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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/IntrinsicInst.h"
     17 #include "llvm/Analysis/InstructionSimplify.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       isPowerOfTwo(PowerOf2, IC.getTargetData())) {
     41     A = IC.Builder->CreateSub(A, B, "tmp");
     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() &&
     49         isPowerOfTwo(I->getOperand(0), IC.getTargetData())) {
     50       // We know that this is an exact/nuw shift and that the input is a
     51       // non-zero context as well.
     52       if (Value *V2 = simplifyValueKnownNonZero(I->getOperand(0), IC)) {
     53         I->setOperand(0, V2);
     54         MadeChange = true;
     55       }
     56 
     57       if (I->getOpcode() == Instruction::LShr && !I->isExact()) {
     58         I->setIsExact();
     59         MadeChange = true;
     60       }
     61 
     62       if (I->getOpcode() == Instruction::Shl && !I->hasNoUnsignedWrap()) {
     63         I->setHasNoUnsignedWrap();
     64         MadeChange = true;
     65       }
     66     }
     67 
     68   // TODO: Lots more we could do here:
     69   //    If V is a phi node, we can call this on each of its operands.
     70   //    "select cond, X, 0" can simplify to "X".
     71 
     72   return MadeChange ? V : 0;
     73 }
     74 
     75 
     76 /// MultiplyOverflows - True if the multiply can not be expressed in an int
     77 /// this size.
     78 static bool MultiplyOverflows(ConstantInt *C1, ConstantInt *C2, bool sign) {
     79   uint32_t W = C1->getBitWidth();
     80   APInt LHSExt = C1->getValue(), RHSExt = C2->getValue();
     81   if (sign) {
     82     LHSExt = LHSExt.sext(W * 2);
     83     RHSExt = RHSExt.sext(W * 2);
     84   } else {
     85     LHSExt = LHSExt.zext(W * 2);
     86     RHSExt = RHSExt.zext(W * 2);
     87   }
     88 
     89   APInt MulExt = LHSExt * RHSExt;
     90 
     91   if (!sign)
     92     return MulExt.ugt(APInt::getLowBitsSet(W * 2, W));
     93 
     94   APInt Min = APInt::getSignedMinValue(W).sext(W * 2);
     95   APInt Max = APInt::getSignedMaxValue(W).sext(W * 2);
     96   return MulExt.slt(Min) || MulExt.sgt(Max);
     97 }
     98 
     99 Instruction *InstCombiner::visitMul(BinaryOperator &I) {
    100   bool Changed = SimplifyAssociativeOrCommutative(I);
    101   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    102 
    103   if (Value *V = SimplifyMulInst(Op0, Op1, TD))
    104     return ReplaceInstUsesWith(I, V);
    105 
    106   if (Value *V = SimplifyUsingDistributiveLaws(I))
    107     return ReplaceInstUsesWith(I, V);
    108 
    109   if (match(Op1, m_AllOnes()))  // X * -1 == 0 - X
    110     return BinaryOperator::CreateNeg(Op0, I.getName());
    111 
    112   if (ConstantInt *CI = dyn_cast<ConstantInt>(Op1)) {
    113 
    114     // ((X << C1)*C2) == (X * (C2 << C1))
    115     if (BinaryOperator *SI = dyn_cast<BinaryOperator>(Op0))
    116       if (SI->getOpcode() == Instruction::Shl)
    117         if (Constant *ShOp = dyn_cast<Constant>(SI->getOperand(1)))
    118           return BinaryOperator::CreateMul(SI->getOperand(0),
    119                                            ConstantExpr::getShl(CI, ShOp));
    120 
    121     const APInt &Val = CI->getValue();
    122     if (Val.isPowerOf2()) {          // Replace X*(2^C) with X << C
    123       Constant *NewCst = ConstantInt::get(Op0->getType(), Val.logBase2());
    124       BinaryOperator *Shl = BinaryOperator::CreateShl(Op0, NewCst);
    125       if (I.hasNoSignedWrap()) Shl->setHasNoSignedWrap();
    126       if (I.hasNoUnsignedWrap()) Shl->setHasNoUnsignedWrap();
    127       return Shl;
    128     }
    129 
    130     // Canonicalize (X+C1)*CI -> X*CI+C1*CI.
    131     { Value *X; ConstantInt *C1;
    132       if (Op0->hasOneUse() &&
    133           match(Op0, m_Add(m_Value(X), m_ConstantInt(C1)))) {
    134         Value *Add = Builder->CreateMul(X, CI, "tmp");
    135         return BinaryOperator::CreateAdd(Add, Builder->CreateMul(C1, CI));
    136       }
    137     }
    138 
    139     // (Y - X) * (-(2**n)) -> (X - Y) * (2**n), for positive nonzero n
    140     // (Y + const) * (-(2**n)) -> (-constY) * (2**n), for positive nonzero n
    141     // The "* (2**n)" thus becomes a potential shifting opportunity.
    142     {
    143       const APInt &   Val = CI->getValue();
    144       const APInt &PosVal = Val.abs();
    145       if (Val.isNegative() && PosVal.isPowerOf2()) {
    146         Value *X = 0, *Y = 0;
    147         if (Op0->hasOneUse()) {
    148           ConstantInt *C1;
    149           Value *Sub = 0;
    150           if (match(Op0, m_Sub(m_Value(Y), m_Value(X))))
    151             Sub = Builder->CreateSub(X, Y, "suba");
    152           else if (match(Op0, m_Add(m_Value(Y), m_ConstantInt(C1))))
    153             Sub = Builder->CreateSub(Builder->CreateNeg(C1), Y, "subc");
    154           if (Sub)
    155             return
    156               BinaryOperator::CreateMul(Sub,
    157                                         ConstantInt::get(Y->getType(), PosVal));
    158         }
    159       }
    160     }
    161   }
    162 
    163   // Simplify mul instructions with a constant RHS.
    164   if (isa<Constant>(Op1)) {
    165     // Try to fold constant mul into select arguments.
    166     if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
    167       if (Instruction *R = FoldOpIntoSelect(I, SI))
    168         return R;
    169 
    170     if (isa<PHINode>(Op0))
    171       if (Instruction *NV = FoldOpIntoPhi(I))
    172         return NV;
    173   }
    174 
    175   if (Value *Op0v = dyn_castNegVal(Op0))     // -X * -Y = X*Y
    176     if (Value *Op1v = dyn_castNegVal(Op1))
    177       return BinaryOperator::CreateMul(Op0v, Op1v);
    178 
    179   // (X / Y) *  Y = X - (X % Y)
    180   // (X / Y) * -Y = (X % Y) - X
    181   {
    182     Value *Op1C = Op1;
    183     BinaryOperator *BO = dyn_cast<BinaryOperator>(Op0);
    184     if (!BO ||
    185         (BO->getOpcode() != Instruction::UDiv &&
    186          BO->getOpcode() != Instruction::SDiv)) {
    187       Op1C = Op0;
    188       BO = dyn_cast<BinaryOperator>(Op1);
    189     }
    190     Value *Neg = dyn_castNegVal(Op1C);
    191     if (BO && BO->hasOneUse() &&
    192         (BO->getOperand(1) == Op1C || BO->getOperand(1) == Neg) &&
    193         (BO->getOpcode() == Instruction::UDiv ||
    194          BO->getOpcode() == Instruction::SDiv)) {
    195       Value *Op0BO = BO->getOperand(0), *Op1BO = BO->getOperand(1);
    196 
    197       // If the division is exact, X % Y is zero, so we end up with X or -X.
    198       if (PossiblyExactOperator *SDiv = dyn_cast<PossiblyExactOperator>(BO))
    199         if (SDiv->isExact()) {
    200           if (Op1BO == Op1C)
    201             return ReplaceInstUsesWith(I, Op0BO);
    202           return BinaryOperator::CreateNeg(Op0BO);
    203         }
    204 
    205       Value *Rem;
    206       if (BO->getOpcode() == Instruction::UDiv)
    207         Rem = Builder->CreateURem(Op0BO, Op1BO);
    208       else
    209         Rem = Builder->CreateSRem(Op0BO, Op1BO);
    210       Rem->takeName(BO);
    211 
    212       if (Op1BO == Op1C)
    213         return BinaryOperator::CreateSub(Op0BO, Rem);
    214       return BinaryOperator::CreateSub(Rem, Op0BO);
    215     }
    216   }
    217 
    218   /// i1 mul -> i1 and.
    219   if (I.getType()->isIntegerTy(1))
    220     return BinaryOperator::CreateAnd(Op0, Op1);
    221 
    222   // X*(1 << Y) --> X << Y
    223   // (1 << Y)*X --> X << Y
    224   {
    225     Value *Y;
    226     if (match(Op0, m_Shl(m_One(), m_Value(Y))))
    227       return BinaryOperator::CreateShl(Op1, Y);
    228     if (match(Op1, m_Shl(m_One(), m_Value(Y))))
    229       return BinaryOperator::CreateShl(Op0, Y);
    230   }
    231 
    232   // If one of the operands of the multiply is a cast from a boolean value, then
    233   // we know the bool is either zero or one, so this is a 'masking' multiply.
    234   //   X * Y (where Y is 0 or 1) -> X & (0-Y)
    235   if (!I.getType()->isVectorTy()) {
    236     // -2 is "-1 << 1" so it is all bits set except the low one.
    237     APInt Negative2(I.getType()->getPrimitiveSizeInBits(), (uint64_t)-2, true);
    238 
    239     Value *BoolCast = 0, *OtherOp = 0;
    240     if (MaskedValueIsZero(Op0, Negative2))
    241       BoolCast = Op0, OtherOp = Op1;
    242     else if (MaskedValueIsZero(Op1, Negative2))
    243       BoolCast = Op1, OtherOp = Op0;
    244 
    245     if (BoolCast) {
    246       Value *V = Builder->CreateSub(Constant::getNullValue(I.getType()),
    247                                     BoolCast, "tmp");
    248       return BinaryOperator::CreateAnd(V, OtherOp);
    249     }
    250   }
    251 
    252   return Changed ? &I : 0;
    253 }
    254 
    255 Instruction *InstCombiner::visitFMul(BinaryOperator &I) {
    256   bool Changed = SimplifyAssociativeOrCommutative(I);
    257   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    258 
    259   // Simplify mul instructions with a constant RHS...
    260   if (Constant *Op1C = dyn_cast<Constant>(Op1)) {
    261     if (ConstantFP *Op1F = dyn_cast<ConstantFP>(Op1C)) {
    262       // "In IEEE floating point, x*1 is not equivalent to x for nans.  However,
    263       // ANSI says we can drop signals, so we can do this anyway." (from GCC)
    264       if (Op1F->isExactlyValue(1.0))
    265         return ReplaceInstUsesWith(I, Op0);  // Eliminate 'fmul double %X, 1.0'
    266     } else if (Op1C->getType()->isVectorTy()) {
    267       if (ConstantVector *Op1V = dyn_cast<ConstantVector>(Op1C)) {
    268         // As above, vector X*splat(1.0) -> X in all defined cases.
    269         if (Constant *Splat = Op1V->getSplatValue()) {
    270           if (ConstantFP *F = dyn_cast<ConstantFP>(Splat))
    271             if (F->isExactlyValue(1.0))
    272               return ReplaceInstUsesWith(I, Op0);
    273         }
    274       }
    275     }
    276 
    277     // Try to fold constant mul into select arguments.
    278     if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
    279       if (Instruction *R = FoldOpIntoSelect(I, SI))
    280         return R;
    281 
    282     if (isa<PHINode>(Op0))
    283       if (Instruction *NV = FoldOpIntoPhi(I))
    284         return NV;
    285   }
    286 
    287   if (Value *Op0v = dyn_castFNegVal(Op0))     // -X * -Y = X*Y
    288     if (Value *Op1v = dyn_castFNegVal(Op1))
    289       return BinaryOperator::CreateFMul(Op0v, Op1v);
    290 
    291   return Changed ? &I : 0;
    292 }
    293 
    294 /// SimplifyDivRemOfSelect - Try to fold a divide or remainder of a select
    295 /// instruction.
    296 bool InstCombiner::SimplifyDivRemOfSelect(BinaryOperator &I) {
    297   SelectInst *SI = cast<SelectInst>(I.getOperand(1));
    298 
    299   // div/rem X, (Cond ? 0 : Y) -> div/rem X, Y
    300   int NonNullOperand = -1;
    301   if (Constant *ST = dyn_cast<Constant>(SI->getOperand(1)))
    302     if (ST->isNullValue())
    303       NonNullOperand = 2;
    304   // div/rem X, (Cond ? Y : 0) -> div/rem X, Y
    305   if (Constant *ST = dyn_cast<Constant>(SI->getOperand(2)))
    306     if (ST->isNullValue())
    307       NonNullOperand = 1;
    308 
    309   if (NonNullOperand == -1)
    310     return false;
    311 
    312   Value *SelectCond = SI->getOperand(0);
    313 
    314   // Change the div/rem to use 'Y' instead of the select.
    315   I.setOperand(1, SI->getOperand(NonNullOperand));
    316 
    317   // Okay, we know we replace the operand of the div/rem with 'Y' with no
    318   // problem.  However, the select, or the condition of the select may have
    319   // multiple uses.  Based on our knowledge that the operand must be non-zero,
    320   // propagate the known value for the select into other uses of it, and
    321   // propagate a known value of the condition into its other users.
    322 
    323   // If the select and condition only have a single use, don't bother with this,
    324   // early exit.
    325   if (SI->use_empty() && SelectCond->hasOneUse())
    326     return true;
    327 
    328   // Scan the current block backward, looking for other uses of SI.
    329   BasicBlock::iterator BBI = &I, BBFront = I.getParent()->begin();
    330 
    331   while (BBI != BBFront) {
    332     --BBI;
    333     // If we found a call to a function, we can't assume it will return, so
    334     // information from below it cannot be propagated above it.
    335     if (isa<CallInst>(BBI) && !isa<IntrinsicInst>(BBI))
    336       break;
    337 
    338     // Replace uses of the select or its condition with the known values.
    339     for (Instruction::op_iterator I = BBI->op_begin(), E = BBI->op_end();
    340          I != E; ++I) {
    341       if (*I == SI) {
    342         *I = SI->getOperand(NonNullOperand);
    343         Worklist.Add(BBI);
    344       } else if (*I == SelectCond) {
    345         *I = NonNullOperand == 1 ? ConstantInt::getTrue(BBI->getContext()) :
    346                                    ConstantInt::getFalse(BBI->getContext());
    347         Worklist.Add(BBI);
    348       }
    349     }
    350 
    351     // If we past the instruction, quit looking for it.
    352     if (&*BBI == SI)
    353       SI = 0;
    354     if (&*BBI == SelectCond)
    355       SelectCond = 0;
    356 
    357     // If we ran out of things to eliminate, break out of the loop.
    358     if (SelectCond == 0 && SI == 0)
    359       break;
    360 
    361   }
    362   return true;
    363 }
    364 
    365 
    366 /// This function implements the transforms common to both integer division
    367 /// instructions (udiv and sdiv). It is called by the visitors to those integer
    368 /// division instructions.
    369 /// @brief Common integer divide transforms
    370 Instruction *InstCombiner::commonIDivTransforms(BinaryOperator &I) {
    371   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    372 
    373   // The RHS is known non-zero.
    374   if (Value *V = simplifyValueKnownNonZero(I.getOperand(1), *this)) {
    375     I.setOperand(1, V);
    376     return &I;
    377   }
    378 
    379   // Handle cases involving: [su]div X, (select Cond, Y, Z)
    380   // This does not apply for fdiv.
    381   if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
    382     return &I;
    383 
    384   if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
    385     // (X / C1) / C2  -> X / (C1*C2)
    386     if (Instruction *LHS = dyn_cast<Instruction>(Op0))
    387       if (Instruction::BinaryOps(LHS->getOpcode()) == I.getOpcode())
    388         if (ConstantInt *LHSRHS = dyn_cast<ConstantInt>(LHS->getOperand(1))) {
    389           if (MultiplyOverflows(RHS, LHSRHS,
    390                                 I.getOpcode()==Instruction::SDiv))
    391             return ReplaceInstUsesWith(I, Constant::getNullValue(I.getType()));
    392           return BinaryOperator::Create(I.getOpcode(), LHS->getOperand(0),
    393                                         ConstantExpr::getMul(RHS, LHSRHS));
    394         }
    395 
    396     if (!RHS->isZero()) { // avoid X udiv 0
    397       if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
    398         if (Instruction *R = FoldOpIntoSelect(I, SI))
    399           return R;
    400       if (isa<PHINode>(Op0))
    401         if (Instruction *NV = FoldOpIntoPhi(I))
    402           return NV;
    403     }
    404   }
    405 
    406   // See if we can fold away this div instruction.
    407   if (SimplifyDemandedInstructionBits(I))
    408     return &I;
    409 
    410   // (X - (X rem Y)) / Y -> X / Y; usually originates as ((X / Y) * Y) / Y
    411   Value *X = 0, *Z = 0;
    412   if (match(Op0, m_Sub(m_Value(X), m_Value(Z)))) { // (X - Z) / Y; Y = Op1
    413     bool isSigned = I.getOpcode() == Instruction::SDiv;
    414     if ((isSigned && match(Z, m_SRem(m_Specific(X), m_Specific(Op1)))) ||
    415         (!isSigned && match(Z, m_URem(m_Specific(X), m_Specific(Op1)))))
    416       return BinaryOperator::Create(I.getOpcode(), X, Op1);
    417   }
    418 
    419   return 0;
    420 }
    421 
    422 /// dyn_castZExtVal - Checks if V is a zext or constant that can
    423 /// be truncated to Ty without losing bits.
    424 static Value *dyn_castZExtVal(Value *V, Type *Ty) {
    425   if (ZExtInst *Z = dyn_cast<ZExtInst>(V)) {
    426     if (Z->getSrcTy() == Ty)
    427       return Z->getOperand(0);
    428   } else if (ConstantInt *C = dyn_cast<ConstantInt>(V)) {
    429     if (C->getValue().getActiveBits() <= cast<IntegerType>(Ty)->getBitWidth())
    430       return ConstantExpr::getTrunc(C, Ty);
    431   }
    432   return 0;
    433 }
    434 
    435 Instruction *InstCombiner::visitUDiv(BinaryOperator &I) {
    436   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    437 
    438   if (Value *V = SimplifyUDivInst(Op0, Op1, TD))
    439     return ReplaceInstUsesWith(I, V);
    440 
    441   // Handle the integer div common cases
    442   if (Instruction *Common = commonIDivTransforms(I))
    443     return Common;
    444 
    445   if (ConstantInt *C = dyn_cast<ConstantInt>(Op1)) {
    446     // X udiv 2^C -> X >> C
    447     // Check to see if this is an unsigned division with an exact power of 2,
    448     // if so, convert to a right shift.
    449     if (C->getValue().isPowerOf2()) { // 0 not included in isPowerOf2
    450       BinaryOperator *LShr =
    451         BinaryOperator::CreateLShr(Op0,
    452             ConstantInt::get(Op0->getType(), C->getValue().logBase2()));
    453       if (I.isExact()) LShr->setIsExact();
    454       return LShr;
    455     }
    456 
    457     // X udiv C, where C >= signbit
    458     if (C->getValue().isNegative()) {
    459       Value *IC = Builder->CreateICmpULT(Op0, C);
    460       return SelectInst::Create(IC, Constant::getNullValue(I.getType()),
    461                                 ConstantInt::get(I.getType(), 1));
    462     }
    463   }
    464 
    465   // X udiv (C1 << N), where C1 is "1<<C2"  -->  X >> (N+C2)
    466   { const APInt *CI; Value *N;
    467     if (match(Op1, m_Shl(m_Power2(CI), m_Value(N)))) {
    468       if (*CI != 1)
    469         N = Builder->CreateAdd(N, ConstantInt::get(I.getType(), CI->logBase2()),
    470                                "tmp");
    471       if (I.isExact())
    472         return BinaryOperator::CreateExactLShr(Op0, N);
    473       return BinaryOperator::CreateLShr(Op0, N);
    474     }
    475   }
    476 
    477   // udiv X, (Select Cond, C1, C2) --> Select Cond, (shr X, C1), (shr X, C2)
    478   // where C1&C2 are powers of two.
    479   { Value *Cond; const APInt *C1, *C2;
    480     if (match(Op1, m_Select(m_Value(Cond), m_Power2(C1), m_Power2(C2)))) {
    481       // Construct the "on true" case of the select
    482       Value *TSI = Builder->CreateLShr(Op0, C1->logBase2(), Op1->getName()+".t",
    483                                        I.isExact());
    484 
    485       // Construct the "on false" case of the select
    486       Value *FSI = Builder->CreateLShr(Op0, C2->logBase2(), Op1->getName()+".f",
    487                                        I.isExact());
    488 
    489       // construct the select instruction and return it.
    490       return SelectInst::Create(Cond, TSI, FSI);
    491     }
    492   }
    493 
    494   // (zext A) udiv (zext B) --> zext (A udiv B)
    495   if (ZExtInst *ZOp0 = dyn_cast<ZExtInst>(Op0))
    496     if (Value *ZOp1 = dyn_castZExtVal(Op1, ZOp0->getSrcTy()))
    497       return new ZExtInst(Builder->CreateUDiv(ZOp0->getOperand(0), ZOp1, "div",
    498                                               I.isExact()),
    499                           I.getType());
    500 
    501   return 0;
    502 }
    503 
    504 Instruction *InstCombiner::visitSDiv(BinaryOperator &I) {
    505   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    506 
    507   if (Value *V = SimplifySDivInst(Op0, Op1, TD))
    508     return ReplaceInstUsesWith(I, V);
    509 
    510   // Handle the integer div common cases
    511   if (Instruction *Common = commonIDivTransforms(I))
    512     return Common;
    513 
    514   if (ConstantInt *RHS = dyn_cast<ConstantInt>(Op1)) {
    515     // sdiv X, -1 == -X
    516     if (RHS->isAllOnesValue())
    517       return BinaryOperator::CreateNeg(Op0);
    518 
    519     // sdiv X, C  -->  ashr exact X, log2(C)
    520     if (I.isExact() && RHS->getValue().isNonNegative() &&
    521         RHS->getValue().isPowerOf2()) {
    522       Value *ShAmt = llvm::ConstantInt::get(RHS->getType(),
    523                                             RHS->getValue().exactLogBase2());
    524       return BinaryOperator::CreateExactAShr(Op0, ShAmt, I.getName());
    525     }
    526 
    527     // -X/C  -->  X/-C  provided the negation doesn't overflow.
    528     if (SubOperator *Sub = dyn_cast<SubOperator>(Op0))
    529       if (match(Sub->getOperand(0), m_Zero()) && Sub->hasNoSignedWrap())
    530         return BinaryOperator::CreateSDiv(Sub->getOperand(1),
    531                                           ConstantExpr::getNeg(RHS));
    532   }
    533 
    534   // If the sign bits of both operands are zero (i.e. we can prove they are
    535   // unsigned inputs), turn this into a udiv.
    536   if (I.getType()->isIntegerTy()) {
    537     APInt Mask(APInt::getSignBit(I.getType()->getPrimitiveSizeInBits()));
    538     if (MaskedValueIsZero(Op0, Mask)) {
    539       if (MaskedValueIsZero(Op1, Mask)) {
    540         // X sdiv Y -> X udiv Y, iff X and Y don't have sign bit set
    541         return BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
    542       }
    543 
    544       if (match(Op1, m_Shl(m_Power2(), m_Value()))) {
    545         // X sdiv (1 << Y) -> X udiv (1 << Y) ( -> X u>> Y)
    546         // Safe because the only negative value (1 << Y) can take on is
    547         // INT_MIN, and X sdiv INT_MIN == X udiv INT_MIN == 0 if X doesn't have
    548         // the sign bit set.
    549         return BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
    550       }
    551     }
    552   }
    553 
    554   return 0;
    555 }
    556 
    557 Instruction *InstCombiner::visitFDiv(BinaryOperator &I) {
    558   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    559 
    560   if (Value *V = SimplifyFDivInst(Op0, Op1, TD))
    561     return ReplaceInstUsesWith(I, V);
    562 
    563   if (ConstantFP *Op1C = dyn_cast<ConstantFP>(Op1)) {
    564     const APFloat &Op1F = Op1C->getValueAPF();
    565 
    566     // If the divisor has an exact multiplicative inverse we can turn the fdiv
    567     // into a cheaper fmul.
    568     APFloat Reciprocal(Op1F.getSemantics());
    569     if (Op1F.getExactInverse(&Reciprocal)) {
    570       ConstantFP *RFP = ConstantFP::get(Builder->getContext(), Reciprocal);
    571       return BinaryOperator::CreateFMul(Op0, RFP);
    572     }
    573   }
    574 
    575   return 0;
    576 }
    577 
    578 /// This function implements the transforms common to both integer remainder
    579 /// instructions (urem and srem). It is called by the visitors to those integer
    580 /// remainder instructions.
    581 /// @brief Common integer remainder transforms
    582 Instruction *InstCombiner::commonIRemTransforms(BinaryOperator &I) {
    583   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    584 
    585   // The RHS is known non-zero.
    586   if (Value *V = simplifyValueKnownNonZero(I.getOperand(1), *this)) {
    587     I.setOperand(1, V);
    588     return &I;
    589   }
    590 
    591   // Handle cases involving: rem X, (select Cond, Y, Z)
    592   if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
    593     return &I;
    594 
    595   if (isa<ConstantInt>(Op1)) {
    596     if (Instruction *Op0I = dyn_cast<Instruction>(Op0)) {
    597       if (SelectInst *SI = dyn_cast<SelectInst>(Op0I)) {
    598         if (Instruction *R = FoldOpIntoSelect(I, SI))
    599           return R;
    600       } else if (isa<PHINode>(Op0I)) {
    601         if (Instruction *NV = FoldOpIntoPhi(I))
    602           return NV;
    603       }
    604 
    605       // See if we can fold away this rem instruction.
    606       if (SimplifyDemandedInstructionBits(I))
    607         return &I;
    608     }
    609   }
    610 
    611   return 0;
    612 }
    613 
    614 Instruction *InstCombiner::visitURem(BinaryOperator &I) {
    615   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    616 
    617   if (Value *V = SimplifyURemInst(Op0, Op1, TD))
    618     return ReplaceInstUsesWith(I, V);
    619 
    620   if (Instruction *common = commonIRemTransforms(I))
    621     return common;
    622 
    623   // X urem C^2 -> X and C-1
    624   { const APInt *C;
    625     if (match(Op1, m_Power2(C)))
    626       return BinaryOperator::CreateAnd(Op0,
    627                                        ConstantInt::get(I.getType(), *C-1));
    628   }
    629 
    630   // Turn A % (C << N), where C is 2^k, into A & ((C << N)-1)
    631   if (match(Op1, m_Shl(m_Power2(), m_Value()))) {
    632     Constant *N1 = Constant::getAllOnesValue(I.getType());
    633     Value *Add = Builder->CreateAdd(Op1, N1, "tmp");
    634     return BinaryOperator::CreateAnd(Op0, Add);
    635   }
    636 
    637   // urem X, (select Cond, 2^C1, 2^C2) -->
    638   //    select Cond, (and X, C1-1), (and X, C2-1)
    639   // when C1&C2 are powers of two.
    640   { Value *Cond; const APInt *C1, *C2;
    641     if (match(Op1, m_Select(m_Value(Cond), m_Power2(C1), m_Power2(C2)))) {
    642       Value *TrueAnd = Builder->CreateAnd(Op0, *C1-1, Op1->getName()+".t");
    643       Value *FalseAnd = Builder->CreateAnd(Op0, *C2-1, Op1->getName()+".f");
    644       return SelectInst::Create(Cond, TrueAnd, FalseAnd);
    645     }
    646   }
    647 
    648   // (zext A) urem (zext B) --> zext (A urem B)
    649   if (ZExtInst *ZOp0 = dyn_cast<ZExtInst>(Op0))
    650     if (Value *ZOp1 = dyn_castZExtVal(Op1, ZOp0->getSrcTy()))
    651       return new ZExtInst(Builder->CreateURem(ZOp0->getOperand(0), ZOp1),
    652                           I.getType());
    653 
    654   return 0;
    655 }
    656 
    657 Instruction *InstCombiner::visitSRem(BinaryOperator &I) {
    658   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    659 
    660   if (Value *V = SimplifySRemInst(Op0, Op1, TD))
    661     return ReplaceInstUsesWith(I, V);
    662 
    663   // Handle the integer rem common cases
    664   if (Instruction *Common = commonIRemTransforms(I))
    665     return Common;
    666 
    667   if (Value *RHSNeg = dyn_castNegVal(Op1))
    668     if (!isa<Constant>(RHSNeg) ||
    669         (isa<ConstantInt>(RHSNeg) &&
    670          cast<ConstantInt>(RHSNeg)->getValue().isStrictlyPositive())) {
    671       // X % -Y -> X % Y
    672       Worklist.AddValue(I.getOperand(1));
    673       I.setOperand(1, RHSNeg);
    674       return &I;
    675     }
    676 
    677   // If the sign bits of both operands are zero (i.e. we can prove they are
    678   // unsigned inputs), turn this into a urem.
    679   if (I.getType()->isIntegerTy()) {
    680     APInt Mask(APInt::getSignBit(I.getType()->getPrimitiveSizeInBits()));
    681     if (MaskedValueIsZero(Op1, Mask) && MaskedValueIsZero(Op0, Mask)) {
    682       // X srem Y -> X urem Y, iff X and Y don't have sign bit set
    683       return BinaryOperator::CreateURem(Op0, Op1, I.getName());
    684     }
    685   }
    686 
    687   // If it's a constant vector, flip any negative values positive.
    688   if (ConstantVector *RHSV = dyn_cast<ConstantVector>(Op1)) {
    689     unsigned VWidth = RHSV->getNumOperands();
    690 
    691     bool hasNegative = false;
    692     for (unsigned i = 0; !hasNegative && i != VWidth; ++i)
    693       if (ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV->getOperand(i)))
    694         if (RHS->isNegative())
    695           hasNegative = true;
    696 
    697     if (hasNegative) {
    698       std::vector<Constant *> Elts(VWidth);
    699       for (unsigned i = 0; i != VWidth; ++i) {
    700         if (ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV->getOperand(i))) {
    701           if (RHS->isNegative())
    702             Elts[i] = cast<ConstantInt>(ConstantExpr::getNeg(RHS));
    703           else
    704             Elts[i] = RHS;
    705         }
    706       }
    707 
    708       Constant *NewRHSV = ConstantVector::get(Elts);
    709       if (NewRHSV != RHSV) {
    710         Worklist.AddValue(I.getOperand(1));
    711         I.setOperand(1, NewRHSV);
    712         return &I;
    713       }
    714     }
    715   }
    716 
    717   return 0;
    718 }
    719 
    720 Instruction *InstCombiner::visitFRem(BinaryOperator &I) {
    721   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
    722 
    723   if (Value *V = SimplifyFRemInst(Op0, Op1, TD))
    724     return ReplaceInstUsesWith(I, V);
    725 
    726   // Handle cases involving: rem X, (select Cond, Y, Z)
    727   if (isa<SelectInst>(Op1) && SimplifyDivRemOfSelect(I))
    728     return &I;
    729 
    730   return 0;
    731 }
    732