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      1 //===- BitstreamWriter.h - Low-level bitstream writer interface -*- C++ -*-===//
      2 //
      3 //                     The LLVM Compiler Infrastructure
      4 //
      5 // This file is distributed under the University of Illinois Open Source
      6 // License. See LICENSE.TXT for details.
      7 //
      8 //===----------------------------------------------------------------------===//
      9 //
     10 // This header defines the BitstreamWriter class.  This class can be used to
     11 // write an arbitrary bitstream, regardless of its contents.
     12 //
     13 //===----------------------------------------------------------------------===//
     14 
     15 #ifndef LLVM_BITCODE_BITSTREAMWRITER_H
     16 #define LLVM_BITCODE_BITSTREAMWRITER_H
     17 
     18 #include "llvm/ADT/ArrayRef.h"
     19 #include "llvm/ADT/Optional.h"
     20 #include "llvm/ADT/SmallVector.h"
     21 #include "llvm/ADT/StringRef.h"
     22 #include "llvm/Bitcode/BitCodes.h"
     23 #include "llvm/Support/Endian.h"
     24 #include <vector>
     25 
     26 namespace llvm {
     27 
     28 class BitstreamWriter {
     29   SmallVectorImpl<char> &Out;
     30 
     31   /// CurBit - Always between 0 and 31 inclusive, specifies the next bit to use.
     32   unsigned CurBit;
     33 
     34   /// CurValue - The current value.  Only bits < CurBit are valid.
     35   uint32_t CurValue;
     36 
     37   /// CurCodeSize - This is the declared size of code values used for the
     38   /// current block, in bits.
     39   unsigned CurCodeSize;
     40 
     41   /// BlockInfoCurBID - When emitting a BLOCKINFO_BLOCK, this is the currently
     42   /// selected BLOCK ID.
     43   unsigned BlockInfoCurBID;
     44 
     45   /// CurAbbrevs - Abbrevs installed at in this block.
     46   std::vector<std::shared_ptr<BitCodeAbbrev>> CurAbbrevs;
     47 
     48   struct Block {
     49     unsigned PrevCodeSize;
     50     size_t StartSizeWord;
     51     std::vector<std::shared_ptr<BitCodeAbbrev>> PrevAbbrevs;
     52     Block(unsigned PCS, size_t SSW) : PrevCodeSize(PCS), StartSizeWord(SSW) {}
     53   };
     54 
     55   /// BlockScope - This tracks the current blocks that we have entered.
     56   std::vector<Block> BlockScope;
     57 
     58   /// BlockInfo - This contains information emitted to BLOCKINFO_BLOCK blocks.
     59   /// These describe abbreviations that all blocks of the specified ID inherit.
     60   struct BlockInfo {
     61     unsigned BlockID;
     62     std::vector<std::shared_ptr<BitCodeAbbrev>> Abbrevs;
     63   };
     64   std::vector<BlockInfo> BlockInfoRecords;
     65 
     66   void WriteByte(unsigned char Value) {
     67     Out.push_back(Value);
     68   }
     69 
     70   void WriteWord(unsigned Value) {
     71     Value = support::endian::byte_swap<uint32_t, support::little>(Value);
     72     Out.append(reinterpret_cast<const char *>(&Value),
     73                reinterpret_cast<const char *>(&Value + 1));
     74   }
     75 
     76   size_t GetBufferOffset() const { return Out.size(); }
     77 
     78   size_t GetWordIndex() const {
     79     size_t Offset = GetBufferOffset();
     80     assert((Offset & 3) == 0 && "Not 32-bit aligned");
     81     return Offset / 4;
     82   }
     83 
     84 public:
     85   explicit BitstreamWriter(SmallVectorImpl<char> &O)
     86     : Out(O), CurBit(0), CurValue(0), CurCodeSize(2) {}
     87 
     88   ~BitstreamWriter() {
     89     assert(CurBit == 0 && "Unflushed data remaining");
     90     assert(BlockScope.empty() && CurAbbrevs.empty() && "Block imbalance");
     91   }
     92 
     93   /// \brief Retrieve the current position in the stream, in bits.
     94   uint64_t GetCurrentBitNo() const { return GetBufferOffset() * 8 + CurBit; }
     95 
     96   /// \brief Retrieve the number of bits currently used to encode an abbrev ID.
     97   unsigned GetAbbrevIDWidth() const { return CurCodeSize; }
     98 
     99   //===--------------------------------------------------------------------===//
    100   // Basic Primitives for emitting bits to the stream.
    101   //===--------------------------------------------------------------------===//
    102 
    103   /// Backpatch a 32-bit word in the output at the given bit offset
    104   /// with the specified value.
    105   void BackpatchWord(uint64_t BitNo, unsigned NewWord) {
    106     using namespace llvm::support;
    107     unsigned ByteNo = BitNo / 8;
    108     assert((!endian::readAtBitAlignment<uint32_t, little, unaligned>(
    109                &Out[ByteNo], BitNo & 7)) &&
    110            "Expected to be patching over 0-value placeholders");
    111     endian::writeAtBitAlignment<uint32_t, little, unaligned>(
    112         &Out[ByteNo], NewWord, BitNo & 7);
    113   }
    114 
    115   void BackpatchWord64(uint64_t BitNo, uint64_t Val) {
    116     BackpatchWord(BitNo, (uint32_t)Val);
    117     BackpatchWord(BitNo + 32, (uint32_t)(Val >> 32));
    118   }
    119 
    120   void Emit(uint32_t Val, unsigned NumBits) {
    121     assert(NumBits && NumBits <= 32 && "Invalid value size!");
    122     assert((Val & ~(~0U >> (32-NumBits))) == 0 && "High bits set!");
    123     CurValue |= Val << CurBit;
    124     if (CurBit + NumBits < 32) {
    125       CurBit += NumBits;
    126       return;
    127     }
    128 
    129     // Add the current word.
    130     WriteWord(CurValue);
    131 
    132     if (CurBit)
    133       CurValue = Val >> (32-CurBit);
    134     else
    135       CurValue = 0;
    136     CurBit = (CurBit+NumBits) & 31;
    137   }
    138 
    139   void FlushToWord() {
    140     if (CurBit) {
    141       WriteWord(CurValue);
    142       CurBit = 0;
    143       CurValue = 0;
    144     }
    145   }
    146 
    147   void EmitVBR(uint32_t Val, unsigned NumBits) {
    148     assert(NumBits <= 32 && "Too many bits to emit!");
    149     uint32_t Threshold = 1U << (NumBits-1);
    150 
    151     // Emit the bits with VBR encoding, NumBits-1 bits at a time.
    152     while (Val >= Threshold) {
    153       Emit((Val & ((1 << (NumBits-1))-1)) | (1 << (NumBits-1)), NumBits);
    154       Val >>= NumBits-1;
    155     }
    156 
    157     Emit(Val, NumBits);
    158   }
    159 
    160   void EmitVBR64(uint64_t Val, unsigned NumBits) {
    161     assert(NumBits <= 32 && "Too many bits to emit!");
    162     if ((uint32_t)Val == Val)
    163       return EmitVBR((uint32_t)Val, NumBits);
    164 
    165     uint32_t Threshold = 1U << (NumBits-1);
    166 
    167     // Emit the bits with VBR encoding, NumBits-1 bits at a time.
    168     while (Val >= Threshold) {
    169       Emit(((uint32_t)Val & ((1 << (NumBits-1))-1)) |
    170            (1 << (NumBits-1)), NumBits);
    171       Val >>= NumBits-1;
    172     }
    173 
    174     Emit((uint32_t)Val, NumBits);
    175   }
    176 
    177   /// EmitCode - Emit the specified code.
    178   void EmitCode(unsigned Val) {
    179     Emit(Val, CurCodeSize);
    180   }
    181 
    182   //===--------------------------------------------------------------------===//
    183   // Block Manipulation
    184   //===--------------------------------------------------------------------===//
    185 
    186   /// getBlockInfo - If there is block info for the specified ID, return it,
    187   /// otherwise return null.
    188   BlockInfo *getBlockInfo(unsigned BlockID) {
    189     // Common case, the most recent entry matches BlockID.
    190     if (!BlockInfoRecords.empty() && BlockInfoRecords.back().BlockID == BlockID)
    191       return &BlockInfoRecords.back();
    192 
    193     for (unsigned i = 0, e = static_cast<unsigned>(BlockInfoRecords.size());
    194          i != e; ++i)
    195       if (BlockInfoRecords[i].BlockID == BlockID)
    196         return &BlockInfoRecords[i];
    197     return nullptr;
    198   }
    199 
    200   void EnterSubblock(unsigned BlockID, unsigned CodeLen) {
    201     // Block header:
    202     //    [ENTER_SUBBLOCK, blockid, newcodelen, <align4bytes>, blocklen]
    203     EmitCode(bitc::ENTER_SUBBLOCK);
    204     EmitVBR(BlockID, bitc::BlockIDWidth);
    205     EmitVBR(CodeLen, bitc::CodeLenWidth);
    206     FlushToWord();
    207 
    208     size_t BlockSizeWordIndex = GetWordIndex();
    209     unsigned OldCodeSize = CurCodeSize;
    210 
    211     // Emit a placeholder, which will be replaced when the block is popped.
    212     Emit(0, bitc::BlockSizeWidth);
    213 
    214     CurCodeSize = CodeLen;
    215 
    216     // Push the outer block's abbrev set onto the stack, start out with an
    217     // empty abbrev set.
    218     BlockScope.emplace_back(OldCodeSize, BlockSizeWordIndex);
    219     BlockScope.back().PrevAbbrevs.swap(CurAbbrevs);
    220 
    221     // If there is a blockinfo for this BlockID, add all the predefined abbrevs
    222     // to the abbrev list.
    223     if (BlockInfo *Info = getBlockInfo(BlockID)) {
    224       CurAbbrevs.insert(CurAbbrevs.end(), Info->Abbrevs.begin(),
    225                         Info->Abbrevs.end());
    226     }
    227   }
    228 
    229   void ExitBlock() {
    230     assert(!BlockScope.empty() && "Block scope imbalance!");
    231     const Block &B = BlockScope.back();
    232 
    233     // Block tail:
    234     //    [END_BLOCK, <align4bytes>]
    235     EmitCode(bitc::END_BLOCK);
    236     FlushToWord();
    237 
    238     // Compute the size of the block, in words, not counting the size field.
    239     size_t SizeInWords = GetWordIndex() - B.StartSizeWord - 1;
    240     uint64_t BitNo = uint64_t(B.StartSizeWord) * 32;
    241 
    242     // Update the block size field in the header of this sub-block.
    243     BackpatchWord(BitNo, SizeInWords);
    244 
    245     // Restore the inner block's code size and abbrev table.
    246     CurCodeSize = B.PrevCodeSize;
    247     CurAbbrevs = std::move(B.PrevAbbrevs);
    248     BlockScope.pop_back();
    249   }
    250 
    251   //===--------------------------------------------------------------------===//
    252   // Record Emission
    253   //===--------------------------------------------------------------------===//
    254 
    255 private:
    256   /// EmitAbbreviatedLiteral - Emit a literal value according to its abbrev
    257   /// record.  This is a no-op, since the abbrev specifies the literal to use.
    258   template<typename uintty>
    259   void EmitAbbreviatedLiteral(const BitCodeAbbrevOp &Op, uintty V) {
    260     assert(Op.isLiteral() && "Not a literal");
    261     // If the abbrev specifies the literal value to use, don't emit
    262     // anything.
    263     assert(V == Op.getLiteralValue() &&
    264            "Invalid abbrev for record!");
    265   }
    266 
    267   /// EmitAbbreviatedField - Emit a single scalar field value with the specified
    268   /// encoding.
    269   template<typename uintty>
    270   void EmitAbbreviatedField(const BitCodeAbbrevOp &Op, uintty V) {
    271     assert(!Op.isLiteral() && "Literals should use EmitAbbreviatedLiteral!");
    272 
    273     // Encode the value as we are commanded.
    274     switch (Op.getEncoding()) {
    275     default: llvm_unreachable("Unknown encoding!");
    276     case BitCodeAbbrevOp::Fixed:
    277       if (Op.getEncodingData())
    278         Emit((unsigned)V, (unsigned)Op.getEncodingData());
    279       break;
    280     case BitCodeAbbrevOp::VBR:
    281       if (Op.getEncodingData())
    282         EmitVBR64(V, (unsigned)Op.getEncodingData());
    283       break;
    284     case BitCodeAbbrevOp::Char6:
    285       Emit(BitCodeAbbrevOp::EncodeChar6((char)V), 6);
    286       break;
    287     }
    288   }
    289 
    290   /// EmitRecordWithAbbrevImpl - This is the core implementation of the record
    291   /// emission code.  If BlobData is non-null, then it specifies an array of
    292   /// data that should be emitted as part of the Blob or Array operand that is
    293   /// known to exist at the end of the record. If Code is specified, then
    294   /// it is the record code to emit before the Vals, which must not contain
    295   /// the code.
    296   template <typename uintty>
    297   void EmitRecordWithAbbrevImpl(unsigned Abbrev, ArrayRef<uintty> Vals,
    298                                 StringRef Blob, Optional<unsigned> Code) {
    299     const char *BlobData = Blob.data();
    300     unsigned BlobLen = (unsigned) Blob.size();
    301     unsigned AbbrevNo = Abbrev-bitc::FIRST_APPLICATION_ABBREV;
    302     assert(AbbrevNo < CurAbbrevs.size() && "Invalid abbrev #!");
    303     const BitCodeAbbrev *Abbv = CurAbbrevs[AbbrevNo].get();
    304 
    305     EmitCode(Abbrev);
    306 
    307     unsigned i = 0, e = static_cast<unsigned>(Abbv->getNumOperandInfos());
    308     if (Code) {
    309       assert(e && "Expected non-empty abbreviation");
    310       const BitCodeAbbrevOp &Op = Abbv->getOperandInfo(i++);
    311 
    312       if (Op.isLiteral())
    313         EmitAbbreviatedLiteral(Op, Code.getValue());
    314       else {
    315         assert(Op.getEncoding() != BitCodeAbbrevOp::Array &&
    316                Op.getEncoding() != BitCodeAbbrevOp::Blob &&
    317                "Expected literal or scalar");
    318         EmitAbbreviatedField(Op, Code.getValue());
    319       }
    320     }
    321 
    322     unsigned RecordIdx = 0;
    323     for (; i != e; ++i) {
    324       const BitCodeAbbrevOp &Op = Abbv->getOperandInfo(i);
    325       if (Op.isLiteral()) {
    326         assert(RecordIdx < Vals.size() && "Invalid abbrev/record");
    327         EmitAbbreviatedLiteral(Op, Vals[RecordIdx]);
    328         ++RecordIdx;
    329       } else if (Op.getEncoding() == BitCodeAbbrevOp::Array) {
    330         // Array case.
    331         assert(i + 2 == e && "array op not second to last?");
    332         const BitCodeAbbrevOp &EltEnc = Abbv->getOperandInfo(++i);
    333 
    334         // If this record has blob data, emit it, otherwise we must have record
    335         // entries to encode this way.
    336         if (BlobData) {
    337           assert(RecordIdx == Vals.size() &&
    338                  "Blob data and record entries specified for array!");
    339           // Emit a vbr6 to indicate the number of elements present.
    340           EmitVBR(static_cast<uint32_t>(BlobLen), 6);
    341 
    342           // Emit each field.
    343           for (unsigned i = 0; i != BlobLen; ++i)
    344             EmitAbbreviatedField(EltEnc, (unsigned char)BlobData[i]);
    345 
    346           // Know that blob data is consumed for assertion below.
    347           BlobData = nullptr;
    348         } else {
    349           // Emit a vbr6 to indicate the number of elements present.
    350           EmitVBR(static_cast<uint32_t>(Vals.size()-RecordIdx), 6);
    351 
    352           // Emit each field.
    353           for (unsigned e = Vals.size(); RecordIdx != e; ++RecordIdx)
    354             EmitAbbreviatedField(EltEnc, Vals[RecordIdx]);
    355         }
    356       } else if (Op.getEncoding() == BitCodeAbbrevOp::Blob) {
    357         // If this record has blob data, emit it, otherwise we must have record
    358         // entries to encode this way.
    359 
    360         if (BlobData) {
    361           assert(RecordIdx == Vals.size() &&
    362                  "Blob data and record entries specified for blob operand!");
    363 
    364           assert(Blob.data() == BlobData && "BlobData got moved");
    365           assert(Blob.size() == BlobLen && "BlobLen got changed");
    366           emitBlob(Blob);
    367           BlobData = nullptr;
    368         } else {
    369           emitBlob(Vals.slice(RecordIdx));
    370         }
    371       } else {  // Single scalar field.
    372         assert(RecordIdx < Vals.size() && "Invalid abbrev/record");
    373         EmitAbbreviatedField(Op, Vals[RecordIdx]);
    374         ++RecordIdx;
    375       }
    376     }
    377     assert(RecordIdx == Vals.size() && "Not all record operands emitted!");
    378     assert(BlobData == nullptr &&
    379            "Blob data specified for record that doesn't use it!");
    380   }
    381 
    382 public:
    383   /// Emit a blob, including flushing before and tail-padding.
    384   template <class UIntTy>
    385   void emitBlob(ArrayRef<UIntTy> Bytes, bool ShouldEmitSize = true) {
    386     // Emit a vbr6 to indicate the number of elements present.
    387     if (ShouldEmitSize)
    388       EmitVBR(static_cast<uint32_t>(Bytes.size()), 6);
    389 
    390     // Flush to a 32-bit alignment boundary.
    391     FlushToWord();
    392 
    393     // Emit literal bytes.
    394     for (const auto &B : Bytes) {
    395       assert(isUInt<8>(B) && "Value too large to emit as byte");
    396       WriteByte((unsigned char)B);
    397     }
    398 
    399     // Align end to 32-bits.
    400     while (GetBufferOffset() & 3)
    401       WriteByte(0);
    402   }
    403   void emitBlob(StringRef Bytes, bool ShouldEmitSize = true) {
    404     emitBlob(makeArrayRef((const uint8_t *)Bytes.data(), Bytes.size()),
    405              ShouldEmitSize);
    406   }
    407 
    408   /// EmitRecord - Emit the specified record to the stream, using an abbrev if
    409   /// we have one to compress the output.
    410   template <typename Container>
    411   void EmitRecord(unsigned Code, const Container &Vals, unsigned Abbrev = 0) {
    412     if (!Abbrev) {
    413       // If we don't have an abbrev to use, emit this in its fully unabbreviated
    414       // form.
    415       auto Count = static_cast<uint32_t>(makeArrayRef(Vals).size());
    416       EmitCode(bitc::UNABBREV_RECORD);
    417       EmitVBR(Code, 6);
    418       EmitVBR(Count, 6);
    419       for (unsigned i = 0, e = Count; i != e; ++i)
    420         EmitVBR64(Vals[i], 6);
    421       return;
    422     }
    423 
    424     EmitRecordWithAbbrevImpl(Abbrev, makeArrayRef(Vals), StringRef(), Code);
    425   }
    426 
    427   /// EmitRecordWithAbbrev - Emit a record with the specified abbreviation.
    428   /// Unlike EmitRecord, the code for the record should be included in Vals as
    429   /// the first entry.
    430   template <typename Container>
    431   void EmitRecordWithAbbrev(unsigned Abbrev, const Container &Vals) {
    432     EmitRecordWithAbbrevImpl(Abbrev, makeArrayRef(Vals), StringRef(), None);
    433   }
    434 
    435   /// EmitRecordWithBlob - Emit the specified record to the stream, using an
    436   /// abbrev that includes a blob at the end.  The blob data to emit is
    437   /// specified by the pointer and length specified at the end.  In contrast to
    438   /// EmitRecord, this routine expects that the first entry in Vals is the code
    439   /// of the record.
    440   template <typename Container>
    441   void EmitRecordWithBlob(unsigned Abbrev, const Container &Vals,
    442                           StringRef Blob) {
    443     EmitRecordWithAbbrevImpl(Abbrev, makeArrayRef(Vals), Blob, None);
    444   }
    445   template <typename Container>
    446   void EmitRecordWithBlob(unsigned Abbrev, const Container &Vals,
    447                           const char *BlobData, unsigned BlobLen) {
    448     return EmitRecordWithAbbrevImpl(Abbrev, makeArrayRef(Vals),
    449                                     StringRef(BlobData, BlobLen), None);
    450   }
    451 
    452   /// EmitRecordWithArray - Just like EmitRecordWithBlob, works with records
    453   /// that end with an array.
    454   template <typename Container>
    455   void EmitRecordWithArray(unsigned Abbrev, const Container &Vals,
    456                            StringRef Array) {
    457     EmitRecordWithAbbrevImpl(Abbrev, makeArrayRef(Vals), Array, None);
    458   }
    459   template <typename Container>
    460   void EmitRecordWithArray(unsigned Abbrev, const Container &Vals,
    461                            const char *ArrayData, unsigned ArrayLen) {
    462     return EmitRecordWithAbbrevImpl(Abbrev, makeArrayRef(Vals),
    463                                     StringRef(ArrayData, ArrayLen), None);
    464   }
    465 
    466   //===--------------------------------------------------------------------===//
    467   // Abbrev Emission
    468   //===--------------------------------------------------------------------===//
    469 
    470 private:
    471   // Emit the abbreviation as a DEFINE_ABBREV record.
    472   void EncodeAbbrev(const BitCodeAbbrev &Abbv) {
    473     EmitCode(bitc::DEFINE_ABBREV);
    474     EmitVBR(Abbv.getNumOperandInfos(), 5);
    475     for (unsigned i = 0, e = static_cast<unsigned>(Abbv.getNumOperandInfos());
    476          i != e; ++i) {
    477       const BitCodeAbbrevOp &Op = Abbv.getOperandInfo(i);
    478       Emit(Op.isLiteral(), 1);
    479       if (Op.isLiteral()) {
    480         EmitVBR64(Op.getLiteralValue(), 8);
    481       } else {
    482         Emit(Op.getEncoding(), 3);
    483         if (Op.hasEncodingData())
    484           EmitVBR64(Op.getEncodingData(), 5);
    485       }
    486     }
    487   }
    488 public:
    489 
    490   /// EmitAbbrev - This emits an abbreviation to the stream.  Note that this
    491   /// method takes ownership of the specified abbrev.
    492   unsigned EmitAbbrev(std::shared_ptr<BitCodeAbbrev> Abbv) {
    493     // Emit the abbreviation as a record.
    494     EncodeAbbrev(*Abbv);
    495     CurAbbrevs.push_back(std::move(Abbv));
    496     return static_cast<unsigned>(CurAbbrevs.size())-1 +
    497       bitc::FIRST_APPLICATION_ABBREV;
    498   }
    499 
    500   //===--------------------------------------------------------------------===//
    501   // BlockInfo Block Emission
    502   //===--------------------------------------------------------------------===//
    503 
    504   /// EnterBlockInfoBlock - Start emitting the BLOCKINFO_BLOCK.
    505   void EnterBlockInfoBlock() {
    506     EnterSubblock(bitc::BLOCKINFO_BLOCK_ID, 2);
    507     BlockInfoCurBID = ~0U;
    508     BlockInfoRecords.clear();
    509   }
    510 private:
    511   /// SwitchToBlockID - If we aren't already talking about the specified block
    512   /// ID, emit a BLOCKINFO_CODE_SETBID record.
    513   void SwitchToBlockID(unsigned BlockID) {
    514     if (BlockInfoCurBID == BlockID) return;
    515     SmallVector<unsigned, 2> V;
    516     V.push_back(BlockID);
    517     EmitRecord(bitc::BLOCKINFO_CODE_SETBID, V);
    518     BlockInfoCurBID = BlockID;
    519   }
    520 
    521   BlockInfo &getOrCreateBlockInfo(unsigned BlockID) {
    522     if (BlockInfo *BI = getBlockInfo(BlockID))
    523       return *BI;
    524 
    525     // Otherwise, add a new record.
    526     BlockInfoRecords.emplace_back();
    527     BlockInfoRecords.back().BlockID = BlockID;
    528     return BlockInfoRecords.back();
    529   }
    530 
    531 public:
    532 
    533   /// EmitBlockInfoAbbrev - Emit a DEFINE_ABBREV record for the specified
    534   /// BlockID.
    535   unsigned EmitBlockInfoAbbrev(unsigned BlockID, std::shared_ptr<BitCodeAbbrev> Abbv) {
    536     SwitchToBlockID(BlockID);
    537     EncodeAbbrev(*Abbv);
    538 
    539     // Add the abbrev to the specified block record.
    540     BlockInfo &Info = getOrCreateBlockInfo(BlockID);
    541     Info.Abbrevs.push_back(std::move(Abbv));
    542 
    543     return Info.Abbrevs.size()-1+bitc::FIRST_APPLICATION_ABBREV;
    544   }
    545 };
    546 
    547 
    548 } // End llvm namespace
    549 
    550 #endif
    551