lib/Transforms/InstCombine/InstCombineMulDivRem.cpp

   1 //===- InstCombineMulDivRem.cpp -------------------------------------------===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // This file implements the visit functions for mul, fmul, sdiv, udiv, fdiv,
  10 // srem, urem, frem.
  11 //
  12 //===----------------------------------------------------------------------===//
  13
  14 #include "InstCombineInternal.h"
  15 #include "llvm/ADT/APFloat.h"
  16 #include "llvm/ADT/APInt.h"
  17 #include "llvm/ADT/SmallVector.h"
  18 #include "llvm/Analysis/InstructionSimplify.h"
  19 #include "llvm/IR/BasicBlock.h"
  20 #include "llvm/IR/Constant.h"
  21 #include "llvm/IR/Constants.h"
  22 #include "llvm/IR/InstrTypes.h"
  23 #include "llvm/IR/Instruction.h"
  24 #include "llvm/IR/Instructions.h"
  25 #include "llvm/IR/IntrinsicInst.h"
  26 #include "llvm/IR/Intrinsics.h"
  27 #include "llvm/IR/Operator.h"
  28 #include "llvm/IR/PatternMatch.h"
  29 #include "llvm/IR/Type.h"
  30 #include "llvm/IR/Value.h"
  31 #include "llvm/Support/Casting.h"
  32 #include "llvm/Support/ErrorHandling.h"
  33 #include "llvm/Support/KnownBits.h"
  34 #include "llvm/Transforms/InstCombine/InstCombineWorklist.h"
  35 #include "llvm/Transforms/Utils/BuildLibCalls.h"
  36 #include <cassert>
  37 #include <cstddef>
  38 #include <cstdint>
  39 #include <utility>
  40
  41 using namespace llvm;
  42 using namespace PatternMatch;
  43
  44 #define DEBUG_TYPE "instcombine"
  45
  46 /// The specific integer value is used in a context where it is known to be
  47 /// non-zero.  If this allows us to simplify the computation, do so and return
  48 /// the new operand, otherwise return null.
  49 static Value *simplifyValueKnownNonZero(Value *V, InstCombiner &IC,
  50                                         Instruction &CxtI) {
  51   // If V has multiple uses, then we would have to do more analysis to determine
  52   // if this is safe.  For example, the use could be in dynamically unreached
  53   // code.
  54   if (!V->hasOneUse()) return nullptr;
  55
  56   bool MadeChange = false;
  57
  58   // ((1 << A) >>u B) --> (1 << (A-B))
  59   // Because V cannot be zero, we know that B is less than A.
  60   Value *A = nullptr, *B = nullptr, *One = nullptr;
  61   if (match(V, m_LShr(m_OneUse(m_Shl(m_Value(One), m_Value(A))), m_Value(B))) &&
  62       match(One, m_One())) {
  63     A = IC.Builder.CreateSub(A, B);
  64     return IC.Builder.CreateShl(One, A);
  65   }
  66
  67   // (PowerOfTwo >>u B) --> isExact since shifting out the result would make it
  68   // inexact.  Similarly for <<.
  69   BinaryOperator *I = dyn_cast<BinaryOperator>(V);
  70   if (I && I->isLogicalShift() &&
  71       IC.isKnownToBeAPowerOfTwo(I->getOperand(0), false, 0, &CxtI)) {
  72     // We know that this is an exact/nuw shift and that the input is a
  73     // non-zero context as well.
  74     if (Value *V2 = simplifyValueKnownNonZero(I->getOperand(0), IC, CxtI)) {
  75       I->setOperand(0, V2);
  76       MadeChange = true;
  77     }
  78
  79     if (I->getOpcode() == Instruction::LShr && !I->isExact()) {
  80       I->setIsExact();
  81       MadeChange = true;
  82     }
  83
  84     if (I->getOpcode() == Instruction::Shl && !I->hasNoUnsignedWrap()) {
  85       I->setHasNoUnsignedWrap();
  86       MadeChange = true;
  87     }
  88   }
  89
  90   // TODO: Lots more we could do here:
  91   //    If V is a phi node, we can call this on each of its operands.
  92   //    "select cond, X, 0" can simplify to "X".
  93
  94   return MadeChange ? V : nullptr;
  95 }
  96
  97 /// A helper routine of InstCombiner::visitMul().
  98 ///
  99 /// If C is a scalar/vector of known powers of 2, then this function returns
 100 /// a new scalar/vector obtained from logBase2 of C.
 101 /// Return a null pointer otherwise.
 102 static Constant *getLogBase2(Type *Ty, Constant *C) {
 103   const APInt *IVal;
 104   if (match(C, m_APInt(IVal)) && IVal->isPowerOf2())
 105     return ConstantInt::get(Ty, IVal->logBase2());
 106
 107   if (!Ty->isVectorTy())
 108     return nullptr;
 109
 110   SmallVector<Constant *, 4> Elts;
 111   for (unsigned I = 0, E = Ty->getVectorNumElements(); I != E; ++I) {
 112     Constant *Elt = C->getAggregateElement(I);
 113     if (!Elt)
 114       return nullptr;
 115     if (isa<UndefValue>(Elt)) {
 116       Elts.push_back(UndefValue::get(Ty->getScalarType()));
 117       continue;
 118     }
 119     if (!match(Elt, m_APInt(IVal)) || !IVal->isPowerOf2())
 120       return nullptr;
 121     Elts.push_back(ConstantInt::get(Ty->getScalarType(), IVal->logBase2()));
 122   }
 123
 124   return ConstantVector::get(Elts);
 125 }
 126
 127 Instruction *InstCombiner::visitMul(BinaryOperator &I) {
 128   if (Value *V = SimplifyMulInst(I.getOperand(0), I.getOperand(1),
 129                                  SQ.getWithInstruction(&I)))
 130     return replaceInstUsesWith(I, V);
 131
 132   if (SimplifyAssociativeOrCommutative(I))
 133     return &I;
 134
 135   if (Instruction *X = foldVectorBinop(I))
 136     return X;
 137
 138   if (Value *V = SimplifyUsingDistributiveLaws(I))
 139     return replaceInstUsesWith(I, V);
 140
 141   // X * -1 == 0 - X
 142   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
 143   if (match(Op1, m_AllOnes())) {
 144     BinaryOperator *BO = BinaryOperator::CreateNeg(Op0, I.getName());
 145     if (I.hasNoSignedWrap())
 146       BO->setHasNoSignedWrap();
 147     return BO;
 148   }
 149
 150   // Also allow combining multiply instructions on vectors.
 151   {
 152     Value *NewOp;
 153     Constant *C1, *C2;
 154     const APInt *IVal;
 155     if (match(&I, m_Mul(m_Shl(m_Value(NewOp), m_Constant(C2)),
 156                         m_Constant(C1))) &&
 157         match(C1, m_APInt(IVal))) {
 158       // ((X << C2)*C1) == (X * (C1 << C2))
 159       Constant *Shl = ConstantExpr::getShl(C1, C2);
 160       BinaryOperator *Mul = cast<BinaryOperator>(I.getOperand(0));
 161       BinaryOperator *BO = BinaryOperator::CreateMul(NewOp, Shl);
 162       if (I.hasNoUnsignedWrap() && Mul->hasNoUnsignedWrap())
 163         BO->setHasNoUnsignedWrap();
 164       if (I.hasNoSignedWrap() && Mul->hasNoSignedWrap() &&
 165           Shl->isNotMinSignedValue())
 166         BO->setHasNoSignedWrap();
 167       return BO;
 168     }
 169
 170     if (match(&I, m_Mul(m_Value(NewOp), m_Constant(C1)))) {
 171       // Replace X*(2^C) with X << C, where C is either a scalar or a vector.
 172       if (Constant *NewCst = getLogBase2(NewOp->getType(), C1)) {
 173         BinaryOperator *Shl = BinaryOperator::CreateShl(NewOp, NewCst);
 174
 175         if (I.hasNoUnsignedWrap())
 176           Shl->setHasNoUnsignedWrap();
 177         if (I.hasNoSignedWrap()) {
 178           const APInt *V;
 179           if (match(NewCst, m_APInt(V)) && *V != V->getBitWidth() - 1)
 180             Shl->setHasNoSignedWrap();
 181         }
 182
 183         return Shl;
 184       }
 185     }
 186   }
 187
 188   if (ConstantInt *CI = dyn_cast<ConstantInt>(Op1)) {
 189     // (Y - X) * (-(2**n)) -> (X - Y) * (2**n), for positive nonzero n
 190     // (Y + const) * (-(2**n)) -> (-constY) * (2**n), for positive nonzero n
 191     // The "* (2**n)" thus becomes a potential shifting opportunity.
 192     {
 193       const APInt &   Val = CI->getValue();
 194       const APInt &PosVal = Val.abs();
 195       if (Val.isNegative() && PosVal.isPowerOf2()) {
 196         Value *X = nullptr, *Y = nullptr;
 197         if (Op0->hasOneUse()) {
 198           ConstantInt *C1;
 199           Value *Sub = nullptr;
 200           if (match(Op0, m_Sub(m_Value(Y), m_Value(X))))
 201             Sub = Builder.CreateSub(X, Y, "suba");
 202           else if (match(Op0, m_Add(m_Value(Y), m_ConstantInt(C1))))
 203             Sub = Builder.CreateSub(Builder.CreateNeg(C1), Y, "subc");
 204           if (Sub)
 205             return
 206               BinaryOperator::CreateMul(Sub,
 207                                         ConstantInt::get(Y->getType(), PosVal));
 208         }
 209       }
 210     }
 211   }
 212
 213   if (Instruction *FoldedMul = foldBinOpIntoSelectOrPhi(I))
 214     return FoldedMul;
 215
 216   // Simplify mul instructions with a constant RHS.
 217   if (isa<Constant>(Op1)) {
 218     // Canonicalize (X+C1)*CI -> X*CI+C1*CI.
 219     Value *X;
 220     Constant *C1;
 221     if (match(Op0, m_OneUse(m_Add(m_Value(X), m_Constant(C1))))) {
 222       Value *Mul = Builder.CreateMul(C1, Op1);
 223       // Only go forward with the transform if C1*CI simplifies to a tidier
 224       // constant.
 225       if (!match(Mul, m_Mul(m_Value(), m_Value())))
 226         return BinaryOperator::CreateAdd(Builder.CreateMul(X, Op1), Mul);
 227     }
 228   }
 229
 230   // -X * C --> X * -C
 231   Value *X, *Y;
 232   Constant *Op1C;
 233   if (match(Op0, m_Neg(m_Value(X))) && match(Op1, m_Constant(Op1C)))
 234     return BinaryOperator::CreateMul(X, ConstantExpr::getNeg(Op1C));
 235
 236   // -X * -Y --> X * Y
 237   if (match(Op0, m_Neg(m_Value(X))) && match(Op1, m_Neg(m_Value(Y)))) {
 238     auto *NewMul = BinaryOperator::CreateMul(X, Y);
 239     if (I.hasNoSignedWrap() &&
 240         cast<OverflowingBinaryOperator>(Op0)->hasNoSignedWrap() &&
 241         cast<OverflowingBinaryOperator>(Op1)->hasNoSignedWrap())
 242       NewMul->setHasNoSignedWrap();
 243     return NewMul;
 244   }
 245
 246   // -X * Y --> -(X * Y)
 247   // X * -Y --> -(X * Y)
 248   if (match(&I, m_c_Mul(m_OneUse(m_Neg(m_Value(X))), m_Value(Y))))
 249     return BinaryOperator::CreateNeg(Builder.CreateMul(X, Y));
 250
 251   // (X / Y) *  Y = X - (X % Y)
 252   // (X / Y) * -Y = (X % Y) - X
 253   {
 254     Value *Y = Op1;
 255     BinaryOperator *Div = dyn_cast<BinaryOperator>(Op0);
 256     if (!Div || (Div->getOpcode() != Instruction::UDiv &&
 257                  Div->getOpcode() != Instruction::SDiv)) {
 258       Y = Op0;
 259       Div = dyn_cast<BinaryOperator>(Op1);
 260     }
 261     Value *Neg = dyn_castNegVal(Y);
 262     if (Div && Div->hasOneUse() &&
 263         (Div->getOperand(1) == Y || Div->getOperand(1) == Neg) &&
 264         (Div->getOpcode() == Instruction::UDiv ||
 265          Div->getOpcode() == Instruction::SDiv)) {
 266       Value *X = Div->getOperand(0), *DivOp1 = Div->getOperand(1);
 267
 268       // If the division is exact, X % Y is zero, so we end up with X or -X.
 269       if (Div->isExact()) {
 270         if (DivOp1 == Y)
 271           return replaceInstUsesWith(I, X);
 272         return BinaryOperator::CreateNeg(X);
 273       }
 274
 275       auto RemOpc = Div->getOpcode() == Instruction::UDiv ? Instruction::URem
 276                                                           : Instruction::SRem;
 277       Value *Rem = Builder.CreateBinOp(RemOpc, X, DivOp1);
 278       if (DivOp1 == Y)
 279         return BinaryOperator::CreateSub(X, Rem);
 280       return BinaryOperator::CreateSub(Rem, X);
 281     }
 282   }
 283
 284   /// i1 mul -> i1 and.
 285   if (I.getType()->isIntOrIntVectorTy(1))
 286     return BinaryOperator::CreateAnd(Op0, Op1);
 287
 288   // X*(1 << Y) --> X << Y
 289   // (1 << Y)*X --> X << Y
 290   {
 291     Value *Y;
 292     BinaryOperator *BO = nullptr;
 293     bool ShlNSW = false;
 294     if (match(Op0, m_Shl(m_One(), m_Value(Y)))) {
 295       BO = BinaryOperator::CreateShl(Op1, Y);
 296       ShlNSW = cast<ShlOperator>(Op0)->hasNoSignedWrap();
 297     } else if (match(Op1, m_Shl(m_One(), m_Value(Y)))) {
 298       BO = BinaryOperator::CreateShl(Op0, Y);
 299       ShlNSW = cast<ShlOperator>(Op1)->hasNoSignedWrap();
 300     }
 301     if (BO) {
 302       if (I.hasNoUnsignedWrap())
 303         BO->setHasNoUnsignedWrap();
 304       if (I.hasNoSignedWrap() && ShlNSW)
 305         BO->setHasNoSignedWrap();
 306       return BO;
 307     }
 308   }
 309
 310   // (bool X) * Y --> X ? Y : 0
 311   // Y * (bool X) --> X ? Y : 0
 312   if (match(Op0, m_ZExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1))
 313     return SelectInst::Create(X, Op1, ConstantInt::get(I.getType(), 0));
 314   if (match(Op1, m_ZExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1))
 315     return SelectInst::Create(X, Op0, ConstantInt::get(I.getType(), 0));
 316
 317   // (lshr X, 31) * Y --> (ashr X, 31) & Y
 318   // Y * (lshr X, 31) --> (ashr X, 31) & Y
 319   // TODO: We are not checking one-use because the elimination of the multiply
 320   //       is better for analysis?
 321   // TODO: Should we canonicalize to '(X < 0) ? Y : 0' instead? That would be
 322   //       more similar to what we're doing above.
 323   const APInt *C;
 324   if (match(Op0, m_LShr(m_Value(X), m_APInt(C))) && *C == C->getBitWidth() - 1)
 325     return BinaryOperator::CreateAnd(Builder.CreateAShr(X, *C), Op1);
 326   if (match(Op1, m_LShr(m_Value(X), m_APInt(C))) && *C == C->getBitWidth() - 1)
 327     return BinaryOperator::CreateAnd(Builder.CreateAShr(X, *C), Op0);
 328
 329   if (Instruction *Ext = narrowMathIfNoOverflow(I))
 330     return Ext;
 331
 332   bool Changed = false;
 333   if (!I.hasNoSignedWrap() && willNotOverflowSignedMul(Op0, Op1, I)) {
 334     Changed = true;
 335     I.setHasNoSignedWrap(true);
 336   }
 337
 338   if (!I.hasNoUnsignedWrap() && willNotOverflowUnsignedMul(Op0, Op1, I)) {
 339     Changed = true;
 340     I.setHasNoUnsignedWrap(true);
 341   }
 342
 343   return Changed ? &I : nullptr;
 344 }
 345
 346 Instruction *InstCombiner::visitFMul(BinaryOperator &I) {
 347   if (Value *V = SimplifyFMulInst(I.getOperand(0), I.getOperand(1),
 348                                   I.getFastMathFlags(),
 349                                   SQ.getWithInstruction(&I)))
 350     return replaceInstUsesWith(I, V);
 351
 352   if (SimplifyAssociativeOrCommutative(I))
 353     return &I;
 354
 355   if (Instruction *X = foldVectorBinop(I))
 356     return X;
 357
 358   if (Instruction *FoldedMul = foldBinOpIntoSelectOrPhi(I))
 359     return FoldedMul;
 360
 361   // X * -1.0 --> -X
 362   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
 363   if (match(Op1, m_SpecificFP(-1.0)))
 364     return BinaryOperator::CreateFNegFMF(Op0, &I);
 365
 366   // -X * -Y --> X * Y
 367   Value *X, *Y;
 368   if (match(Op0, m_FNeg(m_Value(X))) && match(Op1, m_FNeg(m_Value(Y))))
 369     return BinaryOperator::CreateFMulFMF(X, Y, &I);
 370
 371   // -X * C --> X * -C
 372   Constant *C;
 373   if (match(Op0, m_FNeg(m_Value(X))) && match(Op1, m_Constant(C)))
 374     return BinaryOperator::CreateFMulFMF(X, ConstantExpr::getFNeg(C), &I);
 375
 376   // fabs(X) * fabs(X) -> X * X
 377   if (Op0 == Op1 && match(Op0, m_Intrinsic<Intrinsic::fabs>(m_Value(X))))
 378     return BinaryOperator::CreateFMulFMF(X, X, &I);
 379
 380   // (select A, B, C) * (select A, D, E) --> select A, (B*D), (C*E)
 381   if (Value *V = SimplifySelectsFeedingBinaryOp(I, Op0, Op1))
 382     return replaceInstUsesWith(I, V);
 383
 384   if (I.hasAllowReassoc()) {
 385     // Reassociate constant RHS with another constant to form constant
 386     // expression.
 387     if (match(Op1, m_Constant(C)) && C->isFiniteNonZeroFP()) {
 388       Constant *C1;
 389       if (match(Op0, m_OneUse(m_FDiv(m_Constant(C1), m_Value(X))))) {
 390         // (C1 / X) * C --> (C * C1) / X
 391         Constant *CC1 = ConstantExpr::getFMul(C, C1);
 392         if (CC1->isNormalFP())
 393           return BinaryOperator::CreateFDivFMF(CC1, X, &I);
 394       }
 395       if (match(Op0, m_FDiv(m_Value(X), m_Constant(C1)))) {
 396         // (X / C1) * C --> X * (C / C1)
 397         Constant *CDivC1 = ConstantExpr::getFDiv(C, C1);
 398         if (CDivC1->isNormalFP())
 399           return BinaryOperator::CreateFMulFMF(X, CDivC1, &I);
 400
 401         // If the constant was a denormal, try reassociating differently.
 402         // (X / C1) * C --> X / (C1 / C)
 403         Constant *C1DivC = ConstantExpr::getFDiv(C1, C);
 404         if (Op0->hasOneUse() && C1DivC->isNormalFP())
 405           return BinaryOperator::CreateFDivFMF(X, C1DivC, &I);
 406       }
 407
 408       // We do not need to match 'fadd C, X' and 'fsub X, C' because they are
 409       // canonicalized to 'fadd X, C'. Distributing the multiply may allow
 410       // further folds and (X * C) + C2 is 'fma'.
 411       if (match(Op0, m_OneUse(m_FAdd(m_Value(X), m_Constant(C1))))) {
 412         // (X + C1) * C --> (X * C) + (C * C1)
 413         Constant *CC1 = ConstantExpr::getFMul(C, C1);
 414         Value *XC = Builder.CreateFMulFMF(X, C, &I);
 415         return BinaryOperator::CreateFAddFMF(XC, CC1, &I);
 416       }
 417       if (match(Op0, m_OneUse(m_FSub(m_Constant(C1), m_Value(X))))) {
 418         // (C1 - X) * C --> (C * C1) - (X * C)
 419         Constant *CC1 = ConstantExpr::getFMul(C, C1);
 420         Value *XC = Builder.CreateFMulFMF(X, C, &I);
 421         return BinaryOperator::CreateFSubFMF(CC1, XC, &I);
 422       }
 423     }
 424
 425     Value *Z;
 426     if (match(&I, m_c_FMul(m_OneUse(m_FDiv(m_Value(X), m_Value(Y))),
 427                            m_Value(Z)))) {
 428       // Sink division: (X / Y) * Z --> (X * Z) / Y
 429       Value *NewFMul = Builder.CreateFMulFMF(X, Z, &I);
 430       return BinaryOperator::CreateFDivFMF(NewFMul, Y, &I);
 431     }
 432
 433     // sqrt(X) * sqrt(Y) -> sqrt(X * Y)
 434     // nnan disallows the possibility of returning a number if both operands are
 435     // negative (in that case, we should return NaN).
 436     if (I.hasNoNaNs() &&
 437         match(Op0, m_OneUse(m_Intrinsic<Intrinsic::sqrt>(m_Value(X)))) &&
 438         match(Op1, m_OneUse(m_Intrinsic<Intrinsic::sqrt>(m_Value(Y))))) {
 439       Value *XY = Builder.CreateFMulFMF(X, Y, &I);
 440       Value *Sqrt = Builder.CreateUnaryIntrinsic(Intrinsic::sqrt, XY, &I);
 441       return replaceInstUsesWith(I, Sqrt);
 442     }
 443
 444     // Like the similar transform in instsimplify, this requires 'nsz' because
 445     // sqrt(-0.0) = -0.0, and -0.0 * -0.0 does not simplify to -0.0.
 446     if (I.hasNoNaNs() && I.hasNoSignedZeros() && Op0 == Op1 &&
 447         Op0->hasNUses(2)) {
 448       // Peek through fdiv to find squaring of square root:
 449       // (X / sqrt(Y)) * (X / sqrt(Y)) --> (X * X) / Y
 450       if (match(Op0, m_FDiv(m_Value(X),
 451                             m_Intrinsic<Intrinsic::sqrt>(m_Value(Y))))) {
 452         Value *XX = Builder.CreateFMulFMF(X, X, &I);
 453         return BinaryOperator::CreateFDivFMF(XX, Y, &I);
 454       }
 455       // (sqrt(Y) / X) * (sqrt(Y) / X) --> Y / (X * X)
 456       if (match(Op0, m_FDiv(m_Intrinsic<Intrinsic::sqrt>(m_Value(Y)),
 457                             m_Value(X)))) {
 458         Value *XX = Builder.CreateFMulFMF(X, X, &I);
 459         return BinaryOperator::CreateFDivFMF(Y, XX, &I);
 460       }
 461     }
 462
 463     // exp(X) * exp(Y) -> exp(X + Y)
 464     // Match as long as at least one of exp has only one use.
 465     if (match(Op0, m_Intrinsic<Intrinsic::exp>(m_Value(X))) &&
 466         match(Op1, m_Intrinsic<Intrinsic::exp>(m_Value(Y))) &&
 467         (Op0->hasOneUse() || Op1->hasOneUse())) {
 468       Value *XY = Builder.CreateFAddFMF(X, Y, &I);
 469       Value *Exp = Builder.CreateUnaryIntrinsic(Intrinsic::exp, XY, &I);
 470       return replaceInstUsesWith(I, Exp);
 471     }
 472
 473     // exp2(X) * exp2(Y) -> exp2(X + Y)
 474     // Match as long as at least one of exp2 has only one use.
 475     if (match(Op0, m_Intrinsic<Intrinsic::exp2>(m_Value(X))) &&
 476         match(Op1, m_Intrinsic<Intrinsic::exp2>(m_Value(Y))) &&
 477         (Op0->hasOneUse() || Op1->hasOneUse())) {
 478       Value *XY = Builder.CreateFAddFMF(X, Y, &I);
 479       Value *Exp2 = Builder.CreateUnaryIntrinsic(Intrinsic::exp2, XY, &I);
 480       return replaceInstUsesWith(I, Exp2);
 481     }
 482
 483     // (X*Y) * X => (X*X) * Y where Y != X
 484     //  The purpose is two-fold:
 485     //   1) to form a power expression (of X).
 486     //   2) potentially shorten the critical path: After transformation, the
 487     //  latency of the instruction Y is amortized by the expression of X*X,
 488     //  and therefore Y is in a "less critical" position compared to what it
 489     //  was before the transformation.
 490     if (match(Op0, m_OneUse(m_c_FMul(m_Specific(Op1), m_Value(Y)))) &&
 491         Op1 != Y) {
 492       Value *XX = Builder.CreateFMulFMF(Op1, Op1, &I);
 493       return BinaryOperator::CreateFMulFMF(XX, Y, &I);
 494     }
 495     if (match(Op1, m_OneUse(m_c_FMul(m_Specific(Op0), m_Value(Y)))) &&
 496         Op0 != Y) {
 497       Value *XX = Builder.CreateFMulFMF(Op0, Op0, &I);
 498       return BinaryOperator::CreateFMulFMF(XX, Y, &I);
 499     }
 500   }
 501
 502   // log2(X * 0.5) * Y = log2(X) * Y - Y
 503   if (I.isFast()) {
 504     IntrinsicInst *Log2 = nullptr;
 505     if (match(Op0, m_OneUse(m_Intrinsic<Intrinsic::log2>(
 506             m_OneUse(m_FMul(m_Value(X), m_SpecificFP(0.5))))))) {
 507       Log2 = cast<IntrinsicInst>(Op0);
 508       Y = Op1;
 509     }
 510     if (match(Op1, m_OneUse(m_Intrinsic<Intrinsic::log2>(
 511             m_OneUse(m_FMul(m_Value(X), m_SpecificFP(0.5))))))) {
 512       Log2 = cast<IntrinsicInst>(Op1);
 513       Y = Op0;
 514     }
 515     if (Log2) {
 516       Log2->setArgOperand(0, X);
 517       Log2->copyFastMathFlags(&I);
 518       Value *LogXTimesY = Builder.CreateFMulFMF(Log2, Y, &I);
 519       return BinaryOperator::CreateFSubFMF(LogXTimesY, Y, &I);
 520     }
 521   }
 522
 523   return nullptr;
 524 }
 525
 526 /// Fold a divide or remainder with a select instruction divisor when one of the
 527 /// select operands is zero. In that case, we can use the other select operand
 528 /// because div/rem by zero is undefined.
 529 bool InstCombiner::simplifyDivRemOfSelectWithZeroOp(BinaryOperator &I) {
 530   SelectInst *SI = dyn_cast<SelectInst>(I.getOperand(1));
 531   if (!SI)
 532     return false;
 533
 534   int NonNullOperand;
 535   if (match(SI->getTrueValue(), m_Zero()))
 536     // div/rem X, (Cond ? 0 : Y) -> div/rem X, Y
 537     NonNullOperand = 2;
 538   else if (match(SI->getFalseValue(), m_Zero()))
 539     // div/rem X, (Cond ? Y : 0) -> div/rem X, Y
 540     NonNullOperand = 1;
 541   else
 542     return false;
 543
 544   // Change the div/rem to use 'Y' instead of the select.
 545   I.setOperand(1, SI->getOperand(NonNullOperand));
 546
 547   // Okay, we know we replace the operand of the div/rem with 'Y' with no
 548   // problem.  However, the select, or the condition of the select may have
 549   // multiple uses.  Based on our knowledge that the operand must be non-zero,
 550   // propagate the known value for the select into other uses of it, and
 551   // propagate a known value of the condition into its other users.
 552
 553   // If the select and condition only have a single use, don't bother with this,
 554   // early exit.
 555   Value *SelectCond = SI->getCondition();
 556   if (SI->use_empty() && SelectCond->hasOneUse())
 557     return true;
 558
 559   // Scan the current block backward, looking for other uses of SI.
 560   BasicBlock::iterator BBI = I.getIterator(), BBFront = I.getParent()->begin();
 561   Type *CondTy = SelectCond->getType();
 562   while (BBI != BBFront) {
 563     --BBI;
 564     // If we found an instruction that we can't assume will return, so
 565     // information from below it cannot be propagated above it.
 566     if (!isGuaranteedToTransferExecutionToSuccessor(&*BBI))
 567       break;
 568
 569     // Replace uses of the select or its condition with the known values.
 570     for (Instruction::op_iterator I = BBI->op_begin(), E = BBI->op_end();
 571          I != E; ++I) {
 572       if (*I == SI) {
 573         *I = SI->getOperand(NonNullOperand);
 574         Worklist.Add(&*BBI);
 575       } else if (*I == SelectCond) {
 576         *I = NonNullOperand == 1 ? ConstantInt::getTrue(CondTy)
 577                                  : ConstantInt::getFalse(CondTy);
 578         Worklist.Add(&*BBI);
 579       }
 580     }
 581
 582     // If we past the instruction, quit looking for it.
 583     if (&*BBI == SI)
 584       SI = nullptr;
 585     if (&*BBI == SelectCond)
 586       SelectCond = nullptr;
 587
 588     // If we ran out of things to eliminate, break out of the loop.
 589     if (!SelectCond && !SI)
 590       break;
 591
 592   }
 593   return true;
 594 }
 595
 596 /// True if the multiply can not be expressed in an int this size.
 597 static bool multiplyOverflows(const APInt &C1, const APInt &C2, APInt &Product,
 598                               bool IsSigned) {
 599   bool Overflow;
 600   Product = IsSigned ? C1.smul_ov(C2, Overflow) : C1.umul_ov(C2, Overflow);
 601   return Overflow;
 602 }
 603
 604 /// True if C1 is a multiple of C2. Quotient contains C1/C2.
 605 static bool isMultiple(const APInt &C1, const APInt &C2, APInt &Quotient,
 606                        bool IsSigned) {
 607   assert(C1.getBitWidth() == C2.getBitWidth() && "Constant widths not equal");
 608
 609   // Bail if we will divide by zero.
 610   if (C2.isNullValue())
 611     return false;
 612
 613   // Bail if we would divide INT_MIN by -1.
 614   if (IsSigned && C1.isMinSignedValue() && C2.isAllOnesValue())
 615     return false;
 616
 617   APInt Remainder(C1.getBitWidth(), /*val=*/0ULL, IsSigned);
 618   if (IsSigned)
 619     APInt::sdivrem(C1, C2, Quotient, Remainder);
 620   else
 621     APInt::udivrem(C1, C2, Quotient, Remainder);
 622
 623   return Remainder.isMinValue();
 624 }
 625
 626 /// This function implements the transforms common to both integer division
 627 /// instructions (udiv and sdiv). It is called by the visitors to those integer
 628 /// division instructions.
 629 /// Common integer divide transforms
 630 Instruction *InstCombiner::commonIDivTransforms(BinaryOperator &I) {
 631   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
 632   bool IsSigned = I.getOpcode() == Instruction::SDiv;
 633   Type *Ty = I.getType();
 634
 635   // The RHS is known non-zero.
 636   if (Value *V = simplifyValueKnownNonZero(I.getOperand(1), *this, I)) {
 637     I.setOperand(1, V);
 638     return &I;
 639   }
 640
 641   // Handle cases involving: [su]div X, (select Cond, Y, Z)
 642   // This does not apply for fdiv.
 643   if (simplifyDivRemOfSelectWithZeroOp(I))
 644     return &I;
 645
 646   const APInt *C2;
 647   if (match(Op1, m_APInt(C2))) {
 648     Value *X;
 649     const APInt *C1;
 650
 651     // (X / C1) / C2  -> X / (C1*C2)
 652     if ((IsSigned && match(Op0, m_SDiv(m_Value(X), m_APInt(C1)))) ||
 653         (!IsSigned && match(Op0, m_UDiv(m_Value(X), m_APInt(C1))))) {
 654       APInt Product(C1->getBitWidth(), /*val=*/0ULL, IsSigned);
 655       if (!multiplyOverflows(*C1, *C2, Product, IsSigned))
 656         return BinaryOperator::Create(I.getOpcode(), X,
 657                                       ConstantInt::get(Ty, Product));
 658     }
 659
 660     if ((IsSigned && match(Op0, m_NSWMul(m_Value(X), m_APInt(C1)))) ||
 661         (!IsSigned && match(Op0, m_NUWMul(m_Value(X), m_APInt(C1))))) {
 662       APInt Quotient(C1->getBitWidth(), /*val=*/0ULL, IsSigned);
 663
 664       // (X * C1) / C2 -> X / (C2 / C1) if C2 is a multiple of C1.
 665       if (isMultiple(*C2, *C1, Quotient, IsSigned)) {
 666         auto *NewDiv = BinaryOperator::Create(I.getOpcode(), X,
 667                                               ConstantInt::get(Ty, Quotient));
 668         NewDiv->setIsExact(I.isExact());
 669         return NewDiv;
 670       }
 671
 672       // (X * C1) / C2 -> X * (C1 / C2) if C1 is a multiple of C2.
 673       if (isMultiple(*C1, *C2, Quotient, IsSigned)) {
 674         auto *Mul = BinaryOperator::Create(Instruction::Mul, X,
 675                                            ConstantInt::get(Ty, Quotient));
 676         auto *OBO = cast<OverflowingBinaryOperator>(Op0);
 677         Mul->setHasNoUnsignedWrap(!IsSigned && OBO->hasNoUnsignedWrap());
 678         Mul->setHasNoSignedWrap(OBO->hasNoSignedWrap());
 679         return Mul;
 680       }
 681     }
 682
 683     if ((IsSigned && match(Op0, m_NSWShl(m_Value(X), m_APInt(C1))) &&
 684          *C1 != C1->getBitWidth() - 1) ||
 685         (!IsSigned && match(Op0, m_NUWShl(m_Value(X), m_APInt(C1))))) {
 686       APInt Quotient(C1->getBitWidth(), /*val=*/0ULL, IsSigned);
 687       APInt C1Shifted = APInt::getOneBitSet(
 688           C1->getBitWidth(), static_cast<unsigned>(C1->getLimitedValue()));
 689
 690       // (X << C1) / C2 -> X / (C2 >> C1) if C2 is a multiple of 1 << C1.
 691       if (isMultiple(*C2, C1Shifted, Quotient, IsSigned)) {
 692         auto *BO = BinaryOperator::Create(I.getOpcode(), X,
 693                                           ConstantInt::get(Ty, Quotient));
 694         BO->setIsExact(I.isExact());
 695         return BO;
 696       }
 697
 698       // (X << C1) / C2 -> X * ((1 << C1) / C2) if 1 << C1 is a multiple of C2.
 699       if (isMultiple(C1Shifted, *C2, Quotient, IsSigned)) {
 700         auto *Mul = BinaryOperator::Create(Instruction::Mul, X,
 701                                            ConstantInt::get(Ty, Quotient));
 702         auto *OBO = cast<OverflowingBinaryOperator>(Op0);
 703         Mul->setHasNoUnsignedWrap(!IsSigned && OBO->hasNoUnsignedWrap());
 704         Mul->setHasNoSignedWrap(OBO->hasNoSignedWrap());
 705         return Mul;
 706       }
 707     }
 708
 709     if (!C2->isNullValue()) // avoid X udiv 0
 710       if (Instruction *FoldedDiv = foldBinOpIntoSelectOrPhi(I))
 711         return FoldedDiv;
 712   }
 713
 714   if (match(Op0, m_One())) {
 715     assert(!Ty->isIntOrIntVectorTy(1) && "i1 divide not removed?");
 716     if (IsSigned) {
 717       // If Op1 is 0 then it's undefined behaviour, if Op1 is 1 then the
 718       // result is one, if Op1 is -1 then the result is minus one, otherwise
 719       // it's zero.
 720       Value *Inc = Builder.CreateAdd(Op1, Op0);
 721       Value *Cmp = Builder.CreateICmpULT(Inc, ConstantInt::get(Ty, 3));
 722       return SelectInst::Create(Cmp, Op1, ConstantInt::get(Ty, 0));
 723     } else {
 724       // If Op1 is 0 then it's undefined behaviour. If Op1 is 1 then the
 725       // result is one, otherwise it's zero.
 726       return new ZExtInst(Builder.CreateICmpEQ(Op1, Op0), Ty);
 727     }
 728   }
 729
 730   // See if we can fold away this div instruction.
 731   if (SimplifyDemandedInstructionBits(I))
 732     return &I;
 733
 734   // (X - (X rem Y)) / Y -> X / Y; usually originates as ((X / Y) * Y) / Y
 735   Value *X, *Z;
 736   if (match(Op0, m_Sub(m_Value(X), m_Value(Z)))) // (X - Z) / Y; Y = Op1
 737     if ((IsSigned && match(Z, m_SRem(m_Specific(X), m_Specific(Op1)))) ||
 738         (!IsSigned && match(Z, m_URem(m_Specific(X), m_Specific(Op1)))))
 739       return BinaryOperator::Create(I.getOpcode(), X, Op1);
 740
 741   // (X << Y) / X -> 1 << Y
 742   Value *Y;
 743   if (IsSigned && match(Op0, m_NSWShl(m_Specific(Op1), m_Value(Y))))
 744     return BinaryOperator::CreateNSWShl(ConstantInt::get(Ty, 1), Y);
 745   if (!IsSigned && match(Op0, m_NUWShl(m_Specific(Op1), m_Value(Y))))
 746     return BinaryOperator::CreateNUWShl(ConstantInt::get(Ty, 1), Y);
 747
 748   // X / (X * Y) -> 1 / Y if the multiplication does not overflow.
 749   if (match(Op1, m_c_Mul(m_Specific(Op0), m_Value(Y)))) {
 750     bool HasNSW = cast<OverflowingBinaryOperator>(Op1)->hasNoSignedWrap();
 751     bool HasNUW = cast<OverflowingBinaryOperator>(Op1)->hasNoUnsignedWrap();
 752     if ((IsSigned && HasNSW) || (!IsSigned && HasNUW)) {
 753       I.setOperand(0, ConstantInt::get(Ty, 1));
 754       I.setOperand(1, Y);
 755       return &I;
 756     }
 757   }
 758
 759   return nullptr;
 760 }
 761
 762 static const unsigned MaxDepth = 6;
 763
 764 namespace {
 765
 766 using FoldUDivOperandCb = Instruction *(*)(Value *Op0, Value *Op1,
 767                                            const BinaryOperator &I,
 768                                            InstCombiner &IC);
 769
 770 /// Used to maintain state for visitUDivOperand().
 771 struct UDivFoldAction {
 772   /// Informs visitUDiv() how to fold this operand.  This can be zero if this
 773   /// action joins two actions together.
 774   FoldUDivOperandCb FoldAction;
 775
 776   /// Which operand to fold.
 777   Value *OperandToFold;
 778
 779   union {
 780     /// The instruction returned when FoldAction is invoked.
 781     Instruction *FoldResult;
 782
 783     /// Stores the LHS action index if this action joins two actions together.
 784     size_t SelectLHSIdx;
 785   };
 786
 787   UDivFoldAction(FoldUDivOperandCb FA, Value *InputOperand)
 788       : FoldAction(FA), OperandToFold(InputOperand), FoldResult(nullptr) {}
 789   UDivFoldAction(FoldUDivOperandCb FA, Value *InputOperand, size_t SLHS)
 790       : FoldAction(FA), OperandToFold(InputOperand), SelectLHSIdx(SLHS) {}
 791 };
 792
 793 } // end anonymous namespace
 794
 795 // X udiv 2^C -> X >> C
 796 static Instruction *foldUDivPow2Cst(Value *Op0, Value *Op1,
 797                                     const BinaryOperator &I, InstCombiner &IC) {
 798   Constant *C1 = getLogBase2(Op0->getType(), cast<Constant>(Op1));
 799   if (!C1)
 800     llvm_unreachable("Failed to constant fold udiv -> logbase2");
 801   BinaryOperator *LShr = BinaryOperator::CreateLShr(Op0, C1);
 802   if (I.isExact())
 803     LShr->setIsExact();
 804   return LShr;
 805 }
 806
 807 // X udiv (C1 << N), where C1 is "1<<C2"  -->  X >> (N+C2)
 808 // X udiv (zext (C1 << N)), where C1 is "1<<C2"  -->  X >> (N+C2)
 809 static Instruction *foldUDivShl(Value *Op0, Value *Op1, const BinaryOperator &I,
 810                                 InstCombiner &IC) {
 811   Value *ShiftLeft;
 812   if (!match(Op1, m_ZExt(m_Value(ShiftLeft))))
 813     ShiftLeft = Op1;
 814
 815   Constant *CI;
 816   Value *N;
 817   if (!match(ShiftLeft, m_Shl(m_Constant(CI), m_Value(N))))
 818     llvm_unreachable("match should never fail here!");
 819   Constant *Log2Base = getLogBase2(N->getType(), CI);
 820   if (!Log2Base)
 821     llvm_unreachable("getLogBase2 should never fail here!");
 822   N = IC.Builder.CreateAdd(N, Log2Base);
 823   if (Op1 != ShiftLeft)
 824     N = IC.Builder.CreateZExt(N, Op1->getType());
 825   BinaryOperator *LShr = BinaryOperator::CreateLShr(Op0, N);
 826   if (I.isExact())
 827     LShr->setIsExact();
 828   return LShr;
 829 }
 830
 831 // Recursively visits the possible right hand operands of a udiv
 832 // instruction, seeing through select instructions, to determine if we can
 833 // replace the udiv with something simpler.  If we find that an operand is not
 834 // able to simplify the udiv, we abort the entire transformation.
 835 static size_t visitUDivOperand(Value *Op0, Value *Op1, const BinaryOperator &I,
 836                                SmallVectorImpl<UDivFoldAction> &Actions,
 837                                unsigned Depth = 0) {
 838   // Check to see if this is an unsigned division with an exact power of 2,
 839   // if so, convert to a right shift.
 840   if (match(Op1, m_Power2())) {
 841     Actions.push_back(UDivFoldAction(foldUDivPow2Cst, Op1));
 842     return Actions.size();
 843   }
 844
 845   // X udiv (C1 << N), where C1 is "1<<C2"  -->  X >> (N+C2)
 846   if (match(Op1, m_Shl(m_Power2(), m_Value())) ||
 847       match(Op1, m_ZExt(m_Shl(m_Power2(), m_Value())))) {
 848     Actions.push_back(UDivFoldAction(foldUDivShl, Op1));
 849     return Actions.size();
 850   }
 851
 852   // The remaining tests are all recursive, so bail out if we hit the limit.
 853   if (Depth++ == MaxDepth)
 854     return 0;
 855
 856   if (SelectInst *SI = dyn_cast<SelectInst>(Op1))
 857     if (size_t LHSIdx =
 858             visitUDivOperand(Op0, SI->getOperand(1), I, Actions, Depth))
 859       if (visitUDivOperand(Op0, SI->getOperand(2), I, Actions, Depth)) {
 860         Actions.push_back(UDivFoldAction(nullptr, Op1, LHSIdx - 1));
 861         return Actions.size();
 862       }
 863
 864   return 0;
 865 }
 866
 867 /// If we have zero-extended operands of an unsigned div or rem, we may be able
 868 /// to narrow the operation (sink the zext below the math).
 869 static Instruction *narrowUDivURem(BinaryOperator &I,
 870                                    InstCombiner::BuilderTy &Builder) {
 871   Instruction::BinaryOps Opcode = I.getOpcode();
 872   Value *N = I.getOperand(0);
 873   Value *D = I.getOperand(1);
 874   Type *Ty = I.getType();
 875   Value *X, *Y;
 876   if (match(N, m_ZExt(m_Value(X))) && match(D, m_ZExt(m_Value(Y))) &&
 877       X->getType() == Y->getType() && (N->hasOneUse() || D->hasOneUse())) {
 878     // udiv (zext X), (zext Y) --> zext (udiv X, Y)
 879     // urem (zext X), (zext Y) --> zext (urem X, Y)
 880     Value *NarrowOp = Builder.CreateBinOp(Opcode, X, Y);
 881     return new ZExtInst(NarrowOp, Ty);
 882   }
 883
 884   Constant *C;
 885   if ((match(N, m_OneUse(m_ZExt(m_Value(X)))) && match(D, m_Constant(C))) ||
 886       (match(D, m_OneUse(m_ZExt(m_Value(X)))) && match(N, m_Constant(C)))) {
 887     // If the constant is the same in the smaller type, use the narrow version.
 888     Constant *TruncC = ConstantExpr::getTrunc(C, X->getType());
 889     if (ConstantExpr::getZExt(TruncC, Ty) != C)
 890       return nullptr;
 891
 892     // udiv (zext X), C --> zext (udiv X, C')
 893     // urem (zext X), C --> zext (urem X, C')
 894     // udiv C, (zext X) --> zext (udiv C', X)
 895     // urem C, (zext X) --> zext (urem C', X)
 896     Value *NarrowOp = isa<Constant>(D) ? Builder.CreateBinOp(Opcode, X, TruncC)
 897                                        : Builder.CreateBinOp(Opcode, TruncC, X);
 898     return new ZExtInst(NarrowOp, Ty);
 899   }
 900
 901   return nullptr;
 902 }
 903
 904 Instruction *InstCombiner::visitUDiv(BinaryOperator &I) {
 905   if (Value *V = SimplifyUDivInst(I.getOperand(0), I.getOperand(1),
 906                                   SQ.getWithInstruction(&I)))
 907     return replaceInstUsesWith(I, V);
 908
 909   if (Instruction *X = foldVectorBinop(I))
 910     return X;
 911
 912   // Handle the integer div common cases
 913   if (Instruction *Common = commonIDivTransforms(I))
 914     return Common;
 915
 916   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
 917   Value *X;
 918   const APInt *C1, *C2;
 919   if (match(Op0, m_LShr(m_Value(X), m_APInt(C1))) && match(Op1, m_APInt(C2))) {
 920     // (X lshr C1) udiv C2 --> X udiv (C2 << C1)
 921     bool Overflow;
 922     APInt C2ShlC1 = C2->ushl_ov(*C1, Overflow);
 923     if (!Overflow) {
 924       bool IsExact = I.isExact() && match(Op0, m_Exact(m_Value()));
 925       BinaryOperator *BO = BinaryOperator::CreateUDiv(
 926           X, ConstantInt::get(X->getType(), C2ShlC1));
 927       if (IsExact)
 928         BO->setIsExact();
 929       return BO;
 930     }
 931   }
 932
 933   // Op0 / C where C is large (negative) --> zext (Op0 >= C)
 934   // TODO: Could use isKnownNegative() to handle non-constant values.
 935   Type *Ty = I.getType();
 936   if (match(Op1, m_Negative())) {
 937     Value *Cmp = Builder.CreateICmpUGE(Op0, Op1);
 938     return CastInst::CreateZExtOrBitCast(Cmp, Ty);
 939   }
 940   // Op0 / (sext i1 X) --> zext (Op0 == -1) (if X is 0, the div is undefined)
 941   if (match(Op1, m_SExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1)) {
 942     Value *Cmp = Builder.CreateICmpEQ(Op0, ConstantInt::getAllOnesValue(Ty));
 943     return CastInst::CreateZExtOrBitCast(Cmp, Ty);
 944   }
 945
 946   if (Instruction *NarrowDiv = narrowUDivURem(I, Builder))
 947     return NarrowDiv;
 948
 949   // If the udiv operands are non-overflowing multiplies with a common operand,
 950   // then eliminate the common factor:
 951   // (A * B) / (A * X) --> B / X (and commuted variants)
 952   // TODO: The code would be reduced if we had m_c_NUWMul pattern matching.
 953   // TODO: If -reassociation handled this generally, we could remove this.
 954   Value *A, *B;
 955   if (match(Op0, m_NUWMul(m_Value(A), m_Value(B)))) {
 956     if (match(Op1, m_NUWMul(m_Specific(A), m_Value(X))) ||
 957         match(Op1, m_NUWMul(m_Value(X), m_Specific(A))))
 958       return BinaryOperator::CreateUDiv(B, X);
 959     if (match(Op1, m_NUWMul(m_Specific(B), m_Value(X))) ||
 960         match(Op1, m_NUWMul(m_Value(X), m_Specific(B))))
 961       return BinaryOperator::CreateUDiv(A, X);
 962   }
 963
 964   // (LHS udiv (select (select (...)))) -> (LHS >> (select (select (...))))
 965   SmallVector<UDivFoldAction, 6> UDivActions;
 966   if (visitUDivOperand(Op0, Op1, I, UDivActions))
 967     for (unsigned i = 0, e = UDivActions.size(); i != e; ++i) {
 968       FoldUDivOperandCb Action = UDivActions[i].FoldAction;
 969       Value *ActionOp1 = UDivActions[i].OperandToFold;
 970       Instruction *Inst;
 971       if (Action)
 972         Inst = Action(Op0, ActionOp1, I, *this);
 973       else {
 974         // This action joins two actions together.  The RHS of this action is
 975         // simply the last action we processed, we saved the LHS action index in
 976         // the joining action.
 977         size_t SelectRHSIdx = i - 1;
 978         Value *SelectRHS = UDivActions[SelectRHSIdx].FoldResult;
 979         size_t SelectLHSIdx = UDivActions[i].SelectLHSIdx;
 980         Value *SelectLHS = UDivActions[SelectLHSIdx].FoldResult;
 981         Inst = SelectInst::Create(cast<SelectInst>(ActionOp1)->getCondition(),
 982                                   SelectLHS, SelectRHS);
 983       }
 984
 985       // If this is the last action to process, return it to the InstCombiner.
 986       // Otherwise, we insert it before the UDiv and record it so that we may
 987       // use it as part of a joining action (i.e., a SelectInst).
 988       if (e - i != 1) {
 989         Inst->insertBefore(&I);
 990         UDivActions[i].FoldResult = Inst;
 991       } else
 992         return Inst;
 993     }
 994
 995   return nullptr;
 996 }
 997
 998 Instruction *InstCombiner::visitSDiv(BinaryOperator &I) {
 999   if (Value *V = SimplifySDivInst(I.getOperand(0), I.getOperand(1),
1000                                   SQ.getWithInstruction(&I)))
1001     return replaceInstUsesWith(I, V);
1002
1003   if (Instruction *X = foldVectorBinop(I))
1004     return X;
1005
1006   // Handle the integer div common cases
1007   if (Instruction *Common = commonIDivTransforms(I))
1008     return Common;
1009
1010   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
1011   Value *X;
1012   // sdiv Op0, -1 --> -Op0
1013   // sdiv Op0, (sext i1 X) --> -Op0 (because if X is 0, the op is undefined)
1014   if (match(Op1, m_AllOnes()) ||
1015       (match(Op1, m_SExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1)))
1016     return BinaryOperator::CreateNeg(Op0);
1017
1018   // X / INT_MIN --> X == INT_MIN
1019   if (match(Op1, m_SignMask()))
1020     return new ZExtInst(Builder.CreateICmpEQ(Op0, Op1), I.getType());
1021
1022   const APInt *Op1C;
1023   if (match(Op1, m_APInt(Op1C))) {
1024     // sdiv exact X, C  -->  ashr exact X, log2(C)
1025     if (I.isExact() && Op1C->isNonNegative() && Op1C->isPowerOf2()) {
1026       Value *ShAmt = ConstantInt::get(Op1->getType(), Op1C->exactLogBase2());
1027       return BinaryOperator::CreateExactAShr(Op0, ShAmt, I.getName());
1028     }
1029
1030     // If the dividend is sign-extended and the constant divisor is small enough
1031     // to fit in the source type, shrink the division to the narrower type:
1032     // (sext X) sdiv C --> sext (X sdiv C)
1033     Value *Op0Src;
1034     if (match(Op0, m_OneUse(m_SExt(m_Value(Op0Src)))) &&
1035         Op0Src->getType()->getScalarSizeInBits() >= Op1C->getMinSignedBits()) {
1036
1037       // In the general case, we need to make sure that the dividend is not the
1038       // minimum signed value because dividing that by -1 is UB. But here, we
1039       // know that the -1 divisor case is already handled above.
1040
1041       Constant *NarrowDivisor =
1042           ConstantExpr::getTrunc(cast<Constant>(Op1), Op0Src->getType());
1043       Value *NarrowOp = Builder.CreateSDiv(Op0Src, NarrowDivisor);
1044       return new SExtInst(NarrowOp, Op0->getType());
1045     }
1046
1047     // -X / C --> X / -C (if the negation doesn't overflow).
1048     // TODO: This could be enhanced to handle arbitrary vector constants by
1049     //       checking if all elements are not the min-signed-val.
1050     if (!Op1C->isMinSignedValue() &&
1051         match(Op0, m_NSWSub(m_Zero(), m_Value(X)))) {
1052       Constant *NegC = ConstantInt::get(I.getType(), -(*Op1C));
1053       Instruction *BO = BinaryOperator::CreateSDiv(X, NegC);
1054       BO->setIsExact(I.isExact());
1055       return BO;
1056     }
1057   }
1058
1059   // -X / Y --> -(X / Y)
1060   Value *Y;
1061   if (match(&I, m_SDiv(m_OneUse(m_NSWSub(m_Zero(), m_Value(X))), m_Value(Y))))
1062     return BinaryOperator::CreateNSWNeg(
1063         Builder.CreateSDiv(X, Y, I.getName(), I.isExact()));
1064
1065   // If the sign bits of both operands are zero (i.e. we can prove they are
1066   // unsigned inputs), turn this into a udiv.
1067   APInt Mask(APInt::getSignMask(I.getType()->getScalarSizeInBits()));
1068   if (MaskedValueIsZero(Op0, Mask, 0, &I)) {
1069     if (MaskedValueIsZero(Op1, Mask, 0, &I)) {
1070       // X sdiv Y -> X udiv Y, iff X and Y don't have sign bit set
1071       auto *BO = BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
1072       BO->setIsExact(I.isExact());
1073       return BO;
1074     }
1075
1076     if (isKnownToBeAPowerOfTwo(Op1, /*OrZero*/ true, 0, &I)) {
1077       // X sdiv (1 << Y) -> X udiv (1 << Y) ( -> X u>> Y)
1078       // Safe because the only negative value (1 << Y) can take on is
1079       // INT_MIN, and X sdiv INT_MIN == X udiv INT_MIN == 0 if X doesn't have
1080       // the sign bit set.
1081       auto *BO = BinaryOperator::CreateUDiv(Op0, Op1, I.getName());
1082       BO->setIsExact(I.isExact());
1083       return BO;
1084     }
1085   }
1086
1087   return nullptr;
1088 }
1089
1090 /// Remove negation and try to convert division into multiplication.
1091 static Instruction *foldFDivConstantDivisor(BinaryOperator &I) {
1092   Constant *C;
1093   if (!match(I.getOperand(1), m_Constant(C)))
1094     return nullptr;
1095
1096   // -X / C --> X / -C
1097   Value *X;
1098   if (match(I.getOperand(0), m_FNeg(m_Value(X))))
1099     return BinaryOperator::CreateFDivFMF(X, ConstantExpr::getFNeg(C), &I);
1100
1101   // If the constant divisor has an exact inverse, this is always safe. If not,
1102   // then we can still create a reciprocal if fast-math-flags allow it and the
1103   // constant is a regular number (not zero, infinite, or denormal).
1104   if (!(C->hasExactInverseFP() || (I.hasAllowReciprocal() && C->isNormalFP())))
1105     return nullptr;
1106
1107   // Disallow denormal constants because we don't know what would happen
1108   // on all targets.
1109   // TODO: Use Intrinsic::canonicalize or let function attributes tell us that
1110   // denorms are flushed?
1111   auto *RecipC = ConstantExpr::getFDiv(ConstantFP::get(I.getType(), 1.0), C);
1112   if (!RecipC->isNormalFP())
1113     return nullptr;
1114
1115   // X / C --> X * (1 / C)
1116   return BinaryOperator::CreateFMulFMF(I.getOperand(0), RecipC, &I);
1117 }
1118
1119 /// Remove negation and try to reassociate constant math.
1120 static Instruction *foldFDivConstantDividend(BinaryOperator &I) {
1121   Constant *C;
1122   if (!match(I.getOperand(0), m_Constant(C)))
1123     return nullptr;
1124
1125   // C / -X --> -C / X
1126   Value *X;
1127   if (match(I.getOperand(1), m_FNeg(m_Value(X))))
1128     return BinaryOperator::CreateFDivFMF(ConstantExpr::getFNeg(C), X, &I);
1129
1130   if (!I.hasAllowReassoc() || !I.hasAllowReciprocal())
1131     return nullptr;
1132
1133   // Try to reassociate C / X expressions where X includes another constant.
1134   Constant *C2, *NewC = nullptr;
1135   if (match(I.getOperand(1), m_FMul(m_Value(X), m_Constant(C2)))) {
1136     // C / (X * C2) --> (C / C2) / X
1137     NewC = ConstantExpr::getFDiv(C, C2);
1138   } else if (match(I.getOperand(1), m_FDiv(m_Value(X), m_Constant(C2)))) {
1139     // C / (X / C2) --> (C * C2) / X
1140     NewC = ConstantExpr::getFMul(C, C2);
1141   }
1142   // Disallow denormal constants because we don't know what would happen
1143   // on all targets.
1144   // TODO: Use Intrinsic::canonicalize or let function attributes tell us that
1145   // denorms are flushed?
1146   if (!NewC || !NewC->isNormalFP())
1147     return nullptr;
1148
1149   return BinaryOperator::CreateFDivFMF(NewC, X, &I);
1150 }
1151
1152 Instruction *InstCombiner::visitFDiv(BinaryOperator &I) {
1153   if (Value *V = SimplifyFDivInst(I.getOperand(0), I.getOperand(1),
1154                                   I.getFastMathFlags(),
1155                                   SQ.getWithInstruction(&I)))
1156     return replaceInstUsesWith(I, V);
1157
1158   if (Instruction *X = foldVectorBinop(I))
1159     return X;
1160
1161   if (Instruction *R = foldFDivConstantDivisor(I))
1162     return R;
1163
1164   if (Instruction *R = foldFDivConstantDividend(I))
1165     return R;
1166
1167   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
1168   if (isa<Constant>(Op0))
1169     if (SelectInst *SI = dyn_cast<SelectInst>(Op1))
1170       if (Instruction *R = FoldOpIntoSelect(I, SI))
1171         return R;
1172
1173   if (isa<Constant>(Op1))
1174     if (SelectInst *SI = dyn_cast<SelectInst>(Op0))
1175       if (Instruction *R = FoldOpIntoSelect(I, SI))
1176         return R;
1177
1178   if (I.hasAllowReassoc() && I.hasAllowReciprocal()) {
1179     Value *X, *Y;
1180     if (match(Op0, m_OneUse(m_FDiv(m_Value(X), m_Value(Y)))) &&
1181         (!isa<Constant>(Y) || !isa<Constant>(Op1))) {
1182       // (X / Y) / Z => X / (Y * Z)
1183       Value *YZ = Builder.CreateFMulFMF(Y, Op1, &I);
1184       return BinaryOperator::CreateFDivFMF(X, YZ, &I);
1185     }
1186     if (match(Op1, m_OneUse(m_FDiv(m_Value(X), m_Value(Y)))) &&
1187         (!isa<Constant>(Y) || !isa<Constant>(Op0))) {
1188       // Z / (X / Y) => (Y * Z) / X
1189       Value *YZ = Builder.CreateFMulFMF(Y, Op0, &I);
1190       return BinaryOperator::CreateFDivFMF(YZ, X, &I);
1191     }
1192   }
1193
1194   if (I.hasAllowReassoc() && Op0->hasOneUse() && Op1->hasOneUse()) {
1195     // sin(X) / cos(X) -> tan(X)
1196     // cos(X) / sin(X) -> 1/tan(X) (cotangent)
1197     Value *X;
1198     bool IsTan = match(Op0, m_Intrinsic<Intrinsic::sin>(m_Value(X))) &&
1199                  match(Op1, m_Intrinsic<Intrinsic::cos>(m_Specific(X)));
1200     bool IsCot =
1201         !IsTan && match(Op0, m_Intrinsic<Intrinsic::cos>(m_Value(X))) &&
1202                   match(Op1, m_Intrinsic<Intrinsic::sin>(m_Specific(X)));
1203
1204     if ((IsTan || IsCot) &&
1205         hasFloatFn(&TLI, I.getType(), LibFunc_tan, LibFunc_tanf, LibFunc_tanl)) {
1206       IRBuilder<> B(&I);
1207       IRBuilder<>::FastMathFlagGuard FMFGuard(B);
1208       B.setFastMathFlags(I.getFastMathFlags());
1209       AttributeList Attrs =
1210           cast<CallBase>(Op0)->getCalledFunction()->getAttributes();
1211       Value *Res = emitUnaryFloatFnCall(X, &TLI, LibFunc_tan, LibFunc_tanf,
1212                                         LibFunc_tanl, B, Attrs);
1213       if (IsCot)
1214         Res = B.CreateFDiv(ConstantFP::get(I.getType(), 1.0), Res);
1215       return replaceInstUsesWith(I, Res);
1216     }
1217   }
1218
1219   // -X / -Y -> X / Y
1220   Value *X, *Y;
1221   if (match(Op0, m_FNeg(m_Value(X))) && match(Op1, m_FNeg(m_Value(Y)))) {
1222     I.setOperand(0, X);
1223     I.setOperand(1, Y);
1224     return &I;
1225   }
1226
1227   // X / (X * Y) --> 1.0 / Y
1228   // Reassociate to (X / X -> 1.0) is legal when NaNs are not allowed.
1229   // We can ignore the possibility that X is infinity because INF/INF is NaN.
1230   if (I.hasNoNaNs() && I.hasAllowReassoc() &&
1231       match(Op1, m_c_FMul(m_Specific(Op0), m_Value(Y)))) {
1232     I.setOperand(0, ConstantFP::get(I.getType(), 1.0));
1233     I.setOperand(1, Y);
1234     return &I;
1235   }
1236
1237   // X / fabs(X) -> copysign(1.0, X)
1238   // fabs(X) / X -> copysign(1.0, X)
1239   if (I.hasNoNaNs() && I.hasNoInfs() &&
1240       (match(&I,
1241              m_FDiv(m_Value(X), m_Intrinsic<Intrinsic::fabs>(m_Deferred(X)))) ||
1242        match(&I, m_FDiv(m_Intrinsic<Intrinsic::fabs>(m_Value(X)),
1243                         m_Deferred(X))))) {
1244     Value *V = Builder.CreateBinaryIntrinsic(
1245         Intrinsic::copysign, ConstantFP::get(I.getType(), 1.0), X, &I);
1246     return replaceInstUsesWith(I, V);
1247   }
1248   return nullptr;
1249 }
1250
1251 /// This function implements the transforms common to both integer remainder
1252 /// instructions (urem and srem). It is called by the visitors to those integer
1253 /// remainder instructions.
1254 /// Common integer remainder transforms
1255 Instruction *InstCombiner::commonIRemTransforms(BinaryOperator &I) {
1256   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
1257
1258   // The RHS is known non-zero.
1259   if (Value *V = simplifyValueKnownNonZero(I.getOperand(1), *this, I)) {
1260     I.setOperand(1, V);
1261     return &I;
1262   }
1263
1264   // Handle cases involving: rem X, (select Cond, Y, Z)
1265   if (simplifyDivRemOfSelectWithZeroOp(I))
1266     return &I;
1267
1268   if (isa<Constant>(Op1)) {
1269     if (Instruction *Op0I = dyn_cast<Instruction>(Op0)) {
1270       if (SelectInst *SI = dyn_cast<SelectInst>(Op0I)) {
1271         if (Instruction *R = FoldOpIntoSelect(I, SI))
1272           return R;
1273       } else if (auto *PN = dyn_cast<PHINode>(Op0I)) {
1274         const APInt *Op1Int;
1275         if (match(Op1, m_APInt(Op1Int)) && !Op1Int->isMinValue() &&
1276             (I.getOpcode() == Instruction::URem ||
1277              !Op1Int->isMinSignedValue())) {
1278           // foldOpIntoPhi will speculate instructions to the end of the PHI's
1279           // predecessor blocks, so do this only if we know the srem or urem
1280           // will not fault.
1281           if (Instruction *NV = foldOpIntoPhi(I, PN))
1282             return NV;
1283         }
1284       }
1285
1286       // See if we can fold away this rem instruction.
1287       if (SimplifyDemandedInstructionBits(I))
1288         return &I;
1289     }
1290   }
1291
1292   return nullptr;
1293 }
1294
1295 Instruction *InstCombiner::visitURem(BinaryOperator &I) {
1296   if (Value *V = SimplifyURemInst(I.getOperand(0), I.getOperand(1),
1297                                   SQ.getWithInstruction(&I)))
1298     return replaceInstUsesWith(I, V);
1299
1300   if (Instruction *X = foldVectorBinop(I))
1301     return X;
1302
1303   if (Instruction *common = commonIRemTransforms(I))
1304     return common;
1305
1306   if (Instruction *NarrowRem = narrowUDivURem(I, Builder))
1307     return NarrowRem;
1308
1309   // X urem Y -> X and Y-1, where Y is a power of 2,
1310   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
1311   Type *Ty = I.getType();
1312   if (isKnownToBeAPowerOfTwo(Op1, /*OrZero*/ true, 0, &I)) {
1313     // This may increase instruction count, we don't enforce that Y is a
1314     // constant.
1315     Constant *N1 = Constant::getAllOnesValue(Ty);
1316     Value *Add = Builder.CreateAdd(Op1, N1);
1317     return BinaryOperator::CreateAnd(Op0, Add);
1318   }
1319
1320   // 1 urem X -> zext(X != 1)
1321   if (match(Op0, m_One()))
1322     return CastInst::CreateZExtOrBitCast(Builder.CreateICmpNE(Op1, Op0), Ty);
1323
1324   // X urem C -> X < C ? X : X - C, where C >= signbit.
1325   if (match(Op1, m_Negative())) {
1326     Value *Cmp = Builder.CreateICmpULT(Op0, Op1);
1327     Value *Sub = Builder.CreateSub(Op0, Op1);
1328     return SelectInst::Create(Cmp, Op0, Sub);
1329   }
1330
1331   // If the divisor is a sext of a boolean, then the divisor must be max
1332   // unsigned value (-1). Therefore, the remainder is Op0 unless Op0 is also
1333   // max unsigned value. In that case, the remainder is 0:
1334   // urem Op0, (sext i1 X) --> (Op0 == -1) ? 0 : Op0
1335   Value *X;
1336   if (match(Op1, m_SExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1)) {
1337     Value *Cmp = Builder.CreateICmpEQ(Op0, ConstantInt::getAllOnesValue(Ty));
1338     return SelectInst::Create(Cmp, ConstantInt::getNullValue(Ty), Op0);
1339   }
1340
1341   return nullptr;
1342 }
1343
1344 Instruction *InstCombiner::visitSRem(BinaryOperator &I) {
1345   if (Value *V = SimplifySRemInst(I.getOperand(0), I.getOperand(1),
1346                                   SQ.getWithInstruction(&I)))
1347     return replaceInstUsesWith(I, V);
1348
1349   if (Instruction *X = foldVectorBinop(I))
1350     return X;
1351
1352   // Handle the integer rem common cases
1353   if (Instruction *Common = commonIRemTransforms(I))
1354     return Common;
1355
1356   Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
1357   {
1358     const APInt *Y;
1359     // X % -Y -> X % Y
1360     if (match(Op1, m_Negative(Y)) && !Y->isMinSignedValue()) {
1361       Worklist.AddValue(I.getOperand(1));
1362       I.setOperand(1, ConstantInt::get(I.getType(), -*Y));
1363       return &I;
1364     }
1365   }
1366
1367   // -X srem Y --> -(X srem Y)
1368   Value *X, *Y;
1369   if (match(&I, m_SRem(m_OneUse(m_NSWSub(m_Zero(), m_Value(X))), m_Value(Y))))
1370     return BinaryOperator::CreateNSWNeg(Builder.CreateSRem(X, Y));
1371
1372   // If the sign bits of both operands are zero (i.e. we can prove they are
1373   // unsigned inputs), turn this into a urem.
1374   APInt Mask(APInt::getSignMask(I.getType()->getScalarSizeInBits()));
1375   if (MaskedValueIsZero(Op1, Mask, 0, &I) &&
1376       MaskedValueIsZero(Op0, Mask, 0, &I)) {
1377     // X srem Y -> X urem Y, iff X and Y don't have sign bit set
1378     return BinaryOperator::CreateURem(Op0, Op1, I.getName());
1379   }
1380
1381   // If it's a constant vector, flip any negative values positive.
1382   if (isa<ConstantVector>(Op1) || isa<ConstantDataVector>(Op1)) {
1383     Constant *C = cast<Constant>(Op1);
1384     unsigned VWidth = C->getType()->getVectorNumElements();
1385
1386     bool hasNegative = false;
1387     bool hasMissing = false;
1388     for (unsigned i = 0; i != VWidth; ++i) {
1389       Constant *Elt = C->getAggregateElement(i);
1390       if (!Elt) {
1391         hasMissing = true;
1392         break;
1393       }
1394
1395       if (ConstantInt *RHS = dyn_cast<ConstantInt>(Elt))
1396         if (RHS->isNegative())
1397           hasNegative = true;
1398     }
1399
1400     if (hasNegative && !hasMissing) {
1401       SmallVector<Constant *, 16> Elts(VWidth);
1402       for (unsigned i = 0; i != VWidth; ++i) {
1403         Elts[i] = C->getAggregateElement(i);  // Handle undef, etc.
1404         if (ConstantInt *RHS = dyn_cast<ConstantInt>(Elts[i])) {
1405           if (RHS->isNegative())
1406             Elts[i] = cast<ConstantInt>(ConstantExpr::getNeg(RHS));
1407         }
1408       }
1409
1410       Constant *NewRHSV = ConstantVector::get(Elts);
1411       if (NewRHSV != C) {  // Don't loop on -MININT
1412         Worklist.AddValue(I.getOperand(1));
1413         I.setOperand(1, NewRHSV);
1414         return &I;
1415       }
1416     }
1417   }
1418
1419   return nullptr;
1420 }
1421
1422 Instruction *InstCombiner::visitFRem(BinaryOperator &I) {
1423   if (Value *V = SimplifyFRemInst(I.getOperand(0), I.getOperand(1),
1424                                   I.getFastMathFlags(),
1425                                   SQ.getWithInstruction(&I)))
1426     return replaceInstUsesWith(I, V);
1427
1428   if (Instruction *X = foldVectorBinop(I))
1429     return X;
1430
1431   return nullptr;
1432 }