SSize, Count);
288 erase(0, Count, Size);
291 /// transferToRightSib - Transfer elements to a right sibling node.
292 /// @param Size Number of elements in this.
293 /// @param Sib Right sibling node.
294 /// @param SSize Number of elements in sib.
295 /// @param Count Number of elements to transfer.
296 void transferToRightSib(unsigned Size, NodeBase &Sib, unsigned SSize,
298 Sib.moveRight(0, Count, SSize);
299 Sib.copy(*this, Size-Count, 0, Count);
302 /// adjustFromLeftSib - Adjust the number if elements in this node by moving
303 /// elements to or from a left sibling node.
304 /// @param Size Number of elements in this.
305 /// @param Sib Right sibling node.
306 /// @param SSize Number of elements in sib.
307 /// @param Add The number of elements to add to this node, possibly < 0.
308 /// @return Number of elements added to this node, possibly negative.
309 int adjustFromLeftSib(unsigned Size, NodeBase &Sib, unsigned SSize, int Add) {
311 // We want to grow, copy from sib.
312 unsigned Count = std::min(std::min(unsigned(Add), SSize), N - Size);
313 Sib.transferToRightSib(SSize, *this, Size, Count);
316 // We want to shrink, copy to sib.
317 unsigned Count = std::min(std::min(unsigned(-Add), Size), N - SSize);
318 transferToLeftSib(Size, Sib, SSize, Count);
324 /// IntervalMapImpl::adjustSiblingSizes - Move elements between sibling nodes.
325 /// @param Node Array of pointers to sibling nodes.
326 /// @param Nodes Number of nodes.
327 /// @param CurSize Array of current node sizes, will be overwritten.
328 /// @param NewSize Array of desired node sizes.
329 template <typename NodeT>
330 void adjustSiblingSizes(NodeT *Node[], unsigned Nodes,
331 unsigned CurSize[], const unsigned NewSize[]) {
332 // Move elements right.
333 for (int n = Nodes - 1; n; --n) {
334 if (CurSize[n] == NewSize[n])
336 for (int m = n - 1; m != -1; --m) {
337 int d = Node[n]->adjustFromLeftSib(CurSize[n], *Node[m], CurSize[m],
338 NewSize[n] - CurSize[n]);
341 // Keep going if the current node was exhausted.
342 if (CurSize[n] >= NewSize[n])
350 // Move elements left.
351 for (unsigned n = 0; n != Nodes - 1; ++n) {
352 if (CurSize[n] == NewSize[n])
354 for (unsigned m = n + 1; m != Nodes; ++m) {
355 int d = Node[m]->adjustFromLeftSib(CurSize[m], *Node[n], CurSize[n],
356 CurSize[n] - NewSize[n]);
359 // Keep going if the current node was exhausted.
360 if (CurSize[n] >= NewSize[n])
366 for (unsigned n = 0; n != Nodes; n++)
367 assert(CurSize[n] == NewSize[n] && "Insufficient element shuffle");
371 /// IntervalMapImpl::distribute - Compute a new distribution of node elements
372 /// after an overflow or underflow. Reserve space for a new element at Position,
373 /// and compute the node that will hold Position after redistributing node
376 /// It is required that
378 /// Elements == sum(CurSize), and
379 /// Elements + Grow <= Nodes * Capacity.
381 /// NewSize[] will be filled in such that:
383 /// sum(NewSize) == Elements, and
384 /// NewSize[i] <= Capacity.
386 /// The returned index is the node where Position will go, so:
388 /// sum(NewSize[0..idx-1]) <= Position
389 /// sum(NewSize[0..idx]) >= Position
391 /// The last equality, sum(NewSize[0..idx]) == Position, can only happen when
392 /// Grow is set and NewSize[idx] == Capacity-1. The index points to the node
393 /// before the one holding the Position'th element where there is room for an
396 /// @param Nodes The number of nodes.
397 /// @param Elements Total elements in all nodes.
398 /// @param Capacity The capacity of each node.
399 /// @param CurSize Array[Nodes] of current node sizes, or NULL.
400 /// @param NewSize Array[Nodes] to receive the new node sizes.
401 /// @param Position Insert position.
402 /// @param Grow Reserve space for a new element at Position.
403 /// @return (node, offset) for Position.
404 IdxPair distribute(unsigned Nodes, unsigned Elements, unsigned Capacity,
405 const unsigned *CurSize, unsigned NewSize[],
406 unsigned Position, bool Grow);
409 //===----------------------------------------------------------------------===//
410 //--- IntervalMapImpl::NodeSizer ---//
411 //===----------------------------------------------------------------------===//
413 // Compute node sizes from key and value types.
415 // The branching factors are chosen to make nodes fit in three cache lines.
416 // This may not be possible if keys or values are very large. Such large objects
417 // are handled correctly, but a std::map would probably give better performance.
419 //===----------------------------------------------------------------------===//
422 // Cache line size. Most architectures have 32 or 64 byte cache lines.
423 // We use 64 bytes here because it provides good branching factors.
425 CacheLineBytes = 1 << Log2CacheLine,
426 DesiredNodeBytes = 3 * CacheLineBytes
429 template <typename KeyT, typename ValT>
432 // Compute the leaf node branching factor that makes a node fit in three
433 // cache lines. The branching factor must be at least 3, or some B+-tree
434 // balancing algorithms won't work.
435 // LeafSize can't be larger than CacheLineBytes. This is required by the
436 // PointerIntPair used by NodeRef.
437 DesiredLeafSize = DesiredNodeBytes /
438 static_cast<unsigned>(2*sizeof(KeyT)+sizeof(ValT)),
440 LeafSize = DesiredLeafSize > MinLeafSize ? DesiredLeafSize : MinLeafSize
443 typedef NodeBase<std::pair<KeyT, KeyT>, ValT, LeafSize> LeafBase;
446 // Now that we have the leaf branching factor, compute the actual allocation
447 // unit size by rounding up to a whole number of cache lines.
448 AllocBytes = (sizeof(LeafBase) + CacheLineBytes-1) & ~(CacheLineBytes-1),
450 // Determine the branching factor for branch nodes.
451 BranchSize = AllocBytes /
452 static_cast<unsigned>(sizeof(KeyT) + sizeof(void*))
455 /// Allocator - The recycling allocator used for both branch and leaf nodes.
456 /// This typedef is very likely to be identical for all IntervalMaps with
457 /// reasonably sized entries, so the same allocator can be shared among
458 /// different kinds of maps.
459 typedef RecyclingAllocator<BumpPtrAllocator, char,
460 AllocBytes, CacheLineBytes> Allocator;
465 //===----------------------------------------------------------------------===//
466 //--- IntervalMapImpl::NodeRef ---//
467 //===----------------------------------------------------------------------===//
469 // B+-tree nodes can be leaves or branches, so we need a polymorphic node
470 // pointer that can point to both kinds.
472 // All nodes are cache line aligned and the low 6 bits of a node pointer are
473 // always 0. These bits are used to store the number of elements in the
474 // referenced node. Besides saving space, placing node sizes in the parents
475 // allow tree balancing algorithms to run without faulting cache lines for nodes
476 // that may not need to be modified.
478 // A NodeRef doesn't know whether it references a leaf node or a branch node.
479 // It is the responsibility of the caller to use the correct types.
481 // Nodes are never supposed to be empty, and it is invalid to store a node size
482 // of 0 in a NodeRef. The valid range of sizes is 1-64.
484 //===----------------------------------------------------------------------===//
487 struct CacheAlignedPointerTraits {
488 static inline void *getAsVoidPointer(void *P) { return P; }
489 static inline void *getFromVoidPointer(void *P) { return P; }
490 enum { NumLowBitsAvailable = Log2CacheLine };
492 PointerIntPair<void*, Log2CacheLine, unsigned, CacheAlignedPointerTraits> pip;
495 /// NodeRef - Create a null ref.
498 /// operator bool - Detect a null ref.
499 operator bool() const { return pip.getOpaqueValue(); }
501 /// NodeRef - Create a reference to the node p with n elements.
502 template <typename NodeT>
503 NodeRef(NodeT *p, unsigned n) : pip(p, n - 1) {
504 assert(n <= NodeT::Capacity && "Size too big for node");
507 /// size - Return the number of elements in the referenced node.
508 unsigned size() const { return pip.getInt() + 1; }
510 /// setSize - Update the node size.
511 void setSize(unsigned n) { pip.setInt(n - 1); }
513 /// subtree - Access the i'th subtree reference in a branch node.
514 /// This depends on branch nodes storing the NodeRef array as their first
516 NodeRef &subtree(unsigned i) const {
517 return reinterpret_cast<NodeRef*>(pip.getPointer())[i];
520 /// get - Dereference as a NodeT reference.
521 template <typename NodeT>
523 return *reinterpret_cast<NodeT*>(pip.getPointer());
526 bool operator==(const NodeRef &RHS) const {
529 assert(pip.getPointer() != RHS.pip.getPointer() && "Inconsistent NodeRefs");
533 bool operator!=(const NodeRef &RHS) const {
534 return !operator==(RHS);
538 //===----------------------------------------------------------------------===//
539 //--- IntervalMapImpl::LeafNode ---//
540 //===----------------------------------------------------------------------===//
542 // Leaf nodes store up to N disjoint intervals with corresponding values.
544 // The intervals are kept sorted and fully coalesced so there are no adjacent
545 // intervals mapping to the same value.
547 // These constraints are always satisfied:
549 // - Traits::stopLess(start(i), stop(i)) - Non-empty, sane intervals.
551 // - Traits::stopLess(stop(i), start(i + 1) - Sorted.
553 // - value(i) != value(i + 1) || !Traits::adjacent(stop(i), start(i + 1))
554 // - Fully coalesced.
556 //===----------------------------------------------------------------------===//
558 template <typename KeyT, typename ValT, unsigned N, typename Traits>
559 class LeafNode : public NodeBase<std::pair<KeyT, KeyT>, ValT, N> {
561 const KeyT &start(unsigned i) const { return this->first[i].first; }
562 const KeyT &stop(unsigned i) const { return this->first[i].second; }
563 const ValT &value(unsigned i) const { return this->second[i]; }
565 KeyT &start(unsigned i) { return this->first[i].first; }
566 KeyT &stop(unsigned i) { return this->first[i].second; }
567 ValT &value(unsigned i) { return this->second[i]; }
569 /// findFrom - Find the first interval after i that may contain x.
570 /// @param i Starting index for the search.
571 /// @param Size Number of elements in node.
572 /// @param x Key to search for.
573 /// @return First index with !stopLess(key[i].stop, x), or size.
574 /// This is the first interval that can possibly contain x.
575 unsigned findFrom(unsigned i, unsigned Size, KeyT x) const {
576 assert(i <= Size && Size <= N && "Bad indices");
577 assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
578 "Index is past the needed point");
579 while (i != Size && Traits::stopLess(stop(i), x)) ++i;
583 /// safeFind - Find an interval that is known to exist. This is the same as
584 /// findFrom except is it assumed that x is at least within range of the last
586 /// @param i Starting index for the search.
587 /// @param x Key to search for.
588 /// @return First index with !stopLess(key[i].stop, x), never size.
589 /// This is the first interval that can possibly contain x.
590 unsigned safeFind(unsigned i, KeyT x) const {
591 assert(i < N && "Bad index");
592 assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
593 "Index is past the needed point");
594 while (Traits::stopLess(stop(i), x)) ++i;
595 assert(i < N && "Unsafe intervals");
599 /// safeLookup - Lookup mapped value for a safe key.
600 /// It is assumed that x is within range of the last entry.
601 /// @param x Key to search for.
602 /// @param NotFound Value to return if x is not in any interval.
603 /// @return The mapped value at x or NotFound.
604 ValT safeLookup(KeyT x, ValT NotFound) const {
605 unsigned i = safeFind(0, x);
606 return Traits::startLess(x, start(i)) ? NotFound : value(i);
609 unsigned insertFrom(unsigned &Pos, unsigned Size, KeyT a, KeyT b, ValT y);
612 /// insertFrom - Add mapping of [a;b] to y if possible, coalescing as much as
613 /// possible. This may cause the node to grow by 1, or it may cause the node
614 /// to shrink because of coalescing.
615 /// @param i Starting index = insertFrom(0, size, a)
616 /// @param Size Number of elements in node.
617 /// @param a Interval start.
618 /// @param b Interval stop.
619 /// @param y Value be mapped.
620 /// @return (insert position, new size), or (i, Capacity+1) on overflow.
621 template <typename KeyT, typename ValT, unsigned N, typename Traits>
622 unsigned LeafNode<KeyT, ValT, N, Traits>::
623 insertFrom(unsigned &Pos, unsigned Size, KeyT a, KeyT b, ValT y) {
625 assert(i <= Size && Size <= N && "Invalid index");
626 assert(!Traits::stopLess(b, a) && "Invalid interval");
628 // Verify the findFrom invariant.
629 assert((i == 0 || Traits::stopLess(stop(i - 1), a)));
630 assert((i == Size || !Traits::stopLess(stop(i), a)));
631 assert((i == Size || Traits::stopLess(b, start(i))) && "Overlapping insert");
633 // Coalesce with previous interval.
634 if (i && value(i - 1) == y && Traits::adjacent(stop(i - 1), a)) {
636 // Also coalesce with next interval?
637 if (i != Size && value(i) == y && Traits::adjacent(b, start(i))) {
638 stop(i - 1) = stop(i);
639 this->erase(i, Size);
650 // Add new interval at end.
658 // Try to coalesce with following interval.
659 if (value(i) == y && Traits::adjacent(b, start(i))) {
664 // We must insert before i. Detect overflow.
669 this->shift(i, Size);
677 //===----------------------------------------------------------------------===//
678 //--- IntervalMapImpl::BranchNode ---//
679 //===----------------------------------------------------------------------===//
681 // A branch node stores references to 1--N subtrees all of the same height.
683 // The key array in a branch node holds the rightmost stop key of each subtree.
684 // It is redundant to store the last stop key since it can be found in the
685 // parent node, but doing so makes tree balancing a lot simpler.
687 // It is unusual for a branch node to only have one subtree, but it can happen
688 // in the root node if it is smaller than the normal nodes.
690 // When all of the leaf nodes from all the subtrees are concatenated, they must
691 // satisfy the same constraints as a single leaf node. They must be sorted,
692 // sane, and fully coalesced.
694 //===----------------------------------------------------------------------===//
696 template <typename KeyT, typename ValT, unsigned N, typename Traits>
697 class BranchNode : public NodeBase<NodeRef, KeyT, N> {
699 const KeyT &stop(unsigned i) const { return this->second[i]; }
700 const NodeRef &subtree(unsigned i) const { return this->first[i]; }
702 KeyT &stop(unsigned i) { return this->second[i]; }
703 NodeRef &subtree(unsigned i) { return this->first[i]; }
705 /// findFrom - Find the first subtree after i that may contain x.
706 /// @param i Starting index for the search.
707 /// @param Size Number of elements in node.
708 /// @param x Key to search for.
709 /// @return First index with !stopLess(key[i], x), or size.
710 /// This is the first subtree that can possibly contain x.
711 unsigned findFrom(unsigned i, unsigned Size, KeyT x) const {
712 assert(i <= Size && Size <= N && "Bad indices");
713 assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
714 "Index to findFrom is past the needed point");
715 while (i != Size && Traits::stopLess(stop(i), x)) ++i;
719 /// safeFind - Find a subtree that is known to exist. This is the same as
720 /// findFrom except is it assumed that x is in range.
721 /// @param i Starting index for the search.
722 /// @param x Key to search for.
723 /// @return First index with !stopLess(key[i], x), never size.
724 /// This is the first subtree that can possibly contain x.
725 unsigned safeFind(unsigned i, KeyT x) const {
726 assert(i < N && "Bad index");
727 assert((i == 0 || Traits::stopLess(stop(i - 1), x)) &&
728 "Index is past the needed point");
729 while (Traits::stopLess(stop(i), x)) ++i;
730 assert(i < N && "Unsafe intervals");
734 /// safeLookup - Get the subtree containing x, Assuming that x is in range.
735 /// @param x Key to search for.
736 /// @return Subtree containing x
737 NodeRef safeLookup(KeyT x) const {
738 return subtree(safeFind(0, x));
741 /// insert - Insert a new (subtree, stop) pair.
742 /// @param i Insert position, following entries will be shifted.
743 /// @param Size Number of elements in node.
744 /// @param Node Subtree to insert.
745 /// @param Stop Last key in subtree.
746 void insert(unsigned i, unsigned Size, NodeRef Node, KeyT Stop) {
747 assert(Size < N && "branch node overflow");
748 assert(i <= Size && "Bad insert position");
749 this->shift(i, Size);
755 //===----------------------------------------------------------------------===//
756 //--- IntervalMapImpl::Path ---//
757 //===----------------------------------------------------------------------===//
759 // A Path is used by iterators to represent a position in a B+-tree, and the
760 // path to get there from the root.
762 // The Path class also contains the tree navigation code that doesn't have to
765 //===----------------------------------------------------------------------===//
768 /// Entry - Each step in the path is a node pointer and an offset into that
775 Entry(void *Node, unsigned Size, unsigned Offset)
776 : node(Node), size(Size), offset(Offset) {}
778 Entry(NodeRef Node, unsigned Offset)
779 : node(&Node.subtree(0)), size(Node.size()), offset(Offset) {}
781 NodeRef &subtree(unsigned i) const {
782 return reinterpret_cast<NodeRef*>(node)[i];
786 /// path - The path entries, path[0] is the root node, path.back() is a leaf.
787 SmallVector<Entry, 4> path;
791 template <typename NodeT> NodeT &node(unsigned Level) const {
792 return *reinterpret_cast<NodeT*>(path[Level].node);
794 unsigned size(unsigned Level) const { return path[Level].size; }
795 unsigned offset(unsigned Level) const { return path[Level].offset; }
796 unsigned &offset(unsigned Level) { return path[Level].offset; }
799 template <typename NodeT> NodeT &leaf() const {
800 return *reinterpret_cast<NodeT*>(path.back().node);
802 unsigned leafSize() const { return path.back().size; }
803 unsigned leafOffset() const { return path.back().offset; }
804 unsigned &leafOffset() { return path.back().offset; }
806 /// valid - Return true if path is at a valid node, not at end().
808 return !path.empty() && path.front().offset < path.front().size;
811 /// height - Return the height of the tree corresponding to this path.
812 /// This matches map->height in a full path.
813 unsigned height() const { return path.size() - 1; }
815 /// subtree - Get the subtree referenced from Level. When the path is
816 /// consistent, node(Level + 1) == subtree(Level).
817 /// @param Level 0..height-1. The leaves have no subtrees.
818 NodeRef &subtree(unsigned Level) const {
819 return path[Level].subtree(path[Level].offset);
822 /// reset - Reset cached information about node(Level) from subtree(Level -1).
823 /// @param Level 1..height. THe node to update after parent node changed.
824 void reset(unsigned Level) {
825 path[Level] = Entry(subtree(Level - 1), offset(Level));
828 /// push - Add entry to path.
829 /// @param Node Node to add, should be subtree(path.size()-1).
830 /// @param Offset Offset into Node.
831 void push(NodeRef Node, unsigned Offset) {
832 path.push_back(Entry(Node, Offset));
835 /// pop - Remove the last path entry.
840 /// setSize - Set the size of a node both in the path and in the tree.
841 /// @param Level 0..height. Note that setting the root size won't change
843 /// @param Size New node size.
844 void setSize(unsigned Level, unsigned Size) {
845 path[Level].size = Size;
847 subtree(Level - 1).setSize(Size);
850 /// setRoot - Clear the path and set a new root node.
851 /// @param Node New root node.
852 /// @param Size New root size.
853 /// @param Offset Offset into root node.
854 void setRoot(void *Node, unsigned Size, unsigned Offset) {
856 path.push_back(Entry(Node, Size, Offset));
859 /// replaceRoot - Replace the current root node with two new entries after the
860 /// tree height has increased.
861 /// @param Root The new root node.
862 /// @param Size Number of entries in the new root.
863 /// @param Offsets Offsets into the root and first branch nodes.
864 void replaceRoot(void *Root, unsigned Size, IdxPair Offsets);
866 /// getLeftSibling - Get the left sibling node at Level, or a null NodeRef.
867 /// @param Level Get the sibling to node(Level).
868 /// @return Left sibling, or NodeRef().
869 NodeRef getLeftSibling(unsigned Level) const;
871 /// moveLeft - Move path to the left sibling at Level. Leave nodes below Level
873 /// @param Level Move node(Level).
874 void moveLeft(unsigned Level);
876 /// fillLeft - Grow path to Height by taking leftmost branches.
877 /// @param Height The target height.
878 void fillLeft(unsigned Height) {
879 while (height() < Height)
880 push(subtree(height()), 0);
883 /// getLeftSibling - Get the left sibling node at Level, or a null NodeRef.
884 /// @param Level Get the sinbling to node(Level).
885 /// @return Left sibling, or NodeRef().
886 NodeRef getRightSibling(unsigned Level) const;
888 /// moveRight - Move path to the left sibling at Level. Leave nodes below
890 /// @param Level Move node(Level).
891 void moveRight(unsigned Level);
893 /// atBegin - Return true if path is at begin().
894 bool atBegin() const {
895 for (unsigned i = 0, e = path.size(); i != e; ++i)
896 if (path[i].offset != 0)
901 /// atLastEntry - Return true if the path is at the last entry of the node at
903 /// @param Level Node to examine.
904 bool atLastEntry(unsigned Level) const {
905 return path[Level].offset == path[Level].size - 1;
908 /// legalizeForInsert - Prepare the path for an insertion at Level. When the
909 /// path is at end(), node(Level) may not be a legal node. legalizeForInsert
910 /// ensures that node(Level) is real by moving back to the last node at Level,
911 /// and setting offset(Level) to size(Level) if required.
912 /// @param Level The level where an insertion is about to take place.
913 void legalizeForInsert(unsigned Level) {
917 ++path[Level].offset;
921 } // namespace IntervalMapImpl
924 //===----------------------------------------------------------------------===//
925 //--- IntervalMap ----//
926 //===----------------------------------------------------------------------===//
928 template <typename KeyT, typename ValT,
929 unsigned N = IntervalMapImpl::NodeSizer<KeyT, ValT>::LeafSize,
930 typename Traits = IntervalMapInfo<KeyT> >
932 typedef IntervalMapImpl::NodeSizer<KeyT, ValT> Sizer;
933 typedef IntervalMapImpl::LeafNode<KeyT, ValT, Sizer::LeafSize, Traits> Leaf;
934 typedef IntervalMapImpl::BranchNode<KeyT, ValT, Sizer::BranchSize, Traits>
936 typedef IntervalMapImpl::LeafNode<KeyT, ValT, N, Traits> RootLeaf;
937 typedef IntervalMapImpl::IdxPair IdxPair;
939 // The RootLeaf capacity is given as a template parameter. We must compute the
940 // corresponding RootBranch capacity.
942 DesiredRootBranchCap = (sizeof(RootLeaf) - sizeof(KeyT)) /
943 (sizeof(KeyT) + sizeof(IntervalMapImpl::NodeRef)),
944 RootBranchCap = DesiredRootBranchCap ? DesiredRootBranchCap : 1
947 typedef IntervalMapImpl::BranchNode<KeyT, ValT, RootBranchCap, Traits>
950 // When branched, we store a global start key as well as the branch node.
951 struct RootBranchData {
957 RootDataSize = sizeof(RootBranchData) > sizeof(RootLeaf) ?
958 sizeof(RootBranchData) : sizeof(RootLeaf)
962 typedef typename Sizer::Allocator Allocator;
963 typedef KeyT KeyType;
964 typedef ValT ValueType;
965 typedef Traits KeyTraits;
968 // The root data is either a RootLeaf or a RootBranchData instance.
969 // We can't put them in a union since C++03 doesn't allow non-trivial
970 // constructors in unions.
971 // Instead, we use a char array with pointer alignment. The alignment is
972 // ensured by the allocator member in the class, but still verified in the
973 // constructor. We don't support keys or values that are more aligned than a
975 char data[RootDataSize];
978 // 0: Leaves in root.
979 // 1: Root points to leaf.
980 // 2: root->branch->leaf ...
983 // Number of entries in the root node.
986 // Allocator used for creating external nodes.
987 Allocator &allocator;
989 /// dataAs - Represent data as a node type without breaking aliasing rules.
990 template <typename T>
1000 const RootLeaf &rootLeaf() const {
1001 assert(!branched() && "Cannot acces leaf data in branched root");
1002 return dataAs<RootLeaf>();
1004 RootLeaf &rootLeaf() {
1005 assert(!branched() && "Cannot acces leaf data in branched root");
1006 return dataAs<RootLeaf>();
1008 RootBranchData &rootBranchData() const {
1009 assert(branched() && "Cannot access branch data in non-branched root");
1010 return dataAs<RootBranchData>();
1012 RootBranchData &rootBranchData() {
1013 assert(branched() && "Cannot access branch data in non-branched root");
1014 return dataAs<RootBranchData>();
1016 const RootBranch &rootBranch() const { return rootBranchData().node; }
1017 RootBranch &rootBranch() { return rootBranchData().node; }
1018 KeyT rootBranchStart() const { return rootBranchData().start; }
1019 KeyT &rootBranchStart() { return rootBranchData().start; }
1021 template <typename NodeT> NodeT *newNode() {
1022 return new(allocator.template Allocate<NodeT>()) NodeT();
1025 template <typename NodeT> void deleteNode(NodeT *P) {
1027 allocator.Deallocate(P);
1030 IdxPair branchRoot(unsigned Position);
1031 IdxPair splitRoot(unsigned Position);
1033 void switchRootToBranch() {
1034 rootLeaf().~RootLeaf();
1036 new (&rootBranchData()) RootBranchData();
1039 void switchRootToLeaf() {
1040 rootBranchData().~RootBranchData();
1042 new(&rootLeaf()) RootLeaf();
1045 bool branched() const { return height > 0; }
1047 ValT treeSafeLookup(KeyT x, ValT NotFound) const;
1048 void visitNodes(void (IntervalMap::*f)(IntervalMapImpl::NodeRef,
1050 void deleteNode(IntervalMapImpl::NodeRef Node, unsigned Level);
1053 explicit IntervalMap(Allocator &a) : height(0), rootSize(0), allocator(a) {
1054 assert((uintptr_t(data) & (alignOf<RootLeaf>() - 1)) == 0 &&
1055 "Insufficient alignment");
1056 new(&rootLeaf()) RootLeaf();
1061 rootLeaf().~RootLeaf();
1064 /// empty - Return true when no intervals are mapped.
1065 bool empty() const {
1066 return rootSize == 0;
1069 /// start - Return the smallest mapped key in a non-empty map.
1070 KeyT start() const {
1071 assert(!empty() && "Empty IntervalMap has no start");
1072 return !branched() ? rootLeaf().start(0) : rootBranchStart();
1075 /// stop - Return the largest mapped key in a non-empty map.
1077 assert(!empty() && "Empty IntervalMap has no stop");
1078 return !branched() ? rootLeaf().stop(rootSize - 1) :
1079 rootBranch().stop(rootSize - 1);
1082 /// lookup - Return the mapped value at x or NotFound.
1083 ValT lookup(KeyT x, ValT NotFound = ValT()) const {
1084 if (empty() || Traits::startLess(x, start()) || Traits::stopLess(stop(), x))
1086 return branched() ? treeSafeLookup(x, NotFound) :
1087 rootLeaf().safeLookup(x, NotFound);
1090 /// insert - Add a mapping of [a;b] to y, coalesce with adjacent intervals.
1091 /// It is assumed that no key in the interval is mapped to another value, but
1092 /// overlapping intervals already mapped to y will be coalesced.
1093 void insert(KeyT a, KeyT b, ValT y) {
1094 if (branched() || rootSize == RootLeaf::Capacity)
1095 return find(a).insert(a, b, y);
1097 // Easy insert into root leaf.
1098 unsigned p = rootLeaf().findFrom(0, rootSize, a);
1099 rootSize = rootLeaf().insertFrom(p, rootSize, a, b, y);
1102 /// clear - Remove all entries.
1105 class const_iterator;
1107 friend class const_iterator;
1108 friend class iterator;
1110 const_iterator begin() const {
1111 const_iterator I(*this);
1122 const_iterator end() const {
1123 const_iterator I(*this);
1134 /// find - Return an iterator pointing to the first interval ending at or
1135 /// after x, or end().
1136 const_iterator find(KeyT x) const {
1137 const_iterator I(*this);
1142 iterator find(KeyT x) {
1149 /// treeSafeLookup - Return the mapped value at x or NotFound, assuming a
1151 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1152 ValT IntervalMap<KeyT, ValT, N, Traits>::
1153 treeSafeLookup(KeyT x, ValT NotFound) const {
1154 assert(branched() && "treeLookup assumes a branched root");
1156 IntervalMapImpl::NodeRef NR = rootBranch().safeLookup(x);
1157 for (unsigned h = height-1; h; --h)
1158 NR = NR.get<Branch>().safeLookup(x);
1159 return NR.get<Leaf>().safeLookup(x, NotFound);
1163 // branchRoot - Switch from a leaf root to a branched root.
1164 // Return the new (root offset, node offset) corresponding to Position.
1165 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1166 IntervalMapImpl::IdxPair IntervalMap<KeyT, ValT, N, Traits>::
1167 branchRoot(unsigned Position) {
1168 using namespace IntervalMapImpl;
1169 // How many external leaf nodes to hold RootLeaf+1?
1170 const unsigned Nodes = RootLeaf::Capacity / Leaf::Capacity + 1;
1172 // Compute element distribution among new nodes.
1173 unsigned size[Nodes];
1174 IdxPair NewOffset(0, Position);
1176 // Is is very common for the root node to be smaller than external nodes.
1180 NewOffset = distribute(Nodes, rootSize, Leaf::Capacity, NULL, size,
1183 // Allocate new nodes.
1185 NodeRef node[Nodes];
1186 for (unsigned n = 0; n != Nodes; ++n) {
1187 Leaf *L = newNode<Leaf>();
1188 L->copy(rootLeaf(), pos, 0, size[n]);
1189 node[n] = NodeRef(L, size[n]);
1193 // Destroy the old leaf node, construct branch node instead.
1194 switchRootToBranch();
1195 for (unsigned n = 0; n != Nodes; ++n) {
1196 rootBranch().stop(n) = node[n].template get<Leaf>().stop(size[n]-1);
1197 rootBranch().subtree(n) = node[n];
1199 rootBranchStart() = node[0].template get<Leaf>().start(0);
1204 // splitRoot - Split the current BranchRoot into multiple Branch nodes.
1205 // Return the new (root offset, node offset) corresponding to Position.
1206 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1207 IntervalMapImpl::IdxPair IntervalMap<KeyT, ValT, N, Traits>::
1208 splitRoot(unsigned Position) {
1209 using namespace IntervalMapImpl;
1210 // How many external leaf nodes to hold RootBranch+1?
1211 const unsigned Nodes = RootBranch::Capacity / Branch::Capacity + 1;
1213 // Compute element distribution among new nodes.
1214 unsigned Size[Nodes];
1215 IdxPair NewOffset(0, Position);
1217 // Is is very common for the root node to be smaller than external nodes.
1221 NewOffset = distribute(Nodes, rootSize, Leaf::Capacity, NULL, Size,
1224 // Allocate new nodes.
1226 NodeRef Node[Nodes];
1227 for (unsigned n = 0; n != Nodes; ++n) {
1228 Branch *B = newNode<Branch>();
1229 B->copy(rootBranch(), Pos, 0, Size[n]);
1230 Node[n] = NodeRef(B, Size[n]);
1234 for (unsigned n = 0; n != Nodes; ++n) {
1235 rootBranch().stop(n) = Node[n].template get<Branch>().stop(Size[n]-1);
1236 rootBranch().subtree(n) = Node[n];
1243 /// visitNodes - Visit each external node.
1244 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1245 void IntervalMap<KeyT, ValT, N, Traits>::
1246 visitNodes(void (IntervalMap::*f)(IntervalMapImpl::NodeRef, unsigned Height)) {
1249 SmallVector<IntervalMapImpl::NodeRef, 4> Refs, NextRefs;
1251 // Collect level 0 nodes from the root.
1252 for (unsigned i = 0; i != rootSize; ++i)
1253 Refs.push_back(rootBranch().subtree(i));
1255 // Visit all branch nodes.
1256 for (unsigned h = height - 1; h; --h) {
1257 for (unsigned i = 0, e = Refs.size(); i != e; ++i) {
1258 for (unsigned j = 0, s = Refs[i].size(); j != s; ++j)
1259 NextRefs.push_back(Refs[i].subtree(j));
1260 (this->*f)(Refs[i], h);
1263 Refs.swap(NextRefs);
1266 // Visit all leaf nodes.
1267 for (unsigned i = 0, e = Refs.size(); i != e; ++i)
1268 (this->*f)(Refs[i], 0);
1271 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1272 void IntervalMap<KeyT, ValT, N, Traits>::
1273 deleteNode(IntervalMapImpl::NodeRef Node, unsigned Level) {
1275 deleteNode(&Node.get<Branch>());
1277 deleteNode(&Node.get<Leaf>());
1280 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1281 void IntervalMap<KeyT, ValT, N, Traits>::
1284 visitNodes(&IntervalMap::deleteNode);
1290 //===----------------------------------------------------------------------===//
1291 //--- IntervalMap::const_iterator ----//
1292 //===----------------------------------------------------------------------===//
1294 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1295 class IntervalMap<KeyT, ValT, N, Traits>::const_iterator :
1296 public std::iterator<std::bidirectional_iterator_tag, ValT> {
1298 friend class IntervalMap;
1300 // The map referred to.
1303 // We store a full path from the root to the current position.
1304 // The path may be partially filled, but never between iterator calls.
1305 IntervalMapImpl::Path path;
1307 explicit const_iterator(const IntervalMap &map) :
1308 map(const_cast<IntervalMap*>(&map)) {}
1310 bool branched() const {
1311 assert(map && "Invalid iterator");
1312 return map->branched();
1315 void setRoot(unsigned Offset) {
1317 path.setRoot(&map->rootBranch(), map->rootSize, Offset);
1319 path.setRoot(&map->rootLeaf(), map->rootSize, Offset);
1322 void pathFillFind(KeyT x);
1323 void treeFind(KeyT x);
1324 void treeAdvanceTo(KeyT x);
1326 /// unsafeStart - Writable access to start() for iterator.
1327 KeyT &unsafeStart() const {
1328 assert(valid() && "Cannot access invalid iterator");
1329 return branched() ? path.leaf<Leaf>().start(path.leafOffset()) :
1330 path.leaf<RootLeaf>().start(path.leafOffset());
1333 /// unsafeStop - Writable access to stop() for iterator.
1334 KeyT &unsafeStop() const {
1335 assert(valid() && "Cannot access invalid iterator");
1336 return branched() ? path.leaf<Leaf>().stop(path.leafOffset()) :
1337 path.leaf<RootLeaf>().stop(path.leafOffset());
1340 /// unsafeValue - Writable access to value() for iterator.
1341 ValT &unsafeValue() const {
1342 assert(valid() && "Cannot access invalid iterator");
1343 return branched() ? path.leaf<Leaf>().value(path.leafOffset()) :
1344 path.leaf<RootLeaf>().value(path.leafOffset());
1348 /// const_iterator - Create an iterator that isn't pointing anywhere.
1349 const_iterator() : map(0) {}
1351 /// setMap - Change the map iterated over. This call must be followed by a
1352 /// call to goToBegin(), goToEnd(), or find()
1353 void setMap(const IntervalMap &m) { map = const_cast<IntervalMap*>(&m); }
1355 /// valid - Return true if the current position is valid, false for end().
1356 bool valid() const { return path.valid(); }
1358 /// atBegin - Return true if the current position is the first map entry.
1359 bool atBegin() const { return path.atBegin(); }
1361 /// start - Return the beginning of the current interval.
1362 const KeyT &start() const { return unsafeStart(); }
1364 /// stop - Return the end of the current interval.
1365 const KeyT &stop() const { return unsafeStop(); }
1367 /// value - Return the mapped value at the current interval.
1368 const ValT &value() const { return unsafeValue(); }
1370 const ValT &operator*() const { return value(); }
1372 bool operator==(const const_iterator &RHS) const {
1373 assert(map == RHS.map && "Cannot compare iterators from different maps");
1375 return !RHS.valid();
1376 if (path.leafOffset() != RHS.path.leafOffset())
1378 return &path.template leaf<Leaf>() == &RHS.path.template leaf<Leaf>();
1381 bool operator!=(const const_iterator &RHS) const {
1382 return !operator==(RHS);
1385 /// goToBegin - Move to the first interval in map.
1389 path.fillLeft(map->height);
1392 /// goToEnd - Move beyond the last interval in map.
1394 setRoot(map->rootSize);
1397 /// preincrement - move to the next interval.
1398 const_iterator &operator++() {
1399 assert(valid() && "Cannot increment end()");
1400 if (++path.leafOffset() == path.leafSize() && branched())
1401 path.moveRight(map->height);
1405 /// postincrement - Dont do that!
1406 const_iterator operator++(int) {
1407 const_iterator tmp = *this;
1412 /// predecrement - move to the previous interval.
1413 const_iterator &operator--() {
1414 if (path.leafOffset() && (valid() || !branched()))
1415 --path.leafOffset();
1417 path.moveLeft(map->height);
1421 /// postdecrement - Dont do that!
1422 const_iterator operator--(int) {
1423 const_iterator tmp = *this;
1428 /// find - Move to the first interval with stop >= x, or end().
1429 /// This is a full search from the root, the current position is ignored.
1434 setRoot(map->rootLeaf().findFrom(0, map->rootSize, x));
1437 /// advanceTo - Move to the first interval with stop >= x, or end().
1438 /// The search is started from the current position, and no earlier positions
1439 /// can be found. This is much faster than find() for small moves.
1440 void advanceTo(KeyT x) {
1447 map->rootLeaf().findFrom(path.leafOffset(), map->rootSize, x);
1452 /// pathFillFind - Complete path by searching for x.
1453 /// @param x Key to search for.
1454 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1455 void IntervalMap<KeyT, ValT, N, Traits>::
1456 const_iterator::pathFillFind(KeyT x) {
1457 IntervalMapImpl::NodeRef NR = path.subtree(path.height());
1458 for (unsigned i = map->height - path.height() - 1; i; --i) {
1459 unsigned p = NR.get<Branch>().safeFind(0, x);
1463 path.push(NR, NR.get<Leaf>().safeFind(0, x));
1466 /// treeFind - Find in a branched tree.
1467 /// @param x Key to search for.
1468 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1469 void IntervalMap<KeyT, ValT, N, Traits>::
1470 const_iterator::treeFind(KeyT x) {
1471 setRoot(map->rootBranch().findFrom(0, map->rootSize, x));
1476 /// treeAdvanceTo - Find position after the current one.
1477 /// @param x Key to search for.
1478 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1479 void IntervalMap<KeyT, ValT, N, Traits>::
1480 const_iterator::treeAdvanceTo(KeyT x) {
1481 // Can we stay on the same leaf node?
1482 if (!Traits::stopLess(path.leaf<Leaf>().stop(path.leafSize() - 1), x)) {
1483 path.leafOffset() = path.leaf<Leaf>().safeFind(path.leafOffset(), x);
1487 // Drop the current leaf.
1490 // Search towards the root for a usable subtree.
1491 if (path.height()) {
1492 for (unsigned l = path.height() - 1; l; --l) {
1493 if (!Traits::stopLess(path.node<Branch>(l).stop(path.offset(l)), x)) {
1494 // The branch node at l+1 is usable
1495 path.offset(l + 1) =
1496 path.node<Branch>(l + 1).safeFind(path.offset(l + 1), x);
1497 return pathFillFind(x);
1501 // Is the level-1 Branch usable?
1502 if (!Traits::stopLess(map->rootBranch().stop(path.offset(0)), x)) {
1503 path.offset(1) = path.node<Branch>(1).safeFind(path.offset(1), x);
1504 return pathFillFind(x);
1508 // We reached the root.
1509 setRoot(map->rootBranch().findFrom(path.offset(0), map->rootSize, x));
1514 //===----------------------------------------------------------------------===//
1515 //--- IntervalMap::iterator ----//
1516 //===----------------------------------------------------------------------===//
1518 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1519 class IntervalMap<KeyT, ValT, N, Traits>::iterator : public const_iterator {
1520 friend class IntervalMap;
1521 typedef IntervalMapImpl::IdxPair IdxPair;
1523 explicit iterator(IntervalMap &map) : const_iterator(map) {}
1525 void setNodeStop(unsigned Level, KeyT Stop);
1526 bool insertNode(unsigned Level, IntervalMapImpl::NodeRef Node, KeyT Stop);
1527 template <typename NodeT> bool overflow(unsigned Level);
1528 void treeInsert(KeyT a, KeyT b, ValT y);
1529 void eraseNode(unsigned Level);
1530 void treeErase(bool UpdateRoot = true);
1531 bool canCoalesceLeft(KeyT Start, ValT x);
1532 bool canCoalesceRight(KeyT Stop, ValT x);
1535 /// iterator - Create null iterator.
1538 /// setStart - Move the start of the current interval.
1539 /// This may cause coalescing with the previous interval.
1540 /// @param a New start key, must not overlap the previous interval.
1541 void setStart(KeyT a);
1543 /// setStop - Move the end of the current interval.
1544 /// This may cause coalescing with the following interval.
1545 /// @param b New stop key, must not overlap the following interval.
1546 void setStop(KeyT b);
1548 /// setValue - Change the mapped value of the current interval.
1549 /// This may cause coalescing with the previous and following intervals.
1550 /// @param x New value.
1551 void setValue(ValT x);
1553 /// setStartUnchecked - Move the start of the current interval without
1554 /// checking for coalescing or overlaps.
1555 /// This should only be used when it is known that coalescing is not required.
1556 /// @param a New start key.
1557 void setStartUnchecked(KeyT a) { this->unsafeStart() = a; }
1559 /// setStopUnchecked - Move the end of the current interval without checking
1560 /// for coalescing or overlaps.
1561 /// This should only be used when it is known that coalescing is not required.
1562 /// @param b New stop key.
1563 void setStopUnchecked(KeyT b) {
1564 this->unsafeStop() = b;
1565 // Update keys in branch nodes as well.
1566 if (this->path.atLastEntry(this->path.height()))
1567 setNodeStop(this->path.height(), b);
1570 /// setValueUnchecked - Change the mapped value of the current interval
1571 /// without checking for coalescing.
1572 /// @param x New value.
1573 void setValueUnchecked(ValT x) { this->unsafeValue() = x; }
1575 /// insert - Insert mapping [a;b] -> y before the current position.
1576 void insert(KeyT a, KeyT b, ValT y);
1578 /// erase - Erase the current interval.
1581 iterator &operator++() {
1582 const_iterator::operator++();
1586 iterator operator++(int) {
1587 iterator tmp = *this;
1592 iterator &operator--() {
1593 const_iterator::operator--();
1597 iterator operator--(int) {
1598 iterator tmp = *this;
1605 /// canCoalesceLeft - Can the current interval coalesce to the left after
1606 /// changing start or value?
1607 /// @param Start New start of current interval.
1608 /// @param Value New value for current interval.
1609 /// @return True when updating the current interval would enable coalescing.
1610 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1611 bool IntervalMap<KeyT, ValT, N, Traits>::
1612 iterator::canCoalesceLeft(KeyT Start, ValT Value) {
1613 using namespace IntervalMapImpl;
1614 Path &P = this->path;
1615 if (!this->branched()) {
1616 unsigned i = P.leafOffset();
1617 RootLeaf &Node = P.leaf<RootLeaf>();
1618 return i && Node.value(i-1) == Value &&
1619 Traits::adjacent(Node.stop(i-1), Start);
1622 if (unsigned i = P.leafOffset()) {
1623 Leaf &Node = P.leaf<Leaf>();
1624 return Node.value(i-1) == Value && Traits::adjacent(Node.stop(i-1), Start);
1625 } else if (NodeRef NR = P.getLeftSibling(P.height())) {
1626 unsigned i = NR.size() - 1;
1627 Leaf &Node = NR.get<Leaf>();
1628 return Node.value(i) == Value && Traits::adjacent(Node.stop(i), Start);
1633 /// canCoalesceRight - Can the current interval coalesce to the right after
1634 /// changing stop or value?
1635 /// @param Stop New stop of current interval.
1636 /// @param Value New value for current interval.
1637 /// @return True when updating the current interval would enable coalescing.
1638 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1639 bool IntervalMap<KeyT, ValT, N, Traits>::
1640 iterator::canCoalesceRight(KeyT Stop, ValT Value) {
1641 using namespace IntervalMapImpl;
1642 Path &P = this->path;
1643 unsigned i = P.leafOffset() + 1;
1644 if (!this->branched()) {
1645 if (i >= P.leafSize())
1647 RootLeaf &Node = P.leaf<RootLeaf>();
1648 return Node.value(i) == Value && Traits::adjacent(Stop, Node.start(i));
1651 if (i < P.leafSize()) {
1652 Leaf &Node = P.leaf<Leaf>();
1653 return Node.value(i) == Value && Traits::adjacent(Stop, Node.start(i));
1654 } else if (NodeRef NR = P.getRightSibling(P.height())) {
1655 Leaf &Node = NR.get<Leaf>();
1656 return Node.value(0) == Value && Traits::adjacent(Stop, Node.start(0));
1661 /// setNodeStop - Update the stop key of the current node at level and above.
1662 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1663 void IntervalMap<KeyT, ValT, N, Traits>::
1664 iterator::setNodeStop(unsigned Level, KeyT Stop) {
1665 // There are no references to the root node, so nothing to update.
1668 IntervalMapImpl::Path &P = this->path;
1669 // Update nodes pointing to the current node.
1671 P.node<Branch>(Level).stop(P.offset(Level)) = Stop;
1672 if (!P.atLastEntry(Level))
1675 // Update root separately since it has a different layout.
1676 P.node<RootBranch>(Level).stop(P.offset(Level)) = Stop;
1679 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1680 void IntervalMap<KeyT, ValT, N, Traits>::
1681 iterator::setStart(KeyT a) {
1682 assert(Traits::stopLess(a, this->stop()) && "Cannot move start beyond stop");
1683 KeyT &CurStart = this->unsafeStart();
1684 if (!Traits::startLess(a, CurStart) || !canCoalesceLeft(a, this->value())) {
1688 // Coalesce with the interval to the left.
1692 setStartUnchecked(a);
1695 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1696 void IntervalMap<KeyT, ValT, N, Traits>::
1697 iterator::setStop(KeyT b) {
1698 assert(Traits::stopLess(this->start(), b) && "Cannot move stop beyond start");
1699 if (Traits::startLess(b, this->stop()) ||
1700 !canCoalesceRight(b, this->value())) {
1701 setStopUnchecked(b);
1704 // Coalesce with interval to the right.
1705 KeyT a = this->start();
1707 setStartUnchecked(a);
1710 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1711 void IntervalMap<KeyT, ValT, N, Traits>::
1712 iterator::setValue(ValT x) {
1713 setValueUnchecked(x);
1714 if (canCoalesceRight(this->stop(), x)) {
1715 KeyT a = this->start();
1717 setStartUnchecked(a);
1719 if (canCoalesceLeft(this->start(), x)) {
1721 KeyT a = this->start();
1723 setStartUnchecked(a);
1727 /// insertNode - insert a node before the current path at level.
1728 /// Leave the current path pointing at the new node.
1729 /// @param Level path index of the node to be inserted.
1730 /// @param Node The node to be inserted.
1731 /// @param Stop The last index in the new node.
1732 /// @return True if the tree height was increased.
1733 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1734 bool IntervalMap<KeyT, ValT, N, Traits>::
1735 iterator::insertNode(unsigned Level, IntervalMapImpl::NodeRef Node, KeyT Stop) {
1736 assert(Level && "Cannot insert next to the root");
1737 bool SplitRoot = false;
1738 IntervalMap &IM = *this->map;
1739 IntervalMapImpl::Path &P = this->path;
1742 // Insert into the root branch node.
1743 if (IM.rootSize < RootBranch::Capacity) {
1744 IM.rootBranch().insert(P.offset(0), IM.rootSize, Node, Stop);
1745 P.setSize(0, ++IM.rootSize);
1750 // We need to split the root while keeping our position.
1752 IdxPair Offset = IM.splitRoot(P.offset(0));
1753 P.replaceRoot(&IM.rootBranch(), IM.rootSize, Offset);
1755 // Fall through to insert at the new higher level.
1759 // When inserting before end(), make sure we have a valid path.
1760 P.legalizeForInsert(--Level);
1762 // Insert into the branch node at Level-1.
1763 if (P.size(Level) == Branch::Capacity) {
1764 // Branch node is full, handle handle the overflow.
1765 assert(!SplitRoot && "Cannot overflow after splitting the root");
1766 SplitRoot = overflow<Branch>(Level);
1769 P.node<Branch>(Level).insert(P.offset(Level), P.size(Level), Node, Stop);
1770 P.setSize(Level, P.size(Level) + 1);
1771 if (P.atLastEntry(Level))
1772 setNodeStop(Level, Stop);
1778 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1779 void IntervalMap<KeyT, ValT, N, Traits>::
1780 iterator::insert(KeyT a, KeyT b, ValT y) {
1781 if (this->branched())
1782 return treeInsert(a, b, y);
1783 IntervalMap &IM = *this->map;
1784 IntervalMapImpl::Path &P = this->path;
1786 // Try simple root leaf insert.
1787 unsigned Size = IM.rootLeaf().insertFrom(P.leafOffset(), IM.rootSize, a, b, y);
1789 // Was the root node insert successful?
1790 if (Size <= RootLeaf::Capacity) {
1791 P.setSize(0, IM.rootSize = Size);
1795 // Root leaf node is full, we must branch.
1796 IdxPair Offset = IM.branchRoot(P.leafOffset());
1797 P.replaceRoot(&IM.rootBranch(), IM.rootSize, Offset);
1799 // Now it fits in the new leaf.
1800 treeInsert(a, b, y);
1804 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1805 void IntervalMap<KeyT, ValT, N, Traits>::
1806 iterator::treeInsert(KeyT a, KeyT b, ValT y) {
1807 using namespace IntervalMapImpl;
1808 Path &P = this->path;
1811 P.legalizeForInsert(this->map->height);
1813 // Check if this insertion will extend the node to the left.
1814 if (P.leafOffset() == 0 && Traits::startLess(a, P.leaf<Leaf>().start(0))) {
1815 // Node is growing to the left, will it affect a left sibling node?
1816 if (NodeRef Sib = P.getLeftSibling(P.height())) {
1817 Leaf &SibLeaf = Sib.get<Leaf>();
1818 unsigned SibOfs = Sib.size() - 1;
1819 if (SibLeaf.value(SibOfs) == y &&
1820 Traits::adjacent(SibLeaf.stop(SibOfs), a)) {
1821 // This insertion will coalesce with the last entry in SibLeaf. We can
1822 // handle it in two ways:
1823 // 1. Extend SibLeaf.stop to b and be done, or
1824 // 2. Extend a to SibLeaf, erase the SibLeaf entry and continue.
1825 // We prefer 1., but need 2 when coalescing to the right as well.
1826 Leaf &CurLeaf = P.leaf<Leaf>();
1827 P.moveLeft(P.height());
1828 if (Traits::stopLess(b, CurLeaf.start(0)) &&
1829 (y != CurLeaf.value(0) || !Traits::adjacent(b, CurLeaf.start(0)))) {
1830 // Easy, just extend SibLeaf and we're done.
1831 setNodeStop(P.height(), SibLeaf.stop(SibOfs) = b);
1834 // We have both left and right coalescing. Erase the old SibLeaf entry
1835 // and continue inserting the larger interval.
1836 a = SibLeaf.start(SibOfs);
1837 treeErase(/* UpdateRoot= */false);
1841 // No left sibling means we are at begin(). Update cached bound.
1842 this->map->rootBranchStart() = a;
1846 // When we are inserting at the end of a leaf node, we must update stops.
1847 unsigned Size = P.leafSize();
1848 bool Grow = P.leafOffset() == Size;
1849 Size = P.leaf<Leaf>().insertFrom(P.leafOffset(), Size, a, b, y);
1851 // Leaf insertion unsuccessful? Overflow and try again.
1852 if (Size > Leaf::Capacity) {
1853 overflow<Leaf>(P.height());
1854 Grow = P.leafOffset() == P.leafSize();
1855 Size = P.leaf<Leaf>().insertFrom(P.leafOffset(), P.leafSize(), a, b, y);
1856 assert(Size <= Leaf::Capacity && "overflow() didn't make room");
1859 // Inserted, update offset and leaf size.
1860 P.setSize(P.height(), Size);
1862 // Insert was the last node entry, update stops.
1864 setNodeStop(P.height(), b);
1867 /// erase - erase the current interval and move to the next position.
1868 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1869 void IntervalMap<KeyT, ValT, N, Traits>::
1871 IntervalMap &IM = *this->map;
1872 IntervalMapImpl::Path &P = this->path;
1873 assert(P.valid() && "Cannot erase end()");
1874 if (this->branched())
1876 IM.rootLeaf().erase(P.leafOffset(), IM.rootSize);
1877 P.setSize(0, --IM.rootSize);
1880 /// treeErase - erase() for a branched tree.
1881 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1882 void IntervalMap<KeyT, ValT, N, Traits>::
1883 iterator::treeErase(bool UpdateRoot) {
1884 IntervalMap &IM = *this->map;
1885 IntervalMapImpl::Path &P = this->path;
1886 Leaf &Node = P.leaf<Leaf>();
1888 // Nodes are not allowed to become empty.
1889 if (P.leafSize() == 1) {
1890 IM.deleteNode(&Node);
1891 eraseNode(IM.height);
1892 // Update rootBranchStart if we erased begin().
1893 if (UpdateRoot && IM.branched() && P.valid() && P.atBegin())
1894 IM.rootBranchStart() = P.leaf<Leaf>().start(0);
1898 // Erase current entry.
1899 Node.erase(P.leafOffset(), P.leafSize());
1900 unsigned NewSize = P.leafSize() - 1;
1901 P.setSize(IM.height, NewSize);
1902 // When we erase the last entry, update stop and move to a legal position.
1903 if (P.leafOffset() == NewSize) {
1904 setNodeStop(IM.height, Node.stop(NewSize - 1));
1905 P.moveRight(IM.height);
1906 } else if (UpdateRoot && P.atBegin())
1907 IM.rootBranchStart() = P.leaf<Leaf>().start(0);
1910 /// eraseNode - Erase the current node at Level from its parent and move path to
1911 /// the first entry of the next sibling node.
1912 /// The node must be deallocated by the caller.
1913 /// @param Level 1..height, the root node cannot be erased.
1914 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1915 void IntervalMap<KeyT, ValT, N, Traits>::
1916 iterator::eraseNode(unsigned Level) {
1917 assert(Level && "Cannot erase root node");
1918 IntervalMap &IM = *this->map;
1919 IntervalMapImpl::Path &P = this->path;
1922 IM.rootBranch().erase(P.offset(0), IM.rootSize);
1923 P.setSize(0, --IM.rootSize);
1924 // If this cleared the root, switch to height=0.
1926 IM.switchRootToLeaf();
1931 // Remove node ref from branch node at Level.
1932 Branch &Parent = P.node<Branch>(Level);
1933 if (P.size(Level) == 1) {
1934 // Branch node became empty, remove it recursively.
1935 IM.deleteNode(&Parent);
1938 // Branch node won't become empty.
1939 Parent.erase(P.offset(Level), P.size(Level));
1940 unsigned NewSize = P.size(Level) - 1;
1941 P.setSize(Level, NewSize);
1942 // If we removed the last branch, update stop and move to a legal pos.
1943 if (P.offset(Level) == NewSize) {
1944 setNodeStop(Level, Parent.stop(NewSize - 1));
1949 // Update path cache for the new right sibling position.
1952 P.offset(Level + 1) = 0;
1956 /// overflow - Distribute entries of the current node evenly among
1957 /// its siblings and ensure that the current node is not full.
1958 /// This may require allocating a new node.
1959 /// @param NodeT The type of node at Level (Leaf or Branch).
1960 /// @param Level path index of the overflowing node.
1961 /// @return True when the tree height was changed.
1962 template <typename KeyT, typename ValT, unsigned N, typename Traits>
1963 template <typename NodeT>
1964 bool IntervalMap<KeyT, ValT, N, Traits>::
1965 iterator::overflow(unsigned Level) {
1966 using namespace IntervalMapImpl;
1967 Path &P = this->path;
1968 unsigned CurSize[4];
1971 unsigned Elements = 0;
1972 unsigned Offset = P.offset(Level);
1974 // Do we have a left sibling?
1975 NodeRef LeftSib = P.getLeftSibling(Level);
1977 Offset += Elements = CurSize[Nodes] = LeftSib.size();
1978 Node[Nodes++] = &LeftSib.get<NodeT>();
1982 Elements += CurSize[Nodes] = P.size(Level);
1983 Node[Nodes++] = &P.node<NodeT>(Level);
1985 // Do we have a right sibling?
1986 NodeRef RightSib = P.getRightSibling(Level);
1988 Elements += CurSize[Nodes] = RightSib.size();
1989 Node[Nodes++] = &RightSib.get<NodeT>();
1992 // Do we need to allocate a new node?
1993 unsigned NewNode = 0;
1994 if (Elements + 1 > Nodes * NodeT::Capacity) {
1995 // Insert NewNode at the penultimate position, or after a single node.
1996 NewNode = Nodes == 1 ? 1 : Nodes - 1;
1997 CurSize[Nodes] = CurSize[NewNode];
1998 Node[Nodes] = Node[NewNode];
1999 CurSize[NewNode] = 0;
2000 Node[NewNode] = this->map->template newNode<NodeT>();
2004 // Compute the new element distribution.
2005 unsigned NewSize[4];
2006 IdxPair NewOffset = distribute(Nodes, Elements, NodeT::Capacity,
2007 CurSize, NewSize, Offset, true);
2008 adjustSiblingSizes(Node, Nodes, CurSize, NewSize);
2010 // Move current location to the leftmost node.
2014 // Elements have been rearranged, now update node sizes and stops.
2015 bool SplitRoot = false;
2018 KeyT Stop = Node[Pos]->stop(NewSize[Pos]-1);
2019 if (NewNode && Pos == NewNode) {
2020 SplitRoot = insertNode(Level, NodeRef(Node[Pos], NewSize[Pos]), Stop);
2023 P.setSize(Level, NewSize[Pos]);
2024 setNodeStop(Level, Stop);
2026 if (Pos + 1 == Nodes)
2032 // Where was I? Find NewOffset.
2033 while(Pos != NewOffset.first) {
2037 P.offset(Level) = NewOffset.second;
2041 //===----------------------------------------------------------------------===//
2042 //--- IntervalMapOverlaps ----//
2043 //===----------------------------------------------------------------------===//
2045 /// IntervalMapOverlaps - Iterate over the overlaps of mapped intervals in two
2046 /// IntervalMaps. The maps may be different, but the KeyT and Traits types
2047 /// should be the same.
2051 /// 1. Test for overlap:
2052 /// bool overlap = IntervalMapOverlaps(a, b).valid();
2054 /// 2. Enumerate overlaps:
2055 /// for (IntervalMapOverlaps I(a, b); I.valid() ; ++I) { ... }
2057 template <typename MapA, typename MapB>
2058 class IntervalMapOverlaps {
2059 typedef typename MapA::KeyType KeyType;
2060 typedef typename MapA::KeyTraits Traits;
2061 typename MapA::const_iterator posA;
2062 typename MapB::const_iterator posB;
2064 /// advance - Move posA and posB forward until reaching an overlap, or until
2065 /// either meets end.
2066 /// Don't move the iterators if they are already overlapping.
2071 if (Traits::stopLess(posA.stop(), posB.start())) {
2072 // A ends before B begins. Catch up.
2073 posA.advanceTo(posB.start());
2074 if (!posA.valid() || !Traits::stopLess(posB.stop(), posA.start()))
2076 } else if (Traits::stopLess(posB.stop(), posA.start())) {
2077 // B ends before A begins. Catch up.
2078 posB.advanceTo(posA.start());
2079 if (!posB.valid() || !Traits::stopLess(posA.stop(), posB.start()))
2082 // Already overlapping.
2086 // Make a.end > b.start.
2087 posA.advanceTo(posB.start());
2088 if (!posA.valid() || !Traits::stopLess(posB.stop(), posA.start()))
2090 // Make b.end > a.start.
2091 posB.advanceTo(posA.start());
2092 if (!posB.valid() || !Traits::stopLess(posA.stop(), posB.start()))
2098 /// IntervalMapOverlaps - Create an iterator for the overlaps of a and b.
2099 IntervalMapOverlaps(const MapA &a, const MapB &b)
2100 : posA(b.empty() ? a.end() : a.find(b.start())),
2101 posB(posA.valid() ? b.find(posA.start()) : b.end()) { advance(); }
2103 /// valid - Return true if iterator is at an overlap.
2104 bool valid() const {
2105 return posA.valid() && posB.valid();
2108 /// a - access the left hand side in the overlap.
2109 const typename MapA::const_iterator &a() const { return posA; }
2111 /// b - access the right hand side in the overlap.
2112 const typename MapB::const_iterator &b() const { return posB; }
2114 /// start - Beginning of the overlapping interval.
2115 KeyType start() const {
2116 KeyType ak = a().start();
2117 KeyType bk = b().start();
2118 return Traits::startLess(ak, bk) ? bk : ak;
2121 /// stop - End of the overlapping interval.
2122 KeyType stop() const {
2123 KeyType ak = a().stop();
2124 KeyType bk = b().stop();
2125 return Traits::startLess(ak, bk) ? ak : bk;
2128 /// skipA - Move to the next overlap that doesn't involve a().
2134 /// skipB - Move to the next overlap that doesn't involve b().
2140 /// Preincrement - Move to the next overlap.
2141 IntervalMapOverlaps &operator++() {
2142 // Bump the iterator that ends first. The other one may have more overlaps.
2143 if (Traits::startLess(posB.stop(), posA.stop()))
2150 /// advanceTo - Move to the first overlapping interval with
2151 /// stopLess(x, stop()).
2152 void advanceTo(KeyType x) {
2155 // Make sure advanceTo sees monotonic keys.
2156 if (Traits::stopLess(posA.stop(), x))
2158 if (Traits::stopLess(posB.stop(), x))