//===- llvm/ADT/SparseBitVector.h - Efficient Sparse BitVector -*- C++ -*- ===// // // The LLVM Compiler Infrastructure // // This file is distributed under the University of Illinois Open Source // License. See LICENSE.TXT for details. // //===----------------------------------------------------------------------===// // // This file defines the SparseBitVector class. See the doxygen comment for // SparseBitVector for more details on the algorithm used. // //===----------------------------------------------------------------------===// #ifndef LLVM_ADT_SPARSEBITVECTOR_H #define LLVM_ADT_SPARSEBITVECTOR_H #include "llvm/ADT/ilist.h" #include "llvm/ADT/ilist_node.h" #include "llvm/Support/DataTypes.h" #include "llvm/Support/MathExtras.h" #include "llvm/Support/raw_ostream.h" #include <cassert> #include <climits> #include <cstring> namespace llvm { /// SparseBitVector is an implementation of a bitvector that is sparse by only /// storing the elements that have non-zero bits set. In order to make this /// fast for the most common cases, SparseBitVector is implemented as a linked /// list of SparseBitVectorElements. We maintain a pointer to the last /// SparseBitVectorElement accessed (in the form of a list iterator), in order /// to make multiple in-order test/set constant time after the first one is /// executed. Note that using vectors to store SparseBitVectorElement's does /// not work out very well because it causes insertion in the middle to take /// enormous amounts of time with a large amount of bits. Other structures that /// have better worst cases for insertion in the middle (various balanced trees, /// etc) do not perform as well in practice as a linked list with this iterator /// kept up to date. They are also significantly more memory intensive. template <unsigned ElementSize = 128> struct SparseBitVectorElement : public ilist_node<SparseBitVectorElement<ElementSize> > { public: typedef unsigned long BitWord; enum { BITWORD_SIZE = sizeof(BitWord) * CHAR_BIT, BITWORDS_PER_ELEMENT = (ElementSize + BITWORD_SIZE - 1) / BITWORD_SIZE, BITS_PER_ELEMENT = ElementSize }; private: // Index of Element in terms of where first bit starts. unsigned ElementIndex; BitWord Bits[BITWORDS_PER_ELEMENT]; // Needed for sentinels friend struct ilist_sentinel_traits<SparseBitVectorElement>; SparseBitVectorElement() { ElementIndex = ~0U; memset(&Bits[0], 0, sizeof (BitWord) * BITWORDS_PER_ELEMENT); } public: explicit SparseBitVectorElement(unsigned Idx) { ElementIndex = Idx; memset(&Bits[0], 0, sizeof (BitWord) * BITWORDS_PER_ELEMENT); } // Comparison. bool operator==(const SparseBitVectorElement &RHS) const { if (ElementIndex != RHS.ElementIndex) return false; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) if (Bits[i] != RHS.Bits[i]) return false; return true; } bool operator!=(const SparseBitVectorElement &RHS) const { return !(*this == RHS); } // Return the bits that make up word Idx in our element. BitWord word(unsigned Idx) const { assert (Idx < BITWORDS_PER_ELEMENT); return Bits[Idx]; } unsigned index() const { return ElementIndex; } bool empty() const { for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) if (Bits[i]) return false; return true; } void set(unsigned Idx) { Bits[Idx / BITWORD_SIZE] |= 1L << (Idx % BITWORD_SIZE); } bool test_and_set (unsigned Idx) { bool old = test(Idx); if (!old) { set(Idx); return true; } return false; } void reset(unsigned Idx) { Bits[Idx / BITWORD_SIZE] &= ~(1L << (Idx % BITWORD_SIZE)); } bool test(unsigned Idx) const { return Bits[Idx / BITWORD_SIZE] & (1L << (Idx % BITWORD_SIZE)); } unsigned count() const { unsigned NumBits = 0; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) if (sizeof(BitWord) == 4) NumBits += CountPopulation_32(Bits[i]); else if (sizeof(BitWord) == 8) NumBits += CountPopulation_64(Bits[i]); else assert(0 && "Unsupported!"); return NumBits; } /// find_first - Returns the index of the first set bit. int find_first() const { for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) if (Bits[i] != 0) { if (sizeof(BitWord) == 4) return i * BITWORD_SIZE + CountTrailingZeros_32(Bits[i]); else if (sizeof(BitWord) == 8) return i * BITWORD_SIZE + CountTrailingZeros_64(Bits[i]); else assert(0 && "Unsupported!"); } assert(0 && "Illegal empty element"); return 0; // Not reached } /// find_next - Returns the index of the next set bit starting from the /// "Curr" bit. Returns -1 if the next set bit is not found. int find_next(unsigned Curr) const { if (Curr >= BITS_PER_ELEMENT) return -1; unsigned WordPos = Curr / BITWORD_SIZE; unsigned BitPos = Curr % BITWORD_SIZE; BitWord Copy = Bits[WordPos]; assert (WordPos <= BITWORDS_PER_ELEMENT && "Word Position outside of element"); // Mask off previous bits. Copy &= ~0L << BitPos; if (Copy != 0) { if (sizeof(BitWord) == 4) return WordPos * BITWORD_SIZE + CountTrailingZeros_32(Copy); else if (sizeof(BitWord) == 8) return WordPos * BITWORD_SIZE + CountTrailingZeros_64(Copy); else assert(0 && "Unsupported!"); } // Check subsequent words. for (unsigned i = WordPos+1; i < BITWORDS_PER_ELEMENT; ++i) if (Bits[i] != 0) { if (sizeof(BitWord) == 4) return i * BITWORD_SIZE + CountTrailingZeros_32(Bits[i]); else if (sizeof(BitWord) == 8) return i * BITWORD_SIZE + CountTrailingZeros_64(Bits[i]); else assert(0 && "Unsupported!"); } return -1; } // Union this element with RHS and return true if this one changed. bool unionWith(const SparseBitVectorElement &RHS) { bool changed = false; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) { BitWord old = changed ? 0 : Bits[i]; Bits[i] |= RHS.Bits[i]; if (!changed && old != Bits[i]) changed = true; } return changed; } // Return true if we have any bits in common with RHS bool intersects(const SparseBitVectorElement &RHS) const { for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) { if (RHS.Bits[i] & Bits[i]) return true; } return false; } // Intersect this Element with RHS and return true if this one changed. // BecameZero is set to true if this element became all-zero bits. bool intersectWith(const SparseBitVectorElement &RHS, bool &BecameZero) { bool changed = false; bool allzero = true; BecameZero = false; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) { BitWord old = changed ? 0 : Bits[i]; Bits[i] &= RHS.Bits[i]; if (Bits[i] != 0) allzero = false; if (!changed && old != Bits[i]) changed = true; } BecameZero = allzero; return changed; } // Intersect this Element with the complement of RHS and return true if this // one changed. BecameZero is set to true if this element became all-zero // bits. bool intersectWithComplement(const SparseBitVectorElement &RHS, bool &BecameZero) { bool changed = false; bool allzero = true; BecameZero = false; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) { BitWord old = changed ? 0 : Bits[i]; Bits[i] &= ~RHS.Bits[i]; if (Bits[i] != 0) allzero = false; if (!changed && old != Bits[i]) changed = true; } BecameZero = allzero; return changed; } // Three argument version of intersectWithComplement that intersects // RHS1 & ~RHS2 into this element void intersectWithComplement(const SparseBitVectorElement &RHS1, const SparseBitVectorElement &RHS2, bool &BecameZero) { bool allzero = true; BecameZero = false; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) { Bits[i] = RHS1.Bits[i] & ~RHS2.Bits[i]; if (Bits[i] != 0) allzero = false; } BecameZero = allzero; } // Get a hash value for this element; uint64_t getHashValue() const { uint64_t HashVal = 0; for (unsigned i = 0; i < BITWORDS_PER_ELEMENT; ++i) { HashVal ^= Bits[i]; } return HashVal; } }; template <unsigned ElementSize = 128> class SparseBitVector { typedef ilist<SparseBitVectorElement<ElementSize> > ElementList; typedef typename ElementList::iterator ElementListIter; typedef typename ElementList::const_iterator ElementListConstIter; enum { BITWORD_SIZE = SparseBitVectorElement<ElementSize>::BITWORD_SIZE }; // Pointer to our current Element. ElementListIter CurrElementIter; ElementList Elements; // This is like std::lower_bound, except we do linear searching from the // current position. ElementListIter FindLowerBound(unsigned ElementIndex) { if (Elements.empty()) { CurrElementIter = Elements.begin(); return Elements.begin(); } // Make sure our current iterator is valid. if (CurrElementIter == Elements.end()) --CurrElementIter; // Search from our current iterator, either backwards or forwards, // depending on what element we are looking for. ElementListIter ElementIter = CurrElementIter; if (CurrElementIter->index() == ElementIndex) { return ElementIter; } else if (CurrElementIter->index() > ElementIndex) { while (ElementIter != Elements.begin() && ElementIter->index() > ElementIndex) --ElementIter; } else { while (ElementIter != Elements.end() && ElementIter->index() < ElementIndex) ++ElementIter; } CurrElementIter = ElementIter; return ElementIter; } // Iterator to walk set bits in the bitmap. This iterator is a lot uglier // than it would be, in order to be efficient. class SparseBitVectorIterator { private: bool AtEnd; const SparseBitVector<ElementSize> *BitVector; // Current element inside of bitmap. ElementListConstIter Iter; // Current bit number inside of our bitmap. unsigned BitNumber; // Current word number inside of our element. unsigned WordNumber; // Current bits from the element. typename SparseBitVectorElement<ElementSize>::BitWord Bits; // Move our iterator to the first non-zero bit in the bitmap. void AdvanceToFirstNonZero() { if (AtEnd) return; if (BitVector->Elements.empty()) { AtEnd = true; return; } Iter = BitVector->Elements.begin(); BitNumber = Iter->index() * ElementSize; unsigned BitPos = Iter->find_first(); BitNumber += BitPos; WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE; Bits = Iter->word(WordNumber); Bits >>= BitPos % BITWORD_SIZE; } // Move our iterator to the next non-zero bit. void AdvanceToNextNonZero() { if (AtEnd) return; while (Bits && !(Bits & 1)) { Bits >>= 1; BitNumber += 1; } // See if we ran out of Bits in this word. if (!Bits) { int NextSetBitNumber = Iter->find_next(BitNumber % ElementSize) ; // If we ran out of set bits in this element, move to next element. if (NextSetBitNumber == -1 || (BitNumber % ElementSize == 0)) { ++Iter; WordNumber = 0; // We may run out of elements in the bitmap. if (Iter == BitVector->Elements.end()) { AtEnd = true; return; } // Set up for next non zero word in bitmap. BitNumber = Iter->index() * ElementSize; NextSetBitNumber = Iter->find_first(); BitNumber += NextSetBitNumber; WordNumber = (BitNumber % ElementSize) / BITWORD_SIZE; Bits = Iter->word(WordNumber); Bits >>= NextSetBitNumber % BITWORD_SIZE; } else { WordNumber = (NextSetBitNumber % ElementSize) / BITWORD_SIZE; Bits = Iter->word(WordNumber); Bits >>= NextSetBitNumber % BITWORD_SIZE; BitNumber = Iter->index() * ElementSize; BitNumber += NextSetBitNumber; } } } public: // Preincrement. inline SparseBitVectorIterator& operator++() { ++BitNumber; Bits >>= 1; AdvanceToNextNonZero(); return *this; } // Postincrement. inline SparseBitVectorIterator operator++(int) { SparseBitVectorIterator tmp = *this; ++*this; return tmp; } // Return the current set bit number. unsigned operator*() const { return BitNumber; } bool operator==(const SparseBitVectorIterator &RHS) const { // If they are both at the end, ignore the rest of the fields. if (AtEnd && RHS.AtEnd) return true; // Otherwise they are the same if they have the same bit number and // bitmap. return AtEnd == RHS.AtEnd && RHS.BitNumber == BitNumber; } bool operator!=(const SparseBitVectorIterator &RHS) const { return !(*this == RHS); } SparseBitVectorIterator(): BitVector(NULL) { } SparseBitVectorIterator(const SparseBitVector<ElementSize> *RHS, bool end = false):BitVector(RHS) { Iter = BitVector->Elements.begin(); BitNumber = 0; Bits = 0; WordNumber = ~0; AtEnd = end; AdvanceToFirstNonZero(); } }; public: typedef SparseBitVectorIterator iterator; SparseBitVector () { CurrElementIter = Elements.begin (); } ~SparseBitVector() { } // SparseBitVector copy ctor. SparseBitVector(const SparseBitVector &RHS) { ElementListConstIter ElementIter = RHS.Elements.begin(); while (ElementIter != RHS.Elements.end()) { Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter)); ++ElementIter; } CurrElementIter = Elements.begin (); } // Clear. void clear() { Elements.clear(); } // Assignment SparseBitVector& operator=(const SparseBitVector& RHS) { Elements.clear(); ElementListConstIter ElementIter = RHS.Elements.begin(); while (ElementIter != RHS.Elements.end()) { Elements.push_back(SparseBitVectorElement<ElementSize>(*ElementIter)); ++ElementIter; } CurrElementIter = Elements.begin (); return *this; } // Test, Reset, and Set a bit in the bitmap. bool test(unsigned Idx) { if (Elements.empty()) return false; unsigned ElementIndex = Idx / ElementSize; ElementListIter ElementIter = FindLowerBound(ElementIndex); // If we can't find an element that is supposed to contain this bit, there // is nothing more to do. if (ElementIter == Elements.end() || ElementIter->index() != ElementIndex) return false; return ElementIter->test(Idx % ElementSize); } void reset(unsigned Idx) { if (Elements.empty()) return; unsigned ElementIndex = Idx / ElementSize; ElementListIter ElementIter = FindLowerBound(ElementIndex); // If we can't find an element that is supposed to contain this bit, there // is nothing more to do. if (ElementIter == Elements.end() || ElementIter->index() != ElementIndex) return; ElementIter->reset(Idx % ElementSize); // When the element is zeroed out, delete it. if (ElementIter->empty()) { ++CurrElementIter; Elements.erase(ElementIter); } } void set(unsigned Idx) { unsigned ElementIndex = Idx / ElementSize; SparseBitVectorElement<ElementSize> *Element; ElementListIter ElementIter; if (Elements.empty()) { Element = new SparseBitVectorElement<ElementSize>(ElementIndex); ElementIter = Elements.insert(Elements.end(), Element); } else { ElementIter = FindLowerBound(ElementIndex); if (ElementIter == Elements.end() || ElementIter->index() != ElementIndex) { Element = new SparseBitVectorElement<ElementSize>(ElementIndex); // We may have hit the beginning of our SparseBitVector, in which case, // we may need to insert right after this element, which requires moving // the current iterator forward one, because insert does insert before. if (ElementIter != Elements.end() && ElementIter->index() < ElementIndex) ElementIter = Elements.insert(++ElementIter, Element); else ElementIter = Elements.insert(ElementIter, Element); } } CurrElementIter = ElementIter; ElementIter->set(Idx % ElementSize); } bool test_and_set (unsigned Idx) { bool old = test(Idx); if (!old) { set(Idx); return true; } return false; } bool operator!=(const SparseBitVector &RHS) const { return !(*this == RHS); } bool operator==(const SparseBitVector &RHS) const { ElementListConstIter Iter1 = Elements.begin(); ElementListConstIter Iter2 = RHS.Elements.begin(); for (; Iter1 != Elements.end() && Iter2 != RHS.Elements.end(); ++Iter1, ++Iter2) { if (*Iter1 != *Iter2) return false; } return Iter1 == Elements.end() && Iter2 == RHS.Elements.end(); } // Union our bitmap with the RHS and return true if we changed. bool operator|=(const SparseBitVector &RHS) { bool changed = false; ElementListIter Iter1 = Elements.begin(); ElementListConstIter Iter2 = RHS.Elements.begin(); // If RHS is empty, we are done if (RHS.Elements.empty()) return false; while (Iter2 != RHS.Elements.end()) { if (Iter1 == Elements.end() || Iter1->index() > Iter2->index()) { Elements.insert(Iter1, new SparseBitVectorElement<ElementSize>(*Iter2)); ++Iter2; changed = true; } else if (Iter1->index() == Iter2->index()) { changed |= Iter1->unionWith(*Iter2); ++Iter1; ++Iter2; } else { ++Iter1; } } CurrElementIter = Elements.begin(); return changed; } // Intersect our bitmap with the RHS and return true if ours changed. bool operator&=(const SparseBitVector &RHS) { bool changed = false; ElementListIter Iter1 = Elements.begin(); ElementListConstIter Iter2 = RHS.Elements.begin(); // Check if both bitmaps are empty. if (Elements.empty() && RHS.Elements.empty()) return false; // Loop through, intersecting as we go, erasing elements when necessary. while (Iter2 != RHS.Elements.end()) { if (Iter1 == Elements.end()) { CurrElementIter = Elements.begin(); return changed; } if (Iter1->index() > Iter2->index()) { ++Iter2; } else if (Iter1->index() == Iter2->index()) { bool BecameZero; changed |= Iter1->intersectWith(*Iter2, BecameZero); if (BecameZero) { ElementListIter IterTmp = Iter1; ++Iter1; Elements.erase(IterTmp); } else { ++Iter1; } ++Iter2; } else { ElementListIter IterTmp = Iter1; ++Iter1; Elements.erase(IterTmp); } } Elements.erase(Iter1, Elements.end()); CurrElementIter = Elements.begin(); return changed; } // Intersect our bitmap with the complement of the RHS and return true // if ours changed. bool intersectWithComplement(const SparseBitVector &RHS) { bool changed = false; ElementListIter Iter1 = Elements.begin(); ElementListConstIter Iter2 = RHS.Elements.begin(); // If either our bitmap or RHS is empty, we are done if (Elements.empty() || RHS.Elements.empty()) return false; // Loop through, intersecting as we go, erasing elements when necessary. while (Iter2 != RHS.Elements.end()) { if (Iter1 == Elements.end()) { CurrElementIter = Elements.begin(); return changed; } if (Iter1->index() > Iter2->index()) { ++Iter2; } else if (Iter1->index() == Iter2->index()) { bool BecameZero; changed |= Iter1->intersectWithComplement(*Iter2, BecameZero); if (BecameZero) { ElementListIter IterTmp = Iter1; ++Iter1; Elements.erase(IterTmp); } else { ++Iter1; } ++Iter2; } else { ++Iter1; } } CurrElementIter = Elements.begin(); return changed; } bool intersectWithComplement(const SparseBitVector<ElementSize> *RHS) const { return intersectWithComplement(*RHS); } // Three argument version of intersectWithComplement. // Result of RHS1 & ~RHS2 is stored into this bitmap. void intersectWithComplement(const SparseBitVector<ElementSize> &RHS1, const SparseBitVector<ElementSize> &RHS2) { Elements.clear(); CurrElementIter = Elements.begin(); ElementListConstIter Iter1 = RHS1.Elements.begin(); ElementListConstIter Iter2 = RHS2.Elements.begin(); // If RHS1 is empty, we are done // If RHS2 is empty, we still have to copy RHS1 if (RHS1.Elements.empty()) return; // Loop through, intersecting as we go, erasing elements when necessary. while (Iter2 != RHS2.Elements.end()) { if (Iter1 == RHS1.Elements.end()) return; if (Iter1->index() > Iter2->index()) { ++Iter2; } else if (Iter1->index() == Iter2->index()) { bool BecameZero = false; SparseBitVectorElement<ElementSize> *NewElement = new SparseBitVectorElement<ElementSize>(Iter1->index()); NewElement->intersectWithComplement(*Iter1, *Iter2, BecameZero); if (!BecameZero) { Elements.push_back(NewElement); } else delete NewElement; ++Iter1; ++Iter2; } else { SparseBitVectorElement<ElementSize> *NewElement = new SparseBitVectorElement<ElementSize>(*Iter1); Elements.push_back(NewElement); ++Iter1; } } // copy the remaining elements while (Iter1 != RHS1.Elements.end()) { SparseBitVectorElement<ElementSize> *NewElement = new SparseBitVectorElement<ElementSize>(*Iter1); Elements.push_back(NewElement); ++Iter1; } return; } void intersectWithComplement(const SparseBitVector<ElementSize> *RHS1, const SparseBitVector<ElementSize> *RHS2) { intersectWithComplement(*RHS1, *RHS2); } bool intersects(const SparseBitVector<ElementSize> *RHS) const { return intersects(*RHS); } // Return true if we share any bits in common with RHS bool intersects(const SparseBitVector<ElementSize> &RHS) const { ElementListConstIter Iter1 = Elements.begin(); ElementListConstIter Iter2 = RHS.Elements.begin(); // Check if both bitmaps are empty. if (Elements.empty() && RHS.Elements.empty()) return false; // Loop through, intersecting stopping when we hit bits in common. while (Iter2 != RHS.Elements.end()) { if (Iter1 == Elements.end()) return false; if (Iter1->index() > Iter2->index()) { ++Iter2; } else if (Iter1->index() == Iter2->index()) { if (Iter1->intersects(*Iter2)) return true; ++Iter1; ++Iter2; } else { ++Iter1; } } return false; } // Return true iff all bits set in this SparseBitVector are // also set in RHS. bool contains(const SparseBitVector<ElementSize> &RHS) const { SparseBitVector<ElementSize> Result(*this); Result &= RHS; return (Result == RHS); } // Return the first set bit in the bitmap. Return -1 if no bits are set. int find_first() const { if (Elements.empty()) return -1; const SparseBitVectorElement<ElementSize> &First = *(Elements.begin()); return (First.index() * ElementSize) + First.find_first(); } // Return true if the SparseBitVector is empty bool empty() const { return Elements.empty(); } unsigned count() const { unsigned BitCount = 0; for (ElementListConstIter Iter = Elements.begin(); Iter != Elements.end(); ++Iter) BitCount += Iter->count(); return BitCount; } iterator begin() const { return iterator(this); } iterator end() const { return iterator(this, true); } // Get a hash value for this bitmap. uint64_t getHashValue() const { uint64_t HashVal = 0; for (ElementListConstIter Iter = Elements.begin(); Iter != Elements.end(); ++Iter) { HashVal ^= Iter->index(); HashVal ^= Iter->getHashValue(); } return HashVal; } }; // Convenience functions to allow Or and And without dereferencing in the user // code. template <unsigned ElementSize> inline bool operator |=(SparseBitVector<ElementSize> &LHS, const SparseBitVector<ElementSize> *RHS) { return LHS |= *RHS; } template <unsigned ElementSize> inline bool operator |=(SparseBitVector<ElementSize> *LHS, const SparseBitVector<ElementSize> &RHS) { return LHS->operator|=(RHS); } template <unsigned ElementSize> inline bool operator &=(SparseBitVector<ElementSize> *LHS, const SparseBitVector<ElementSize> &RHS) { return LHS->operator&=(RHS); } template <unsigned ElementSize> inline bool operator &=(SparseBitVector<ElementSize> &LHS, const SparseBitVector<ElementSize> *RHS) { return LHS &= *RHS; } // Convenience functions for infix union, intersection, difference operators. template <unsigned ElementSize> inline SparseBitVector<ElementSize> operator|(const SparseBitVector<ElementSize> &LHS, const SparseBitVector<ElementSize> &RHS) { SparseBitVector<ElementSize> Result(LHS); Result |= RHS; return Result; } template <unsigned ElementSize> inline SparseBitVector<ElementSize> operator&(const SparseBitVector<ElementSize> &LHS, const SparseBitVector<ElementSize> &RHS) { SparseBitVector<ElementSize> Result(LHS); Result &= RHS; return Result; } template <unsigned ElementSize> inline SparseBitVector<ElementSize> operator-(const SparseBitVector<ElementSize> &LHS, const SparseBitVector<ElementSize> &RHS) { SparseBitVector<ElementSize> Result; Result.intersectWithComplement(LHS, RHS); return Result; } // Dump a SparseBitVector to a stream template <unsigned ElementSize> void dump(const SparseBitVector<ElementSize> &LHS, raw_ostream &out) { out << "["; typename SparseBitVector<ElementSize>::iterator bi = LHS.begin(), be = LHS.end(); if (bi != be) { out << *bi; for (++bi; bi != be; ++bi) { out << " " << *bi; } } out << "]\n"; } } // end namespace llvm #endif