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
21 #include "llvm/ADT/STLExtras.h"
22 #include "llvm/ADT/ilist.h"
23 #include "llvm/ADT/ilist_node.h"
24 #include "llvm/Support/DataTypes.h"
25 #include "llvm/Support/MathExtras.h"
26 #include "llvm/Support/raw_ostream.h"
30 /// SparseBitVector is an implementation of a bitvector that is sparse by only
31 /// storing the elements that have non-zero bits set. In order to make this
32 /// fast for the most common cases, SparseBitVector is implemented as a linked
33 /// list of SparseBitVectorElements. We maintain a pointer to the last
34 /// SparseBitVectorElement accessed (in the form of a list iterator), in order
35 /// to make multiple in-order test/set constant time after the first one is
36 /// executed. Note that using vectors to store SparseBitVectorElement's does
37 /// not work out very well because it causes insertion in the middle to take
38 /// enormous amounts of time with a large amount of bits. Other structures that
39 /// have better worst cases for insertion in the middle (various balanced trees,
40 /// etc) do not perform as well in practice as a linked list with this iterator
41 /// kept up to date. They are also significantly more memory intensive.
44 template <unsigned ElementSize = 128>
45 struct SparseBitVectorElement
46 : ilist_node<SparseBitVectorElement<ElementSize> > {
48 typedef unsigned long BitWord;
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 unsigned 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 assert(0 && "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_32(Bits[i]);
142 else if (sizeof(BitWord) == 8)
143 return i * BITWORD_SIZE + CountTrailingZeros_64(Bits[i]);
145 assert(0 && "Unsupported!");
147 assert(0 && "Illegal empty element");
148 return 0; // Not reached
151 /// find_next - Returns the index of the next set bit starting from the
152 /// "Curr" bit. Returns -1 if the next set bit is not found.
153 int find_next(unsigned Curr) const {
154 if (Curr >= BITS_PER_ELEMENT)
157 unsigned WordPos = Curr / BITWORD_SIZE;
158 unsigned BitPos = Curr % BITWORD_SIZE;
159 BitWord Copy = Bits[WordPos];
160 assert (WordPos <= BITWORDS_PER_ELEMENT
161 && "Word Position outside of element");
163 // Mask off previous bits.
164 Copy &= ~0L << BitPos;
167 if (sizeof(BitWord) == 4)
168 return WordPos * BITWORD_SIZE + CountTrailingZeros_32(Copy);
169 else if (sizeof(BitWord) == 8)
170 return WordPos * BITWORD_SIZE + CountTrailingZeros_64(Copy);
172 assert(0 && "Unsupported!");
175 // Check subsequent words.
176 for (unsigned i = WordPos+1; i < BITWORDS_PER_ELEMENT; ++i)
178 if (sizeof(BitWord) == 4)
179 return i * BITWORD_SIZE + CountTrailingZeros_32(Bits[i]);
180 else if (sizeof(BitWord) == 8)
181 return i * BITWORD_SIZE + CountTrailingZeros_64(Bits[i]);
183 assert(0 && "Unsupported!");
188 // Union this element with RHS and return true if this one changed.
189 bool unionWith(const SparseBitVectorElement &RHS) {
190 bool changed = false;
191 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
192 BitWord old = changed ? 0 : Bits[i];
194 Bits[i] |= RHS.Bits[i];
195 if (!changed && old != Bits[i])
201 // Return true if we have any bits in common with RHS
202 bool intersects(const SparseBitVectorElement &RHS) const {
203 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
204 if (RHS.Bits[i] & Bits[i])
210 // Intersect this Element with RHS and return true if this one changed.
211 // BecameZero is set to true if this element became all-zero bits.
212 bool intersectWith(const SparseBitVectorElement &RHS,
214 bool changed = false;
218 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
219 BitWord old = changed ? 0 : Bits[i];
221 Bits[i] &= RHS.Bits[i];
225 if (!changed && old != Bits[i])
228 BecameZero = allzero;
231 // Intersect this Element with the complement of RHS and return true if this
232 // one changed. BecameZero is set to true if this element became all-zero
234 bool intersectWithComplement(const SparseBitVectorElement &RHS,
236 bool changed = false;
240 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
241 BitWord old = changed ? 0 : Bits[i];
243 Bits[i] &= ~RHS.Bits[i];
247 if (!changed && old != Bits[i])
250 BecameZero = allzero;
253 // Three argument version of intersectWithComplement that intersects
254 // RHS1 & ~RHS2 into this element
255 void intersectWithComplement(const SparseBitVectorElement &RHS1,
256 const SparseBitVectorElement &RHS2,
261 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
262 Bits[i] = RHS1.Bits[i] & ~RHS2.Bits[i];
266 BecameZero = allzero;
269 // Get a hash value for this element;
270 uint64_t getHashValue() const {
271 uint64_t HashVal = 0;
272 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
279 template <unsigned ElementSize = 128>
280 class SparseBitVector {
281 typedef ilist<SparseBitVectorElement<ElementSize> > ElementList;
282 typedef typename ElementList::iterator ElementListIter;
283 typedef typename ElementList::const_iterator ElementListConstIter;
285 BITWORD_SIZE = SparseBitVectorElement<ElementSize>::BITWORD_SIZE
288 // Pointer to our current Element.
289 ElementListIter CurrElementIter;
290 ElementList Elements;
292 // This is like std::lower_bound, except we do linear searching from the
294 ElementListIter FindLowerBound(unsigned ElementIndex) {
296 if (Elements.empty()) {
297 CurrElementIter = Elements.begin();
298 return Elements.begin();
301 // Make sure our current iterator is valid.
302 if (CurrElementIter == Elements.end())
305 // Search from our current iterator, either backwards or forwards,
306 // depending on what element we are looking for.
307 ElementListIter ElementIter = CurrElementIter;
308 if (CurrElementIter->index() == ElementIndex) {
310 } else if (CurrElementIter->index() > ElementIndex) {
311 while (ElementIter != Elements.begin()
312 && ElementIter->index() > ElementIndex)
315 while (ElementIter != Elements.end() &&
316 ElementIter->index() < ElementIndex)
319 CurrElementIter = ElementIter;
323 // Iterator to walk set bits in the bitmap. This iterator is a lot uglier
324 // than it would be, in order to be efficient.
325 class SparseBitVectorIterator {
329 const SparseBitVector<ElementSize> *BitVector;
331 // Current element inside of bitmap.
332 ElementListConstIter Iter;
334 // Current bit number inside of our bitmap.
337 // Current word number inside of our element.
340 // Current bits from the element.
341 typename SparseBitVectorElement<ElementSize>::BitWord Bits;
343 // Move our iterator to the first non-zero bit in the bitmap.
344 void AdvanceToFirstNonZero() {
347 if (BitVector->Elements.empty()) {
351 Iter = BitVector->Elements.begin();
352 BitNumber = Iter->index() * ElementSize;
353 unsigned BitPos = Iter->find_first();
355 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
356 Bits = Iter->word(WordNumber);
357 Bits >>= BitPos % BITWORD_SIZE;
360 // Move our iterator to the next non-zero bit.
361 void AdvanceToNextNonZero() {
365 while (Bits && !(Bits & 1)) {
370 // See if we ran out of Bits in this word.
372 int NextSetBitNumber = Iter->find_next(BitNumber % ElementSize) ;
373 // If we ran out of set bits in this element, move to next element.
374 if (NextSetBitNumber == -1 || (BitNumber % ElementSize == 0)) {
378 // We may run out of elements in the bitmap.
379 if (Iter == BitVector->Elements.end()) {
383 // Set up for next non zero word in bitmap.
384 BitNumber = Iter->index() * ElementSize;
385 NextSetBitNumber = Iter->find_first();
386 BitNumber += NextSetBitNumber;
387 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
388 Bits = Iter->word(WordNumber);
389 Bits >>= NextSetBitNumber % BITWORD_SIZE;
391 WordNumber = (NextSetBitNumber % ElementSize) / BITWORD_SIZE;
392 Bits = Iter->word(WordNumber);
393 Bits >>= NextSetBitNumber % BITWORD_SIZE;
394 BitNumber = Iter->index() * ElementSize;
395 BitNumber += NextSetBitNumber;
401 inline SparseBitVectorIterator& operator++() {
404 AdvanceToNextNonZero();
409 inline SparseBitVectorIterator operator++(int) {
410 SparseBitVectorIterator tmp = *this;
415 // Return the current set bit number.
416 unsigned operator*() const {
420 bool operator==(const SparseBitVectorIterator &RHS) const {
421 // If they are both at the end, ignore the rest of the fields.
422 if (AtEnd && RHS.AtEnd)
424 // Otherwise they are the same if they have the same bit number and
426 return AtEnd == RHS.AtEnd && RHS.BitNumber == BitNumber;
428 bool operator!=(const SparseBitVectorIterator &RHS) const {
429 return !(*this == RHS);
431 SparseBitVectorIterator(): BitVector(NULL) {
435 SparseBitVectorIterator(const SparseBitVector<ElementSize> *RHS,
436 bool end = false):BitVector(RHS) {
437 Iter = BitVector->Elements.begin();
442 AdvanceToFirstNonZero();
446 typedef SparseBitVectorIterator iterator;
449 CurrElementIter = Elements.begin ();
455 // SparseBitVector copy ctor.
456 SparseBitVector(const SparseBitVector &RHS) {
457 ElementListConstIter ElementIter = RHS.Elements.begin();
458 while (ElementIter != RHS.Elements.end()) {
459 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
463 CurrElementIter = Elements.begin ();
472 SparseBitVector& operator=(const SparseBitVector& RHS) {
475 ElementListConstIter ElementIter = RHS.Elements.begin();
476 while (ElementIter != RHS.Elements.end()) {
477 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
481 CurrElementIter = Elements.begin ();
486 // Test, Reset, and Set a bit in the bitmap.
487 bool test(unsigned Idx) {
488 if (Elements.empty())
491 unsigned ElementIndex = Idx / ElementSize;
492 ElementListIter ElementIter = FindLowerBound(ElementIndex);
494 // If we can't find an element that is supposed to contain this bit, there
495 // is nothing more to do.
496 if (ElementIter == Elements.end() ||
497 ElementIter->index() != ElementIndex)
499 return ElementIter->test(Idx % ElementSize);
502 void reset(unsigned Idx) {
503 if (Elements.empty())
506 unsigned ElementIndex = Idx / ElementSize;
507 ElementListIter ElementIter = FindLowerBound(ElementIndex);
509 // If we can't find an element that is supposed to contain this bit, there
510 // is nothing more to do.
511 if (ElementIter == Elements.end() ||
512 ElementIter->index() != ElementIndex)
514 ElementIter->reset(Idx % ElementSize);
516 // When the element is zeroed out, delete it.
517 if (ElementIter->empty()) {
519 Elements.erase(ElementIter);
523 void set(unsigned Idx) {
524 unsigned ElementIndex = Idx / ElementSize;
525 SparseBitVectorElement<ElementSize> *Element;
526 ElementListIter ElementIter;
527 if (Elements.empty()) {
528 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
529 ElementIter = Elements.insert(Elements.end(), Element);
532 ElementIter = FindLowerBound(ElementIndex);
534 if (ElementIter == Elements.end() ||
535 ElementIter->index() != ElementIndex) {
536 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
537 // We may have hit the beginning of our SparseBitVector, in which case,
538 // we may need to insert right after this element, which requires moving
539 // the current iterator forward one, because insert does insert before.
540 if (ElementIter != Elements.end() &&
541 ElementIter->index() < ElementIndex)
542 ElementIter = Elements.insert(++ElementIter, Element);
544 ElementIter = Elements.insert(ElementIter, Element);
547 CurrElementIter = ElementIter;
549 ElementIter->set(Idx % ElementSize);
552 bool test_and_set (unsigned Idx) {
553 bool old = test(Idx);
561 bool operator!=(const SparseBitVector &RHS) const {
562 return !(*this == RHS);
565 bool operator==(const SparseBitVector &RHS) const {
566 ElementListConstIter Iter1 = Elements.begin();
567 ElementListConstIter Iter2 = RHS.Elements.begin();
569 for (; Iter1 != Elements.end() && Iter2 != RHS.Elements.end();
571 if (*Iter1 != *Iter2)
574 return Iter1 == Elements.end() && Iter2 == RHS.Elements.end();
577 // Union our bitmap with the RHS and return true if we changed.
578 bool operator|=(const SparseBitVector &RHS) {
579 bool changed = false;
580 ElementListIter Iter1 = Elements.begin();
581 ElementListConstIter Iter2 = RHS.Elements.begin();
583 // If RHS is empty, we are done
584 if (RHS.Elements.empty())
587 while (Iter2 != RHS.Elements.end()) {
588 if (Iter1 == Elements.end() || Iter1->index() > Iter2->index()) {
589 Elements.insert(Iter1,
590 new SparseBitVectorElement<ElementSize>(*Iter2));
593 } else if (Iter1->index() == Iter2->index()) {
594 changed |= Iter1->unionWith(*Iter2);
601 CurrElementIter = Elements.begin();
605 // Intersect our bitmap with the RHS and return true if ours changed.
606 bool operator&=(const SparseBitVector &RHS) {
607 bool changed = false;
608 ElementListIter Iter1 = Elements.begin();
609 ElementListConstIter Iter2 = RHS.Elements.begin();
611 // Check if both bitmaps are empty.
612 if (Elements.empty() && RHS.Elements.empty())
615 // Loop through, intersecting as we go, erasing elements when necessary.
616 while (Iter2 != RHS.Elements.end()) {
617 if (Iter1 == Elements.end()) {
618 CurrElementIter = Elements.begin();
622 if (Iter1->index() > Iter2->index()) {
624 } else if (Iter1->index() == Iter2->index()) {
626 changed |= Iter1->intersectWith(*Iter2, BecameZero);
628 ElementListIter IterTmp = Iter1;
630 Elements.erase(IterTmp);
636 ElementListIter IterTmp = Iter1;
638 Elements.erase(IterTmp);
641 Elements.erase(Iter1, Elements.end());
642 CurrElementIter = Elements.begin();
646 // Intersect our bitmap with the complement of the RHS and return true
648 bool intersectWithComplement(const SparseBitVector &RHS) {
649 bool changed = false;
650 ElementListIter Iter1 = Elements.begin();
651 ElementListConstIter Iter2 = RHS.Elements.begin();
653 // If either our bitmap or RHS is empty, we are done
654 if (Elements.empty() || RHS.Elements.empty())
657 // Loop through, intersecting as we go, erasing elements when necessary.
658 while (Iter2 != RHS.Elements.end()) {
659 if (Iter1 == Elements.end()) {
660 CurrElementIter = Elements.begin();
664 if (Iter1->index() > Iter2->index()) {
666 } else if (Iter1->index() == Iter2->index()) {
668 changed |= Iter1->intersectWithComplement(*Iter2, BecameZero);
670 ElementListIter IterTmp = Iter1;
672 Elements.erase(IterTmp);
681 CurrElementIter = Elements.begin();
685 bool intersectWithComplement(const SparseBitVector<ElementSize> *RHS) const {
686 return intersectWithComplement(*RHS);
690 // Three argument version of intersectWithComplement.
691 // Result of RHS1 & ~RHS2 is stored into this bitmap.
692 void intersectWithComplement(const SparseBitVector<ElementSize> &RHS1,
693 const SparseBitVector<ElementSize> &RHS2)
696 CurrElementIter = Elements.begin();
697 ElementListConstIter Iter1 = RHS1.Elements.begin();
698 ElementListConstIter Iter2 = RHS2.Elements.begin();
700 // If RHS1 is empty, we are done
701 // If RHS2 is empty, we still have to copy RHS1
702 if (RHS1.Elements.empty())
705 // Loop through, intersecting as we go, erasing elements when necessary.
706 while (Iter2 != RHS2.Elements.end()) {
707 if (Iter1 == RHS1.Elements.end())
710 if (Iter1->index() > Iter2->index()) {
712 } else if (Iter1->index() == Iter2->index()) {
713 bool BecameZero = false;
714 SparseBitVectorElement<ElementSize> *NewElement =
715 new SparseBitVectorElement<ElementSize>(Iter1->index());
716 NewElement->intersectWithComplement(*Iter1, *Iter2, BecameZero);
718 Elements.push_back(NewElement);
725 SparseBitVectorElement<ElementSize> *NewElement =
726 new SparseBitVectorElement<ElementSize>(*Iter1);
727 Elements.push_back(NewElement);
732 // copy the remaining elements
733 while (Iter1 != RHS1.Elements.end()) {
734 SparseBitVectorElement<ElementSize> *NewElement =
735 new SparseBitVectorElement<ElementSize>(*Iter1);
736 Elements.push_back(NewElement);
743 void intersectWithComplement(const SparseBitVector<ElementSize> *RHS1,
744 const SparseBitVector<ElementSize> *RHS2) {
745 intersectWithComplement(*RHS1, *RHS2);
748 bool intersects(const SparseBitVector<ElementSize> *RHS) const {
749 return intersects(*RHS);
752 // Return true if we share any bits in common with RHS
753 bool intersects(const SparseBitVector<ElementSize> &RHS) const {
754 ElementListConstIter Iter1 = Elements.begin();
755 ElementListConstIter Iter2 = RHS.Elements.begin();
757 // Check if both bitmaps are empty.
758 if (Elements.empty() && RHS.Elements.empty())
761 // Loop through, intersecting stopping when we hit bits in common.
762 while (Iter2 != RHS.Elements.end()) {
763 if (Iter1 == Elements.end())
766 if (Iter1->index() > Iter2->index()) {
768 } else if (Iter1->index() == Iter2->index()) {
769 if (Iter1->intersects(*Iter2))
780 // Return true iff all bits set in this SparseBitVector are
782 bool contains(const SparseBitVector<ElementSize> &RHS) const {
783 SparseBitVector<ElementSize> Result(*this);
785 return (Result == RHS);
788 // Return the first set bit in the bitmap. Return -1 if no bits are set.
789 int find_first() const {
790 if (Elements.empty())
792 const SparseBitVectorElement<ElementSize> &First = *(Elements.begin());
793 return (First.index() * ElementSize) + First.find_first();
796 // Return true if the SparseBitVector is empty
798 return Elements.empty();
801 unsigned count() const {
802 unsigned BitCount = 0;
803 for (ElementListConstIter Iter = Elements.begin();
804 Iter != Elements.end();
806 BitCount += Iter->count();
810 iterator begin() const {
811 return iterator(this);
814 iterator end() const {
815 return iterator(this, true);
818 // Get a hash value for this bitmap.
819 uint64_t getHashValue() const {
820 uint64_t HashVal = 0;
821 for (ElementListConstIter Iter = Elements.begin();
822 Iter != Elements.end();
824 HashVal ^= Iter->index();
825 HashVal ^= Iter->getHashValue();
831 // Convenience functions to allow Or and And without dereferencing in the user
834 template <unsigned ElementSize>
835 inline bool operator |=(SparseBitVector<ElementSize> &LHS,
836 const SparseBitVector<ElementSize> *RHS) {
840 template <unsigned ElementSize>
841 inline bool operator |=(SparseBitVector<ElementSize> *LHS,
842 const SparseBitVector<ElementSize> &RHS) {
843 return LHS->operator|=(RHS);
846 template <unsigned ElementSize>
847 inline bool operator &=(SparseBitVector<ElementSize> *LHS,
848 const SparseBitVector<ElementSize> &RHS) {
849 return LHS->operator&=(RHS);
852 template <unsigned ElementSize>
853 inline bool operator &=(SparseBitVector<ElementSize> &LHS,
854 const SparseBitVector<ElementSize> *RHS) {
858 // Convenience functions for infix union, intersection, difference operators.
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(LHS);
878 template <unsigned ElementSize>
879 inline SparseBitVector<ElementSize>
880 operator-(const SparseBitVector<ElementSize> &LHS,
881 const SparseBitVector<ElementSize> &RHS) {
882 SparseBitVector<ElementSize> Result;
883 Result.intersectWithComplement(LHS, RHS);
890 // Dump a SparseBitVector to a stream
891 template <unsigned ElementSize>
892 void dump(const SparseBitVector<ElementSize> &LHS, raw_ostream &out) {
895 typename SparseBitVector<ElementSize>::iterator bi;
896 for (bi = LHS.begin(); bi != LHS.end(); ++bi) {
901 } // end namespace llvm