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/MathExtras.h"
22 #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 assert(0 && "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_32(Bits[i]);
141 else if (sizeof(BitWord) == 8)
142 return i * BITWORD_SIZE + CountTrailingZeros_64(Bits[i]);
144 assert(0 && "Unsupported!");
146 assert(0 && "Illegal empty element");
147 return 0; // Not reached
150 /// find_next - Returns the index of the next set bit starting from the
151 /// "Curr" bit. Returns -1 if the next set bit is not found.
152 int find_next(unsigned Curr) const {
153 if (Curr >= BITS_PER_ELEMENT)
156 unsigned WordPos = Curr / BITWORD_SIZE;
157 unsigned BitPos = Curr % BITWORD_SIZE;
158 BitWord Copy = Bits[WordPos];
159 assert (WordPos <= BITWORDS_PER_ELEMENT
160 && "Word Position outside of element");
162 // Mask off previous bits.
163 Copy &= ~0L << BitPos;
166 if (sizeof(BitWord) == 4)
167 return WordPos * BITWORD_SIZE + CountTrailingZeros_32(Copy);
168 else if (sizeof(BitWord) == 8)
169 return WordPos * BITWORD_SIZE + CountTrailingZeros_64(Copy);
171 assert(0 && "Unsupported!");
174 // Check subsequent words.
175 for (unsigned i = WordPos+1; i < BITWORDS_PER_ELEMENT; ++i)
177 if (sizeof(BitWord) == 4)
178 return i * BITWORD_SIZE + CountTrailingZeros_32(Bits[i]);
179 else if (sizeof(BitWord) == 8)
180 return i * BITWORD_SIZE + CountTrailingZeros_64(Bits[i]);
182 assert(0 && "Unsupported!");
187 // Union this element with RHS and return true if this one changed.
188 bool unionWith(const SparseBitVectorElement &RHS) {
189 bool changed = false;
190 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
191 BitWord old = changed ? 0 : Bits[i];
193 Bits[i] |= RHS.Bits[i];
194 if (!changed && old != Bits[i])
200 // Return true if we have any bits in common with RHS
201 bool intersects(const SparseBitVectorElement &RHS) const {
202 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
203 if (RHS.Bits[i] & Bits[i])
209 // Intersect this Element with RHS and return true if this one changed.
210 // BecameZero is set to true if this element became all-zero bits.
211 bool intersectWith(const SparseBitVectorElement &RHS,
213 bool changed = false;
217 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
218 BitWord old = changed ? 0 : Bits[i];
220 Bits[i] &= RHS.Bits[i];
224 if (!changed && old != Bits[i])
227 BecameZero = allzero;
230 // Intersect this Element with the complement of RHS and return true if this
231 // one changed. BecameZero is set to true if this element became all-zero
233 bool intersectWithComplement(const SparseBitVectorElement &RHS,
235 bool changed = false;
239 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
240 BitWord old = changed ? 0 : Bits[i];
242 Bits[i] &= ~RHS.Bits[i];
246 if (!changed && old != Bits[i])
249 BecameZero = allzero;
252 // Three argument version of intersectWithComplement that intersects
253 // RHS1 & ~RHS2 into this element
254 void intersectWithComplement(const SparseBitVectorElement &RHS1,
255 const SparseBitVectorElement &RHS2,
260 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
261 Bits[i] = RHS1.Bits[i] & ~RHS2.Bits[i];
265 BecameZero = allzero;
268 // Get a hash value for this element;
269 uint64_t getHashValue() const {
270 uint64_t HashVal = 0;
271 for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) {
278 template <unsigned ElementSize = 128>
279 class SparseBitVector {
280 typedef ilist<SparseBitVectorElement<ElementSize> > ElementList;
281 typedef typename ElementList::iterator ElementListIter;
282 typedef typename ElementList::const_iterator ElementListConstIter;
284 BITWORD_SIZE = SparseBitVectorElement<ElementSize>::BITWORD_SIZE
287 // Pointer to our current Element.
288 ElementListIter CurrElementIter;
289 ElementList Elements;
291 // This is like std::lower_bound, except we do linear searching from the
293 ElementListIter FindLowerBound(unsigned ElementIndex) {
295 if (Elements.empty()) {
296 CurrElementIter = Elements.begin();
297 return Elements.begin();
300 // Make sure our current iterator is valid.
301 if (CurrElementIter == Elements.end())
304 // Search from our current iterator, either backwards or forwards,
305 // depending on what element we are looking for.
306 ElementListIter ElementIter = CurrElementIter;
307 if (CurrElementIter->index() == ElementIndex) {
309 } else if (CurrElementIter->index() > ElementIndex) {
310 while (ElementIter != Elements.begin()
311 && ElementIter->index() > ElementIndex)
314 while (ElementIter != Elements.end() &&
315 ElementIter->index() < ElementIndex)
318 CurrElementIter = ElementIter;
322 // Iterator to walk set bits in the bitmap. This iterator is a lot uglier
323 // than it would be, in order to be efficient.
324 class SparseBitVectorIterator {
328 const SparseBitVector<ElementSize> *BitVector;
330 // Current element inside of bitmap.
331 ElementListConstIter Iter;
333 // Current bit number inside of our bitmap.
336 // Current word number inside of our element.
339 // Current bits from the element.
340 typename SparseBitVectorElement<ElementSize>::BitWord Bits;
342 // Move our iterator to the first non-zero bit in the bitmap.
343 void AdvanceToFirstNonZero() {
346 if (BitVector->Elements.empty()) {
350 Iter = BitVector->Elements.begin();
351 BitNumber = Iter->index() * ElementSize;
352 unsigned BitPos = Iter->find_first();
354 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
355 Bits = Iter->word(WordNumber);
356 Bits >>= BitPos % BITWORD_SIZE;
359 // Move our iterator to the next non-zero bit.
360 void AdvanceToNextNonZero() {
364 while (Bits && !(Bits & 1)) {
369 // See if we ran out of Bits in this word.
371 int NextSetBitNumber = Iter->find_next(BitNumber % ElementSize) ;
372 // If we ran out of set bits in this element, move to next element.
373 if (NextSetBitNumber == -1 || (BitNumber % ElementSize == 0)) {
377 // We may run out of elements in the bitmap.
378 if (Iter == BitVector->Elements.end()) {
382 // Set up for next non zero word in bitmap.
383 BitNumber = Iter->index() * ElementSize;
384 NextSetBitNumber = Iter->find_first();
385 BitNumber += NextSetBitNumber;
386 WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE;
387 Bits = Iter->word(WordNumber);
388 Bits >>= NextSetBitNumber % BITWORD_SIZE;
390 WordNumber = (NextSetBitNumber % ElementSize) / BITWORD_SIZE;
391 Bits = Iter->word(WordNumber);
392 Bits >>= NextSetBitNumber % BITWORD_SIZE;
393 BitNumber = Iter->index() * ElementSize;
394 BitNumber += NextSetBitNumber;
400 inline SparseBitVectorIterator& operator++() {
403 AdvanceToNextNonZero();
408 inline SparseBitVectorIterator operator++(int) {
409 SparseBitVectorIterator tmp = *this;
414 // Return the current set bit number.
415 unsigned operator*() const {
419 bool operator==(const SparseBitVectorIterator &RHS) const {
420 // If they are both at the end, ignore the rest of the fields.
421 if (AtEnd && RHS.AtEnd)
423 // Otherwise they are the same if they have the same bit number and
425 return AtEnd == RHS.AtEnd && RHS.BitNumber == BitNumber;
427 bool operator!=(const SparseBitVectorIterator &RHS) const {
428 return !(*this == RHS);
430 SparseBitVectorIterator(): BitVector(NULL) {
434 SparseBitVectorIterator(const SparseBitVector<ElementSize> *RHS,
435 bool end = false):BitVector(RHS) {
436 Iter = BitVector->Elements.begin();
441 AdvanceToFirstNonZero();
445 typedef SparseBitVectorIterator iterator;
448 CurrElementIter = Elements.begin ();
454 // SparseBitVector copy ctor.
455 SparseBitVector(const SparseBitVector &RHS) {
456 ElementListConstIter ElementIter = RHS.Elements.begin();
457 while (ElementIter != RHS.Elements.end()) {
458 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
462 CurrElementIter = Elements.begin ();
471 SparseBitVector& operator=(const SparseBitVector& RHS) {
474 ElementListConstIter ElementIter = RHS.Elements.begin();
475 while (ElementIter != RHS.Elements.end()) {
476 Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter));
480 CurrElementIter = Elements.begin ();
485 // Test, Reset, and Set a bit in the bitmap.
486 bool test(unsigned Idx) {
487 if (Elements.empty())
490 unsigned ElementIndex = Idx / ElementSize;
491 ElementListIter ElementIter = FindLowerBound(ElementIndex);
493 // If we can't find an element that is supposed to contain this bit, there
494 // is nothing more to do.
495 if (ElementIter == Elements.end() ||
496 ElementIter->index() != ElementIndex)
498 return ElementIter->test(Idx % ElementSize);
501 void reset(unsigned Idx) {
502 if (Elements.empty())
505 unsigned ElementIndex = Idx / ElementSize;
506 ElementListIter ElementIter = FindLowerBound(ElementIndex);
508 // If we can't find an element that is supposed to contain this bit, there
509 // is nothing more to do.
510 if (ElementIter == Elements.end() ||
511 ElementIter->index() != ElementIndex)
513 ElementIter->reset(Idx % ElementSize);
515 // When the element is zeroed out, delete it.
516 if (ElementIter->empty()) {
518 Elements.erase(ElementIter);
522 void set(unsigned Idx) {
523 unsigned ElementIndex = Idx / ElementSize;
524 SparseBitVectorElement<ElementSize> *Element;
525 ElementListIter ElementIter;
526 if (Elements.empty()) {
527 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
528 ElementIter = Elements.insert(Elements.end(), Element);
531 ElementIter = FindLowerBound(ElementIndex);
533 if (ElementIter == Elements.end() ||
534 ElementIter->index() != ElementIndex) {
535 Element = new SparseBitVectorElement<ElementSize>(ElementIndex);
536 // We may have hit the beginning of our SparseBitVector, in which case,
537 // we may need to insert right after this element, which requires moving
538 // the current iterator forward one, because insert does insert before.
539 if (ElementIter != Elements.end() &&
540 ElementIter->index() < ElementIndex)
541 ElementIter = Elements.insert(++ElementIter, Element);
543 ElementIter = Elements.insert(ElementIter, Element);
546 CurrElementIter = ElementIter;
548 ElementIter->set(Idx % ElementSize);
551 bool test_and_set (unsigned Idx) {
552 bool old = test(Idx);
560 bool operator!=(const SparseBitVector &RHS) const {
561 return !(*this == RHS);
564 bool operator==(const SparseBitVector &RHS) const {
565 ElementListConstIter Iter1 = Elements.begin();
566 ElementListConstIter Iter2 = RHS.Elements.begin();
568 for (; Iter1 != Elements.end() && Iter2 != RHS.Elements.end();
570 if (*Iter1 != *Iter2)
573 return Iter1 == Elements.end() && Iter2 == RHS.Elements.end();
576 // Union our bitmap with the RHS and return true if we changed.
577 bool operator|=(const SparseBitVector &RHS) {
578 bool changed = false;
579 ElementListIter Iter1 = Elements.begin();
580 ElementListConstIter Iter2 = RHS.Elements.begin();
582 // If RHS is empty, we are done
583 if (RHS.Elements.empty())
586 while (Iter2 != RHS.Elements.end()) {
587 if (Iter1 == Elements.end() || Iter1->index() > Iter2->index()) {
588 Elements.insert(Iter1,
589 new SparseBitVectorElement<ElementSize>(*Iter2));
592 } else if (Iter1->index() == Iter2->index()) {
593 changed |= Iter1->unionWith(*Iter2);
600 CurrElementIter = Elements.begin();
604 // Intersect our bitmap with the RHS and return true if ours changed.
605 bool operator&=(const SparseBitVector &RHS) {
606 bool changed = false;
607 ElementListIter Iter1 = Elements.begin();
608 ElementListConstIter Iter2 = RHS.Elements.begin();
610 // Check if both bitmaps are empty.
611 if (Elements.empty() && RHS.Elements.empty())
614 // Loop through, intersecting as we go, erasing elements when necessary.
615 while (Iter2 != RHS.Elements.end()) {
616 if (Iter1 == Elements.end()) {
617 CurrElementIter = Elements.begin();
621 if (Iter1->index() > Iter2->index()) {
623 } else if (Iter1->index() == Iter2->index()) {
625 changed |= Iter1->intersectWith(*Iter2, BecameZero);
627 ElementListIter IterTmp = Iter1;
629 Elements.erase(IterTmp);
635 ElementListIter IterTmp = Iter1;
637 Elements.erase(IterTmp);
640 Elements.erase(Iter1, Elements.end());
641 CurrElementIter = Elements.begin();
645 // Intersect our bitmap with the complement of the RHS and return true
647 bool intersectWithComplement(const SparseBitVector &RHS) {
648 bool changed = false;
649 ElementListIter Iter1 = Elements.begin();
650 ElementListConstIter Iter2 = RHS.Elements.begin();
652 // If either our bitmap or RHS is empty, we are done
653 if (Elements.empty() || RHS.Elements.empty())
656 // Loop through, intersecting as we go, erasing elements when necessary.
657 while (Iter2 != RHS.Elements.end()) {
658 if (Iter1 == Elements.end()) {
659 CurrElementIter = Elements.begin();
663 if (Iter1->index() > Iter2->index()) {
665 } else if (Iter1->index() == Iter2->index()) {
667 changed |= Iter1->intersectWithComplement(*Iter2, BecameZero);
669 ElementListIter IterTmp = Iter1;
671 Elements.erase(IterTmp);
680 CurrElementIter = Elements.begin();
684 bool intersectWithComplement(const SparseBitVector<ElementSize> *RHS) const {
685 return intersectWithComplement(*RHS);
689 // Three argument version of intersectWithComplement.
690 // Result of RHS1 & ~RHS2 is stored into this bitmap.
691 void intersectWithComplement(const SparseBitVector<ElementSize> &RHS1,
692 const SparseBitVector<ElementSize> &RHS2)
695 CurrElementIter = Elements.begin();
696 ElementListConstIter Iter1 = RHS1.Elements.begin();
697 ElementListConstIter Iter2 = RHS2.Elements.begin();
699 // If RHS1 is empty, we are done
700 // If RHS2 is empty, we still have to copy RHS1
701 if (RHS1.Elements.empty())
704 // Loop through, intersecting as we go, erasing elements when necessary.
705 while (Iter2 != RHS2.Elements.end()) {
706 if (Iter1 == RHS1.Elements.end())
709 if (Iter1->index() > Iter2->index()) {
711 } else if (Iter1->index() == Iter2->index()) {
712 bool BecameZero = false;
713 SparseBitVectorElement<ElementSize> *NewElement =
714 new SparseBitVectorElement<ElementSize>(Iter1->index());
715 NewElement->intersectWithComplement(*Iter1, *Iter2, BecameZero);
717 Elements.push_back(NewElement);
724 SparseBitVectorElement<ElementSize> *NewElement =
725 new SparseBitVectorElement<ElementSize>(*Iter1);
726 Elements.push_back(NewElement);
731 // copy the remaining elements
732 while (Iter1 != RHS1.Elements.end()) {
733 SparseBitVectorElement<ElementSize> *NewElement =
734 new SparseBitVectorElement<ElementSize>(*Iter1);
735 Elements.push_back(NewElement);
742 void intersectWithComplement(const SparseBitVector<ElementSize> *RHS1,
743 const SparseBitVector<ElementSize> *RHS2) {
744 intersectWithComplement(*RHS1, *RHS2);
747 bool intersects(const SparseBitVector<ElementSize> *RHS) const {
748 return intersects(*RHS);
751 // Return true if we share any bits in common with RHS
752 bool intersects(const SparseBitVector<ElementSize> &RHS) const {
753 ElementListConstIter Iter1 = Elements.begin();
754 ElementListConstIter Iter2 = RHS.Elements.begin();
756 // Check if both bitmaps are empty.
757 if (Elements.empty() && RHS.Elements.empty())
760 // Loop through, intersecting stopping when we hit bits in common.
761 while (Iter2 != RHS.Elements.end()) {
762 if (Iter1 == Elements.end())
765 if (Iter1->index() > Iter2->index()) {
767 } else if (Iter1->index() == Iter2->index()) {
768 if (Iter1->intersects(*Iter2))
779 // Return true iff all bits set in this SparseBitVector are
781 bool contains(const SparseBitVector<ElementSize> &RHS) const {
782 SparseBitVector<ElementSize> Result(*this);
784 return (Result == RHS);
787 // Return the first set bit in the bitmap. Return -1 if no bits are set.
788 int find_first() const {
789 if (Elements.empty())
791 const SparseBitVectorElement<ElementSize> &First = *(Elements.begin());
792 return (First.index() * ElementSize) + First.find_first();
795 // Return true if the SparseBitVector is empty
797 return Elements.empty();
800 unsigned count() const {
801 unsigned BitCount = 0;
802 for (ElementListConstIter Iter = Elements.begin();
803 Iter != Elements.end();
805 BitCount += Iter->count();
809 iterator begin() const {
810 return iterator(this);
813 iterator end() const {
814 return iterator(this, true);
817 // Get a hash value for this bitmap.
818 uint64_t getHashValue() const {
819 uint64_t HashVal = 0;
820 for (ElementListConstIter Iter = Elements.begin();
821 Iter != Elements.end();
823 HashVal ^= Iter->index();
824 HashVal ^= Iter->getHashValue();
830 // Convenience functions to allow Or and And without dereferencing in the user
833 template <unsigned ElementSize>
834 inline bool operator |=(SparseBitVector<ElementSize> &LHS,
835 const SparseBitVector<ElementSize> *RHS) {
839 template <unsigned ElementSize>
840 inline bool operator |=(SparseBitVector<ElementSize> *LHS,
841 const SparseBitVector<ElementSize> &RHS) {
842 return LHS->operator|=(RHS);
845 template <unsigned ElementSize>
846 inline bool operator &=(SparseBitVector<ElementSize> *LHS,
847 const SparseBitVector<ElementSize> &RHS) {
848 return LHS->operator&=(RHS);
851 template <unsigned ElementSize>
852 inline bool operator &=(SparseBitVector<ElementSize> &LHS,
853 const SparseBitVector<ElementSize> *RHS) {
857 // Convenience functions for infix union, intersection, difference operators.
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(LHS);
877 template <unsigned ElementSize>
878 inline SparseBitVector<ElementSize>
879 operator-(const SparseBitVector<ElementSize> &LHS,
880 const SparseBitVector<ElementSize> &RHS) {
881 SparseBitVector<ElementSize> Result;
882 Result.intersectWithComplement(LHS, RHS);
889 // Dump a SparseBitVector to a stream
890 template <unsigned ElementSize>
891 void dump(const SparseBitVector<ElementSize> &LHS, raw_ostream &out) {
894 typename SparseBitVector<ElementSize>::iterator bi;
895 for (bi = LHS.begin(); bi != LHS.end(); ++bi) {
900 } // end namespace llvm