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;
49 BITWORD_SIZE = sizeof(BitWord) * CHAR_BIT,
50 BITWORDS_PER_ELEMENT = (ElementSize + BITWORD_SIZE - 1) / BITWORD_SIZE,
51 BITS_PER_ELEMENT = ElementSize
55 // Index of Element in terms of where first bit starts.
56 unsigned ElementIndex;
57 BitWord Bits[BITWORDS_PER_ELEMENT];
58 // Needed for sentinels
59 friend struct ilist_sentinel_traits<SparseBitVectorElement>;
60 SparseBitVectorElement() {
62 memset(&Bits[0], 0, sizeof (BitWord) * BITWORDS_PER_ELEMENT);
66 explicit SparseBitVectorElement(unsigned Idx) {
68 memset(&Bits[0], 0, sizeof (BitWord) * BITWORDS_PER_ELEMENT);
72 bool operator==(const SparseBitVectorElement &RHS) const {
73 if (ElementIndex != RHS.ElementIndex)
75 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
76 if (Bits[i] != RHS.Bits[i])
81 bool operator!=(const SparseBitVectorElement &RHS) const {
82 return !(*this == RHS);
85 // Return the bits that make up word Idx in our element.
86 BitWord word(unsigned Idx) const {
87 assert (Idx < BITWORDS_PER_ELEMENT);
91 unsigned index() const {
96 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
102 void set(unsigned Idx) {
103 Bits[Idx / BITWORD_SIZE] |= 1L << (Idx % BITWORD_SIZE);
106 bool test_and_set (unsigned Idx) {
107 bool old = test(Idx);
115 void reset(unsigned Idx) {
116 Bits[Idx / BITWORD_SIZE] &= ~(1L << (Idx % BITWORD_SIZE));
119 bool test(unsigned Idx) const {
120 return Bits[Idx / BITWORD_SIZE] & (1L << (Idx % BITWORD_SIZE));
123 unsigned count() const {
124 unsigned NumBits = 0;
125 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
126 if (sizeof(BitWord) == 4)
127 NumBits += CountPopulation_32(Bits[i]);
128 else if (sizeof(BitWord) == 8)
129 NumBits += CountPopulation_64(Bits[i]);
131 llvm_unreachable("Unsupported!");
135 /// find_first - Returns the index of the first set bit.
136 int find_first() const {
137 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i)
139 if (sizeof(BitWord) == 4)
140 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
141 if (sizeof(BitWord) == 8)
142 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
143 llvm_unreachable("Unsupported!");
145 llvm_unreachable("Illegal empty element");
148 /// find_next - Returns the index of the next set bit starting from the
149 /// "Curr" bit. Returns -1 if the next set bit is not found.
150 int find_next(unsigned Curr) const {
151 if (Curr >= BITS_PER_ELEMENT)
154 unsigned WordPos = Curr / BITWORD_SIZE;
155 unsigned BitPos = Curr % BITWORD_SIZE;
156 BitWord Copy = Bits[WordPos];
157 assert (WordPos <= BITWORDS_PER_ELEMENT
158 && "Word Position outside of element");
160 // Mask off previous bits.
161 Copy &= ~0UL << BitPos;
164 if (sizeof(BitWord) == 4)
165 return WordPos * BITWORD_SIZE + countTrailingZeros(Copy);
166 if (sizeof(BitWord) == 8)
167 return WordPos * BITWORD_SIZE + countTrailingZeros(Copy);
168 llvm_unreachable("Unsupported!");
171 // Check subsequent words.
172 for (unsigned i = WordPos+1; i < BITWORDS_PER_ELEMENT; ++i)
174 if (sizeof(BitWord) == 4)
175 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
176 if (sizeof(BitWord) == 8)
177 return i * BITWORD_SIZE + countTrailingZeros(Bits[i]);
178 llvm_unreachable("Unsupported!");
183 // Union this element with RHS and return true if this one changed.
184 bool unionWith(const SparseBitVectorElement &RHS) {
185 bool changed = false;
186 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
187 BitWord old = changed ? 0 : Bits[i];
189 Bits[i] |= RHS.Bits[i];
190 if (!changed && old != Bits[i])
196 // Return true if we have any bits in common with RHS
197 bool intersects(const SparseBitVectorElement &RHS) const {
198 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
199 if (RHS.Bits[i] & Bits[i])
205 // Intersect this Element with RHS and return true if this one changed.
206 // BecameZero is set to true if this element became all-zero bits.
207 bool intersectWith(const SparseBitVectorElement &RHS,
209 bool changed = false;
213 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
214 BitWord old = changed ? 0 : Bits[i];
216 Bits[i] &= RHS.Bits[i];
220 if (!changed && old != Bits[i])
223 BecameZero = allzero;
226 // Intersect this Element with the complement of RHS and return true if this
227 // one changed. BecameZero is set to true if this element became all-zero
229 bool intersectWithComplement(const SparseBitVectorElement &RHS,
231 bool changed = false;
235 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
236 BitWord old = changed ? 0 : Bits[i];
238 Bits[i] &= ~RHS.Bits[i];
242 if (!changed && old != Bits[i])
245 BecameZero = allzero;
248 // Three argument version of intersectWithComplement that intersects
249 // RHS1 & ~RHS2 into this element
250 void intersectWithComplement(const SparseBitVectorElement &RHS1,
251 const SparseBitVectorElement &RHS2,
256 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
257 Bits[i] = RHS1.Bits[i] & ~RHS2.Bits[i];
261 BecameZero = allzero;
265 template <unsigned ElementSize>
266 struct ilist_traits<SparseBitVectorElement<ElementSize> >
267 : public ilist_default_traits<SparseBitVectorElement<ElementSize> > {
268 typedef SparseBitVectorElement<ElementSize> Element;
270 Element *createSentinel() const { return static_cast<Element *>(&Sentinel); }
271 static void destroySentinel(Element *) {}
273 Element *provideInitialHead() const { return createSentinel(); }
274 Element *ensureHead(Element *) const { return createSentinel(); }
275 static void noteHead(Element *, Element *) {}
278 mutable ilist_half_node<Element> Sentinel;
281 template <unsigned ElementSize = 128>
282 class SparseBitVector {
283 typedef ilist<SparseBitVectorElement<ElementSize> > ElementList;
284 typedef typename ElementList::iterator ElementListIter;
285 typedef typename ElementList::const_iterator ElementListConstIter;
287 BITWORD_SIZE = SparseBitVectorElement<ElementSize>::BITWORD_SIZE
290 // Pointer to our current Element.
291 ElementListIter CurrElementIter;
292 ElementList Elements;
294 // This is like std::lower_bound, except we do linear searching from the
296 ElementListIter FindLowerBound(unsigned ElementIndex) {
298 if (Elements.empty()) {
299 CurrElementIter = Elements.begin();
300 return Elements.begin();
303 // Make sure our current iterator is valid.
304 if (CurrElementIter == Elements.end())
307 // Search from our current iterator, either backwards or forwards,
308 // depending on what element we are looking for.
309 ElementListIter ElementIter = CurrElementIter;
310 if (CurrElementIter->index() == ElementIndex) {
312 } else if (CurrElementIter->index() > ElementIndex) {
313 while (ElementIter != Elements.begin()
314 && ElementIter->index() > ElementIndex)
317 while (ElementIter != Elements.end() &&
318 ElementIter->index() < ElementIndex)
321 CurrElementIter = ElementIter;
325 // Iterator to walk set bits in the bitmap. This iterator is a lot uglier
326 // than it would be, in order to be efficient.
327 class SparseBitVectorIterator {
331 const SparseBitVector<ElementSize> *BitVector;
333 // Current element inside of bitmap.
334 ElementListConstIter Iter;
336 // Current bit number inside of our bitmap.
339 // Current word number inside of our element.
342 // Current bits from the element.
343 typename SparseBitVectorElement<ElementSize>::BitWord Bits;
345 // Move our iterator to the first non-zero bit in the bitmap.
346 void AdvanceToFirstNonZero() {
349 if (BitVector->Elements.empty()) {
353 Iter = BitVector->Elements.begin();
354 BitNumber = Iter->index() * ElementSize;
355 unsigned BitPos = Iter->find_first();
357 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
358 Bits = Iter->word(WordNumber);
359 Bits >>= BitPos % BITWORD_SIZE;
362 // Move our iterator to the next non-zero bit.
363 void AdvanceToNextNonZero() {
367 while (Bits && !(Bits & 1)) {
372 // See if we ran out of Bits in this word.
374 int NextSetBitNumber = Iter->find_next(BitNumber % ElementSize) ;
375 // If we ran out of set bits in this element, move to next element.
376 if (NextSetBitNumber == -1 || (BitNumber % ElementSize == 0)) {
380 // We may run out of elements in the bitmap.
381 if (Iter == BitVector->Elements.end()) {
385 // Set up for next non-zero word in bitmap.
386 BitNumber = Iter->index() * ElementSize;
387 NextSetBitNumber = Iter->find_first();
388 BitNumber += NextSetBitNumber;
389 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
390 Bits = Iter->word(WordNumber);
391 Bits >>= NextSetBitNumber % BITWORD_SIZE;
393 WordNumber = (NextSetBitNumber % ElementSize) / BITWORD_SIZE;
394 Bits = Iter->word(WordNumber);
395 Bits >>= NextSetBitNumber % BITWORD_SIZE;
396 BitNumber = Iter->index() * ElementSize;
397 BitNumber += NextSetBitNumber;
403 inline SparseBitVectorIterator& operator++() {
406 AdvanceToNextNonZero();
411 inline SparseBitVectorIterator operator++(int) {
412 SparseBitVectorIterator tmp = *this;
417 // Return the current set bit number.
418 unsigned operator*() const {
422 bool operator==(const SparseBitVectorIterator &RHS) const {
423 // If they are both at the end, ignore the rest of the fields.
424 if (AtEnd && RHS.AtEnd)
426 // Otherwise they are the same if they have the same bit number and
428 return AtEnd == RHS.AtEnd && RHS.BitNumber == BitNumber;
430 bool operator!=(const SparseBitVectorIterator &RHS) const {
431 return !(*this == RHS);
433 SparseBitVectorIterator(): BitVector(NULL) {
437 SparseBitVectorIterator(const SparseBitVector<ElementSize> *RHS,
438 bool end = false):BitVector(RHS) {
439 Iter = BitVector->Elements.begin();
444 AdvanceToFirstNonZero();
448 typedef SparseBitVectorIterator iterator;
451 CurrElementIter = Elements.begin ();
457 // SparseBitVector copy ctor.
458 SparseBitVector(const SparseBitVector &RHS) {
459 ElementListConstIter ElementIter = RHS.Elements.begin();
460 while (ElementIter != RHS.Elements.end()) {
461 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
465 CurrElementIter = Elements.begin ();
474 SparseBitVector& operator=(const SparseBitVector& RHS) {
477 ElementListConstIter ElementIter = RHS.Elements.begin();
478 while (ElementIter != RHS.Elements.end()) {
479 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
483 CurrElementIter = Elements.begin ();
488 // Test, Reset, and Set a bit in the bitmap.
489 bool test(unsigned Idx) {
490 if (Elements.empty())
493 unsigned ElementIndex = Idx / ElementSize;
494 ElementListIter ElementIter = FindLowerBound(ElementIndex);
496 // If we can't find an element that is supposed to contain this bit, there
497 // is nothing more to do.
498 if (ElementIter == Elements.end() ||
499 ElementIter->index() != ElementIndex)
501 return ElementIter->test(Idx % ElementSize);
504 void reset(unsigned Idx) {
505 if (Elements.empty())
508 unsigned ElementIndex = Idx / ElementSize;
509 ElementListIter ElementIter = FindLowerBound(ElementIndex);
511 // If we can't find an element that is supposed to contain this bit, there
512 // is nothing more to do.
513 if (ElementIter == Elements.end() ||
514 ElementIter->index() != ElementIndex)
516 ElementIter->reset(Idx % ElementSize);
518 // When the element is zeroed out, delete it.
519 if (ElementIter->empty()) {
521 Elements.erase(ElementIter);
525 void set(unsigned Idx) {
526 unsigned ElementIndex = Idx / ElementSize;
527 SparseBitVectorElement<ElementSize> *Element;
528 ElementListIter ElementIter;
529 if (Elements.empty()) {
530 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
531 ElementIter = Elements.insert(Elements.end(), Element);
534 ElementIter = FindLowerBound(ElementIndex);
536 if (ElementIter == Elements.end() ||
537 ElementIter->index() != ElementIndex) {
538 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
539 // We may have hit the beginning of our SparseBitVector, in which case,
540 // we may need to insert right after this element, which requires moving
541 // the current iterator forward one, because insert does insert before.
542 if (ElementIter != Elements.end() &&
543 ElementIter->index() < ElementIndex)
544 ElementIter = Elements.insert(++ElementIter, Element);
546 ElementIter = Elements.insert(ElementIter, Element);
549 CurrElementIter = ElementIter;
551 ElementIter->set(Idx % ElementSize);
554 bool test_and_set (unsigned Idx) {
555 bool old = test(Idx);
563 bool operator!=(const SparseBitVector &RHS) const {
564 return !(*this == RHS);
567 bool operator==(const SparseBitVector &RHS) const {
568 ElementListConstIter Iter1 = Elements.begin();
569 ElementListConstIter Iter2 = RHS.Elements.begin();
571 for (; Iter1 != Elements.end() && Iter2 != RHS.Elements.end();
573 if (*Iter1 != *Iter2)
576 return Iter1 == Elements.end() && Iter2 == RHS.Elements.end();
579 // Union our bitmap with the RHS and return true if we changed.
580 bool operator|=(const SparseBitVector &RHS) {
581 bool changed = false;
582 ElementListIter Iter1 = Elements.begin();
583 ElementListConstIter Iter2 = RHS.Elements.begin();
585 // If RHS is empty, we are done
586 if (RHS.Elements.empty())
589 while (Iter2 != RHS.Elements.end()) {
590 if (Iter1 == Elements.end() || Iter1->index() > Iter2->index()) {
591 Elements.insert(Iter1,
592 new SparseBitVectorElement<ElementSize>(*Iter2));
595 } else if (Iter1->index() == Iter2->index()) {
596 changed |= Iter1->unionWith(*Iter2);
603 CurrElementIter = Elements.begin();
607 // Intersect our bitmap with the RHS and return true if ours changed.
608 bool operator&=(const SparseBitVector &RHS) {
609 bool changed = false;
610 ElementListIter Iter1 = Elements.begin();
611 ElementListConstIter Iter2 = RHS.Elements.begin();
613 // Check if both bitmaps are empty.
614 if (Elements.empty() && RHS.Elements.empty())
617 // Loop through, intersecting as we go, erasing elements when necessary.
618 while (Iter2 != RHS.Elements.end()) {
619 if (Iter1 == Elements.end()) {
620 CurrElementIter = Elements.begin();
624 if (Iter1->index() > Iter2->index()) {
626 } else if (Iter1->index() == Iter2->index()) {
628 changed |= Iter1->intersectWith(*Iter2, BecameZero);
630 ElementListIter IterTmp = Iter1;
632 Elements.erase(IterTmp);
638 ElementListIter IterTmp = Iter1;
640 Elements.erase(IterTmp);
643 Elements.erase(Iter1, Elements.end());
644 CurrElementIter = Elements.begin();
648 // Intersect our bitmap with the complement of the RHS and return true
650 bool intersectWithComplement(const SparseBitVector &RHS) {
651 bool changed = false;
652 ElementListIter Iter1 = Elements.begin();
653 ElementListConstIter Iter2 = RHS.Elements.begin();
655 // If either our bitmap or RHS is empty, we are done
656 if (Elements.empty() || RHS.Elements.empty())
659 // Loop through, intersecting as we go, erasing elements when necessary.
660 while (Iter2 != RHS.Elements.end()) {
661 if (Iter1 == Elements.end()) {
662 CurrElementIter = Elements.begin();
666 if (Iter1->index() > Iter2->index()) {
668 } else if (Iter1->index() == Iter2->index()) {
670 changed |= Iter1->intersectWithComplement(*Iter2, BecameZero);
672 ElementListIter IterTmp = Iter1;
674 Elements.erase(IterTmp);
683 CurrElementIter = Elements.begin();
687 bool intersectWithComplement(const SparseBitVector<ElementSize> *RHS) const {
688 return intersectWithComplement(*RHS);
692 // Three argument version of intersectWithComplement.
693 // Result of RHS1 & ~RHS2 is stored into this bitmap.
694 void intersectWithComplement(const SparseBitVector<ElementSize> &RHS1,
695 const SparseBitVector<ElementSize> &RHS2)
698 CurrElementIter = Elements.begin();
699 ElementListConstIter Iter1 = RHS1.Elements.begin();
700 ElementListConstIter Iter2 = RHS2.Elements.begin();
702 // If RHS1 is empty, we are done
703 // If RHS2 is empty, we still have to copy RHS1
704 if (RHS1.Elements.empty())
707 // Loop through, intersecting as we go, erasing elements when necessary.
708 while (Iter2 != RHS2.Elements.end()) {
709 if (Iter1 == RHS1.Elements.end())
712 if (Iter1->index() > Iter2->index()) {
714 } else if (Iter1->index() == Iter2->index()) {
715 bool BecameZero = false;
716 SparseBitVectorElement<ElementSize> *NewElement =
717 new SparseBitVectorElement<ElementSize>(Iter1->index());
718 NewElement->intersectWithComplement(*Iter1, *Iter2, BecameZero);
720 Elements.push_back(NewElement);
727 SparseBitVectorElement<ElementSize> *NewElement =
728 new SparseBitVectorElement<ElementSize>(*Iter1);
729 Elements.push_back(NewElement);
734 // copy the remaining elements
735 while (Iter1 != RHS1.Elements.end()) {
736 SparseBitVectorElement<ElementSize> *NewElement =
737 new SparseBitVectorElement<ElementSize>(*Iter1);
738 Elements.push_back(NewElement);
745 void intersectWithComplement(const SparseBitVector<ElementSize> *RHS1,
746 const SparseBitVector<ElementSize> *RHS2) {
747 intersectWithComplement(*RHS1, *RHS2);
750 bool intersects(const SparseBitVector<ElementSize> *RHS) const {
751 return intersects(*RHS);
754 // Return true if we share any bits in common with RHS
755 bool intersects(const SparseBitVector<ElementSize> &RHS) const {
756 ElementListConstIter Iter1 = Elements.begin();
757 ElementListConstIter Iter2 = RHS.Elements.begin();
759 // Check if both bitmaps are empty.
760 if (Elements.empty() && RHS.Elements.empty())
763 // Loop through, intersecting stopping when we hit bits in common.
764 while (Iter2 != RHS.Elements.end()) {
765 if (Iter1 == Elements.end())
768 if (Iter1->index() > Iter2->index()) {
770 } else if (Iter1->index() == Iter2->index()) {
771 if (Iter1->intersects(*Iter2))
782 // Return true iff all bits set in this SparseBitVector are
784 bool contains(const SparseBitVector<ElementSize> &RHS) const {
785 SparseBitVector<ElementSize> Result(*this);
787 return (Result == RHS);
790 // Return the first set bit in the bitmap. Return -1 if no bits are set.
791 int find_first() const {
792 if (Elements.empty())
794 const SparseBitVectorElement<ElementSize> &First = *(Elements.begin());
795 return (First.index() * ElementSize) + First.find_first();
798 // Return true if the SparseBitVector is empty
800 return Elements.empty();
803 unsigned count() const {
804 unsigned BitCount = 0;
805 for (ElementListConstIter Iter = Elements.begin();
806 Iter != Elements.end();
808 BitCount += Iter->count();
812 iterator begin() const {
813 return iterator(this);
816 iterator end() const {
817 return iterator(this, true);
821 // Convenience functions to allow Or and And without dereferencing in the user
824 template <unsigned ElementSize>
825 inline bool operator |=(SparseBitVector<ElementSize> &LHS,
826 const SparseBitVector<ElementSize> *RHS) {
830 template <unsigned ElementSize>
831 inline bool operator |=(SparseBitVector<ElementSize> *LHS,
832 const SparseBitVector<ElementSize> &RHS) {
833 return LHS->operator|=(RHS);
836 template <unsigned ElementSize>
837 inline bool operator &=(SparseBitVector<ElementSize> *LHS,
838 const SparseBitVector<ElementSize> &RHS) {
839 return LHS->operator&=(RHS);
842 template <unsigned ElementSize>
843 inline bool operator &=(SparseBitVector<ElementSize> &LHS,
844 const SparseBitVector<ElementSize> *RHS) {
848 // Convenience functions for infix union, intersection, difference operators.
850 template <unsigned ElementSize>
851 inline SparseBitVector<ElementSize>
852 operator|(const SparseBitVector<ElementSize> &LHS,
853 const SparseBitVector<ElementSize> &RHS) {
854 SparseBitVector<ElementSize> Result(LHS);
859 template <unsigned ElementSize>
860 inline SparseBitVector<ElementSize>
861 operator&(const SparseBitVector<ElementSize> &LHS,
862 const SparseBitVector<ElementSize> &RHS) {
863 SparseBitVector<ElementSize> Result(LHS);
868 template <unsigned ElementSize>
869 inline SparseBitVector<ElementSize>
870 operator-(const SparseBitVector<ElementSize> &LHS,
871 const SparseBitVector<ElementSize> &RHS) {
872 SparseBitVector<ElementSize> Result;
873 Result.intersectWithComplement(LHS, RHS);
880 // Dump a SparseBitVector to a stream
881 template <unsigned ElementSize>
882 void dump(const SparseBitVector<ElementSize> &LHS, raw_ostream &out) {
885 typename SparseBitVector<ElementSize>::iterator bi = LHS.begin(),
889 for (++bi; bi != be; ++bi) {
895 } // end namespace llvm