1 //===- llvm/ADT/SparseBitVector.h - Efficient Sparse BitVector -*- 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 defines the SparseBitVector class. See the doxygen comment for
11 // SparseBitVector for more details on the algorithm used.
13 //===----------------------------------------------------------------------===//
15 #ifndef LLVM_ADT_SPARSEBITVECTOR_H
16 #define LLVM_ADT_SPARSEBITVECTOR_H
18 #include "llvm/ADT/ilist.h"
19 #include "llvm/ADT/ilist_node.h"
20 #include "llvm/Support/DataTypes.h"
21 #include "llvm/Support/ErrorHandling.h"
22 #include "llvm/Support/MathExtras.h"
23 #include "llvm/Support/raw_ostream.h"
29 /// SparseBitVector is an implementation of a bitvector that is sparse by only
30 /// storing the elements that have non-zero bits set. In order to make this
31 /// fast for the most common cases, SparseBitVector is implemented as a linked
32 /// list of SparseBitVectorElements. We maintain a pointer to the last
33 /// SparseBitVectorElement accessed (in the form of a list iterator), in order
34 /// to make multiple in-order test/set constant time after the first one is
35 /// executed. Note that using vectors to store SparseBitVectorElement's does
36 /// not work out very well because it causes insertion in the middle to take
37 /// enormous amounts of time with a large amount of bits. Other structures that
38 /// have better worst cases for insertion in the middle (various balanced trees,
39 /// etc) do not perform as well in practice as a linked list with this iterator
40 /// kept up to date. They are also significantly more memory intensive.
43 template <unsigned ElementSize = 128>
44 struct SparseBitVectorElement
45 : public ilist_node<SparseBitVectorElement<ElementSize> > {
47 typedef unsigned long BitWord;
48 typedef unsigned size_type;
50 BITWORD_SIZE = sizeof(BitWord) * CHAR_BIT,
51 BITWORDS_PER_ELEMENT = (ElementSize + BITWORD_SIZE - 1) / BITWORD_SIZE,
52 BITS_PER_ELEMENT = ElementSize
56 // Index of Element in terms of where first bit starts.
57 unsigned ElementIndex;
58 BitWord Bits[BITWORDS_PER_ELEMENT];
59 // Needed for sentinels
60 friend struct ilist_sentinel_traits<SparseBitVectorElement>;
61 SparseBitVectorElement() {
63 memset(&Bits[0], 0, sizeof (BitWord) * BITWORDS_PER_ELEMENT);
67 explicit SparseBitVectorElement(unsigned Idx) {
69 memset(&Bits[0], 0, sizeof (BitWord) * BITWORDS_PER_ELEMENT);
73 bool operator==(const SparseBitVectorElement &RHS) const {
74 if (ElementIndex != RHS.ElementIndex)
76 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
77 if (Bits[i] != RHS.Bits[i])
82 bool operator!=(const SparseBitVectorElement &RHS) const {
83 return !(*this == RHS);
86 // Return the bits that make up word Idx in our element.
87 BitWord word(unsigned Idx) const {
88 assert (Idx < BITWORDS_PER_ELEMENT);
92 unsigned index() const {
97 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
103 void set(unsigned Idx) {
104 Bits[Idx / BITWORD_SIZE] |= 1L << (Idx % BITWORD_SIZE);
107 bool test_and_set (unsigned Idx) {
108 bool old = test(Idx);
116 void reset(unsigned Idx) {
117 Bits[Idx / BITWORD_SIZE] &= ~(1L << (Idx % BITWORD_SIZE));
120 bool test(unsigned Idx) const {
121 return Bits[Idx / BITWORD_SIZE] & (1L << (Idx % BITWORD_SIZE));
124 size_type count() const {
125 unsigned NumBits = 0;
126 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
127 if (sizeof(BitWord) == 4)
128 NumBits += CountPopulation_32(Bits[i]);
129 else if (sizeof(BitWord) == 8)
130 NumBits += CountPopulation_64(Bits[i]);
132 llvm_unreachable("Unsupported!");
136 /// find_first - Returns the index of the first set bit.
137 int find_first() const {
138 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
140 if (sizeof(BitWord) == 4)
141 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
142 if (sizeof(BitWord) == 8)
143 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
144 llvm_unreachable("Unsupported!");
146 llvm_unreachable("Illegal empty element");
149 /// find_next - Returns the index of the next set bit starting from the
150 /// "Curr" bit. Returns -1 if the next set bit is not found.
151 int find_next(unsigned Curr) const {
152 if (Curr >= BITS_PER_ELEMENT)
155 unsigned WordPos = Curr / BITWORD_SIZE;
156 unsigned BitPos = Curr % BITWORD_SIZE;
157 BitWord Copy = Bits[WordPos];
158 assert (WordPos <= BITWORDS_PER_ELEMENT
159 && "Word Position outside of element");
161 // Mask off previous bits.
162 Copy &= ~0UL << BitPos;
165 if (sizeof(BitWord) == 4)
166 return WordPos * BITWORD_SIZE + countTrailingZeros(Copy);
167 if (sizeof(BitWord) == 8)
168 return WordPos * BITWORD_SIZE + countTrailingZeros(Copy);
169 llvm_unreachable("Unsupported!");
172 // Check subsequent words.
173 for (unsigned i = WordPos+1; i < BITWORDS_PER_ELEMENT; ++i)
175 if (sizeof(BitWord) == 4)
176 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
177 if (sizeof(BitWord) == 8)
178 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
179 llvm_unreachable("Unsupported!");
184 // Union this element with RHS and return true if this one changed.
185 bool unionWith(const SparseBitVectorElement &RHS) {
186 bool changed = false;
187 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
188 BitWord old = changed ? 0 : Bits[i];
190 Bits[i] |= RHS.Bits[i];
191 if (!changed && old != Bits[i])
197 // Return true if we have any bits in common with RHS
198 bool intersects(const SparseBitVectorElement &RHS) const {
199 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
200 if (RHS.Bits[i] & Bits[i])
206 // Intersect this Element with RHS and return true if this one changed.
207 // BecameZero is set to true if this element became all-zero bits.
208 bool intersectWith(const SparseBitVectorElement &RHS,
210 bool changed = false;
214 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
215 BitWord old = changed ? 0 : Bits[i];
217 Bits[i] &= RHS.Bits[i];
221 if (!changed && old != Bits[i])
224 BecameZero = allzero;
227 // Intersect this Element with the complement of RHS and return true if this
228 // one changed. BecameZero is set to true if this element became all-zero
230 bool intersectWithComplement(const SparseBitVectorElement &RHS,
232 bool changed = false;
236 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
237 BitWord old = changed ? 0 : Bits[i];
239 Bits[i] &= ~RHS.Bits[i];
243 if (!changed && old != Bits[i])
246 BecameZero = allzero;
249 // Three argument version of intersectWithComplement that intersects
250 // RHS1 & ~RHS2 into this element
251 void intersectWithComplement(const SparseBitVectorElement &RHS1,
252 const SparseBitVectorElement &RHS2,
257 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
258 Bits[i] = RHS1.Bits[i] & ~RHS2.Bits[i];
262 BecameZero = allzero;
266 template <unsigned ElementSize>
267 struct ilist_traits<SparseBitVectorElement<ElementSize> >
268 : public ilist_default_traits<SparseBitVectorElement<ElementSize> > {
269 typedef SparseBitVectorElement<ElementSize> Element;
271 Element *createSentinel() const { return static_cast<Element *>(&Sentinel); }
272 static void destroySentinel(Element *) {}
274 Element *provideInitialHead() const { return createSentinel(); }
275 Element *ensureHead(Element *) const { return createSentinel(); }
276 static void noteHead(Element *, Element *) {}
279 mutable ilist_half_node<Element> Sentinel;
282 template <unsigned ElementSize = 128>
283 class SparseBitVector {
284 typedef ilist<SparseBitVectorElement<ElementSize> > ElementList;
285 typedef typename ElementList::iterator ElementListIter;
286 typedef typename ElementList::const_iterator ElementListConstIter;
288 BITWORD_SIZE = SparseBitVectorElement<ElementSize>::BITWORD_SIZE
291 // Pointer to our current Element.
292 ElementListIter CurrElementIter;
293 ElementList Elements;
295 // This is like std::lower_bound, except we do linear searching from the
297 ElementListIter FindLowerBound(unsigned ElementIndex) {
299 if (Elements.empty()) {
300 CurrElementIter = Elements.begin();
301 return Elements.begin();
304 // Make sure our current iterator is valid.
305 if (CurrElementIter == Elements.end())
308 // Search from our current iterator, either backwards or forwards,
309 // depending on what element we are looking for.
310 ElementListIter ElementIter = CurrElementIter;
311 if (CurrElementIter->index() == ElementIndex) {
313 } else if (CurrElementIter->index() > ElementIndex) {
314 while (ElementIter != Elements.begin()
315 && ElementIter->index() > ElementIndex)
318 while (ElementIter != Elements.end() &&
319 ElementIter->index() < ElementIndex)
322 CurrElementIter = ElementIter;
326 // Iterator to walk set bits in the bitmap. This iterator is a lot uglier
327 // than it would be, in order to be efficient.
328 class SparseBitVectorIterator {
332 const SparseBitVector<ElementSize> *BitVector;
334 // Current element inside of bitmap.
335 ElementListConstIter Iter;
337 // Current bit number inside of our bitmap.
340 // Current word number inside of our element.
343 // Current bits from the element.
344 typename SparseBitVectorElement<ElementSize>::BitWord Bits;
346 // Move our iterator to the first non-zero bit in the bitmap.
347 void AdvanceToFirstNonZero() {
350 if (BitVector->Elements.empty()) {
354 Iter = BitVector->Elements.begin();
355 BitNumber = Iter->index() * ElementSize;
356 unsigned BitPos = Iter->find_first();
358 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
359 Bits = Iter->word(WordNumber);
360 Bits >>= BitPos % BITWORD_SIZE;
363 // Move our iterator to the next non-zero bit.
364 void AdvanceToNextNonZero() {
368 while (Bits && !(Bits & 1)) {
373 // See if we ran out of Bits in this word.
375 int NextSetBitNumber = Iter->find_next(BitNumber % ElementSize) ;
376 // If we ran out of set bits in this element, move to next element.
377 if (NextSetBitNumber == -1 || (BitNumber % ElementSize == 0)) {
381 // We may run out of elements in the bitmap.
382 if (Iter == BitVector->Elements.end()) {
386 // Set up for next non-zero word in bitmap.
387 BitNumber = Iter->index() * ElementSize;
388 NextSetBitNumber = Iter->find_first();
389 BitNumber += NextSetBitNumber;
390 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
391 Bits = Iter->word(WordNumber);
392 Bits >>= NextSetBitNumber % BITWORD_SIZE;
394 WordNumber = (NextSetBitNumber % ElementSize) / BITWORD_SIZE;
395 Bits = Iter->word(WordNumber);
396 Bits >>= NextSetBitNumber % BITWORD_SIZE;
397 BitNumber = Iter->index() * ElementSize;
398 BitNumber += NextSetBitNumber;
404 inline SparseBitVectorIterator& operator++() {
407 AdvanceToNextNonZero();
412 inline SparseBitVectorIterator operator++(int) {
413 SparseBitVectorIterator tmp = *this;
418 // Return the current set bit number.
419 unsigned operator*() const {
423 bool operator==(const SparseBitVectorIterator &RHS) const {
424 // If they are both at the end, ignore the rest of the fields.
425 if (AtEnd && RHS.AtEnd)
427 // Otherwise they are the same if they have the same bit number and
429 return AtEnd == RHS.AtEnd && RHS.BitNumber == BitNumber;
431 bool operator!=(const SparseBitVectorIterator &RHS) const {
432 return !(*this == RHS);
434 SparseBitVectorIterator(): BitVector(NULL) {
438 SparseBitVectorIterator(const SparseBitVector<ElementSize> *RHS,
439 bool end = false):BitVector(RHS) {
440 Iter = BitVector->Elements.begin();
445 AdvanceToFirstNonZero();
449 typedef SparseBitVectorIterator iterator;
452 CurrElementIter = Elements.begin ();
458 // SparseBitVector copy ctor.
459 SparseBitVector(const SparseBitVector &RHS) {
460 ElementListConstIter ElementIter = RHS.Elements.begin();
461 while (ElementIter != RHS.Elements.end()) {
462 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
466 CurrElementIter = Elements.begin ();
475 SparseBitVector& operator=(const SparseBitVector& RHS) {
478 ElementListConstIter ElementIter = RHS.Elements.begin();
479 while (ElementIter != RHS.Elements.end()) {
480 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
484 CurrElementIter = Elements.begin ();
489 // Test, Reset, and Set a bit in the bitmap.
490 bool test(unsigned Idx) {
491 if (Elements.empty())
494 unsigned ElementIndex = Idx / ElementSize;
495 ElementListIter ElementIter = FindLowerBound(ElementIndex);
497 // If we can't find an element that is supposed to contain this bit, there
498 // is nothing more to do.
499 if (ElementIter == Elements.end() ||
500 ElementIter->index() != ElementIndex)
502 return ElementIter->test(Idx % ElementSize);
505 void reset(unsigned Idx) {
506 if (Elements.empty())
509 unsigned ElementIndex = Idx / ElementSize;
510 ElementListIter ElementIter = FindLowerBound(ElementIndex);
512 // If we can't find an element that is supposed to contain this bit, there
513 // is nothing more to do.
514 if (ElementIter == Elements.end() ||
515 ElementIter->index() != ElementIndex)
517 ElementIter->reset(Idx % ElementSize);
519 // When the element is zeroed out, delete it.
520 if (ElementIter->empty()) {
522 Elements.erase(ElementIter);
526 void set(unsigned Idx) {
527 unsigned ElementIndex = Idx / ElementSize;
528 SparseBitVectorElement<ElementSize> *Element;
529 ElementListIter ElementIter;
530 if (Elements.empty()) {
531 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
532 ElementIter = Elements.insert(Elements.end(), Element);
535 ElementIter = FindLowerBound(ElementIndex);
537 if (ElementIter == Elements.end() ||
538 ElementIter->index() != ElementIndex) {
539 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
540 // We may have hit the beginning of our SparseBitVector, in which case,
541 // we may need to insert right after this element, which requires moving
542 // the current iterator forward one, because insert does insert before.
543 if (ElementIter != Elements.end() &&
544 ElementIter->index() < ElementIndex)
545 ElementIter = Elements.insert(++ElementIter, Element);
547 ElementIter = Elements.insert(ElementIter, Element);
550 CurrElementIter = ElementIter;
552 ElementIter->set(Idx % ElementSize);
555 bool test_and_set (unsigned Idx) {
556 bool old = test(Idx);
564 bool operator!=(const SparseBitVector &RHS) const {
565 return !(*this == RHS);
568 bool operator==(const SparseBitVector &RHS) const {
569 ElementListConstIter Iter1 = Elements.begin();
570 ElementListConstIter Iter2 = RHS.Elements.begin();
572 for (; Iter1 != Elements.end() && Iter2 != RHS.Elements.end();
574 if (*Iter1 != *Iter2)
577 return Iter1 == Elements.end() && Iter2 == RHS.Elements.end();
580 // Union our bitmap with the RHS and return true if we changed.
581 bool operator|=(const SparseBitVector &RHS) {
582 bool changed = false;
583 ElementListIter Iter1 = Elements.begin();
584 ElementListConstIter Iter2 = RHS.Elements.begin();
586 // If RHS is empty, we are done
587 if (RHS.Elements.empty())
590 while (Iter2 != RHS.Elements.end()) {
591 if (Iter1 == Elements.end() || Iter1->index() > Iter2->index()) {
592 Elements.insert(Iter1,
593 new SparseBitVectorElement<ElementSize>(*Iter2));
596 } else if (Iter1->index() == Iter2->index()) {
597 changed |= Iter1->unionWith(*Iter2);
604 CurrElementIter = Elements.begin();
608 // Intersect our bitmap with the RHS and return true if ours changed.
609 bool operator&=(const SparseBitVector &RHS) {
610 bool changed = false;
611 ElementListIter Iter1 = Elements.begin();
612 ElementListConstIter Iter2 = RHS.Elements.begin();
614 // Check if both bitmaps are empty.
615 if (Elements.empty() && RHS.Elements.empty())
618 // Loop through, intersecting as we go, erasing elements when necessary.
619 while (Iter2 != RHS.Elements.end()) {
620 if (Iter1 == Elements.end()) {
621 CurrElementIter = Elements.begin();
625 if (Iter1->index() > Iter2->index()) {
627 } else if (Iter1->index() == Iter2->index()) {
629 changed |= Iter1->intersectWith(*Iter2, BecameZero);
631 ElementListIter IterTmp = Iter1;
633 Elements.erase(IterTmp);
639 ElementListIter IterTmp = Iter1;
641 Elements.erase(IterTmp);
644 Elements.erase(Iter1, Elements.end());
645 CurrElementIter = Elements.begin();
649 // Intersect our bitmap with the complement of the RHS and return true
651 bool intersectWithComplement(const SparseBitVector &RHS) {
652 bool changed = false;
653 ElementListIter Iter1 = Elements.begin();
654 ElementListConstIter Iter2 = RHS.Elements.begin();
656 // If either our bitmap or RHS is empty, we are done
657 if (Elements.empty() || RHS.Elements.empty())
660 // Loop through, intersecting as we go, erasing elements when necessary.
661 while (Iter2 != RHS.Elements.end()) {
662 if (Iter1 == Elements.end()) {
663 CurrElementIter = Elements.begin();
667 if (Iter1->index() > Iter2->index()) {
669 } else if (Iter1->index() == Iter2->index()) {
671 changed |= Iter1->intersectWithComplement(*Iter2, BecameZero);
673 ElementListIter IterTmp = Iter1;
675 Elements.erase(IterTmp);
684 CurrElementIter = Elements.begin();
688 bool intersectWithComplement(const SparseBitVector<ElementSize> *RHS) const {
689 return intersectWithComplement(*RHS);
693 // Three argument version of intersectWithComplement.
694 // Result of RHS1 & ~RHS2 is stored into this bitmap.
695 void intersectWithComplement(const SparseBitVector<ElementSize> &RHS1,
696 const SparseBitVector<ElementSize> &RHS2)
699 CurrElementIter = Elements.begin();
700 ElementListConstIter Iter1 = RHS1.Elements.begin();
701 ElementListConstIter Iter2 = RHS2.Elements.begin();
703 // If RHS1 is empty, we are done
704 // If RHS2 is empty, we still have to copy RHS1
705 if (RHS1.Elements.empty())
708 // Loop through, intersecting as we go, erasing elements when necessary.
709 while (Iter2 != RHS2.Elements.end()) {
710 if (Iter1 == RHS1.Elements.end())
713 if (Iter1->index() > Iter2->index()) {
715 } else if (Iter1->index() == Iter2->index()) {
716 bool BecameZero = false;
717 SparseBitVectorElement<ElementSize> *NewElement =
718 new SparseBitVectorElement<ElementSize>(Iter1->index());
719 NewElement->intersectWithComplement(*Iter1, *Iter2, BecameZero);
721 Elements.push_back(NewElement);
728 SparseBitVectorElement<ElementSize> *NewElement =
729 new SparseBitVectorElement<ElementSize>(*Iter1);
730 Elements.push_back(NewElement);
735 // copy the remaining elements
736 while (Iter1 != RHS1.Elements.end()) {
737 SparseBitVectorElement<ElementSize> *NewElement =
738 new SparseBitVectorElement<ElementSize>(*Iter1);
739 Elements.push_back(NewElement);
746 void intersectWithComplement(const SparseBitVector<ElementSize> *RHS1,
747 const SparseBitVector<ElementSize> *RHS2) {
748 intersectWithComplement(*RHS1, *RHS2);
751 bool intersects(const SparseBitVector<ElementSize> *RHS) const {
752 return intersects(*RHS);
755 // Return true if we share any bits in common with RHS
756 bool intersects(const SparseBitVector<ElementSize> &RHS) const {
757 ElementListConstIter Iter1 = Elements.begin();
758 ElementListConstIter Iter2 = RHS.Elements.begin();
760 // Check if both bitmaps are empty.
761 if (Elements.empty() && RHS.Elements.empty())
764 // Loop through, intersecting stopping when we hit bits in common.
765 while (Iter2 != RHS.Elements.end()) {
766 if (Iter1 == Elements.end())
769 if (Iter1->index() > Iter2->index()) {
771 } else if (Iter1->index() == Iter2->index()) {
772 if (Iter1->intersects(*Iter2))
783 // Return true iff all bits set in this SparseBitVector are
785 bool contains(const SparseBitVector<ElementSize> &RHS) const {
786 SparseBitVector<ElementSize> Result(*this);
788 return (Result == RHS);
791 // Return the first set bit in the bitmap. Return -1 if no bits are set.
792 int find_first() const {
793 if (Elements.empty())
795 const SparseBitVectorElement<ElementSize> &First = *(Elements.begin());
796 return (First.index() * ElementSize) + First.find_first();
799 // Return true if the SparseBitVector is empty
801 return Elements.empty();
804 unsigned count() const {
805 unsigned BitCount = 0;
806 for (ElementListConstIter Iter = Elements.begin();
807 Iter != Elements.end();
809 BitCount += Iter->count();
813 iterator begin() const {
814 return iterator(this);
817 iterator end() const {
818 return iterator(this, true);
822 // Convenience functions to allow Or and And without dereferencing in the user
825 template <unsigned ElementSize>
826 inline bool operator |=(SparseBitVector<ElementSize> &LHS,
827 const SparseBitVector<ElementSize> *RHS) {
831 template <unsigned ElementSize>
832 inline bool operator |=(SparseBitVector<ElementSize> *LHS,
833 const SparseBitVector<ElementSize> &RHS) {
834 return LHS->operator|=(RHS);
837 template <unsigned ElementSize>
838 inline bool operator &=(SparseBitVector<ElementSize> *LHS,
839 const SparseBitVector<ElementSize> &RHS) {
840 return LHS->operator&=(RHS);
843 template <unsigned ElementSize>
844 inline bool operator &=(SparseBitVector<ElementSize> &LHS,
845 const SparseBitVector<ElementSize> *RHS) {
849 // Convenience functions for infix union, intersection, difference operators.
851 template <unsigned ElementSize>
852 inline SparseBitVector<ElementSize>
853 operator|(const SparseBitVector<ElementSize> &LHS,
854 const SparseBitVector<ElementSize> &RHS) {
855 SparseBitVector<ElementSize> Result(LHS);
860 template <unsigned ElementSize>
861 inline SparseBitVector<ElementSize>
862 operator&(const SparseBitVector<ElementSize> &LHS,
863 const SparseBitVector<ElementSize> &RHS) {
864 SparseBitVector<ElementSize> Result(LHS);
869 template <unsigned ElementSize>
870 inline SparseBitVector<ElementSize>
871 operator-(const SparseBitVector<ElementSize> &LHS,
872 const SparseBitVector<ElementSize> &RHS) {
873 SparseBitVector<ElementSize> Result;
874 Result.intersectWithComplement(LHS, RHS);
881 // Dump a SparseBitVector to a stream
882 template <unsigned ElementSize>
883 void dump(const SparseBitVector<ElementSize> &LHS, raw_ostream &out) {
886 typename SparseBitVector<ElementSize>::iterator bi = LHS.begin(),
890 for (++bi; bi != be; ++bi) {
896 } // end namespace llvm