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      1 //===- InstCombineMulDivRem.cpp -------------------------------------------===//
      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 file implements the visit functions for mul, fmul, sdiv, udiv, fdiv,
     11 // srem, urem, frem.
     12 //
     13 //===----------------------------------------------------------------------===//
     14 
     15 #include "InstCombine.h"
     16 #include "llvm/Analysis/InstructionSimplify.h"
     17 #include "llvm/IR/IntrinsicInst.h"
     18 #include "llvm/Support/PatternMatch.h"
     19 using namespace llvm;
     20 using namespace PatternMatch;
     21 
     22 
     23 /// simplifyValueKnownNonZero - The specific integer value is used in a context
     24 /// where it is known to be non-zero.  If this allows us to simplify the
     25 /// computation, do so and return the new operand, otherwise return null.
     26 static Value *simplifyValueKnownNonZero(Value *V, InstCombiner &IC) {
     27   // If V has multiple uses, then we would have to do more analysis to determine
     28   // if this is safe.  For example, the use could be in dynamically unreached
     29   // code.
     30   if (!V->hasOneUse()) return 0;
     31 
     32   bool MadeChange = false;
     33 
     34   // ((1 << A) >>u B) --> (1 << (A-B))
     35   // Because V cannot be zero, we know that B is less than A.
     36   Value *A = 0, *B = 0, *PowerOf2 = 0;
     37   if (match(V, m_LShr(m_OneUse(m_Shl(m_Value(PowerOf2), m_Value(A))),
     38                       m_Value(B))) &&
     39       // The "1" can be any value known to be a power of 2.
     40       isKnownToBeAPowerOfTwo(PowerOf2)) {
     41     A = IC.Builder->CreateSub(A, B);
     42     return IC.Builder->CreateShl(PowerOf2, A);
     43   }
     44 
     45   // (PowerOfTwo >>u B) --> isExact since shifting out the result would make it
     46   // inexact.  Similarly for <<.
     47   if (BinaryOperator *I = dyn_cast<BinaryOperator>(V))
     48     if (I->isLogicalShift() && isKnownToBeAPowerOfTwo(I->getOperand(0))) {
     49       // We know that this is an exact/nuw shift and that the input is a
     50       // non-zero context as well.
     51       if (Value *V2 = simplifyValueKnownNonZero(I->getOperand(0), IC)) {
     52         I->setOperand(0, V2);
     53         MadeChange = true;
     54       }
     55 
     56       if (I->getOpcode() == Instruction::LShr && !I->isExact()) {
     57         I->setIsExact();
     58         MadeChange = true;
     59       }
     60 
     61       if (I->getOpcode() == Instruction::Shl && !I->hasNoUnsignedWrap()) {
     62         I->setHasNoUnsignedWrap();
     63         MadeChange = true;
     64       }
     65     }
     66 
     67   // TODO: Lots more we could do here:
     68   //    If V is a phi node, we can call this on each of its operands.
     69   //    "select cond, X, 0" can simplify to "X".
     70 
     71   return MadeChange ? V : 0;
     72 }
     73 
     74 
     75 /// MultiplyOverflows - True if the multiply can not be expressed in an int
     76 /// this size.
     77 static bool MultiplyOverflows(ConstantInt *C1, ConstantInt *C2, bool sign) {
     78   uint32_t W = C1->getBitWidth();
     79   APInt LHSExt = C1->getValue(), RHSExt = C2->getValue();
     80   if (sign) {
     81     LHSExt = LHSExt.sext(W * 2);
     82     RHSExt = RHSExt.sext(W * 2);
     83   } else {
     84     LHSExt = LHSExt.zext(W * 2);
     85     RHSExt = RHSExt.zext(W * 2);
     86   }
     87 
     88   APInt MulExt = LHSExt * RHSExt;
     89 
     90   if (!sign)
     91     return MulExt.ugt(APInt::getLowBitsSet(W * 2, W));
     92 
     93   APInt Min = APInt::getSignedMinValue(W).sext(W * 2);
     94   APInt Max = APInt::getSignedMaxValue(W).sext(W * 2);
     95   return MulExt.slt(Min) || MulExt.sgt(Max);
     96 }
     97 
     98 /// \brief A helper routine of InstCombiner::visitMul().
     99 ///
    100 /// If C is a vector of known powers of 2, then this function returns
    101 /// a new vector obtained from C replacing each element with its logBase2.
    102 /// Return a null pointer otherwise.
    103 static Constant *getLogBase2Vector(ConstantDataVector *CV) {
    104   const APInt *IVal;
    105   SmallVector<Constant *, 4> Elts;
    106 
    107   for (unsigned I = 0, E = CV->getNumElements(); I != E; ++I) {
    108     Constant *Elt = CV->getElementAsConstant(I);
    109     if (!match(Elt, m_APInt(IVal)) || !IVal->isPowerOf2())
    110       return 0;
    111     Elts.push_back(ConstantInt::get(Elt->getType(), IVal->logBase2()));
    112   }
    113 
    114   return ConstantVector::get(Elts);
    115 }
    116 
    117 Instruction *InstCombiner::visitMul(BinaryOperator &I) {
    118   bool Changed = SimplifyAssociativeOrCommutative(I);
    119   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    120 
    121   if (Value *V = SimplifyMulInst(Op0, Op1, TD))
    122     return ReplaceInstUsesWith(I, V);
    123 
    124   if (Value *V = SimplifyUsingDistributiveLaws(I))
    125     return ReplaceInstUsesWith(I, V);
    126 
    127   if (match(Op1, m_AllOnes()))  // X * -1 == 0 - X
    128     return BinaryOperator::CreateNeg(Op0, I.getName());
    129 
    130   // Also allow combining multiply instructions on vectors.
    131   {
    132     Value *NewOp;
    133     Constant *C1, *C2;
    134     const APInt *IVal;
    135     if (match(&I, m_Mul(m_Shl(m_Value(NewOp), m_Constant(C2)),
    136                         m_Constant(C1))) &&
    137         match(C1, m_APInt(IVal)))
    138       // ((X << C1)*C2) == (X * (C2 << C1))
    139       return BinaryOperator::CreateMul(NewOp, ConstantExpr::getShl(C1, C2));
    140 
    141     if (match(&I, m_Mul(m_Value(NewOp), m_Constant(C1)))) {
    142       Constant *NewCst = 0;
    143       if (match(C1, m_APInt(IVal)) && IVal->isPowerOf2())
    144         // Replace X*(2^C) with X << C, where C is either a scalar or a splat.
    145         NewCst = ConstantInt::get(NewOp->getType(), IVal->logBase2());
    146       else if (ConstantDataVector *CV = dyn_cast<ConstantDataVector>(C1))
    147         // Replace X*(2^C) with X << C, where C is a vector of known
    148         // constant powers of 2.
    149         NewCst = getLogBase2Vector(CV);
    150 
    151       if (NewCst) {
    152         BinaryOperator *Shl = BinaryOperator::CreateShl(NewOp, NewCst);
    153         if (I.hasNoSignedWrap()) Shl->setHasNoSignedWrap();
    154         if (I.hasNoUnsignedWrap()) Shl->setHasNoUnsignedWrap();
    155         return Shl;
    156       }
    157     }
    158   }
    159 
    160   if (ConstantInt *CI = dyn_cast<ConstantInt>(Op1)) {
    161     // Canonicalize (X+C1)*CI -> X*CI+C1*CI.
    162     { Value *X; ConstantInt *C1;
    163       if (Op0->hasOneUse() &&
    164           match(Op0, m_Add(m_Value(X), m_ConstantInt(C1)))) {
    165         Value *Add = Builder->CreateMul(X, CI);
    166         return BinaryOperator::CreateAdd(Add, Builder->CreateMul(C1, CI));
    167       }
    168     }
    169 
    170     // (Y - X) * (-(2**n)) -> (X - Y) * (2**n), for positive nonzero n
    171     // (Y + const) * (-(2**n)) -> (-constY) * (2**n), for positive nonzero n
    172     // The "* (2**n)" thus becomes a potential shifting opportunity.
    173     {
    174       const APInt &   Val = CI->getValue();
    175       const APInt &PosVal = Val.abs();
    176       if (Val.isNegative() && PosVal.isPowerOf2()) {
    177         Value *X = 0, *Y = 0;
    178         if (Op0->hasOneUse()) {
    179           ConstantInt *C1;
    180           Value *Sub = 0;
    181           if (match(Op0, m_Sub(m_Value(Y), m_Value(X))))
    182             Sub = Builder->CreateSub(X, Y, "suba");
    183           else if (match(Op0, m_Add(m_Value(Y), m_ConstantInt(C1))))
    184             Sub = Builder->CreateSub(Builder->CreateNeg(C1), Y, "subc");
    185           if (Sub)
    186             return
    187               BinaryOperator::CreateMul(Sub,
    188                                         ConstantInt::get(Y->getType(), PosVal));
    189         }
    190       }
    191     }
    192   }
    193 
    194   // Simplify mul instructions with a constant RHS.
    195   if (isa<Constant>(Op1)) {
    196     // Try to fold constant mul into select arguments.
    197     if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
    198       if (Instruction *R = FoldOpIntoSelect(I, SI))
    199         return R;
    200 
    201     if (isa<PHINode>(Op0))
    202       if (Instruction *NV = FoldOpIntoPhi(I))
    203         return NV;
    204   }
    205 
    206   if (Value *Op0v = dyn_castNegVal(Op0))     // -X * -Y = X*Y
    207     if (Value *Op1v = dyn_castNegVal(Op1))
    208       return BinaryOperator::CreateMul(Op0v, Op1v);
    209 
    210   // (X / Y) *  Y = X - (X % Y)
    211   // (X / Y) * -Y = (X % Y) - X
    212   {
    213     Value *Op1C = Op1;
    214     BinaryOperator *BO = dyn_cast<BinaryOperator>(Op0);
    215     if (!BO ||
    216         (BO->getOpcode() != Instruction::UDiv &&
    217          BO->getOpcode() != Instruction::SDiv)) {
    218       Op1C = Op0;
    219       BO = dyn_cast<BinaryOperator>(Op1);
    220     }
    221     Value *Neg = dyn_castNegVal(Op1C);
    222     if (BO && BO->hasOneUse() &&
    223         (BO->getOperand(1) == Op1C || BO->getOperand(1) == Neg) &&
    224         (BO->getOpcode() == Instruction::UDiv ||
    225          BO->getOpcode() == Instruction::SDiv)) {
    226       Value *Op0BO = BO->getOperand(0), *Op1BO = BO->getOperand(1);
    227 
    228       // If the division is exact, X % Y is zero, so we end up with X or -X.
    229       if (PossiblyExactOperator *SDiv = dyn_cast<PossiblyExactOperator>(BO))
    230         if (SDiv->isExact()) {
    231           if (Op1BO == Op1C)
    232             return ReplaceInstUsesWith(I, Op0BO);
    233           return BinaryOperator::CreateNeg(Op0BO);
    234         }
    235 
    236       Value *Rem;
    237       if (BO->getOpcode() == Instruction::UDiv)
    238         Rem = Builder->CreateURem(Op0BO, Op1BO);
    239       else
    240         Rem = Builder->CreateSRem(Op0BO, Op1BO);
    241       Rem->takeName(BO);
    242 
    243       if (Op1BO == Op1C)
    244         return BinaryOperator::CreateSub(Op0BO, Rem);
    245       return BinaryOperator::CreateSub(Rem, Op0BO);
    246     }
    247   }
    248 
    249   /// i1 mul -> i1 and.
    250   if (I.getType()->isIntegerTy(1))
    251     return BinaryOperator::CreateAnd(Op0, Op1);
    252 
    253   // X*(1 << Y) --> X << Y
    254   // (1 << Y)*X --> X << Y
    255   {
    256     Value *Y;
    257     if (match(Op0, m_Shl(m_One(), m_Value(Y))))
    258       return BinaryOperator::CreateShl(Op1, Y);
    259     if (match(Op1, m_Shl(m_One(), m_Value(Y))))
    260       return BinaryOperator::CreateShl(Op0, Y);
    261   }
    262 
    263   // If one of the operands of the multiply is a cast from a boolean value, then
    264   // we know the bool is either zero or one, so this is a 'masking' multiply.
    265   //   X * Y (where Y is 0 or 1) -> X & (0-Y)
    266   if (!I.getType()->isVectorTy()) {
    267     // -2 is "-1 << 1" so it is all bits set except the low one.
    268     APInt Negative2(I.getType()->getPrimitiveSizeInBits(), (uint64_t)-2, true);
    269 
    270     Value *BoolCast = 0, *OtherOp = 0;
    271     if (MaskedValueIsZero(Op0, Negative2))
    272       BoolCast = Op0, OtherOp = Op1;
    273     else if (MaskedValueIsZero(Op1, Negative2))
    274       BoolCast = Op1, OtherOp = Op0;
    275 
    276     if (BoolCast) {
    277       Value *V = Builder->CreateSub(Constant::getNullValue(I.getType()),
    278                                     BoolCast);
    279       return BinaryOperator::CreateAnd(V, OtherOp);
    280     }
    281   }
    282 
    283   return Changed ? &I : 0;
    284 }
    285 
    286 //
    287 // Detect pattern:
    288 //
    289 // log2(Y*0.5)
    290 //
    291 // And check for corresponding fast math flags
    292 //
    293 
    294 static void detectLog2OfHalf(Value *&Op, Value *&Y, IntrinsicInst *&Log2) {
    295 
    296    if (!Op->hasOneUse())
    297      return;
    298 
    299    IntrinsicInst *II = dyn_cast<IntrinsicInst>(Op);
    300    if (!II)
    301      return;
    302    if (II->getIntrinsicID() != Intrinsic::log2 || !II->hasUnsafeAlgebra())
    303      return;
    304    Log2 = II;
    305 
    306    Value *OpLog2Of = II->getArgOperand(0);
    307    if (!OpLog2Of->hasOneUse())
    308      return;
    309 
    310    Instruction *I = dyn_cast<Instruction>(OpLog2Of);
    311    if (!I)
    312      return;
    313    if (I->getOpcode() != Instruction::FMul || !I->hasUnsafeAlgebra())
    314      return;
    315 
    316    ConstantFP *CFP = dyn_cast<ConstantFP>(I->getOperand(0));
    317    if (CFP && CFP->isExactlyValue(0.5)) {
    318      Y = I->getOperand(1);
    319      return;
    320    }
    321    CFP = dyn_cast<ConstantFP>(I->getOperand(1));
    322    if (CFP && CFP->isExactlyValue(0.5))
    323      Y = I->getOperand(0);
    324 }
    325 
    326 /// Helper function of InstCombiner::visitFMul(BinaryOperator(). It returns
    327 /// true iff the given value is FMul or FDiv with one and only one operand
    328 /// being a normal constant (i.e. not Zero/NaN/Infinity).
    329 static bool isFMulOrFDivWithConstant(Value *V) {
    330   Instruction *I = dyn_cast<Instruction>(V);
    331   if (!I || (I->getOpcode() != Instruction::FMul &&
    332              I->getOpcode() != Instruction::FDiv))
    333     return false;
    334 
    335   ConstantFP *C0 = dyn_cast<ConstantFP>(I->getOperand(0));
    336   ConstantFP *C1 = dyn_cast<ConstantFP>(I->getOperand(1));
    337 
    338   if (C0 && C1)
    339     return false;
    340 
    341   return (C0 && C0->getValueAPF().isFiniteNonZero()) ||
    342          (C1 && C1->getValueAPF().isFiniteNonZero());
    343 }
    344 
    345 static bool isNormalFp(const ConstantFP *C) {
    346   const APFloat &Flt = C->getValueAPF();
    347   return Flt.isNormal();
    348 }
    349 
    350 /// foldFMulConst() is a helper routine of InstCombiner::visitFMul().
    351 /// The input \p FMulOrDiv is a FMul/FDiv with one and only one operand
    352 /// being a constant (i.e. isFMulOrFDivWithConstant(FMulOrDiv) == true).
    353 /// This function is to simplify "FMulOrDiv * C" and returns the
    354 /// resulting expression. Note that this function could return NULL in
    355 /// case the constants cannot be folded into a normal floating-point.
    356 ///
    357 Value *InstCombiner::foldFMulConst(Instruction *FMulOrDiv, ConstantFP *C,
    358                                    Instruction *InsertBefore) {
    359   assert(isFMulOrFDivWithConstant(FMulOrDiv) && "V is invalid");
    360 
    361   Value *Opnd0 = FMulOrDiv->getOperand(0);
    362   Value *Opnd1 = FMulOrDiv->getOperand(1);
    363 
    364   ConstantFP *C0 = dyn_cast<ConstantFP>(Opnd0);
    365   ConstantFP *C1 = dyn_cast<ConstantFP>(Opnd1);
    366 
    367   BinaryOperator *R = 0;
    368 
    369   // (X * C0) * C => X * (C0*C)
    370   if (FMulOrDiv->getOpcode() == Instruction::FMul) {
    371     Constant *F = ConstantExpr::getFMul(C1 ? C1 : C0, C);
    372     if (isNormalFp(cast<ConstantFP>(F)))
    373       R = BinaryOperator::CreateFMul(C1 ? Opnd0 : Opnd1, F);
    374   } else {
    375     if (C0) {
    376       // (C0 / X) * C => (C0 * C) / X
    377       ConstantFP *F = cast<ConstantFP>(ConstantExpr::getFMul(C0, C));
    378       if (isNormalFp(F))
    379         R = BinaryOperator::CreateFDiv(F, Opnd1);
    380     } else {
    381       // (X / C1) * C => X * (C/C1) if C/C1 is not a denormal
    382       ConstantFP *F = cast<ConstantFP>(ConstantExpr::getFDiv(C, C1));
    383       if (isNormalFp(F)) {
    384         R = BinaryOperator::CreateFMul(Opnd0, F);
    385       } else {
    386         // (X / C1) * C => X / (C1/C)
    387         Constant *F = ConstantExpr::getFDiv(C1, C);
    388         if (isNormalFp(cast<ConstantFP>(F)))
    389           R = BinaryOperator::CreateFDiv(Opnd0, F);
    390       }
    391     }
    392   }
    393 
    394   if (R) {
    395     R->setHasUnsafeAlgebra(true);
    396     InsertNewInstWith(R, *InsertBefore);
    397   }
    398 
    399   return R;
    400 }
    401 
    402 Instruction *InstCombiner::visitFMul(BinaryOperator &I) {
    403   bool Changed = SimplifyAssociativeOrCommutative(I);
    404   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    405 
    406   if (isa<Constant>(Op0))
    407     std::swap(Op0, Op1);
    408 
    409   if (Value *V = SimplifyFMulInst(Op0, Op1, I.getFastMathFlags(), TD))
    410     return ReplaceInstUsesWith(I, V);
    411 
    412   bool AllowReassociate = I.hasUnsafeAlgebra();
    413 
    414   // Simplify mul instructions with a constant RHS.
    415   if (isa<Constant>(Op1)) {
    416     // Try to fold constant mul into select arguments.
    417     if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
    418       if (Instruction *R = FoldOpIntoSelect(I, SI))
    419         return R;
    420 
    421     if (isa<PHINode>(Op0))
    422       if (Instruction *NV = FoldOpIntoPhi(I))
    423         return NV;
    424 
    425     ConstantFP *C = dyn_cast<ConstantFP>(Op1);
    426     if (C && AllowReassociate && C->getValueAPF().isFiniteNonZero()) {
    427       // Let MDC denote an expression in one of these forms:
    428       // X * C, C/X, X/C, where C is a constant.
    429       //
    430       // Try to simplify "MDC * Constant"
    431       if (isFMulOrFDivWithConstant(Op0)) {
    432         Value *V = foldFMulConst(cast<Instruction>(Op0), C, &I);
    433         if (V)
    434           return ReplaceInstUsesWith(I, V);
    435       }
    436 
    437       // (MDC +/- C1) * C => (MDC * C) +/- (C1 * C)
    438       Instruction *FAddSub = dyn_cast<Instruction>(Op0);
    439       if (FAddSub &&
    440           (FAddSub->getOpcode() == Instruction::FAdd ||
    441            FAddSub->getOpcode() == Instruction::FSub)) {
    442         Value *Opnd0 = FAddSub->getOperand(0);
    443         Value *Opnd1 = FAddSub->getOperand(1);
    444         ConstantFP *C0 = dyn_cast<ConstantFP>(Opnd0);
    445         ConstantFP *C1 = dyn_cast<ConstantFP>(Opnd1);
    446         bool Swap = false;
    447         if (C0) {
    448           std::swap(C0, C1);
    449           std::swap(Opnd0, Opnd1);
    450           Swap = true;
    451         }
    452 
    453         if (C1 && C1->getValueAPF().isFiniteNonZero() &&
    454             isFMulOrFDivWithConstant(Opnd0)) {
    455           Value *M1 = ConstantExpr::getFMul(C1, C);
    456           Value *M0 = isNormalFp(cast<ConstantFP>(M1)) ?
    457                       foldFMulConst(cast<Instruction>(Opnd0), C, &I) :
    458                       0;
    459           if (M0 && M1) {
    460             if (Swap && FAddSub->getOpcode() == Instruction::FSub)
    461               std::swap(M0, M1);
    462 
    463             Value *R = (FAddSub->getOpcode() == Instruction::FAdd) ?
    464                         BinaryOperator::CreateFAdd(M0, M1) :
    465                         BinaryOperator::CreateFSub(M0, M1);
    466             Instruction *RI = cast<Instruction>(R);
    467             RI->copyFastMathFlags(&I);
    468             return RI;
    469           }
    470         }
    471       }
    472     }
    473   }
    474 
    475 
    476   // Under unsafe algebra do:
    477   // X * log2(0.5*Y) = X*log2(Y) - X
    478   if (I.hasUnsafeAlgebra()) {
    479     Value *OpX = NULL;
    480     Value *OpY = NULL;
    481     IntrinsicInst *Log2;
    482     detectLog2OfHalf(Op0, OpY, Log2);
    483     if (OpY) {
    484       OpX = Op1;
    485     } else {
    486       detectLog2OfHalf(Op1, OpY, Log2);
    487       if (OpY) {
    488         OpX = Op0;
    489       }
    490     }
    491     // if pattern detected emit alternate sequence
    492     if (OpX && OpY) {
    493       Log2->setArgOperand(0, OpY);
    494       Value *FMulVal = Builder->CreateFMul(OpX, Log2);
    495       Instruction *FMul = cast<Instruction>(FMulVal);
    496       FMul->copyFastMathFlags(Log2);
    497       Instruction *FSub = BinaryOperator::CreateFSub(FMulVal, OpX);
    498       FSub->copyFastMathFlags(Log2);
    499       return FSub;
    500     }
    501   }
    502 
    503   // Handle symmetric situation in a 2-iteration loop
    504   Value *Opnd0 = Op0;
    505   Value *Opnd1 = Op1;
    506   for (int i = 0; i < 2; i++) {
    507     bool IgnoreZeroSign = I.hasNoSignedZeros();
    508     if (BinaryOperator::isFNeg(Opnd0, IgnoreZeroSign)) {
    509       Value *N0 = dyn_castFNegVal(Opnd0, IgnoreZeroSign);
    510       Value *N1 = dyn_castFNegVal(Opnd1, IgnoreZeroSign);
    511 
    512       // -X * -Y => X*Y
    513       if (N1)
    514         return BinaryOperator::CreateFMul(N0, N1);
    515 
    516       if (Opnd0->hasOneUse()) {
    517         // -X * Y => -(X*Y) (Promote negation as high as possible)
    518         Value *T = Builder->CreateFMul(N0, Opnd1);
    519         cast<Instruction>(T)->setDebugLoc(I.getDebugLoc());
    520         Instruction *Neg = BinaryOperator::CreateFNeg(T);
    521         if (I.getFastMathFlags().any()) {
    522           cast<Instruction>(T)->copyFastMathFlags(&I);
    523           Neg->copyFastMathFlags(&I);
    524         }
    525         return Neg;
    526       }
    527     }
    528 
    529     // (X*Y) * X => (X*X) * Y where Y != X
    530     //  The purpose is two-fold:
    531     //   1) to form a power expression (of X).
    532     //   2) potentially shorten the critical path: After transformation, the
    533     //  latency of the instruction Y is amortized by the expression of X*X,
    534     //  and therefore Y is in a "less critical" position compared to what it
    535     //  was before the transformation.
    536     //
    537     if (AllowReassociate) {
    538       Value *Opnd0_0, *Opnd0_1;
    539       if (Opnd0->hasOneUse() &&
    540           match(Opnd0, m_FMul(m_Value(Opnd0_0), m_Value(Opnd0_1)))) {
    541         Value *Y = 0;
    542         if (Opnd0_0 == Opnd1 && Opnd0_1 != Opnd1)
    543           Y = Opnd0_1;
    544         else if (Opnd0_1 == Opnd1 && Opnd0_0 != Opnd1)
    545           Y = Opnd0_0;
    546 
    547         if (Y) {
    548           Instruction *T = cast<Instruction>(Builder->CreateFMul(Opnd1, Opnd1));
    549           T->copyFastMathFlags(&I);
    550           T->setDebugLoc(I.getDebugLoc());
    551 
    552           Instruction *R = BinaryOperator::CreateFMul(T, Y);
    553           R->copyFastMathFlags(&I);
    554           return R;
    555         }
    556       }
    557     }
    558 
    559     // B * (uitofp i1 C) -> select C, B, 0
    560     if (I.hasNoNaNs() && I.hasNoInfs() && I.hasNoSignedZeros()) {
    561       Value *LHS = Op0, *RHS = Op1;
    562       Value *B, *C;
    563       if (!match(RHS, m_UIToFP(m_Value(C))))
    564         std::swap(LHS, RHS);
    565 
    566       if (match(RHS, m_UIToFP(m_Value(C))) && C->getType()->isIntegerTy(1)) {
    567         B = LHS;
    568         Value *Zero = ConstantFP::getNegativeZero(B->getType());
    569         return SelectInst::Create(C, B, Zero);
    570       }
    571     }
    572 
    573     // A * (1 - uitofp i1 C) -> select C, 0, A
    574     if (I.hasNoNaNs() && I.hasNoInfs() && I.hasNoSignedZeros()) {
    575       Value *LHS = Op0, *RHS = Op1;
    576       Value *A, *C;
    577       if (!match(RHS, m_FSub(m_FPOne(), m_UIToFP(m_Value(C)))))
    578         std::swap(LHS, RHS);
    579 
    580       if (match(RHS, m_FSub(m_FPOne(), m_UIToFP(m_Value(C)))) &&
    581           C->getType()->isIntegerTy(1)) {
    582         A = LHS;
    583         Value *Zero = ConstantFP::getNegativeZero(A->getType());
    584         return SelectInst::Create(C, Zero, A);
    585       }
    586     }
    587 
    588     if (!isa<Constant>(Op1))
    589       std::swap(Opnd0, Opnd1);
    590     else
    591       break;
    592   }
    593 
    594   return Changed ? &I : 0;
    595 }
    596 
    597 /// SimplifyDivRemOfSelect - Try to fold a divide or remainder of a select
    598 /// instruction.
    599 bool InstCombiner::SimplifyDivRemOfSelect(BinaryOperator &I) {
    600   SelectInst *SI = cast<SelectInst>(I.getOperand(1));
    601 
    602   // div/rem X, (Cond ? 0 : Y) -> div/rem X, Y
    603   int NonNullOperand = -1;
    604   if (Constant *ST = dyn_cast<Constant>(SI->getOperand(1)))
    605     if (ST->isNullValue())
    606       NonNullOperand = 2;
    607   // div/rem X, (Cond ? Y : 0) -> div/rem X, Y
    608   if (Constant *ST = dyn_cast<Constant>(SI->getOperand(2)))
    609     if (ST->isNullValue())
    610       NonNullOperand = 1;
    611 
    612   if (NonNullOperand == -1)
    613     return false;
    614 
    615   Value *SelectCond = SI->getOperand(0);
    616 
    617   // Change the div/rem to use 'Y' instead of the select.
    618   I.setOperand(1, SI->getOperand(NonNullOperand));
    619 
    620   // Okay, we know we replace the operand of the div/rem with 'Y' with no
    621   // problem.  However, the select, or the condition of the select may have
    622   // multiple uses.  Based on our knowledge that the operand must be non-zero,
    623   // propagate the known value for the select into other uses of it, and
    624   // propagate a known value of the condition into its other users.
    625 
    626   // If the select and condition only have a single use, don't bother with this,
    627   // early exit.
    628   if (SI->use_empty() && SelectCond->hasOneUse())
    629     return true;
    630 
    631   // Scan the current block backward, looking for other uses of SI.
    632   BasicBlock::iterator BBI = &I, BBFront = I.getParent()->begin();
    633 
    634   while (BBI != BBFront) {
    635     --BBI;
    636     // If we found a call to a function, we can't assume it will return, so
    637     // information from below it cannot be propagated above it.
    638     if (isa<CallInst>(BBI) && !isa<IntrinsicInst>(BBI))
    639       break;
    640 
    641     // Replace uses of the select or its condition with the known values.
    642     for (Instruction::op_iterator I = BBI->op_begin(), E = BBI->op_end();
    643          I != E; ++I) {
    644       if (*I == SI) {
    645         *I = SI->getOperand(NonNullOperand);
    646         Worklist.Add(BBI);
    647       } else if (*I == SelectCond) {
    648         *I = Builder->getInt1(NonNullOperand == 1);
    649         Worklist.Add(BBI);
    650       }
    651     }
    652 
    653     // If we past the instruction, quit looking for it.
    654     if (&*BBI == SI)
    655       SI = 0;
    656     if (&*BBI == SelectCond)
    657       SelectCond = 0;
    658 
    659     // If we ran out of things to eliminate, break out of the loop.
    660     if (SelectCond == 0 && SI == 0)
    661       break;
    662 
    663   }
    664   return true;
    665 }
    666 
    667 
    668 /// This function implements the transforms common to both integer division
    669 /// instructions (udiv and sdiv). It is called by the visitors to those integer
    670 /// division instructions.
    671 /// @brief Common integer divide transforms
    672 Instruction *InstCombiner::commonIDivTransforms(BinaryOperator &I) {
    673   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    674 
    675   // The RHS is known non-zero.
    676   if (Value *V = simplifyValueKnownNonZero(I.getOperand(1), *this)) {
    677     I.setOperand(1, V);
    678     return &I;
    679   }
    680 
    681   // Handle cases involving: [su]div X, (select Cond, Y, Z)
    682   // This does not apply for fdiv.
    683   if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
    684     return &I;
    685 
    686   if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
    687     // (X / C1) / C2  -> X / (C1*C2)
    688     if (Instruction *LHS = dyn_cast<Instruction>(Op0))
    689       if (Instruction::BinaryOps(LHS->getOpcode()) == I.getOpcode())
    690         if (ConstantInt *LHSRHS = dyn_cast<ConstantInt>(LHS->getOperand(1))) {
    691           if (MultiplyOverflows(RHS, LHSRHS,
    692                                 I.getOpcode()==Instruction::SDiv))
    693             return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
    694           return BinaryOperator::Create(I.getOpcode(), LHS->getOperand(0),
    695                                         ConstantExpr::getMul(RHS, LHSRHS));
    696         }
    697 
    698     if (!RHS->isZero()) { // avoid X udiv 0
    699       if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
    700         if (Instruction *R = FoldOpIntoSelect(I, SI))
    701           return R;
    702       if (isa<PHINode>(Op0))
    703         if (Instruction *NV = FoldOpIntoPhi(I))
    704           return NV;
    705     }
    706   }
    707 
    708   // See if we can fold away this div instruction.
    709   if (SimplifyDemandedInstructionBits(I))
    710     return &I;
    711 
    712   // (X - (X rem Y)) / Y -> X / Y; usually originates as ((X / Y) * Y) / Y
    713   Value *X = 0, *Z = 0;
    714   if (match(Op0, m_Sub(m_Value(X), m_Value(Z)))) { // (X - Z) / Y; Y = Op1
    715     bool isSigned = I.getOpcode() == Instruction::SDiv;
    716     if ((isSigned && match(Z, m_SRem(m_Specific(X), m_Specific(Op1)))) ||
    717         (!isSigned && match(Z, m_URem(m_Specific(X), m_Specific(Op1)))))
    718       return BinaryOperator::Create(I.getOpcode(), X, Op1);
    719   }
    720 
    721   return 0;
    722 }
    723 
    724 /// dyn_castZExtVal - Checks if V is a zext or constant that can
    725 /// be truncated to Ty without losing bits.
    726 static Value *dyn_castZExtVal(Value *V, Type *Ty) {
    727   if (ZExtInst *Z = dyn_cast<ZExtInst>(V)) {
    728     if (Z->getSrcTy() == Ty)
    729       return Z->getOperand(0);
    730   } else if (ConstantInt *C = dyn_cast<ConstantInt>(V)) {
    731     if (C->getValue().getActiveBits() <= cast<IntegerType>(Ty)->getBitWidth())
    732       return ConstantExpr::getTrunc(C, Ty);
    733   }
    734   return 0;
    735 }
    736 
    737 namespace {
    738 const unsigned MaxDepth = 6;
    739 typedef Instruction *(*FoldUDivOperandCb)(Value *Op0, Value *Op1,
    740                                           const BinaryOperator &I,
    741                                           InstCombiner &IC);
    742 
    743 /// \brief Used to maintain state for visitUDivOperand().
    744 struct UDivFoldAction {
    745   FoldUDivOperandCb FoldAction; ///< Informs visitUDiv() how to fold this
    746                                 ///< operand.  This can be zero if this action
    747                                 ///< joins two actions together.
    748 
    749   Value *OperandToFold;         ///< Which operand to fold.
    750   union {
    751     Instruction *FoldResult;    ///< The instruction returned when FoldAction is
    752                                 ///< invoked.
    753 
    754     size_t SelectLHSIdx;        ///< Stores the LHS action index if this action
    755                                 ///< joins two actions together.
    756   };
    757 
    758   UDivFoldAction(FoldUDivOperandCb FA, Value *InputOperand)
    759       : FoldAction(FA), OperandToFold(InputOperand), FoldResult(0) {}
    760   UDivFoldAction(FoldUDivOperandCb FA, Value *InputOperand, size_t SLHS)
    761       : FoldAction(FA), OperandToFold(InputOperand), SelectLHSIdx(SLHS) {}
    762 };
    763 }
    764 
    765 // X udiv 2^C -> X >> C
    766 static Instruction *foldUDivPow2Cst(Value *Op0, Value *Op1,
    767                                     const BinaryOperator &I, InstCombiner &IC) {
    768   const APInt &C = cast<Constant>(Op1)->getUniqueInteger();
    769   BinaryOperator *LShr = BinaryOperator::CreateLShr(
    770       Op0, ConstantInt::get(Op0->getType(), C.logBase2()));
    771   if (I.isExact()) LShr->setIsExact();
    772   return LShr;
    773 }
    774 
    775 // X udiv C, where C >= signbit
    776 static Instruction *foldUDivNegCst(Value *Op0, Value *Op1,
    777                                    const BinaryOperator &I, InstCombiner &IC) {
    778   Value *ICI = IC.Builder->CreateICmpULT(Op0, cast<ConstantInt>(Op1));
    779 
    780   return SelectInst::Create(ICI, Constant::getNullValue(I.getType()),
    781                             ConstantInt::get(I.getType(), 1));
    782 }
    783 
    784 // X udiv (C1 << N), where C1 is "1<<C2"  -->  X >> (N+C2)
    785 static Instruction *foldUDivShl(Value *Op0, Value *Op1, const BinaryOperator &I,
    786                                 InstCombiner &IC) {
    787   Instruction *ShiftLeft = cast<Instruction>(Op1);
    788   if (isa<ZExtInst>(ShiftLeft))
    789     ShiftLeft = cast<Instruction>(ShiftLeft->getOperand(0));
    790 
    791   const APInt &CI =
    792       cast<Constant>(ShiftLeft->getOperand(0))->getUniqueInteger();
    793   Value *N = ShiftLeft->getOperand(1);
    794   if (CI != 1)
    795     N = IC.Builder->CreateAdd(N, ConstantInt::get(N->getType(), CI.logBase2()));
    796   if (ZExtInst *Z = dyn_cast<ZExtInst>(Op1))
    797     N = IC.Builder->CreateZExt(N, Z->getDestTy());
    798   BinaryOperator *LShr = BinaryOperator::CreateLShr(Op0, N);
    799   if (I.isExact()) LShr->setIsExact();
    800   return LShr;
    801 }
    802 
    803 // \brief Recursively visits the possible right hand operands of a udiv
    804 // instruction, seeing through select instructions, to determine if we can
    805 // replace the udiv with something simpler.  If we find that an operand is not
    806 // able to simplify the udiv, we abort the entire transformation.
    807 static size_t visitUDivOperand(Value *Op0, Value *Op1, const BinaryOperator &I,
    808                                SmallVectorImpl<UDivFoldAction> &Actions,
    809                                unsigned Depth = 0) {
    810   // Check to see if this is an unsigned division with an exact power of 2,
    811   // if so, convert to a right shift.
    812   if (match(Op1, m_Power2())) {
    813     Actions.push_back(UDivFoldAction(foldUDivPow2Cst, Op1));
    814     return Actions.size();
    815   }
    816 
    817   if (ConstantInt *C = dyn_cast<ConstantInt>(Op1))
    818     // X udiv C, where C >= signbit
    819     if (C->getValue().isNegative()) {
    820       Actions.push_back(UDivFoldAction(foldUDivNegCst, C));
    821       return Actions.size();
    822     }
    823 
    824   // X udiv (C1 << N), where C1 is "1<<C2"  -->  X >> (N+C2)
    825   if (match(Op1, m_Shl(m_Power2(), m_Value())) ||
    826       match(Op1, m_ZExt(m_Shl(m_Power2(), m_Value())))) {
    827     Actions.push_back(UDivFoldAction(foldUDivShl, Op1));
    828     return Actions.size();
    829   }
    830 
    831   // The remaining tests are all recursive, so bail out if we hit the limit.
    832   if (Depth++ == MaxDepth)
    833     return 0;
    834 
    835   if (SelectInst *SI = dyn_cast<SelectInst>(Op1))
    836     if (size_t LHSIdx = visitUDivOperand(Op0, SI->getOperand(1), I, Actions))
    837       if (visitUDivOperand(Op0, SI->getOperand(2), I, Actions)) {
    838         Actions.push_back(UDivFoldAction((FoldUDivOperandCb)0, Op1, LHSIdx-1));
    839         return Actions.size();
    840       }
    841 
    842   return 0;
    843 }
    844 
    845 Instruction *InstCombiner::visitUDiv(BinaryOperator &I) {
    846   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    847 
    848   if (Value *V = SimplifyUDivInst(Op0, Op1, TD))
    849     return ReplaceInstUsesWith(I, V);
    850 
    851   // Handle the integer div common cases
    852   if (Instruction *Common = commonIDivTransforms(I))
    853     return Common;
    854 
    855   // (x lshr C1) udiv C2 --> x udiv (C2 << C1)
    856   if (ConstantInt *C2 = dyn_cast<ConstantInt>(Op1)) {
    857     Value *X;
    858     ConstantInt *C1;
    859     if (match(Op0, m_LShr(m_Value(X), m_ConstantInt(C1)))) {
    860       APInt NC = C2->getValue().shl(C1->getLimitedValue(C1->getBitWidth()-1));
    861       return BinaryOperator::CreateUDiv(X, Builder->getInt(NC));
    862     }
    863   }
    864 
    865   // (zext A) udiv (zext B) --> zext (A udiv B)
    866   if (ZExtInst *ZOp0 = dyn_cast<ZExtInst>(Op0))
    867     if (Value *ZOp1 = dyn_castZExtVal(Op1, ZOp0->getSrcTy()))
    868       return new ZExtInst(Builder->CreateUDiv(ZOp0->getOperand(0), ZOp1, "div",
    869                                               I.isExact()),
    870                           I.getType());
    871 
    872   // (LHS udiv (select (select (...)))) -> (LHS >> (select (select (...))))
    873   SmallVector<UDivFoldAction, 6> UDivActions;
    874   if (visitUDivOperand(Op0, Op1, I, UDivActions))
    875     for (unsigned i = 0, e = UDivActions.size(); i != e; ++i) {
    876       FoldUDivOperandCb Action = UDivActions[i].FoldAction;
    877       Value *ActionOp1 = UDivActions[i].OperandToFold;
    878       Instruction *Inst;
    879       if (Action)
    880         Inst = Action(Op0, ActionOp1, I, *this);
    881       else {
    882         // This action joins two actions together.  The RHS of this action is
    883         // simply the last action we processed, we saved the LHS action index in
    884         // the joining action.
    885         size_t SelectRHSIdx = i - 1;
    886         Value *SelectRHS = UDivActions[SelectRHSIdx].FoldResult;
    887         size_t SelectLHSIdx = UDivActions[i].SelectLHSIdx;
    888         Value *SelectLHS = UDivActions[SelectLHSIdx].FoldResult;
    889         Inst = SelectInst::Create(cast<SelectInst>(ActionOp1)->getCondition(),
    890                                   SelectLHS, SelectRHS);
    891       }
    892 
    893       // If this is the last action to process, return it to the InstCombiner.
    894       // Otherwise, we insert it before the UDiv and record it so that we may
    895       // use it as part of a joining action (i.e., a SelectInst).
    896       if (e - i != 1) {
    897         Inst->insertBefore(&I);
    898         UDivActions[i].FoldResult = Inst;
    899       } else
    900         return Inst;
    901     }
    902 
    903   return 0;
    904 }
    905 
    906 Instruction *InstCombiner::visitSDiv(BinaryOperator &I) {
    907   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    908 
    909   if (Value *V = SimplifySDivInst(Op0, Op1, TD))
    910     return ReplaceInstUsesWith(I, V);
    911 
    912   // Handle the integer div common cases
    913   if (Instruction *Common = commonIDivTransforms(I))
    914     return Common;
    915 
    916   if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
    917     // sdiv X, -1 == -X
    918     if (RHS->isAllOnesValue())
    919       return BinaryOperator::CreateNeg(Op0);
    920 
    921     // sdiv X, C  -->  ashr exact X, log2(C)
    922     if (I.isExact() && RHS->getValue().isNonNegative() &&
    923         RHS->getValue().isPowerOf2()) {
    924       Value *ShAmt = llvm::ConstantInt::get(RHS->getType(),
    925                                             RHS->getValue().exactLogBase2());
    926       return BinaryOperator::CreateExactAShr(Op0, ShAmt, I.getName());
    927     }
    928 
    929     // -X/C  -->  X/-C  provided the negation doesn't overflow.
    930     if (SubOperator *Sub = dyn_cast<SubOperator>(Op0))
    931       if (match(Sub->getOperand(0), m_Zero()) && Sub->hasNoSignedWrap())
    932         return BinaryOperator::CreateSDiv(Sub->getOperand(1),
    933                                           ConstantExpr::getNeg(RHS));
    934   }
    935 
    936   // If the sign bits of both operands are zero (i.e. we can prove they are
    937   // unsigned inputs), turn this into a udiv.
    938   if (I.getType()->isIntegerTy()) {
    939     APInt Mask(APInt::getSignBit(I.getType()->getPrimitiveSizeInBits()));
    940     if (MaskedValueIsZero(Op0, Mask)) {
    941       if (MaskedValueIsZero(Op1, Mask)) {
    942         // X sdiv Y -> X udiv Y, iff X and Y don't have sign bit set
    943         return BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
    944       }
    945 
    946       if (match(Op1, m_Shl(m_Power2(), m_Value()))) {
    947         // X sdiv (1 << Y) -> X udiv (1 << Y) ( -> X u>> Y)
    948         // Safe because the only negative value (1 << Y) can take on is
    949         // INT_MIN, and X sdiv INT_MIN == X udiv INT_MIN == 0 if X doesn't have
    950         // the sign bit set.
    951         return BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
    952       }
    953     }
    954   }
    955 
    956   return 0;
    957 }
    958 
    959 /// CvtFDivConstToReciprocal tries to convert X/C into X*1/C if C not a special
    960 /// FP value and:
    961 ///    1) 1/C is exact, or
    962 ///    2) reciprocal is allowed.
    963 /// If the conversion was successful, the simplified expression "X * 1/C" is
    964 /// returned; otherwise, NULL is returned.
    965 ///
    966 static Instruction *CvtFDivConstToReciprocal(Value *Dividend,
    967                                              ConstantFP *Divisor,
    968                                              bool AllowReciprocal) {
    969   const APFloat &FpVal = Divisor->getValueAPF();
    970   APFloat Reciprocal(FpVal.getSemantics());
    971   bool Cvt = FpVal.getExactInverse(&Reciprocal);
    972 
    973   if (!Cvt && AllowReciprocal && FpVal.isFiniteNonZero()) {
    974     Reciprocal = APFloat(FpVal.getSemantics(), 1.0f);
    975     (void)Reciprocal.divide(FpVal, APFloat::rmNearestTiesToEven);
    976     Cvt = !Reciprocal.isDenormal();
    977   }
    978 
    979   if (!Cvt)
    980     return 0;
    981 
    982   ConstantFP *R;
    983   R = ConstantFP::get(Dividend->getType()->getContext(), Reciprocal);
    984   return BinaryOperator::CreateFMul(Dividend, R);
    985 }
    986 
    987 Instruction *InstCombiner::visitFDiv(BinaryOperator &I) {
    988   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    989 
    990   if (Value *V = SimplifyFDivInst(Op0, Op1, TD))
    991     return ReplaceInstUsesWith(I, V);
    992 
    993   if (isa<Constant>(Op0))
    994     if (SelectInst *SI = dyn_cast<SelectInst>(Op1))
    995       if (Instruction *R = FoldOpIntoSelect(I, SI))
    996         return R;
    997 
    998   bool AllowReassociate = I.hasUnsafeAlgebra();
    999   bool AllowReciprocal = I.hasAllowReciprocal();
   1000 
   1001   if (ConstantFP *Op1C = dyn_cast<ConstantFP>(Op1)) {
   1002     if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
   1003       if (Instruction *R = FoldOpIntoSelect(I, SI))
   1004         return R;
   1005 
   1006     if (AllowReassociate) {
   1007       ConstantFP *C1 = 0;
   1008       ConstantFP *C2 = Op1C;
   1009       Value *X;
   1010       Instruction *Res = 0;
   1011 
   1012       if (match(Op0, m_FMul(m_Value(X), m_ConstantFP(C1)))) {
   1013         // (X*C1)/C2 => X * (C1/C2)
   1014         //
   1015         Constant *C = ConstantExpr::getFDiv(C1, C2);
   1016         const APFloat &F = cast<ConstantFP>(C)->getValueAPF();
   1017         if (F.isNormal())
   1018           Res = BinaryOperator::CreateFMul(X, C);
   1019       } else if (match(Op0, m_FDiv(m_Value(X), m_ConstantFP(C1)))) {
   1020         // (X/C1)/C2 => X /(C2*C1) [=> X * 1/(C2*C1) if reciprocal is allowed]
   1021         //
   1022         Constant *C = ConstantExpr::getFMul(C1, C2);
   1023         const APFloat &F = cast<ConstantFP>(C)->getValueAPF();
   1024         if (F.isNormal()) {
   1025           Res = CvtFDivConstToReciprocal(X, cast<ConstantFP>(C),
   1026                                          AllowReciprocal);
   1027           if (!Res)
   1028             Res = BinaryOperator::CreateFDiv(X, C);
   1029         }
   1030       }
   1031 
   1032       if (Res) {
   1033         Res->setFastMathFlags(I.getFastMathFlags());
   1034         return Res;
   1035       }
   1036     }
   1037 
   1038     // X / C => X * 1/C
   1039     if (Instruction *T = CvtFDivConstToReciprocal(Op0, Op1C, AllowReciprocal))
   1040       return T;
   1041 
   1042     return 0;
   1043   }
   1044 
   1045   if (AllowReassociate && isa<ConstantFP>(Op0)) {
   1046     ConstantFP *C1 = cast<ConstantFP>(Op0), *C2;
   1047     Constant *Fold = 0;
   1048     Value *X;
   1049     bool CreateDiv = true;
   1050 
   1051     // C1 / (X*C2) => (C1/C2) / X
   1052     if (match(Op1, m_FMul(m_Value(X), m_ConstantFP(C2))))
   1053       Fold = ConstantExpr::getFDiv(C1, C2);
   1054     else if (match(Op1, m_FDiv(m_Value(X), m_ConstantFP(C2)))) {
   1055       // C1 / (X/C2) => (C1*C2) / X
   1056       Fold = ConstantExpr::getFMul(C1, C2);
   1057     } else if (match(Op1, m_FDiv(m_ConstantFP(C2), m_Value(X)))) {
   1058       // C1 / (C2/X) => (C1/C2) * X
   1059       Fold = ConstantExpr::getFDiv(C1, C2);
   1060       CreateDiv = false;
   1061     }
   1062 
   1063     if (Fold) {
   1064       const APFloat &FoldC = cast<ConstantFP>(Fold)->getValueAPF();
   1065       if (FoldC.isNormal()) {
   1066         Instruction *R = CreateDiv ?
   1067                          BinaryOperator::CreateFDiv(Fold, X) :
   1068                          BinaryOperator::CreateFMul(X, Fold);
   1069         R->setFastMathFlags(I.getFastMathFlags());
   1070         return R;
   1071       }
   1072     }
   1073     return 0;
   1074   }
   1075 
   1076   if (AllowReassociate) {
   1077     Value *X, *Y;
   1078     Value *NewInst = 0;
   1079     Instruction *SimpR = 0;
   1080 
   1081     if (Op0->hasOneUse() && match(Op0, m_FDiv(m_Value(X), m_Value(Y)))) {
   1082       // (X/Y) / Z => X / (Y*Z)
   1083       //
   1084       if (!isa<ConstantFP>(Y) || !isa<ConstantFP>(Op1)) {
   1085         NewInst = Builder->CreateFMul(Y, Op1);
   1086         SimpR = BinaryOperator::CreateFDiv(X, NewInst);
   1087       }
   1088     } else if (Op1->hasOneUse() && match(Op1, m_FDiv(m_Value(X), m_Value(Y)))) {
   1089       // Z / (X/Y) => Z*Y / X
   1090       //
   1091       if (!isa<ConstantFP>(Y) || !isa<ConstantFP>(Op0)) {
   1092         NewInst = Builder->CreateFMul(Op0, Y);
   1093         SimpR = BinaryOperator::CreateFDiv(NewInst, X);
   1094       }
   1095     }
   1096 
   1097     if (NewInst) {
   1098       if (Instruction *T = dyn_cast<Instruction>(NewInst))
   1099         T->setDebugLoc(I.getDebugLoc());
   1100       SimpR->setFastMathFlags(I.getFastMathFlags());
   1101       return SimpR;
   1102     }
   1103   }
   1104 
   1105   return 0;
   1106 }
   1107 
   1108 /// This function implements the transforms common to both integer remainder
   1109 /// instructions (urem and srem). It is called by the visitors to those integer
   1110 /// remainder instructions.
   1111 /// @brief Common integer remainder transforms
   1112 Instruction *InstCombiner::commonIRemTransforms(BinaryOperator &I) {
   1113   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
   1114 
   1115   // The RHS is known non-zero.
   1116   if (Value *V = simplifyValueKnownNonZero(I.getOperand(1), *this)) {
   1117     I.setOperand(1, V);
   1118     return &I;
   1119   }
   1120 
   1121   // Handle cases involving: rem X, (select Cond, Y, Z)
   1122   if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
   1123     return &I;
   1124 
   1125   if (isa<ConstantInt>(Op1)) {
   1126     if (Instruction *Op0I = dyn_cast<Instruction>(Op0)) {
   1127       if (SelectInst *SI = dyn_cast<SelectInst>(Op0I)) {
   1128         if (Instruction *R = FoldOpIntoSelect(I, SI))
   1129           return R;
   1130       } else if (isa<PHINode>(Op0I)) {
   1131         if (Instruction *NV = FoldOpIntoPhi(I))
   1132           return NV;
   1133       }
   1134 
   1135       // See if we can fold away this rem instruction.
   1136       if (SimplifyDemandedInstructionBits(I))
   1137         return &I;
   1138     }
   1139   }
   1140 
   1141   return 0;
   1142 }
   1143 
   1144 Instruction *InstCombiner::visitURem(BinaryOperator &I) {
   1145   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
   1146 
   1147   if (Value *V = SimplifyURemInst(Op0, Op1, TD))
   1148     return ReplaceInstUsesWith(I, V);
   1149 
   1150   if (Instruction *common = commonIRemTransforms(I))
   1151     return common;
   1152 
   1153   // (zext A) urem (zext B) --> zext (A urem B)
   1154   if (ZExtInst *ZOp0 = dyn_cast<ZExtInst>(Op0))
   1155     if (Value *ZOp1 = dyn_castZExtVal(Op1, ZOp0->getSrcTy()))
   1156       return new ZExtInst(Builder->CreateURem(ZOp0->getOperand(0), ZOp1),
   1157                           I.getType());
   1158 
   1159   // X urem Y -> X and Y-1, where Y is a power of 2,
   1160   if (isKnownToBeAPowerOfTwo(Op1, /*OrZero*/true)) {
   1161     Constant *N1 = Constant::getAllOnesValue(I.getType());
   1162     Value *Add = Builder->CreateAdd(Op1, N1);
   1163     return BinaryOperator::CreateAnd(Op0, Add);
   1164   }
   1165 
   1166   // 1 urem X -> zext(X != 1)
   1167   if (match(Op0, m_One())) {
   1168     Value *Cmp = Builder->CreateICmpNE(Op1, Op0);
   1169     Value *Ext = Builder->CreateZExt(Cmp, I.getType());
   1170     return ReplaceInstUsesWith(I, Ext);
   1171   }
   1172 
   1173   return 0;
   1174 }
   1175 
   1176 Instruction *InstCombiner::visitSRem(BinaryOperator &I) {
   1177   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
   1178 
   1179   if (Value *V = SimplifySRemInst(Op0, Op1, TD))
   1180     return ReplaceInstUsesWith(I, V);
   1181 
   1182   // Handle the integer rem common cases
   1183   if (Instruction *Common = commonIRemTransforms(I))
   1184     return Common;
   1185 
   1186   if (Value *RHSNeg = dyn_castNegVal(Op1))
   1187     if (!isa<Constant>(RHSNeg) ||
   1188         (isa<ConstantInt>(RHSNeg) &&
   1189          cast<ConstantInt>(RHSNeg)->getValue().isStrictlyPositive())) {
   1190       // X % -Y -> X % Y
   1191       Worklist.AddValue(I.getOperand(1));
   1192       I.setOperand(1, RHSNeg);
   1193       return &I;
   1194     }
   1195 
   1196   // If the sign bits of both operands are zero (i.e. we can prove they are
   1197   // unsigned inputs), turn this into a urem.
   1198   if (I.getType()->isIntegerTy()) {
   1199     APInt Mask(APInt::getSignBit(I.getType()->getPrimitiveSizeInBits()));
   1200     if (MaskedValueIsZero(Op1, Mask) && MaskedValueIsZero(Op0, Mask)) {
   1201       // X srem Y -> X urem Y, iff X and Y don't have sign bit set
   1202       return BinaryOperator::CreateURem(Op0, Op1, I.getName());
   1203     }
   1204   }
   1205 
   1206   // If it's a constant vector, flip any negative values positive.
   1207   if (isa<ConstantVector>(Op1) || isa<ConstantDataVector>(Op1)) {
   1208     Constant *C = cast<Constant>(Op1);
   1209     unsigned VWidth = C->getType()->getVectorNumElements();
   1210 
   1211     bool hasNegative = false;
   1212     bool hasMissing = false;
   1213     for (unsigned i = 0; i != VWidth; ++i) {
   1214       Constant *Elt = C->getAggregateElement(i);
   1215       if (Elt == 0) {
   1216         hasMissing = true;
   1217         break;
   1218       }
   1219 
   1220       if (ConstantInt *RHS = dyn_cast<ConstantInt>(Elt))
   1221         if (RHS->isNegative())
   1222           hasNegative = true;
   1223     }
   1224 
   1225     if (hasNegative && !hasMissing) {
   1226       SmallVector<Constant *, 16> Elts(VWidth);
   1227       for (unsigned i = 0; i != VWidth; ++i) {
   1228         Elts[i] = C->getAggregateElement(i);  // Handle undef, etc.
   1229         if (ConstantInt *RHS = dyn_cast<ConstantInt>(Elts[i])) {
   1230           if (RHS->isNegative())
   1231             Elts[i] = cast<ConstantInt>(ConstantExpr::getNeg(RHS));
   1232         }
   1233       }
   1234 
   1235       Constant *NewRHSV = ConstantVector::get(Elts);
   1236       if (NewRHSV != C) {  // Don't loop on -MININT
   1237         Worklist.AddValue(I.getOperand(1));
   1238         I.setOperand(1, NewRHSV);
   1239         return &I;
   1240       }
   1241     }
   1242   }
   1243 
   1244   return 0;
   1245 }
   1246 
   1247 Instruction *InstCombiner::visitFRem(BinaryOperator &I) {
   1248   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
   1249 
   1250   if (Value *V = SimplifyFRemInst(Op0, Op1, TD))
   1251     return ReplaceInstUsesWith(I, V);
   1252 
   1253   // Handle cases involving: rem X, (select Cond, Y, Z)
   1254   if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
   1255     return &I;
   1256 
   1257   return 0;
   1258 }
   1259