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diff --git a/contrib/llvm-project/llvm/lib/Analysis/ValueTracking.cpp b/contrib/llvm-project/llvm/lib/Analysis/ValueTracking.cpp
new file mode 100644
index 000000000000..c70906dcc629
--- /dev/null
+++ b/contrib/llvm-project/llvm/lib/Analysis/ValueTracking.cpp
@@ -0,0 +1,5706 @@
+//===- ValueTracking.cpp - Walk computations to compute properties --------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// This file contains routines that help analyze properties that chains of
+// computations have.
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/ValueTracking.h"
+#include "llvm/ADT/APFloat.h"
+#include "llvm/ADT/APInt.h"
+#include "llvm/ADT/ArrayRef.h"
+#include "llvm/ADT/None.h"
+#include "llvm/ADT/Optional.h"
+#include "llvm/ADT/STLExtras.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include "llvm/ADT/SmallSet.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/ADT/StringRef.h"
+#include "llvm/ADT/iterator_range.h"
+#include "llvm/Analysis/AliasAnalysis.h"
+#include "llvm/Analysis/AssumptionCache.h"
+#include "llvm/Analysis/GuardUtils.h"
+#include "llvm/Analysis/InstructionSimplify.h"
+#include "llvm/Analysis/Loads.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Analysis/OptimizationRemarkEmitter.h"
+#include "llvm/Analysis/TargetLibraryInfo.h"
+#include "llvm/IR/Argument.h"
+#include "llvm/IR/Attributes.h"
+#include "llvm/IR/BasicBlock.h"
+#include "llvm/IR/CallSite.h"
+#include "llvm/IR/Constant.h"
+#include "llvm/IR/ConstantRange.h"
+#include "llvm/IR/Constants.h"
+#include "llvm/IR/DerivedTypes.h"
+#include "llvm/IR/DiagnosticInfo.h"
+#include "llvm/IR/Dominators.h"
+#include "llvm/IR/Function.h"
+#include "llvm/IR/GetElementPtrTypeIterator.h"
+#include "llvm/IR/GlobalAlias.h"
+#include "llvm/IR/GlobalValue.h"
+#include "llvm/IR/GlobalVariable.h"
+#include "llvm/IR/InstrTypes.h"
+#include "llvm/IR/Instruction.h"
+#include "llvm/IR/Instructions.h"
+#include "llvm/IR/IntrinsicInst.h"
+#include "llvm/IR/Intrinsics.h"
+#include "llvm/IR/LLVMContext.h"
+#include "llvm/IR/Metadata.h"
+#include "llvm/IR/Module.h"
+#include "llvm/IR/Operator.h"
+#include "llvm/IR/PatternMatch.h"
+#include "llvm/IR/Type.h"
+#include "llvm/IR/User.h"
+#include "llvm/IR/Value.h"
+#include "llvm/Support/Casting.h"
+#include "llvm/Support/CommandLine.h"
+#include "llvm/Support/Compiler.h"
+#include "llvm/Support/ErrorHandling.h"
+#include "llvm/Support/KnownBits.h"
+#include "llvm/Support/MathExtras.h"
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cstdint>
+#include <iterator>
+#include <utility>
+
+using namespace llvm;
+using namespace llvm::PatternMatch;
+
+const unsigned MaxDepth = 6;
+
+// Controls the number of uses of the value searched for possible
+// dominating comparisons.
+static cl::opt<unsigned> DomConditionsMaxUses("dom-conditions-max-uses",
+                                              cl::Hidden, cl::init(20));
+
+/// Returns the bitwidth of the given scalar or pointer type. For vector types,
+/// returns the element type's bitwidth.
+static unsigned getBitWidth(Type *Ty, const DataLayout &DL) {
+  if (unsigned BitWidth = Ty->getScalarSizeInBits())
+    return BitWidth;
+
+  return DL.getIndexTypeSizeInBits(Ty);
+}
+
+namespace {
+
+// Simplifying using an assume can only be done in a particular control-flow
+// context (the context instruction provides that context). If an assume and
+// the context instruction are not in the same block then the DT helps in
+// figuring out if we can use it.
+struct Query {
+  const DataLayout &DL;
+  AssumptionCache *AC;
+  const Instruction *CxtI;
+  const DominatorTree *DT;
+
+  // Unlike the other analyses, this may be a nullptr because not all clients
+  // provide it currently.
+  OptimizationRemarkEmitter *ORE;
+
+  /// Set of assumptions that should be excluded from further queries.
+  /// This is because of the potential for mutual recursion to cause
+  /// computeKnownBits to repeatedly visit the same assume intrinsic. The
+  /// classic case of this is assume(x = y), which will attempt to determine
+  /// bits in x from bits in y, which will attempt to determine bits in y from
+  /// bits in x, etc. Regarding the mutual recursion, computeKnownBits can call
+  /// isKnownNonZero, which calls computeKnownBits and isKnownToBeAPowerOfTwo
+  /// (all of which can call computeKnownBits), and so on.
+  std::array<const Value *, MaxDepth> Excluded;
+
+  /// If true, it is safe to use metadata during simplification.
+  InstrInfoQuery IIQ;
+
+  unsigned NumExcluded = 0;
+
+  Query(const DataLayout &DL, AssumptionCache *AC, const Instruction *CxtI,
+        const DominatorTree *DT, bool UseInstrInfo,
+        OptimizationRemarkEmitter *ORE = nullptr)
+      : DL(DL), AC(AC), CxtI(CxtI), DT(DT), ORE(ORE), IIQ(UseInstrInfo) {}
+
+  Query(const Query &Q, const Value *NewExcl)
+      : DL(Q.DL), AC(Q.AC), CxtI(Q.CxtI), DT(Q.DT), ORE(Q.ORE), IIQ(Q.IIQ),
+        NumExcluded(Q.NumExcluded) {
+    Excluded = Q.Excluded;
+    Excluded[NumExcluded++] = NewExcl;
+    assert(NumExcluded <= Excluded.size());
+  }
+
+  bool isExcluded(const Value *Value) const {
+    if (NumExcluded == 0)
+      return false;
+    auto End = Excluded.begin() + NumExcluded;
+    return std::find(Excluded.begin(), End, Value) != End;
+  }
+};
+
+} // end anonymous namespace
+
+// Given the provided Value and, potentially, a context instruction, return
+// the preferred context instruction (if any).
+static const Instruction *safeCxtI(const Value *V, const Instruction *CxtI) {
+  // If we've been provided with a context instruction, then use that (provided
+  // it has been inserted).
+  if (CxtI && CxtI->getParent())
+    return CxtI;
+
+  // If the value is really an already-inserted instruction, then use that.
+  CxtI = dyn_cast<Instruction>(V);
+  if (CxtI && CxtI->getParent())
+    return CxtI;
+
+  return nullptr;
+}
+
+static void computeKnownBits(const Value *V, KnownBits &Known,
+                             unsigned Depth, const Query &Q);
+
+void llvm::computeKnownBits(const Value *V, KnownBits &Known,
+                            const DataLayout &DL, unsigned Depth,
+                            AssumptionCache *AC, const Instruction *CxtI,
+                            const DominatorTree *DT,
+                            OptimizationRemarkEmitter *ORE, bool UseInstrInfo) {
+  ::computeKnownBits(V, Known, Depth,
+                     Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo, ORE));
+}
+
+static KnownBits computeKnownBits(const Value *V, unsigned Depth,
+                                  const Query &Q);
+
+KnownBits llvm::computeKnownBits(const Value *V, const DataLayout &DL,
+                                 unsigned Depth, AssumptionCache *AC,
+                                 const Instruction *CxtI,
+                                 const DominatorTree *DT,
+                                 OptimizationRemarkEmitter *ORE,
+                                 bool UseInstrInfo) {
+  return ::computeKnownBits(
+      V, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo, ORE));
+}
+
+bool llvm::haveNoCommonBitsSet(const Value *LHS, const Value *RHS,
+                               const DataLayout &DL, AssumptionCache *AC,
+                               const Instruction *CxtI, const DominatorTree *DT,
+                               bool UseInstrInfo) {
+  assert(LHS->getType() == RHS->getType() &&
+         "LHS and RHS should have the same type");
+  assert(LHS->getType()->isIntOrIntVectorTy() &&
+         "LHS and RHS should be integers");
+  // Look for an inverted mask: (X & ~M) op (Y & M).
+  Value *M;
+  if (match(LHS, m_c_And(m_Not(m_Value(M)), m_Value())) &&
+      match(RHS, m_c_And(m_Specific(M), m_Value())))
+    return true;
+  if (match(RHS, m_c_And(m_Not(m_Value(M)), m_Value())) &&
+      match(LHS, m_c_And(m_Specific(M), m_Value())))
+    return true;
+  IntegerType *IT = cast<IntegerType>(LHS->getType()->getScalarType());
+  KnownBits LHSKnown(IT->getBitWidth());
+  KnownBits RHSKnown(IT->getBitWidth());
+  computeKnownBits(LHS, LHSKnown, DL, 0, AC, CxtI, DT, nullptr, UseInstrInfo);
+  computeKnownBits(RHS, RHSKnown, DL, 0, AC, CxtI, DT, nullptr, UseInstrInfo);
+  return (LHSKnown.Zero | RHSKnown.Zero).isAllOnesValue();
+}
+
+bool llvm::isOnlyUsedInZeroEqualityComparison(const Instruction *CxtI) {
+  for (const User *U : CxtI->users()) {
+    if (const ICmpInst *IC = dyn_cast<ICmpInst>(U))
+      if (IC->isEquality())
+        if (Constant *C = dyn_cast<Constant>(IC->getOperand(1)))
+          if (C->isNullValue())
+            continue;
+    return false;
+  }
+  return true;
+}
+
+static bool isKnownToBeAPowerOfTwo(const Value *V, bool OrZero, unsigned Depth,
+                                   const Query &Q);
+
+bool llvm::isKnownToBeAPowerOfTwo(const Value *V, const DataLayout &DL,
+                                  bool OrZero, unsigned Depth,
+                                  AssumptionCache *AC, const Instruction *CxtI,
+                                  const DominatorTree *DT, bool UseInstrInfo) {
+  return ::isKnownToBeAPowerOfTwo(
+      V, OrZero, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
+}
+
+static bool isKnownNonZero(const Value *V, unsigned Depth, const Query &Q);
+
+bool llvm::isKnownNonZero(const Value *V, const DataLayout &DL, unsigned Depth,
+                          AssumptionCache *AC, const Instruction *CxtI,
+                          const DominatorTree *DT, bool UseInstrInfo) {
+  return ::isKnownNonZero(V, Depth,
+                          Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
+}
+
+bool llvm::isKnownNonNegative(const Value *V, const DataLayout &DL,
+                              unsigned Depth, AssumptionCache *AC,
+                              const Instruction *CxtI, const DominatorTree *DT,
+                              bool UseInstrInfo) {
+  KnownBits Known =
+      computeKnownBits(V, DL, Depth, AC, CxtI, DT, nullptr, UseInstrInfo);
+  return Known.isNonNegative();
+}
+
+bool llvm::isKnownPositive(const Value *V, const DataLayout &DL, unsigned Depth,
+                           AssumptionCache *AC, const Instruction *CxtI,
+                           const DominatorTree *DT, bool UseInstrInfo) {
+  if (auto *CI = dyn_cast<ConstantInt>(V))
+    return CI->getValue().isStrictlyPositive();
+
+  // TODO: We'd doing two recursive queries here.  We should factor this such
+  // that only a single query is needed.
+  return isKnownNonNegative(V, DL, Depth, AC, CxtI, DT, UseInstrInfo) &&
+         isKnownNonZero(V, DL, Depth, AC, CxtI, DT, UseInstrInfo);
+}
+
+bool llvm::isKnownNegative(const Value *V, const DataLayout &DL, unsigned Depth,
+                           AssumptionCache *AC, const Instruction *CxtI,
+                           const DominatorTree *DT, bool UseInstrInfo) {
+  KnownBits Known =
+      computeKnownBits(V, DL, Depth, AC, CxtI, DT, nullptr, UseInstrInfo);
+  return Known.isNegative();
+}
+
+static bool isKnownNonEqual(const Value *V1, const Value *V2, const Query &Q);
+
+bool llvm::isKnownNonEqual(const Value *V1, const Value *V2,
+                           const DataLayout &DL, AssumptionCache *AC,
+                           const Instruction *CxtI, const DominatorTree *DT,
+                           bool UseInstrInfo) {
+  return ::isKnownNonEqual(V1, V2,
+                           Query(DL, AC, safeCxtI(V1, safeCxtI(V2, CxtI)), DT,
+                                 UseInstrInfo, /*ORE=*/nullptr));
+}
+
+static bool MaskedValueIsZero(const Value *V, const APInt &Mask, unsigned Depth,
+                              const Query &Q);
+
+bool llvm::MaskedValueIsZero(const Value *V, const APInt &Mask,
+                             const DataLayout &DL, unsigned Depth,
+                             AssumptionCache *AC, const Instruction *CxtI,
+                             const DominatorTree *DT, bool UseInstrInfo) {
+  return ::MaskedValueIsZero(
+      V, Mask, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
+}
+
+static unsigned ComputeNumSignBits(const Value *V, unsigned Depth,
+                                   const Query &Q);
+
+unsigned llvm::ComputeNumSignBits(const Value *V, const DataLayout &DL,
+                                  unsigned Depth, AssumptionCache *AC,
+                                  const Instruction *CxtI,
+                                  const DominatorTree *DT, bool UseInstrInfo) {
+  return ::ComputeNumSignBits(
+      V, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
+}
+
+static void computeKnownBitsAddSub(bool Add, const Value *Op0, const Value *Op1,
+                                   bool NSW,
+                                   KnownBits &KnownOut, KnownBits &Known2,
+                                   unsigned Depth, const Query &Q) {
+  unsigned BitWidth = KnownOut.getBitWidth();
+
+  // If an initial sequence of bits in the result is not needed, the
+  // corresponding bits in the operands are not needed.
+  KnownBits LHSKnown(BitWidth);
+  computeKnownBits(Op0, LHSKnown, Depth + 1, Q);
+  computeKnownBits(Op1, Known2, Depth + 1, Q);
+
+  KnownOut = KnownBits::computeForAddSub(Add, NSW, LHSKnown, Known2);
+}
+
+static void computeKnownBitsMul(const Value *Op0, const Value *Op1, bool NSW,
+                                KnownBits &Known, KnownBits &Known2,
+                                unsigned Depth, const Query &Q) {
+  unsigned BitWidth = Known.getBitWidth();
+  computeKnownBits(Op1, Known, Depth + 1, Q);
+  computeKnownBits(Op0, Known2, Depth + 1, Q);
+
+  bool isKnownNegative = false;
+  bool isKnownNonNegative = false;
+  // If the multiplication is known not to overflow, compute the sign bit.
+  if (NSW) {
+    if (Op0 == Op1) {
+      // The product of a number with itself is non-negative.
+      isKnownNonNegative = true;
+    } else {
+      bool isKnownNonNegativeOp1 = Known.isNonNegative();
+      bool isKnownNonNegativeOp0 = Known2.isNonNegative();
+      bool isKnownNegativeOp1 = Known.isNegative();
+      bool isKnownNegativeOp0 = Known2.isNegative();
+      // The product of two numbers with the same sign is non-negative.
+      isKnownNonNegative = (isKnownNegativeOp1 && isKnownNegativeOp0) ||
+        (isKnownNonNegativeOp1 && isKnownNonNegativeOp0);
+      // The product of a negative number and a non-negative number is either
+      // negative or zero.
+      if (!isKnownNonNegative)
+        isKnownNegative = (isKnownNegativeOp1 && isKnownNonNegativeOp0 &&
+                           isKnownNonZero(Op0, Depth, Q)) ||
+                          (isKnownNegativeOp0 && isKnownNonNegativeOp1 &&
+                           isKnownNonZero(Op1, Depth, Q));
+    }
+  }
+
+  assert(!Known.hasConflict() && !Known2.hasConflict());
+  // Compute a conservative estimate for high known-0 bits.
+  unsigned LeadZ =  std::max(Known.countMinLeadingZeros() +
+                             Known2.countMinLeadingZeros(),
+                             BitWidth) - BitWidth;
+  LeadZ = std::min(LeadZ, BitWidth);
+
+  // The result of the bottom bits of an integer multiply can be
+  // inferred by looking at the bottom bits of both operands and
+  // multiplying them together.
+  // We can infer at least the minimum number of known trailing bits
+  // of both operands. Depending on number of trailing zeros, we can
+  // infer more bits, because (a*b) <=> ((a/m) * (b/n)) * (m*n) assuming
+  // a and b are divisible by m and n respectively.
+  // We then calculate how many of those bits are inferrable and set
+  // the output. For example, the i8 mul:
+  //  a = XXXX1100 (12)
+  //  b = XXXX1110 (14)
+  // We know the bottom 3 bits are zero since the first can be divided by
+  // 4 and the second by 2, thus having ((12/4) * (14/2)) * (2*4).
+  // Applying the multiplication to the trimmed arguments gets:
+  //    XX11 (3)
+  //    X111 (7)
+  // -------
+  //    XX11
+  //   XX11
+  //  XX11
+  // XX11
+  // -------
+  // XXXXX01
+  // Which allows us to infer the 2 LSBs. Since we're multiplying the result
+  // by 8, the bottom 3 bits will be 0, so we can infer a total of 5 bits.
+  // The proof for this can be described as:
+  // Pre: (C1 >= 0) && (C1 < (1 << C5)) && (C2 >= 0) && (C2 < (1 << C6)) &&
+  //      (C7 == (1 << (umin(countTrailingZeros(C1), C5) +
+  //                    umin(countTrailingZeros(C2), C6) +
+  //                    umin(C5 - umin(countTrailingZeros(C1), C5),
+  //                         C6 - umin(countTrailingZeros(C2), C6)))) - 1)
+  // %aa = shl i8 %a, C5
+  // %bb = shl i8 %b, C6
+  // %aaa = or i8 %aa, C1
+  // %bbb = or i8 %bb, C2
+  // %mul = mul i8 %aaa, %bbb
+  // %mask = and i8 %mul, C7
+  //   =>
+  // %mask = i8 ((C1*C2)&C7)
+  // Where C5, C6 describe the known bits of %a, %b
+  // C1, C2 describe the known bottom bits of %a, %b.
+  // C7 describes the mask of the known bits of the result.
+  APInt Bottom0 = Known.One;
+  APInt Bottom1 = Known2.One;
+
+  // How many times we'd be able to divide each argument by 2 (shr by 1).
+  // This gives us the number of trailing zeros on the multiplication result.
+  unsigned TrailBitsKnown0 = (Known.Zero | Known.One).countTrailingOnes();
+  unsigned TrailBitsKnown1 = (Known2.Zero | Known2.One).countTrailingOnes();
+  unsigned TrailZero0 = Known.countMinTrailingZeros();
+  unsigned TrailZero1 = Known2.countMinTrailingZeros();
+  unsigned TrailZ = TrailZero0 + TrailZero1;
+
+  // Figure out the fewest known-bits operand.
+  unsigned SmallestOperand = std::min(TrailBitsKnown0 - TrailZero0,
+                                      TrailBitsKnown1 - TrailZero1);
+  unsigned ResultBitsKnown = std::min(SmallestOperand + TrailZ, BitWidth);
+
+  APInt BottomKnown = Bottom0.getLoBits(TrailBitsKnown0) *
+                      Bottom1.getLoBits(TrailBitsKnown1);
+
+  Known.resetAll();
+  Known.Zero.setHighBits(LeadZ);
+  Known.Zero |= (~BottomKnown).getLoBits(ResultBitsKnown);
+  Known.One |= BottomKnown.getLoBits(ResultBitsKnown);
+
+  // Only make use of no-wrap flags if we failed to compute the sign bit
+  // directly.  This matters if the multiplication always overflows, in
+  // which case we prefer to follow the result of the direct computation,
+  // though as the program is invoking undefined behaviour we can choose
+  // whatever we like here.
+  if (isKnownNonNegative && !Known.isNegative())
+    Known.makeNonNegative();
+  else if (isKnownNegative && !Known.isNonNegative())
+    Known.makeNegative();
+}
+
+void llvm::computeKnownBitsFromRangeMetadata(const MDNode &Ranges,
+                                             KnownBits &Known) {
+  unsigned BitWidth = Known.getBitWidth();
+  unsigned NumRanges = Ranges.getNumOperands() / 2;
+  assert(NumRanges >= 1);
+
+  Known.Zero.setAllBits();
+  Known.One.setAllBits();
+
+  for (unsigned i = 0; i < NumRanges; ++i) {
+    ConstantInt *Lower =
+        mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 0));
+    ConstantInt *Upper =
+        mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 1));
+    ConstantRange Range(Lower->getValue(), Upper->getValue());
+
+    // The first CommonPrefixBits of all values in Range are equal.
+    unsigned CommonPrefixBits =
+        (Range.getUnsignedMax() ^ Range.getUnsignedMin()).countLeadingZeros();
+
+    APInt Mask = APInt::getHighBitsSet(BitWidth, CommonPrefixBits);
+    Known.One &= Range.getUnsignedMax() & Mask;
+    Known.Zero &= ~Range.getUnsignedMax() & Mask;
+  }
+}
+
+static bool isEphemeralValueOf(const Instruction *I, const Value *E) {
+  SmallVector<const Value *, 16> WorkSet(1, I);
+  SmallPtrSet<const Value *, 32> Visited;
+  SmallPtrSet<const Value *, 16> EphValues;
+
+  // The instruction defining an assumption's condition itself is always
+  // considered ephemeral to that assumption (even if it has other
+  // non-ephemeral users). See r246696's test case for an example.
+  if (is_contained(I->operands(), E))
+    return true;
+
+  while (!WorkSet.empty()) {
+    const Value *V = WorkSet.pop_back_val();
+    if (!Visited.insert(V).second)
+      continue;
+
+    // If all uses of this value are ephemeral, then so is this value.
+    if (llvm::all_of(V->users(), [&](const User *U) {
+                                   return EphValues.count(U);
+                                 })) {
+      if (V == E)
+        return true;
+
+      if (V == I || isSafeToSpeculativelyExecute(V)) {
+       EphValues.insert(V);
+       if (const User *U = dyn_cast<User>(V))
+         for (User::const_op_iterator J = U->op_begin(), JE = U->op_end();
+              J != JE; ++J)
+           WorkSet.push_back(*J);
+      }
+    }
+  }
+
+  return false;
+}
+
+// Is this an intrinsic that cannot be speculated but also cannot trap?
+bool llvm::isAssumeLikeIntrinsic(const Instruction *I) {
+  if (const CallInst *CI = dyn_cast<CallInst>(I))
+    if (Function *F = CI->getCalledFunction())
+      switch (F->getIntrinsicID()) {
+      default: break;
+      // FIXME: This list is repeated from NoTTI::getIntrinsicCost.
+      case Intrinsic::assume:
+      case Intrinsic::sideeffect:
+      case Intrinsic::dbg_declare:
+      case Intrinsic::dbg_value:
+      case Intrinsic::dbg_label:
+      case Intrinsic::invariant_start:
+      case Intrinsic::invariant_end:
+      case Intrinsic::lifetime_start:
+      case Intrinsic::lifetime_end:
+      case Intrinsic::objectsize:
+      case Intrinsic::ptr_annotation:
+      case Intrinsic::var_annotation:
+        return true;
+      }
+
+  return false;
+}
+
+bool llvm::isValidAssumeForContext(const Instruction *Inv,
+                                   const Instruction *CxtI,
+                                   const DominatorTree *DT) {
+  // There are two restrictions on the use of an assume:
+  //  1. The assume must dominate the context (or the control flow must
+  //     reach the assume whenever it reaches the context).
+  //  2. The context must not be in the assume's set of ephemeral values
+  //     (otherwise we will use the assume to prove that the condition
+  //     feeding the assume is trivially true, thus causing the removal of
+  //     the assume).
+
+  if (DT) {
+    if (DT->dominates(Inv, CxtI))
+      return true;
+  } else if (Inv->getParent() == CxtI->getParent()->getSinglePredecessor()) {
+    // We don't have a DT, but this trivially dominates.
+    return true;
+  }
+
+  // With or without a DT, the only remaining case we will check is if the
+  // instructions are in the same BB.  Give up if that is not the case.
+  if (Inv->getParent() != CxtI->getParent())
+    return false;
+
+  // If we have a dom tree, then we now know that the assume doesn't dominate
+  // the other instruction.  If we don't have a dom tree then we can check if
+  // the assume is first in the BB.
+  if (!DT) {
+    // Search forward from the assume until we reach the context (or the end
+    // of the block); the common case is that the assume will come first.
+    for (auto I = std::next(BasicBlock::const_iterator(Inv)),
+         IE = Inv->getParent()->end(); I != IE; ++I)
+      if (&*I == CxtI)
+        return true;
+  }
+
+  // The context comes first, but they're both in the same block. Make sure
+  // there is nothing in between that might interrupt the control flow.
+  for (BasicBlock::const_iterator I =
+         std::next(BasicBlock::const_iterator(CxtI)), IE(Inv);
+       I != IE; ++I)
+    if (!isSafeToSpeculativelyExecute(&*I) && !isAssumeLikeIntrinsic(&*I))
+      return false;
+
+  return !isEphemeralValueOf(Inv, CxtI);
+}
+
+static void computeKnownBitsFromAssume(const Value *V, KnownBits &Known,
+                                       unsigned Depth, const Query &Q) {
+  // Use of assumptions is context-sensitive. If we don't have a context, we
+  // cannot use them!
+  if (!Q.AC || !Q.CxtI)
+    return;
+
+  unsigned BitWidth = Known.getBitWidth();
+
+  // Note that the patterns below need to be kept in sync with the code
+  // in AssumptionCache::updateAffectedValues.
+
+  for (auto &AssumeVH : Q.AC->assumptionsFor(V)) {
+    if (!AssumeVH)
+      continue;
+    CallInst *I = cast<CallInst>(AssumeVH);
+    assert(I->getParent()->getParent() == Q.CxtI->getParent()->getParent() &&
+           "Got assumption for the wrong function!");
+    if (Q.isExcluded(I))
+      continue;
+
+    // Warning: This loop can end up being somewhat performance sensitive.
+    // We're running this loop for once for each value queried resulting in a
+    // runtime of ~O(#assumes * #values).
+
+    assert(I->getCalledFunction()->getIntrinsicID() == Intrinsic::assume &&
+           "must be an assume intrinsic");
+
+    Value *Arg = I->getArgOperand(0);
+
+    if (Arg == V && isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+      assert(BitWidth == 1 && "assume operand is not i1?");
+      Known.setAllOnes();
+      return;
+    }
+    if (match(Arg, m_Not(m_Specific(V))) &&
+        isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+      assert(BitWidth == 1 && "assume operand is not i1?");
+      Known.setAllZero();
+      return;
+    }
+
+    // The remaining tests are all recursive, so bail out if we hit the limit.
+    if (Depth == MaxDepth)
+      continue;
+
+    ICmpInst *Cmp = dyn_cast<ICmpInst>(Arg);
+    if (!Cmp)
+      continue;
+
+    Value *A, *B;
+    auto m_V = m_CombineOr(m_Specific(V), m_PtrToInt(m_Specific(V)));
+
+    CmpInst::Predicate Pred;
+    uint64_t C;
+    switch (Cmp->getPredicate()) {
+    default:
+      break;
+    case ICmpInst::ICMP_EQ:
+      // assume(v = a)
+      if (match(Cmp, m_c_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        Known.Zero |= RHSKnown.Zero;
+        Known.One  |= RHSKnown.One;
+      // assume(v & b = a)
+      } else if (match(Cmp,
+                       m_c_ICmp(Pred, m_c_And(m_V, m_Value(B)), m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        KnownBits MaskKnown(BitWidth);
+        computeKnownBits(B, MaskKnown, Depth+1, Query(Q, I));
+
+        // For those bits in the mask that are known to be one, we can propagate
+        // known bits from the RHS to V.
+        Known.Zero |= RHSKnown.Zero & MaskKnown.One;
+        Known.One  |= RHSKnown.One  & MaskKnown.One;
+      // assume(~(v & b) = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_c_And(m_V, m_Value(B))),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        KnownBits MaskKnown(BitWidth);
+        computeKnownBits(B, MaskKnown, Depth+1, Query(Q, I));
+
+        // For those bits in the mask that are known to be one, we can propagate
+        // inverted known bits from the RHS to V.
+        Known.Zero |= RHSKnown.One  & MaskKnown.One;
+        Known.One  |= RHSKnown.Zero & MaskKnown.One;
+      // assume(v | b = a)
+      } else if (match(Cmp,
+                       m_c_ICmp(Pred, m_c_Or(m_V, m_Value(B)), m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        KnownBits BKnown(BitWidth);
+        computeKnownBits(B, BKnown, Depth+1, Query(Q, I));
+
+        // For those bits in B that are known to be zero, we can propagate known
+        // bits from the RHS to V.
+        Known.Zero |= RHSKnown.Zero & BKnown.Zero;
+        Known.One  |= RHSKnown.One  & BKnown.Zero;
+      // assume(~(v | b) = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_c_Or(m_V, m_Value(B))),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        KnownBits BKnown(BitWidth);
+        computeKnownBits(B, BKnown, Depth+1, Query(Q, I));
+
+        // For those bits in B that are known to be zero, we can propagate
+        // inverted known bits from the RHS to V.
+        Known.Zero |= RHSKnown.One  & BKnown.Zero;
+        Known.One  |= RHSKnown.Zero & BKnown.Zero;
+      // assume(v ^ b = a)
+      } else if (match(Cmp,
+                       m_c_ICmp(Pred, m_c_Xor(m_V, m_Value(B)), m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        KnownBits BKnown(BitWidth);
+        computeKnownBits(B, BKnown, Depth+1, Query(Q, I));
+
+        // For those bits in B that are known to be zero, we can propagate known
+        // bits from the RHS to V. For those bits in B that are known to be one,
+        // we can propagate inverted known bits from the RHS to V.
+        Known.Zero |= RHSKnown.Zero & BKnown.Zero;
+        Known.One  |= RHSKnown.One  & BKnown.Zero;
+        Known.Zero |= RHSKnown.One  & BKnown.One;
+        Known.One  |= RHSKnown.Zero & BKnown.One;
+      // assume(~(v ^ b) = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_c_Xor(m_V, m_Value(B))),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        KnownBits BKnown(BitWidth);
+        computeKnownBits(B, BKnown, Depth+1, Query(Q, I));
+
+        // For those bits in B that are known to be zero, we can propagate
+        // inverted known bits from the RHS to V. For those bits in B that are
+        // known to be one, we can propagate known bits from the RHS to V.
+        Known.Zero |= RHSKnown.One  & BKnown.Zero;
+        Known.One  |= RHSKnown.Zero & BKnown.Zero;
+        Known.Zero |= RHSKnown.Zero & BKnown.One;
+        Known.One  |= RHSKnown.One  & BKnown.One;
+      // assume(v << c = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Shl(m_V, m_ConstantInt(C)),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        // For those bits in RHS that are known, we can propagate them to known
+        // bits in V shifted to the right by C.
+        RHSKnown.Zero.lshrInPlace(C);
+        Known.Zero |= RHSKnown.Zero;
+        RHSKnown.One.lshrInPlace(C);
+        Known.One  |= RHSKnown.One;
+      // assume(~(v << c) = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_Shl(m_V, m_ConstantInt(C))),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        // For those bits in RHS that are known, we can propagate them inverted
+        // to known bits in V shifted to the right by C.
+        RHSKnown.One.lshrInPlace(C);
+        Known.Zero |= RHSKnown.One;
+        RHSKnown.Zero.lshrInPlace(C);
+        Known.One  |= RHSKnown.Zero;
+      // assume(v >> c = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Shr(m_V, m_ConstantInt(C)),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        // For those bits in RHS that are known, we can propagate them to known
+        // bits in V shifted to the right by C.
+        Known.Zero |= RHSKnown.Zero << C;
+        Known.One  |= RHSKnown.One  << C;
+      // assume(~(v >> c) = a)
+      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_Shr(m_V, m_ConstantInt(C))),
+                                     m_Value(A))) &&
+                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+        // For those bits in RHS that are known, we can propagate them inverted
+        // to known bits in V shifted to the right by C.
+        Known.Zero |= RHSKnown.One  << C;
+        Known.One  |= RHSKnown.Zero << C;
+      }
+      break;
+    case ICmpInst::ICMP_SGE:
+      // assume(v >=_s c) where c is non-negative
+      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth + 1, Query(Q, I));
+
+        if (RHSKnown.isNonNegative()) {
+          // We know that the sign bit is zero.
+          Known.makeNonNegative();
+        }
+      }
+      break;
+    case ICmpInst::ICMP_SGT:
+      // assume(v >_s c) where c is at least -1.
+      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth + 1, Query(Q, I));
+
+        if (RHSKnown.isAllOnes() || RHSKnown.isNonNegative()) {
+          // We know that the sign bit is zero.
+          Known.makeNonNegative();
+        }
+      }
+      break;
+    case ICmpInst::ICMP_SLE:
+      // assume(v <=_s c) where c is negative
+      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth + 1, Query(Q, I));
+
+        if (RHSKnown.isNegative()) {
+          // We know that the sign bit is one.
+          Known.makeNegative();
+        }
+      }
+      break;
+    case ICmpInst::ICMP_SLT:
+      // assume(v <_s c) where c is non-positive
+      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+
+        if (RHSKnown.isZero() || RHSKnown.isNegative()) {
+          // We know that the sign bit is one.
+          Known.makeNegative();
+        }
+      }
+      break;
+    case ICmpInst::ICMP_ULE:
+      // assume(v <=_u c)
+      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+
+        // Whatever high bits in c are zero are known to be zero.
+        Known.Zero.setHighBits(RHSKnown.countMinLeadingZeros());
+      }
+      break;
+    case ICmpInst::ICMP_ULT:
+      // assume(v <_u c)
+      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
+          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
+        KnownBits RHSKnown(BitWidth);
+        computeKnownBits(A, RHSKnown, Depth+1, Query(Q, I));
+
+        // If the RHS is known zero, then this assumption must be wrong (nothing
+        // is unsigned less than zero). Signal a conflict and get out of here.
+        if (RHSKnown.isZero()) {
+          Known.Zero.setAllBits();
+          Known.One.setAllBits();
+          break;
+        }
+
+        // Whatever high bits in c are zero are known to be zero (if c is a power
+        // of 2, then one more).
+        if (isKnownToBeAPowerOfTwo(A, false, Depth + 1, Query(Q, I)))
+          Known.Zero.setHighBits(RHSKnown.countMinLeadingZeros() + 1);
+        else
+          Known.Zero.setHighBits(RHSKnown.countMinLeadingZeros());
+      }
+      break;
+    }
+  }
+
+  // If assumptions conflict with each other or previous known bits, then we
+  // have a logical fallacy. It's possible that the assumption is not reachable,
+  // so this isn't a real bug. On the other hand, the program may have undefined
+  // behavior, or we might have a bug in the compiler. We can't assert/crash, so
+  // clear out the known bits, try to warn the user, and hope for the best.
+  if (Known.Zero.intersects(Known.One)) {
+    Known.resetAll();
+
+    if (Q.ORE)
+      Q.ORE->emit([&]() {
+        auto *CxtI = const_cast<Instruction *>(Q.CxtI);
+        return OptimizationRemarkAnalysis("value-tracking", "BadAssumption",
+                                          CxtI)
+               << "Detected conflicting code assumptions. Program may "
+                  "have undefined behavior, or compiler may have "
+                  "internal error.";
+      });
+  }
+}
+
+/// Compute known bits from a shift operator, including those with a
+/// non-constant shift amount. Known is the output of this function. Known2 is a
+/// pre-allocated temporary with the same bit width as Known. KZF and KOF are
+/// operator-specific functions that, given the known-zero or known-one bits
+/// respectively, and a shift amount, compute the implied known-zero or
+/// known-one bits of the shift operator's result respectively for that shift
+/// amount. The results from calling KZF and KOF are conservatively combined for
+/// all permitted shift amounts.
+static void computeKnownBitsFromShiftOperator(
+    const Operator *I, KnownBits &Known, KnownBits &Known2,
+    unsigned Depth, const Query &Q,
+    function_ref<APInt(const APInt &, unsigned)> KZF,
+    function_ref<APInt(const APInt &, unsigned)> KOF) {
+  unsigned BitWidth = Known.getBitWidth();
+
+  if (auto *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
+    unsigned ShiftAmt = SA->getLimitedValue(BitWidth-1);
+
+    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+    Known.Zero = KZF(Known.Zero, ShiftAmt);
+    Known.One  = KOF(Known.One, ShiftAmt);
+    // If the known bits conflict, this must be an overflowing left shift, so
+    // the shift result is poison. We can return anything we want. Choose 0 for
+    // the best folding opportunity.
+    if (Known.hasConflict())
+      Known.setAllZero();
+
+    return;
+  }
+
+  computeKnownBits(I->getOperand(1), Known, Depth + 1, Q);
+
+  // If the shift amount could be greater than or equal to the bit-width of the
+  // LHS, the value could be poison, but bail out because the check below is
+  // expensive. TODO: Should we just carry on?
+  if ((~Known.Zero).uge(BitWidth)) {
+    Known.resetAll();
+    return;
+  }
+
+  // Note: We cannot use Known.Zero.getLimitedValue() here, because if
+  // BitWidth > 64 and any upper bits are known, we'll end up returning the
+  // limit value (which implies all bits are known).
+  uint64_t ShiftAmtKZ = Known.Zero.zextOrTrunc(64).getZExtValue();
+  uint64_t ShiftAmtKO = Known.One.zextOrTrunc(64).getZExtValue();
+
+  // It would be more-clearly correct to use the two temporaries for this
+  // calculation. Reusing the APInts here to prevent unnecessary allocations.
+  Known.resetAll();
+
+  // If we know the shifter operand is nonzero, we can sometimes infer more
+  // known bits. However this is expensive to compute, so be lazy about it and
+  // only compute it when absolutely necessary.
+  Optional<bool> ShifterOperandIsNonZero;
+
+  // Early exit if we can't constrain any well-defined shift amount.
+  if (!(ShiftAmtKZ & (PowerOf2Ceil(BitWidth) - 1)) &&
+      !(ShiftAmtKO & (PowerOf2Ceil(BitWidth) - 1))) {
+    ShifterOperandIsNonZero = isKnownNonZero(I->getOperand(1), Depth + 1, Q);
+    if (!*ShifterOperandIsNonZero)
+      return;
+  }
+
+  computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+
+  Known.Zero.setAllBits();
+  Known.One.setAllBits();
+  for (unsigned ShiftAmt = 0; ShiftAmt < BitWidth; ++ShiftAmt) {
+    // Combine the shifted known input bits only for those shift amounts
+    // compatible with its known constraints.
+    if ((ShiftAmt & ~ShiftAmtKZ) != ShiftAmt)
+      continue;
+    if ((ShiftAmt | ShiftAmtKO) != ShiftAmt)
+      continue;
+    // If we know the shifter is nonzero, we may be able to infer more known
+    // bits. This check is sunk down as far as possible to avoid the expensive
+    // call to isKnownNonZero if the cheaper checks above fail.
+    if (ShiftAmt == 0) {
+      if (!ShifterOperandIsNonZero.hasValue())
+        ShifterOperandIsNonZero =
+            isKnownNonZero(I->getOperand(1), Depth + 1, Q);
+      if (*ShifterOperandIsNonZero)
+        continue;
+    }
+
+    Known.Zero &= KZF(Known2.Zero, ShiftAmt);
+    Known.One  &= KOF(Known2.One, ShiftAmt);
+  }
+
+  // If the known bits conflict, the result is poison. Return a 0 and hope the
+  // caller can further optimize that.
+  if (Known.hasConflict())
+    Known.setAllZero();
+}
+
+static void computeKnownBitsFromOperator(const Operator *I, KnownBits &Known,
+                                         unsigned Depth, const Query &Q) {
+  unsigned BitWidth = Known.getBitWidth();
+
+  KnownBits Known2(Known);
+  switch (I->getOpcode()) {
+  default: break;
+  case Instruction::Load:
+    if (MDNode *MD =
+            Q.IIQ.getMetadata(cast<LoadInst>(I), LLVMContext::MD_range))
+      computeKnownBitsFromRangeMetadata(*MD, Known);
+    break;
+  case Instruction::And: {
+    // If either the LHS or the RHS are Zero, the result is zero.
+    computeKnownBits(I->getOperand(1), Known, Depth + 1, Q);
+    computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+
+    // Output known-1 bits are only known if set in both the LHS & RHS.
+    Known.One &= Known2.One;
+    // Output known-0 are known to be clear if zero in either the LHS | RHS.
+    Known.Zero |= Known2.Zero;
+
+    // and(x, add (x, -1)) is a common idiom that always clears the low bit;
+    // here we handle the more general case of adding any odd number by
+    // matching the form add(x, add(x, y)) where y is odd.
+    // TODO: This could be generalized to clearing any bit set in y where the
+    // following bit is known to be unset in y.
+    Value *X = nullptr, *Y = nullptr;
+    if (!Known.Zero[0] && !Known.One[0] &&
+        match(I, m_c_BinOp(m_Value(X), m_Add(m_Deferred(X), m_Value(Y))))) {
+      Known2.resetAll();
+      computeKnownBits(Y, Known2, Depth + 1, Q);
+      if (Known2.countMinTrailingOnes() > 0)
+        Known.Zero.setBit(0);
+    }
+    break;
+  }
+  case Instruction::Or:
+    computeKnownBits(I->getOperand(1), Known, Depth + 1, Q);
+    computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+
+    // Output known-0 bits are only known if clear in both the LHS & RHS.
+    Known.Zero &= Known2.Zero;
+    // Output known-1 are known to be set if set in either the LHS | RHS.
+    Known.One |= Known2.One;
+    break;
+  case Instruction::Xor: {
+    computeKnownBits(I->getOperand(1), Known, Depth + 1, Q);
+    computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+
+    // Output known-0 bits are known if clear or set in both the LHS & RHS.
+    APInt KnownZeroOut = (Known.Zero & Known2.Zero) | (Known.One & Known2.One);
+    // Output known-1 are known to be set if set in only one of the LHS, RHS.
+    Known.One = (Known.Zero & Known2.One) | (Known.One & Known2.Zero);
+    Known.Zero = std::move(KnownZeroOut);
+    break;
+  }
+  case Instruction::Mul: {
+    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
+    computeKnownBitsMul(I->getOperand(0), I->getOperand(1), NSW, Known,
+                        Known2, Depth, Q);
+    break;
+  }
+  case Instruction::UDiv: {
+    // For the purposes of computing leading zeros we can conservatively
+    // treat a udiv as a logical right shift by the power of 2 known to
+    // be less than the denominator.
+    computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+    unsigned LeadZ = Known2.countMinLeadingZeros();
+
+    Known2.resetAll();
+    computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
+    unsigned RHSMaxLeadingZeros = Known2.countMaxLeadingZeros();
+    if (RHSMaxLeadingZeros != BitWidth)
+      LeadZ = std::min(BitWidth, LeadZ + BitWidth - RHSMaxLeadingZeros - 1);
+
+    Known.Zero.setHighBits(LeadZ);
+    break;
+  }
+  case Instruction::Select: {
+    const Value *LHS, *RHS;
+    SelectPatternFlavor SPF = matchSelectPattern(I, LHS, RHS).Flavor;
+    if (SelectPatternResult::isMinOrMax(SPF)) {
+      computeKnownBits(RHS, Known, Depth + 1, Q);
+      computeKnownBits(LHS, Known2, Depth + 1, Q);
+    } else {
+      computeKnownBits(I->getOperand(2), Known, Depth + 1, Q);
+      computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
+    }
+
+    unsigned MaxHighOnes = 0;
+    unsigned MaxHighZeros = 0;
+    if (SPF == SPF_SMAX) {
+      // If both sides are negative, the result is negative.
+      if (Known.isNegative() && Known2.isNegative())
+        // We can derive a lower bound on the result by taking the max of the
+        // leading one bits.
+        MaxHighOnes =
+            std::max(Known.countMinLeadingOnes(), Known2.countMinLeadingOnes());
+      // If either side is non-negative, the result is non-negative.
+      else if (Known.isNonNegative() || Known2.isNonNegative())
+        MaxHighZeros = 1;
+    } else if (SPF == SPF_SMIN) {
+      // If both sides are non-negative, the result is non-negative.
+      if (Known.isNonNegative() && Known2.isNonNegative())
+        // We can derive an upper bound on the result by taking the max of the
+        // leading zero bits.
+        MaxHighZeros = std::max(Known.countMinLeadingZeros(),
+                                Known2.countMinLeadingZeros());
+      // If either side is negative, the result is negative.
+      else if (Known.isNegative() || Known2.isNegative())
+        MaxHighOnes = 1;
+    } else if (SPF == SPF_UMAX) {
+      // We can derive a lower bound on the result by taking the max of the
+      // leading one bits.
+      MaxHighOnes =
+          std::max(Known.countMinLeadingOnes(), Known2.countMinLeadingOnes());
+    } else if (SPF == SPF_UMIN) {
+      // We can derive an upper bound on the result by taking the max of the
+      // leading zero bits.
+      MaxHighZeros =
+          std::max(Known.countMinLeadingZeros(), Known2.countMinLeadingZeros());
+    } else if (SPF == SPF_ABS) {
+      // RHS from matchSelectPattern returns the negation part of abs pattern.
+      // If the negate has an NSW flag we can assume the sign bit of the result
+      // will be 0 because that makes abs(INT_MIN) undefined.
+      if (Q.IIQ.hasNoSignedWrap(cast<Instruction>(RHS)))
+        MaxHighZeros = 1;
+    }
+
+    // Only known if known in both the LHS and RHS.
+    Known.One &= Known2.One;
+    Known.Zero &= Known2.Zero;
+    if (MaxHighOnes > 0)
+      Known.One.setHighBits(MaxHighOnes);
+    if (MaxHighZeros > 0)
+      Known.Zero.setHighBits(MaxHighZeros);
+    break;
+  }
+  case Instruction::FPTrunc:
+  case Instruction::FPExt:
+  case Instruction::FPToUI:
+  case Instruction::FPToSI:
+  case Instruction::SIToFP:
+  case Instruction::UIToFP:
+    break; // Can't work with floating point.
+  case Instruction::PtrToInt:
+  case Instruction::IntToPtr:
+    // Fall through and handle them the same as zext/trunc.
+    LLVM_FALLTHROUGH;
+  case Instruction::ZExt:
+  case Instruction::Trunc: {
+    Type *SrcTy = I->getOperand(0)->getType();
+
+    unsigned SrcBitWidth;
+    // Note that we handle pointer operands here because of inttoptr/ptrtoint
+    // which fall through here.
+    Type *ScalarTy = SrcTy->getScalarType();
+    SrcBitWidth = ScalarTy->isPointerTy() ?
+      Q.DL.getIndexTypeSizeInBits(ScalarTy) :
+      Q.DL.getTypeSizeInBits(ScalarTy);
+
+    assert(SrcBitWidth && "SrcBitWidth can't be zero");
+    Known = Known.zextOrTrunc(SrcBitWidth, false);
+    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+    Known = Known.zextOrTrunc(BitWidth, true /* ExtendedBitsAreKnownZero */);
+    break;
+  }
+  case Instruction::BitCast: {
+    Type *SrcTy = I->getOperand(0)->getType();
+    if (SrcTy->isIntOrPtrTy() &&
+        // TODO: For now, not handling conversions like:
+        // (bitcast i64 %x to <2 x i32>)
+        !I->getType()->isVectorTy()) {
+      computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+      break;
+    }
+    break;
+  }
+  case Instruction::SExt: {
+    // Compute the bits in the result that are not present in the input.
+    unsigned SrcBitWidth = I->getOperand(0)->getType()->getScalarSizeInBits();
+
+    Known = Known.trunc(SrcBitWidth);
+    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+    // If the sign bit of the input is known set or clear, then we know the
+    // top bits of the result.
+    Known = Known.sext(BitWidth);
+    break;
+  }
+  case Instruction::Shl: {
+    // (shl X, C1) & C2 == 0   iff   (X & C2 >>u C1) == 0
+    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
+    auto KZF = [NSW](const APInt &KnownZero, unsigned ShiftAmt) {
+      APInt KZResult = KnownZero << ShiftAmt;
+      KZResult.setLowBits(ShiftAmt); // Low bits known 0.
+      // If this shift has "nsw" keyword, then the result is either a poison
+      // value or has the same sign bit as the first operand.
+      if (NSW && KnownZero.isSignBitSet())
+        KZResult.setSignBit();
+      return KZResult;
+    };
+
+    auto KOF = [NSW](const APInt &KnownOne, unsigned ShiftAmt) {
+      APInt KOResult = KnownOne << ShiftAmt;
+      if (NSW && KnownOne.isSignBitSet())
+        KOResult.setSignBit();
+      return KOResult;
+    };
+
+    computeKnownBitsFromShiftOperator(I, Known, Known2, Depth, Q, KZF, KOF);
+    break;
+  }
+  case Instruction::LShr: {
+    // (lshr X, C1) & C2 == 0   iff  (-1 >> C1) & C2 == 0
+    auto KZF = [](const APInt &KnownZero, unsigned ShiftAmt) {
+      APInt KZResult = KnownZero.lshr(ShiftAmt);
+      // High bits known zero.
+      KZResult.setHighBits(ShiftAmt);
+      return KZResult;
+    };
+
+    auto KOF = [](const APInt &KnownOne, unsigned ShiftAmt) {
+      return KnownOne.lshr(ShiftAmt);
+    };
+
+    computeKnownBitsFromShiftOperator(I, Known, Known2, Depth, Q, KZF, KOF);
+    break;
+  }
+  case Instruction::AShr: {
+    // (ashr X, C1) & C2 == 0   iff  (-1 >> C1) & C2 == 0
+    auto KZF = [](const APInt &KnownZero, unsigned ShiftAmt) {
+      return KnownZero.ashr(ShiftAmt);
+    };
+
+    auto KOF = [](const APInt &KnownOne, unsigned ShiftAmt) {
+      return KnownOne.ashr(ShiftAmt);
+    };
+
+    computeKnownBitsFromShiftOperator(I, Known, Known2, Depth, Q, KZF, KOF);
+    break;
+  }
+  case Instruction::Sub: {
+    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
+    computeKnownBitsAddSub(false, I->getOperand(0), I->getOperand(1), NSW,
+                           Known, Known2, Depth, Q);
+    break;
+  }
+  case Instruction::Add: {
+    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
+    computeKnownBitsAddSub(true, I->getOperand(0), I->getOperand(1), NSW,
+                           Known, Known2, Depth, Q);
+    break;
+  }
+  case Instruction::SRem:
+    if (ConstantInt *Rem = dyn_cast<ConstantInt>(I->getOperand(1))) {
+      APInt RA = Rem->getValue().abs();
+      if (RA.isPowerOf2()) {
+        APInt LowBits = RA - 1;
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+
+        // The low bits of the first operand are unchanged by the srem.
+        Known.Zero = Known2.Zero & LowBits;
+        Known.One = Known2.One & LowBits;
+
+        // If the first operand is non-negative or has all low bits zero, then
+        // the upper bits are all zero.
+        if (Known2.isNonNegative() || LowBits.isSubsetOf(Known2.Zero))
+          Known.Zero |= ~LowBits;
+
+        // If the first operand is negative and not all low bits are zero, then
+        // the upper bits are all one.
+        if (Known2.isNegative() && LowBits.intersects(Known2.One))
+          Known.One |= ~LowBits;
+
+        assert((Known.Zero & Known.One) == 0 && "Bits known to be one AND zero?");
+        break;
+      }
+    }
+
+    // The sign bit is the LHS's sign bit, except when the result of the
+    // remainder is zero.
+    computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+    // If it's known zero, our sign bit is also zero.
+    if (Known2.isNonNegative())
+      Known.makeNonNegative();
+
+    break;
+  case Instruction::URem: {
+    if (ConstantInt *Rem = dyn_cast<ConstantInt>(I->getOperand(1))) {
+      const APInt &RA = Rem->getValue();
+      if (RA.isPowerOf2()) {
+        APInt LowBits = (RA - 1);
+        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+        Known.Zero |= ~LowBits;
+        Known.One &= LowBits;
+        break;
+      }
+    }
+
+    // Since the result is less than or equal to either operand, any leading
+    // zero bits in either operand must also exist in the result.
+    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+    computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
+
+    unsigned Leaders =
+        std::max(Known.countMinLeadingZeros(), Known2.countMinLeadingZeros());
+    Known.resetAll();
+    Known.Zero.setHighBits(Leaders);
+    break;
+  }
+
+  case Instruction::Alloca: {
+    const AllocaInst *AI = cast<AllocaInst>(I);
+    unsigned Align = AI->getAlignment();
+    if (Align == 0)
+      Align = Q.DL.getABITypeAlignment(AI->getAllocatedType());
+
+    if (Align > 0)
+      Known.Zero.setLowBits(countTrailingZeros(Align));
+    break;
+  }
+  case Instruction::GetElementPtr: {
+    // Analyze all of the subscripts of this getelementptr instruction
+    // to determine if we can prove known low zero bits.
+    KnownBits LocalKnown(BitWidth);
+    computeKnownBits(I->getOperand(0), LocalKnown, Depth + 1, Q);
+    unsigned TrailZ = LocalKnown.countMinTrailingZeros();
+
+    gep_type_iterator GTI = gep_type_begin(I);
+    for (unsigned i = 1, e = I->getNumOperands(); i != e; ++i, ++GTI) {
+      Value *Index = I->getOperand(i);
+      if (StructType *STy = GTI.getStructTypeOrNull()) {
+        // Handle struct member offset arithmetic.
+
+        // Handle case when index is vector zeroinitializer
+        Constant *CIndex = cast<Constant>(Index);
+        if (CIndex->isZeroValue())
+          continue;
+
+        if (CIndex->getType()->isVectorTy())
+          Index = CIndex->getSplatValue();
+
+        unsigned Idx = cast<ConstantInt>(Index)->getZExtValue();
+        const StructLayout *SL = Q.DL.getStructLayout(STy);
+        uint64_t Offset = SL->getElementOffset(Idx);
+        TrailZ = std::min<unsigned>(TrailZ,
+                                    countTrailingZeros(Offset));
+      } else {
+        // Handle array index arithmetic.
+        Type *IndexedTy = GTI.getIndexedType();
+        if (!IndexedTy->isSized()) {
+          TrailZ = 0;
+          break;
+        }
+        unsigned GEPOpiBits = Index->getType()->getScalarSizeInBits();
+        uint64_t TypeSize = Q.DL.getTypeAllocSize(IndexedTy);
+        LocalKnown.Zero = LocalKnown.One = APInt(GEPOpiBits, 0);
+        computeKnownBits(Index, LocalKnown, Depth + 1, Q);
+        TrailZ = std::min(TrailZ,
+                          unsigned(countTrailingZeros(TypeSize) +
+                                   LocalKnown.countMinTrailingZeros()));
+      }
+    }
+
+    Known.Zero.setLowBits(TrailZ);
+    break;
+  }
+  case Instruction::PHI: {
+    const PHINode *P = cast<PHINode>(I);
+    // Handle the case of a simple two-predecessor recurrence PHI.
+    // There's a lot more that could theoretically be done here, but
+    // this is sufficient to catch some interesting cases.
+    if (P->getNumIncomingValues() == 2) {
+      for (unsigned i = 0; i != 2; ++i) {
+        Value *L = P->getIncomingValue(i);
+        Value *R = P->getIncomingValue(!i);
+        Operator *LU = dyn_cast<Operator>(L);
+        if (!LU)
+          continue;
+        unsigned Opcode = LU->getOpcode();
+        // Check for operations that have the property that if
+        // both their operands have low zero bits, the result
+        // will have low zero bits.
+        if (Opcode == Instruction::Add ||
+            Opcode == Instruction::Sub ||
+            Opcode == Instruction::And ||
+            Opcode == Instruction::Or ||
+            Opcode == Instruction::Mul) {
+          Value *LL = LU->getOperand(0);
+          Value *LR = LU->getOperand(1);
+          // Find a recurrence.
+          if (LL == I)
+            L = LR;
+          else if (LR == I)
+            L = LL;
+          else
+            break;
+          // Ok, we have a PHI of the form L op= R. Check for low
+          // zero bits.
+          computeKnownBits(R, Known2, Depth + 1, Q);
+
+          // We need to take the minimum number of known bits
+          KnownBits Known3(Known);
+          computeKnownBits(L, Known3, Depth + 1, Q);
+
+          Known.Zero.setLowBits(std::min(Known2.countMinTrailingZeros(),
+                                         Known3.countMinTrailingZeros()));
+
+          auto *OverflowOp = dyn_cast<OverflowingBinaryOperator>(LU);
+          if (OverflowOp && Q.IIQ.hasNoSignedWrap(OverflowOp)) {
+            // If initial value of recurrence is nonnegative, and we are adding
+            // a nonnegative number with nsw, the result can only be nonnegative
+            // or poison value regardless of the number of times we execute the
+            // add in phi recurrence. If initial value is negative and we are
+            // adding a negative number with nsw, the result can only be
+            // negative or poison value. Similar arguments apply to sub and mul.
+            //
+            // (add non-negative, non-negative) --> non-negative
+            // (add negative, negative) --> negative
+            if (Opcode == Instruction::Add) {
+              if (Known2.isNonNegative() && Known3.isNonNegative())
+                Known.makeNonNegative();
+              else if (Known2.isNegative() && Known3.isNegative())
+                Known.makeNegative();
+            }
+
+            // (sub nsw non-negative, negative) --> non-negative
+            // (sub nsw negative, non-negative) --> negative
+            else if (Opcode == Instruction::Sub && LL == I) {
+              if (Known2.isNonNegative() && Known3.isNegative())
+                Known.makeNonNegative();
+              else if (Known2.isNegative() && Known3.isNonNegative())
+                Known.makeNegative();
+            }
+
+            // (mul nsw non-negative, non-negative) --> non-negative
+            else if (Opcode == Instruction::Mul && Known2.isNonNegative() &&
+                     Known3.isNonNegative())
+              Known.makeNonNegative();
+          }
+
+          break;
+        }
+      }
+    }
+
+    // Unreachable blocks may have zero-operand PHI nodes.
+    if (P->getNumIncomingValues() == 0)
+      break;
+
+    // Otherwise take the unions of the known bit sets of the operands,
+    // taking conservative care to avoid excessive recursion.
+    if (Depth < MaxDepth - 1 && !Known.Zero && !Known.One) {
+      // Skip if every incoming value references to ourself.
+      if (dyn_cast_or_null<UndefValue>(P->hasConstantValue()))
+        break;
+
+      Known.Zero.setAllBits();
+      Known.One.setAllBits();
+      for (Value *IncValue : P->incoming_values()) {
+        // Skip direct self references.
+        if (IncValue == P) continue;
+
+        Known2 = KnownBits(BitWidth);
+        // Recurse, but cap the recursion to one level, because we don't
+        // want to waste time spinning around in loops.
+        computeKnownBits(IncValue, Known2, MaxDepth - 1, Q);
+        Known.Zero &= Known2.Zero;
+        Known.One &= Known2.One;
+        // If all bits have been ruled out, there's no need to check
+        // more operands.
+        if (!Known.Zero && !Known.One)
+          break;
+      }
+    }
+    break;
+  }
+  case Instruction::Call:
+  case Instruction::Invoke:
+    // If range metadata is attached to this call, set known bits from that,
+    // and then intersect with known bits based on other properties of the
+    // function.
+    if (MDNode *MD =
+            Q.IIQ.getMetadata(cast<Instruction>(I), LLVMContext::MD_range))
+      computeKnownBitsFromRangeMetadata(*MD, Known);
+    if (const Value *RV = ImmutableCallSite(I).getReturnedArgOperand()) {
+      computeKnownBits(RV, Known2, Depth + 1, Q);
+      Known.Zero |= Known2.Zero;
+      Known.One |= Known2.One;
+    }
+    if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(I)) {
+      switch (II->getIntrinsicID()) {
+      default: break;
+      case Intrinsic::bitreverse:
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+        Known.Zero |= Known2.Zero.reverseBits();
+        Known.One |= Known2.One.reverseBits();
+        break;
+      case Intrinsic::bswap:
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+        Known.Zero |= Known2.Zero.byteSwap();
+        Known.One |= Known2.One.byteSwap();
+        break;
+      case Intrinsic::ctlz: {
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+        // If we have a known 1, its position is our upper bound.
+        unsigned PossibleLZ = Known2.One.countLeadingZeros();
+        // If this call is undefined for 0, the result will be less than 2^n.
+        if (II->getArgOperand(1) == ConstantInt::getTrue(II->getContext()))
+          PossibleLZ = std::min(PossibleLZ, BitWidth - 1);
+        unsigned LowBits = Log2_32(PossibleLZ)+1;
+        Known.Zero.setBitsFrom(LowBits);
+        break;
+      }
+      case Intrinsic::cttz: {
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+        // If we have a known 1, its position is our upper bound.
+        unsigned PossibleTZ = Known2.One.countTrailingZeros();
+        // If this call is undefined for 0, the result will be less than 2^n.
+        if (II->getArgOperand(1) == ConstantInt::getTrue(II->getContext()))
+          PossibleTZ = std::min(PossibleTZ, BitWidth - 1);
+        unsigned LowBits = Log2_32(PossibleTZ)+1;
+        Known.Zero.setBitsFrom(LowBits);
+        break;
+      }
+      case Intrinsic::ctpop: {
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+        // We can bound the space the count needs.  Also, bits known to be zero
+        // can't contribute to the population.
+        unsigned BitsPossiblySet = Known2.countMaxPopulation();
+        unsigned LowBits = Log2_32(BitsPossiblySet)+1;
+        Known.Zero.setBitsFrom(LowBits);
+        // TODO: we could bound KnownOne using the lower bound on the number
+        // of bits which might be set provided by popcnt KnownOne2.
+        break;
+      }
+      case Intrinsic::fshr:
+      case Intrinsic::fshl: {
+        const APInt *SA;
+        if (!match(I->getOperand(2), m_APInt(SA)))
+          break;
+
+        // Normalize to funnel shift left.
+        uint64_t ShiftAmt = SA->urem(BitWidth);
+        if (II->getIntrinsicID() == Intrinsic::fshr)
+          ShiftAmt = BitWidth - ShiftAmt;
+
+        KnownBits Known3(Known);
+        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
+        computeKnownBits(I->getOperand(1), Known3, Depth + 1, Q);
+
+        Known.Zero =
+            Known2.Zero.shl(ShiftAmt) | Known3.Zero.lshr(BitWidth - ShiftAmt);
+        Known.One =
+            Known2.One.shl(ShiftAmt) | Known3.One.lshr(BitWidth - ShiftAmt);
+        break;
+      }
+      case Intrinsic::uadd_sat:
+      case Intrinsic::usub_sat: {
+        bool IsAdd = II->getIntrinsicID() == Intrinsic::uadd_sat;
+        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+        computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
+
+        // Add: Leading ones of either operand are preserved.
+        // Sub: Leading zeros of LHS and leading ones of RHS are preserved
+        // as leading zeros in the result.
+        unsigned LeadingKnown;
+        if (IsAdd)
+          LeadingKnown = std::max(Known.countMinLeadingOnes(),
+                                  Known2.countMinLeadingOnes());
+        else
+          LeadingKnown = std::max(Known.countMinLeadingZeros(),
+                                  Known2.countMinLeadingOnes());
+
+        Known = KnownBits::computeForAddSub(
+            IsAdd, /* NSW */ false, Known, Known2);
+
+        // We select between the operation result and all-ones/zero
+        // respectively, so we can preserve known ones/zeros.
+        if (IsAdd) {
+          Known.One.setHighBits(LeadingKnown);
+          Known.Zero.clearAllBits();
+        } else {
+          Known.Zero.setHighBits(LeadingKnown);
+          Known.One.clearAllBits();
+        }
+        break;
+      }
+      case Intrinsic::x86_sse42_crc32_64_64:
+        Known.Zero.setBitsFrom(32);
+        break;
+      }
+    }
+    break;
+  case Instruction::ExtractElement:
+    // Look through extract element. At the moment we keep this simple and skip
+    // tracking the specific element. But at least we might find information
+    // valid for all elements of the vector (for example if vector is sign
+    // extended, shifted, etc).
+    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
+    break;
+  case Instruction::ExtractValue:
+    if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(I->getOperand(0))) {
+      const ExtractValueInst *EVI = cast<ExtractValueInst>(I);
+      if (EVI->getNumIndices() != 1) break;
+      if (EVI->getIndices()[0] == 0) {
+        switch (II->getIntrinsicID()) {
+        default: break;
+        case Intrinsic::uadd_with_overflow:
+        case Intrinsic::sadd_with_overflow:
+          computeKnownBitsAddSub(true, II->getArgOperand(0),
+                                 II->getArgOperand(1), false, Known, Known2,
+                                 Depth, Q);
+          break;
+        case Intrinsic::usub_with_overflow:
+        case Intrinsic::ssub_with_overflow:
+          computeKnownBitsAddSub(false, II->getArgOperand(0),
+                                 II->getArgOperand(1), false, Known, Known2,
+                                 Depth, Q);
+          break;
+        case Intrinsic::umul_with_overflow:
+        case Intrinsic::smul_with_overflow:
+          computeKnownBitsMul(II->getArgOperand(0), II->getArgOperand(1), false,
+                              Known, Known2, Depth, Q);
+          break;
+        }
+      }
+    }
+  }
+}
+
+/// Determine which bits of V are known to be either zero or one and return
+/// them.
+KnownBits computeKnownBits(const Value *V, unsigned Depth, const Query &Q) {
+  KnownBits Known(getBitWidth(V->getType(), Q.DL));
+  computeKnownBits(V, Known, Depth, Q);
+  return Known;
+}
+
+/// Determine which bits of V are known to be either zero or one and return
+/// them in the Known bit set.
+///
+/// NOTE: we cannot consider 'undef' to be "IsZero" here.  The problem is that
+/// we cannot optimize based on the assumption that it is zero without changing
+/// it to be an explicit zero.  If we don't change it to zero, other code could
+/// optimized based on the contradictory assumption that it is non-zero.
+/// Because instcombine aggressively folds operations with undef args anyway,
+/// this won't lose us code quality.
+///
+/// This function is defined on values with integer type, values with pointer
+/// type, and vectors of integers.  In the case
+/// where V is a vector, known zero, and known one values are the
+/// same width as the vector element, and the bit is set only if it is true
+/// for all of the elements in the vector.
+void computeKnownBits(const Value *V, KnownBits &Known, unsigned Depth,
+                      const Query &Q) {
+  assert(V && "No Value?");
+  assert(Depth <= MaxDepth && "Limit Search Depth");
+  unsigned BitWidth = Known.getBitWidth();
+
+  assert((V->getType()->isIntOrIntVectorTy(BitWidth) ||
+          V->getType()->isPtrOrPtrVectorTy()) &&
+         "Not integer or pointer type!");
+
+  Type *ScalarTy = V->getType()->getScalarType();
+  unsigned ExpectedWidth = ScalarTy->isPointerTy() ?
+    Q.DL.getIndexTypeSizeInBits(ScalarTy) : Q.DL.getTypeSizeInBits(ScalarTy);
+  assert(ExpectedWidth == BitWidth && "V and Known should have same BitWidth");
+  (void)BitWidth;
+  (void)ExpectedWidth;
+
+  const APInt *C;
+  if (match(V, m_APInt(C))) {
+    // We know all of the bits for a scalar constant or a splat vector constant!
+    Known.One = *C;
+    Known.Zero = ~Known.One;
+    return;
+  }
+  // Null and aggregate-zero are all-zeros.
+  if (isa<ConstantPointerNull>(V) || isa<ConstantAggregateZero>(V)) {
+    Known.setAllZero();
+    return;
+  }
+  // Handle a constant vector by taking the intersection of the known bits of
+  // each element.
+  if (const ConstantDataSequential *CDS = dyn_cast<ConstantDataSequential>(V)) {
+    // We know that CDS must be a vector of integers. Take the intersection of
+    // each element.
+    Known.Zero.setAllBits(); Known.One.setAllBits();
+    for (unsigned i = 0, e = CDS->getNumElements(); i != e; ++i) {
+      APInt Elt = CDS->getElementAsAPInt(i);
+      Known.Zero &= ~Elt;
+      Known.One &= Elt;
+    }
+    return;
+  }
+
+  if (const auto *CV = dyn_cast<ConstantVector>(V)) {
+    // We know that CV must be a vector of integers. Take the intersection of
+    // each element.
+    Known.Zero.setAllBits(); Known.One.setAllBits();
+    for (unsigned i = 0, e = CV->getNumOperands(); i != e; ++i) {
+      Constant *Element = CV->getAggregateElement(i);
+      auto *ElementCI = dyn_cast_or_null<ConstantInt>(Element);
+      if (!ElementCI) {
+        Known.resetAll();
+        return;
+      }
+      const APInt &Elt = ElementCI->getValue();
+      Known.Zero &= ~Elt;
+      Known.One &= Elt;
+    }
+    return;
+  }
+
+  // Start out not knowing anything.
+  Known.resetAll();
+
+  // We can't imply anything about undefs.
+  if (isa<UndefValue>(V))
+    return;
+
+  // There's no point in looking through other users of ConstantData for
+  // assumptions.  Confirm that we've handled them all.
+  assert(!isa<ConstantData>(V) && "Unhandled constant data!");
+
+  // Limit search depth.
+  // All recursive calls that increase depth must come after this.
+  if (Depth == MaxDepth)
+    return;
+
+  // A weak GlobalAlias is totally unknown. A non-weak GlobalAlias has
+  // the bits of its aliasee.
+  if (const GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
+    if (!GA->isInterposable())
+      computeKnownBits(GA->getAliasee(), Known, Depth + 1, Q);
+    return;
+  }
+
+  if (const Operator *I = dyn_cast<Operator>(V))
+    computeKnownBitsFromOperator(I, Known, Depth, Q);
+
+  // Aligned pointers have trailing zeros - refine Known.Zero set
+  if (V->getType()->isPointerTy()) {
+    unsigned Align = V->getPointerAlignment(Q.DL);
+    if (Align)
+      Known.Zero.setLowBits(countTrailingZeros(Align));
+  }
+
+  // computeKnownBitsFromAssume strictly refines Known.
+  // Therefore, we run them after computeKnownBitsFromOperator.
+
+  // Check whether a nearby assume intrinsic can determine some known bits.
+  computeKnownBitsFromAssume(V, Known, Depth, Q);
+
+  assert((Known.Zero & Known.One) == 0 && "Bits known to be one AND zero?");
+}
+
+/// Return true if the given value is known to have exactly one
+/// bit set when defined. For vectors return true if every element is known to
+/// be a power of two when defined. Supports values with integer or pointer
+/// types and vectors of integers.
+bool isKnownToBeAPowerOfTwo(const Value *V, bool OrZero, unsigned Depth,
+                            const Query &Q) {
+  assert(Depth <= MaxDepth && "Limit Search Depth");
+
+  // Attempt to match against constants.
+  if (OrZero && match(V, m_Power2OrZero()))
+      return true;
+  if (match(V, m_Power2()))
+      return true;
+
+  // 1 << X is clearly a power of two if the one is not shifted off the end.  If
+  // it is shifted off the end then the result is undefined.
+  if (match(V, m_Shl(m_One(), m_Value())))
+    return true;
+
+  // (signmask) >>l X is clearly a power of two if the one is not shifted off
+  // the bottom.  If it is shifted off the bottom then the result is undefined.
+  if (match(V, m_LShr(m_SignMask(), m_Value())))
+    return true;
+
+  // The remaining tests are all recursive, so bail out if we hit the limit.
+  if (Depth++ == MaxDepth)
+    return false;
+
+  Value *X = nullptr, *Y = nullptr;
+  // A shift left or a logical shift right of a power of two is a power of two
+  // or zero.
+  if (OrZero && (match(V, m_Shl(m_Value(X), m_Value())) ||
+                 match(V, m_LShr(m_Value(X), m_Value()))))
+    return isKnownToBeAPowerOfTwo(X, /*OrZero*/ true, Depth, Q);
+
+  if (const ZExtInst *ZI = dyn_cast<ZExtInst>(V))
+    return isKnownToBeAPowerOfTwo(ZI->getOperand(0), OrZero, Depth, Q);
+
+  if (const SelectInst *SI = dyn_cast<SelectInst>(V))
+    return isKnownToBeAPowerOfTwo(SI->getTrueValue(), OrZero, Depth, Q) &&
+           isKnownToBeAPowerOfTwo(SI->getFalseValue(), OrZero, Depth, Q);
+
+  if (OrZero && match(V, m_And(m_Value(X), m_Value(Y)))) {
+    // A power of two and'd with anything is a power of two or zero.
+    if (isKnownToBeAPowerOfTwo(X, /*OrZero*/ true, Depth, Q) ||
+        isKnownToBeAPowerOfTwo(Y, /*OrZero*/ true, Depth, Q))
+      return true;
+    // X & (-X) is always a power of two or zero.
+    if (match(X, m_Neg(m_Specific(Y))) || match(Y, m_Neg(m_Specific(X))))
+      return true;
+    return false;
+  }
+
+  // Adding a power-of-two or zero to the same power-of-two or zero yields
+  // either the original power-of-two, a larger power-of-two or zero.
+  if (match(V, m_Add(m_Value(X), m_Value(Y)))) {
+    const OverflowingBinaryOperator *VOBO = cast<OverflowingBinaryOperator>(V);
+    if (OrZero || Q.IIQ.hasNoUnsignedWrap(VOBO) ||
+        Q.IIQ.hasNoSignedWrap(VOBO)) {
+      if (match(X, m_And(m_Specific(Y), m_Value())) ||
+          match(X, m_And(m_Value(), m_Specific(Y))))
+        if (isKnownToBeAPowerOfTwo(Y, OrZero, Depth, Q))
+          return true;
+      if (match(Y, m_And(m_Specific(X), m_Value())) ||
+          match(Y, m_And(m_Value(), m_Specific(X))))
+        if (isKnownToBeAPowerOfTwo(X, OrZero, Depth, Q))
+          return true;
+
+      unsigned BitWidth = V->getType()->getScalarSizeInBits();
+      KnownBits LHSBits(BitWidth);
+      computeKnownBits(X, LHSBits, Depth, Q);
+
+      KnownBits RHSBits(BitWidth);
+      computeKnownBits(Y, RHSBits, Depth, Q);
+      // If i8 V is a power of two or zero:
+      //  ZeroBits: 1 1 1 0 1 1 1 1
+      // ~ZeroBits: 0 0 0 1 0 0 0 0
+      if ((~(LHSBits.Zero & RHSBits.Zero)).isPowerOf2())
+        // If OrZero isn't set, we cannot give back a zero result.
+        // Make sure either the LHS or RHS has a bit set.
+        if (OrZero || RHSBits.One.getBoolValue() || LHSBits.One.getBoolValue())
+          return true;
+    }
+  }
+
+  // An exact divide or right shift can only shift off zero bits, so the result
+  // is a power of two only if the first operand is a power of two and not
+  // copying a sign bit (sdiv int_min, 2).
+  if (match(V, m_Exact(m_LShr(m_Value(), m_Value()))) ||
+      match(V, m_Exact(m_UDiv(m_Value(), m_Value())))) {
+    return isKnownToBeAPowerOfTwo(cast<Operator>(V)->getOperand(0), OrZero,
+                                  Depth, Q);
+  }
+
+  return false;
+}
+
+/// Test whether a GEP's result is known to be non-null.
+///
+/// Uses properties inherent in a GEP to try to determine whether it is known
+/// to be non-null.
+///
+/// Currently this routine does not support vector GEPs.
+static bool isGEPKnownNonNull(const GEPOperator *GEP, unsigned Depth,
+                              const Query &Q) {
+  const Function *F = nullptr;
+  if (const Instruction *I = dyn_cast<Instruction>(GEP))
+    F = I->getFunction();
+
+  if (!GEP->isInBounds() ||
+      NullPointerIsDefined(F, GEP->getPointerAddressSpace()))
+    return false;
+
+  // FIXME: Support vector-GEPs.
+  assert(GEP->getType()->isPointerTy() && "We only support plain pointer GEP");
+
+  // If the base pointer is non-null, we cannot walk to a null address with an
+  // inbounds GEP in address space zero.
+  if (isKnownNonZero(GEP->getPointerOperand(), Depth, Q))
+    return true;
+
+  // Walk the GEP operands and see if any operand introduces a non-zero offset.
+  // If so, then the GEP cannot produce a null pointer, as doing so would
+  // inherently violate the inbounds contract within address space zero.
+  for (gep_type_iterator GTI = gep_type_begin(GEP), GTE = gep_type_end(GEP);
+       GTI != GTE; ++GTI) {
+    // Struct types are easy -- they must always be indexed by a constant.
+    if (StructType *STy = GTI.getStructTypeOrNull()) {
+      ConstantInt *OpC = cast<ConstantInt>(GTI.getOperand());
+      unsigned ElementIdx = OpC->getZExtValue();
+      const StructLayout *SL = Q.DL.getStructLayout(STy);
+      uint64_t ElementOffset = SL->getElementOffset(ElementIdx);
+      if (ElementOffset > 0)
+        return true;
+      continue;
+    }
+
+    // If we have a zero-sized type, the index doesn't matter. Keep looping.
+    if (Q.DL.getTypeAllocSize(GTI.getIndexedType()) == 0)
+      continue;
+
+    // Fast path the constant operand case both for efficiency and so we don't
+    // increment Depth when just zipping down an all-constant GEP.
+    if (ConstantInt *OpC = dyn_cast<ConstantInt>(GTI.getOperand())) {
+      if (!OpC->isZero())
+        return true;
+      continue;
+    }
+
+    // We post-increment Depth here because while isKnownNonZero increments it
+    // as well, when we pop back up that increment won't persist. We don't want
+    // to recurse 10k times just because we have 10k GEP operands. We don't
+    // bail completely out because we want to handle constant GEPs regardless
+    // of depth.
+    if (Depth++ >= MaxDepth)
+      continue;
+
+    if (isKnownNonZero(GTI.getOperand(), Depth, Q))
+      return true;
+  }
+
+  return false;
+}
+
+static bool isKnownNonNullFromDominatingCondition(const Value *V,
+                                                  const Instruction *CtxI,
+                                                  const DominatorTree *DT) {
+  assert(V->getType()->isPointerTy() && "V must be pointer type");
+  assert(!isa<ConstantData>(V) && "Did not expect ConstantPointerNull");
+
+  if (!CtxI || !DT)
+    return false;
+
+  unsigned NumUsesExplored = 0;
+  for (auto *U : V->users()) {
+    // Avoid massive lists
+    if (NumUsesExplored >= DomConditionsMaxUses)
+      break;
+    NumUsesExplored++;
+
+    // If the value is used as an argument to a call or invoke, then argument
+    // attributes may provide an answer about null-ness.
+    if (auto CS = ImmutableCallSite(U))
+      if (auto *CalledFunc = CS.getCalledFunction())
+        for (const Argument &Arg : CalledFunc->args())
+          if (CS.getArgOperand(Arg.getArgNo()) == V &&
+              Arg.hasNonNullAttr() && DT->dominates(CS.getInstruction(), CtxI))
+            return true;
+
+    // Consider only compare instructions uniquely controlling a branch
+    CmpInst::Predicate Pred;
+    if (!match(const_cast<User *>(U),
+               m_c_ICmp(Pred, m_Specific(V), m_Zero())) ||
+        (Pred != ICmpInst::ICMP_EQ && Pred != ICmpInst::ICMP_NE))
+      continue;
+
+    SmallVector<const User *, 4> WorkList;
+    SmallPtrSet<const User *, 4> Visited;
+    for (auto *CmpU : U->users()) {
+      assert(WorkList.empty() && "Should be!");
+      if (Visited.insert(CmpU).second)
+        WorkList.push_back(CmpU);
+
+      while (!WorkList.empty()) {
+        auto *Curr = WorkList.pop_back_val();
+
+        // If a user is an AND, add all its users to the work list. We only
+        // propagate "pred != null" condition through AND because it is only
+        // correct to assume that all conditions of AND are met in true branch.
+        // TODO: Support similar logic of OR and EQ predicate?
+        if (Pred == ICmpInst::ICMP_NE)
+          if (auto *BO = dyn_cast<BinaryOperator>(Curr))
+            if (BO->getOpcode() == Instruction::And) {
+              for (auto *BOU : BO->users())
+                if (Visited.insert(BOU).second)
+                  WorkList.push_back(BOU);
+              continue;
+            }
+
+        if (const BranchInst *BI = dyn_cast<BranchInst>(Curr)) {
+          assert(BI->isConditional() && "uses a comparison!");
+
+          BasicBlock *NonNullSuccessor =
+              BI->getSuccessor(Pred == ICmpInst::ICMP_EQ ? 1 : 0);
+          BasicBlockEdge Edge(BI->getParent(), NonNullSuccessor);
+          if (Edge.isSingleEdge() && DT->dominates(Edge, CtxI->getParent()))
+            return true;
+        } else if (Pred == ICmpInst::ICMP_NE && isGuard(Curr) &&
+                   DT->dominates(cast<Instruction>(Curr), CtxI)) {
+          return true;
+        }
+      }
+    }
+  }
+
+  return false;
+}
+
+/// Does the 'Range' metadata (which must be a valid MD_range operand list)
+/// ensure that the value it's attached to is never Value?  'RangeType' is
+/// is the type of the value described by the range.
+static bool rangeMetadataExcludesValue(const MDNode* Ranges, const APInt& Value) {
+  const unsigned NumRanges = Ranges->getNumOperands() / 2;
+  assert(NumRanges >= 1);
+  for (unsigned i = 0; i < NumRanges; ++i) {
+    ConstantInt *Lower =
+        mdconst::extract<ConstantInt>(Ranges->getOperand(2 * i + 0));
+    ConstantInt *Upper =
+        mdconst::extract<ConstantInt>(Ranges->getOperand(2 * i + 1));
+    ConstantRange Range(Lower->getValue(), Upper->getValue());
+    if (Range.contains(Value))
+      return false;
+  }
+  return true;
+}
+
+/// Return true if the given value is known to be non-zero when defined. For
+/// vectors, return true if every element is known to be non-zero when
+/// defined. For pointers, if the context instruction and dominator tree are
+/// specified, perform context-sensitive analysis and return true if the
+/// pointer couldn't possibly be null at the specified instruction.
+/// Supports values with integer or pointer type and vectors of integers.
+bool isKnownNonZero(const Value *V, unsigned Depth, const Query &Q) {
+  if (auto *C = dyn_cast<Constant>(V)) {
+    if (C->isNullValue())
+      return false;
+    if (isa<ConstantInt>(C))
+      // Must be non-zero due to null test above.
+      return true;
+
+    if (auto *CE = dyn_cast<ConstantExpr>(C)) {
+      // See the comment for IntToPtr/PtrToInt instructions below.
+      if (CE->getOpcode() == Instruction::IntToPtr ||
+          CE->getOpcode() == Instruction::PtrToInt)
+        if (Q.DL.getTypeSizeInBits(CE->getOperand(0)->getType()) <=
+            Q.DL.getTypeSizeInBits(CE->getType()))
+          return isKnownNonZero(CE->getOperand(0), Depth, Q);
+    }
+
+    // For constant vectors, check that all elements are undefined or known
+    // non-zero to determine that the whole vector is known non-zero.
+    if (auto *VecTy = dyn_cast<VectorType>(C->getType())) {
+      for (unsigned i = 0, e = VecTy->getNumElements(); i != e; ++i) {
+        Constant *Elt = C->getAggregateElement(i);
+        if (!Elt || Elt->isNullValue())
+          return false;
+        if (!isa<UndefValue>(Elt) && !isa<ConstantInt>(Elt))
+          return false;
+      }
+      return true;
+    }
+
+    // A global variable in address space 0 is non null unless extern weak
+    // or an absolute symbol reference. Other address spaces may have null as a
+    // valid address for a global, so we can't assume anything.
+    if (const GlobalValue *GV = dyn_cast<GlobalValue>(V)) {
+      if (!GV->isAbsoluteSymbolRef() && !GV->hasExternalWeakLinkage() &&
+          GV->getType()->getAddressSpace() == 0)
+        return true;
+    } else
+      return false;
+  }
+
+  if (auto *I = dyn_cast<Instruction>(V)) {
+    if (MDNode *Ranges = Q.IIQ.getMetadata(I, LLVMContext::MD_range)) {
+      // If the possible ranges don't contain zero, then the value is
+      // definitely non-zero.
+      if (auto *Ty = dyn_cast<IntegerType>(V->getType())) {
+        const APInt ZeroValue(Ty->getBitWidth(), 0);
+        if (rangeMetadataExcludesValue(Ranges, ZeroValue))
+          return true;
+      }
+    }
+  }
+
+  // Some of the tests below are recursive, so bail out if we hit the limit.
+  if (Depth++ >= MaxDepth)
+    return false;
+
+  // Check for pointer simplifications.
+  if (V->getType()->isPointerTy()) {
+    // Alloca never returns null, malloc might.
+    if (isa<AllocaInst>(V) && Q.DL.getAllocaAddrSpace() == 0)
+      return true;
+
+    // A byval, inalloca, or nonnull argument is never null.
+    if (const Argument *A = dyn_cast<Argument>(V))
+      if (A->hasByValOrInAllocaAttr() || A->hasNonNullAttr())
+        return true;
+
+    // A Load tagged with nonnull metadata is never null.
+    if (const LoadInst *LI = dyn_cast<LoadInst>(V))
+      if (Q.IIQ.getMetadata(LI, LLVMContext::MD_nonnull))
+        return true;
+
+    if (const auto *Call = dyn_cast<CallBase>(V)) {
+      if (Call->isReturnNonNull())
+        return true;
+      if (const auto *RP = getArgumentAliasingToReturnedPointer(Call))
+        return isKnownNonZero(RP, Depth, Q);
+    }
+  }
+
+
+  // Check for recursive pointer simplifications.
+  if (V->getType()->isPointerTy()) {
+    if (isKnownNonNullFromDominatingCondition(V, Q.CxtI, Q.DT))
+      return true;
+
+    // Look through bitcast operations, GEPs, and int2ptr instructions as they
+    // do not alter the value, or at least not the nullness property of the
+    // value, e.g., int2ptr is allowed to zero/sign extend the value.
+    //
+    // Note that we have to take special care to avoid looking through
+    // truncating casts, e.g., int2ptr/ptr2int with appropriate sizes, as well
+    // as casts that can alter the value, e.g., AddrSpaceCasts.
+    if (const GEPOperator *GEP = dyn_cast<GEPOperator>(V))
+      if (isGEPKnownNonNull(GEP, Depth, Q))
+        return true;
+
+    if (auto *BCO = dyn_cast<BitCastOperator>(V))
+      return isKnownNonZero(BCO->getOperand(0), Depth, Q);
+
+    if (auto *I2P = dyn_cast<IntToPtrInst>(V))
+      if (Q.DL.getTypeSizeInBits(I2P->getSrcTy()) <=
+          Q.DL.getTypeSizeInBits(I2P->getDestTy()))
+        return isKnownNonZero(I2P->getOperand(0), Depth, Q);
+  }
+
+  // Similar to int2ptr above, we can look through ptr2int here if the cast
+  // is a no-op or an extend and not a truncate.
+  if (auto *P2I = dyn_cast<PtrToIntInst>(V))
+    if (Q.DL.getTypeSizeInBits(P2I->getSrcTy()) <=
+        Q.DL.getTypeSizeInBits(P2I->getDestTy()))
+      return isKnownNonZero(P2I->getOperand(0), Depth, Q);
+
+  unsigned BitWidth = getBitWidth(V->getType()->getScalarType(), Q.DL);
+
+  // X | Y != 0 if X != 0 or Y != 0.
+  Value *X = nullptr, *Y = nullptr;
+  if (match(V, m_Or(m_Value(X), m_Value(Y))))
+    return isKnownNonZero(X, Depth, Q) || isKnownNonZero(Y, Depth, Q);
+
+  // ext X != 0 if X != 0.
+  if (isa<SExtInst>(V) || isa<ZExtInst>(V))
+    return isKnownNonZero(cast<Instruction>(V)->getOperand(0), Depth, Q);
+
+  // shl X, Y != 0 if X is odd.  Note that the value of the shift is undefined
+  // if the lowest bit is shifted off the end.
+  if (match(V, m_Shl(m_Value(X), m_Value(Y)))) {
+    // shl nuw can't remove any non-zero bits.
+    const OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
+    if (Q.IIQ.hasNoUnsignedWrap(BO))
+      return isKnownNonZero(X, Depth, Q);
+
+    KnownBits Known(BitWidth);
+    computeKnownBits(X, Known, Depth, Q);
+    if (Known.One[0])
+      return true;
+  }
+  // shr X, Y != 0 if X is negative.  Note that the value of the shift is not
+  // defined if the sign bit is shifted off the end.
+  else if (match(V, m_Shr(m_Value(X), m_Value(Y)))) {
+    // shr exact can only shift out zero bits.
+    const PossiblyExactOperator *BO = cast<PossiblyExactOperator>(V);
+    if (BO->isExact())
+      return isKnownNonZero(X, Depth, Q);
+
+    KnownBits Known = computeKnownBits(X, Depth, Q);
+    if (Known.isNegative())
+      return true;
+
+    // If the shifter operand is a constant, and all of the bits shifted
+    // out are known to be zero, and X is known non-zero then at least one
+    // non-zero bit must remain.
+    if (ConstantInt *Shift = dyn_cast<ConstantInt>(Y)) {
+      auto ShiftVal = Shift->getLimitedValue(BitWidth - 1);
+      // Is there a known one in the portion not shifted out?
+      if (Known.countMaxLeadingZeros() < BitWidth - ShiftVal)
+        return true;
+      // Are all the bits to be shifted out known zero?
+      if (Known.countMinTrailingZeros() >= ShiftVal)
+        return isKnownNonZero(X, Depth, Q);
+    }
+  }
+  // div exact can only produce a zero if the dividend is zero.
+  else if (match(V, m_Exact(m_IDiv(m_Value(X), m_Value())))) {
+    return isKnownNonZero(X, Depth, Q);
+  }
+  // X + Y.
+  else if (match(V, m_Add(m_Value(X), m_Value(Y)))) {
+    KnownBits XKnown = computeKnownBits(X, Depth, Q);
+    KnownBits YKnown = computeKnownBits(Y, Depth, Q);
+
+    // If X and Y are both non-negative (as signed values) then their sum is not
+    // zero unless both X and Y are zero.
+    if (XKnown.isNonNegative() && YKnown.isNonNegative())
+      if (isKnownNonZero(X, Depth, Q) || isKnownNonZero(Y, Depth, Q))
+        return true;
+
+    // If X and Y are both negative (as signed values) then their sum is not
+    // zero unless both X and Y equal INT_MIN.
+    if (XKnown.isNegative() && YKnown.isNegative()) {
+      APInt Mask = APInt::getSignedMaxValue(BitWidth);
+      // The sign bit of X is set.  If some other bit is set then X is not equal
+      // to INT_MIN.
+      if (XKnown.One.intersects(Mask))
+        return true;
+      // The sign bit of Y is set.  If some other bit is set then Y is not equal
+      // to INT_MIN.
+      if (YKnown.One.intersects(Mask))
+        return true;
+    }
+
+    // The sum of a non-negative number and a power of two is not zero.
+    if (XKnown.isNonNegative() &&
+        isKnownToBeAPowerOfTwo(Y, /*OrZero*/ false, Depth, Q))
+      return true;
+    if (YKnown.isNonNegative() &&
+        isKnownToBeAPowerOfTwo(X, /*OrZero*/ false, Depth, Q))
+      return true;
+  }
+  // X * Y.
+  else if (match(V, m_Mul(m_Value(X), m_Value(Y)))) {
+    const OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
+    // If X and Y are non-zero then so is X * Y as long as the multiplication
+    // does not overflow.
+    if ((Q.IIQ.hasNoSignedWrap(BO) || Q.IIQ.hasNoUnsignedWrap(BO)) &&
+        isKnownNonZero(X, Depth, Q) && isKnownNonZero(Y, Depth, Q))
+      return true;
+  }
+  // (C ? X : Y) != 0 if X != 0 and Y != 0.
+  else if (const SelectInst *SI = dyn_cast<SelectInst>(V)) {
+    if (isKnownNonZero(SI->getTrueValue(), Depth, Q) &&
+        isKnownNonZero(SI->getFalseValue(), Depth, Q))
+      return true;
+  }
+  // PHI
+  else if (const PHINode *PN = dyn_cast<PHINode>(V)) {
+    // Try and detect a recurrence that monotonically increases from a
+    // starting value, as these are common as induction variables.
+    if (PN->getNumIncomingValues() == 2) {
+      Value *Start = PN->getIncomingValue(0);
+      Value *Induction = PN->getIncomingValue(1);
+      if (isa<ConstantInt>(Induction) && !isa<ConstantInt>(Start))
+        std::swap(Start, Induction);
+      if (ConstantInt *C = dyn_cast<ConstantInt>(Start)) {
+        if (!C->isZero() && !C->isNegative()) {
+          ConstantInt *X;
+          if (Q.IIQ.UseInstrInfo &&
+              (match(Induction, m_NSWAdd(m_Specific(PN), m_ConstantInt(X))) ||
+               match(Induction, m_NUWAdd(m_Specific(PN), m_ConstantInt(X)))) &&
+              !X->isNegative())
+            return true;
+        }
+      }
+    }
+    // Check if all incoming values are non-zero constant.
+    bool AllNonZeroConstants = llvm::all_of(PN->operands(), [](Value *V) {
+      return isa<ConstantInt>(V) && !cast<ConstantInt>(V)->isZero();
+    });
+    if (AllNonZeroConstants)
+      return true;
+  }
+
+  KnownBits Known(BitWidth);
+  computeKnownBits(V, Known, Depth, Q);
+  return Known.One != 0;
+}
+
+/// Return true if V2 == V1 + X, where X is known non-zero.
+static bool isAddOfNonZero(const Value *V1, const Value *V2, const Query &Q) {
+  const BinaryOperator *BO = dyn_cast<BinaryOperator>(V1);
+  if (!BO || BO->getOpcode() != Instruction::Add)
+    return false;
+  Value *Op = nullptr;
+  if (V2 == BO->getOperand(0))
+    Op = BO->getOperand(1);
+  else if (V2 == BO->getOperand(1))
+    Op = BO->getOperand(0);
+  else
+    return false;
+  return isKnownNonZero(Op, 0, Q);
+}
+
+/// Return true if it is known that V1 != V2.
+static bool isKnownNonEqual(const Value *V1, const Value *V2, const Query &Q) {
+  if (V1 == V2)
+    return false;
+  if (V1->getType() != V2->getType())
+    // We can't look through casts yet.
+    return false;
+  if (isAddOfNonZero(V1, V2, Q) || isAddOfNonZero(V2, V1, Q))
+    return true;
+
+  if (V1->getType()->isIntOrIntVectorTy()) {
+    // Are any known bits in V1 contradictory to known bits in V2? If V1
+    // has a known zero where V2 has a known one, they must not be equal.
+    KnownBits Known1 = computeKnownBits(V1, 0, Q);
+    KnownBits Known2 = computeKnownBits(V2, 0, Q);
+
+    if (Known1.Zero.intersects(Known2.One) ||
+        Known2.Zero.intersects(Known1.One))
+      return true;
+  }
+  return false;
+}
+
+/// Return true if 'V & Mask' is known to be zero.  We use this predicate to
+/// simplify operations downstream. Mask is known to be zero for bits that V
+/// cannot have.
+///
+/// This function is defined on values with integer type, values with pointer
+/// type, and vectors of integers.  In the case
+/// where V is a vector, the mask, known zero, and known one values are the
+/// same width as the vector element, and the bit is set only if it is true
+/// for all of the elements in the vector.
+bool MaskedValueIsZero(const Value *V, const APInt &Mask, unsigned Depth,
+                       const Query &Q) {
+  KnownBits Known(Mask.getBitWidth());
+  computeKnownBits(V, Known, Depth, Q);
+  return Mask.isSubsetOf(Known.Zero);
+}
+
+// Match a signed min+max clamp pattern like smax(smin(In, CHigh), CLow).
+// Returns the input and lower/upper bounds.
+static bool isSignedMinMaxClamp(const Value *Select, const Value *&In,
+                                const APInt *&CLow, const APInt *&CHigh) {
+  assert(isa<Operator>(Select) &&
+         cast<Operator>(Select)->getOpcode() == Instruction::Select &&
+         "Input should be a Select!");
+
+  const Value *LHS, *RHS, *LHS2, *RHS2;
+  SelectPatternFlavor SPF = matchSelectPattern(Select, LHS, RHS).Flavor;
+  if (SPF != SPF_SMAX && SPF != SPF_SMIN)
+    return false;
+
+  if (!match(RHS, m_APInt(CLow)))
+    return false;
+
+  SelectPatternFlavor SPF2 = matchSelectPattern(LHS, LHS2, RHS2).Flavor;
+  if (getInverseMinMaxFlavor(SPF) != SPF2)
+    return false;
+
+  if (!match(RHS2, m_APInt(CHigh)))
+    return false;
+
+  if (SPF == SPF_SMIN)
+    std::swap(CLow, CHigh);
+
+  In = LHS2;
+  return CLow->sle(*CHigh);
+}
+
+/// For vector constants, loop over the elements and find the constant with the
+/// minimum number of sign bits. Return 0 if the value is not a vector constant
+/// or if any element was not analyzed; otherwise, return the count for the
+/// element with the minimum number of sign bits.
+static unsigned computeNumSignBitsVectorConstant(const Value *V,
+                                                 unsigned TyBits) {
+  const auto *CV = dyn_cast<Constant>(V);
+  if (!CV || !CV->getType()->isVectorTy())
+    return 0;
+
+  unsigned MinSignBits = TyBits;
+  unsigned NumElts = CV->getType()->getVectorNumElements();
+  for (unsigned i = 0; i != NumElts; ++i) {
+    // If we find a non-ConstantInt, bail out.
+    auto *Elt = dyn_cast_or_null<ConstantInt>(CV->getAggregateElement(i));
+    if (!Elt)
+      return 0;
+
+    MinSignBits = std::min(MinSignBits, Elt->getValue().getNumSignBits());
+  }
+
+  return MinSignBits;
+}
+
+static unsigned ComputeNumSignBitsImpl(const Value *V, unsigned Depth,
+                                       const Query &Q);
+
+static unsigned ComputeNumSignBits(const Value *V, unsigned Depth,
+                                   const Query &Q) {
+  unsigned Result = ComputeNumSignBitsImpl(V, Depth, Q);
+  assert(Result > 0 && "At least one sign bit needs to be present!");
+  return Result;
+}
+
+/// Return the number of times the sign bit of the register is replicated into
+/// the other bits. We know that at least 1 bit is always equal to the sign bit
+/// (itself), but other cases can give us information. For example, immediately
+/// after an "ashr X, 2", we know that the top 3 bits are all equal to each
+/// other, so we return 3. For vectors, return the number of sign bits for the
+/// vector element with the minimum number of known sign bits.
+static unsigned ComputeNumSignBitsImpl(const Value *V, unsigned Depth,
+                                       const Query &Q) {
+  assert(Depth <= MaxDepth && "Limit Search Depth");
+
+  // We return the minimum number of sign bits that are guaranteed to be present
+  // in V, so for undef we have to conservatively return 1.  We don't have the
+  // same behavior for poison though -- that's a FIXME today.
+
+  Type *ScalarTy = V->getType()->getScalarType();
+  unsigned TyBits = ScalarTy->isPointerTy() ?
+    Q.DL.getIndexTypeSizeInBits(ScalarTy) :
+    Q.DL.getTypeSizeInBits(ScalarTy);
+
+  unsigned Tmp, Tmp2;
+  unsigned FirstAnswer = 1;
+
+  // Note that ConstantInt is handled by the general computeKnownBits case
+  // below.
+
+  if (Depth == MaxDepth)
+    return 1;  // Limit search depth.
+
+  const Operator *U = dyn_cast<Operator>(V);
+  switch (Operator::getOpcode(V)) {
+  default: break;
+  case Instruction::SExt:
+    Tmp = TyBits - U->getOperand(0)->getType()->getScalarSizeInBits();
+    return ComputeNumSignBits(U->getOperand(0), Depth + 1, Q) + Tmp;
+
+  case Instruction::SDiv: {
+    const APInt *Denominator;
+    // sdiv X, C -> adds log(C) sign bits.
+    if (match(U->getOperand(1), m_APInt(Denominator))) {
+
+      // Ignore non-positive denominator.
+      if (!Denominator->isStrictlyPositive())
+        break;
+
+      // Calculate the incoming numerator bits.
+      unsigned NumBits = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+
+      // Add floor(log(C)) bits to the numerator bits.
+      return std::min(TyBits, NumBits + Denominator->logBase2());
+    }
+    break;
+  }
+
+  case Instruction::SRem: {
+    const APInt *Denominator;
+    // srem X, C -> we know that the result is within [-C+1,C) when C is a
+    // positive constant.  This let us put a lower bound on the number of sign
+    // bits.
+    if (match(U->getOperand(1), m_APInt(Denominator))) {
+
+      // Ignore non-positive denominator.
+      if (!Denominator->isStrictlyPositive())
+        break;
+
+      // Calculate the incoming numerator bits. SRem by a positive constant
+      // can't lower the number of sign bits.
+      unsigned NumrBits =
+          ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+
+      // Calculate the leading sign bit constraints by examining the
+      // denominator.  Given that the denominator is positive, there are two
+      // cases:
+      //
+      //  1. the numerator is positive.  The result range is [0,C) and [0,C) u<
+      //     (1 << ceilLogBase2(C)).
+      //
+      //  2. the numerator is negative.  Then the result range is (-C,0] and
+      //     integers in (-C,0] are either 0 or >u (-1 << ceilLogBase2(C)).
+      //
+      // Thus a lower bound on the number of sign bits is `TyBits -
+      // ceilLogBase2(C)`.
+
+      unsigned ResBits = TyBits - Denominator->ceilLogBase2();
+      return std::max(NumrBits, ResBits);
+    }
+    break;
+  }
+
+  case Instruction::AShr: {
+    Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+    // ashr X, C   -> adds C sign bits.  Vectors too.
+    const APInt *ShAmt;
+    if (match(U->getOperand(1), m_APInt(ShAmt))) {
+      if (ShAmt->uge(TyBits))
+        break;  // Bad shift.
+      unsigned ShAmtLimited = ShAmt->getZExtValue();
+      Tmp += ShAmtLimited;
+      if (Tmp > TyBits) Tmp = TyBits;
+    }
+    return Tmp;
+  }
+  case Instruction::Shl: {
+    const APInt *ShAmt;
+    if (match(U->getOperand(1), m_APInt(ShAmt))) {
+      // shl destroys sign bits.
+      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+      if (ShAmt->uge(TyBits) ||      // Bad shift.
+          ShAmt->uge(Tmp)) break;    // Shifted all sign bits out.
+      Tmp2 = ShAmt->getZExtValue();
+      return Tmp - Tmp2;
+    }
+    break;
+  }
+  case Instruction::And:
+  case Instruction::Or:
+  case Instruction::Xor:    // NOT is handled here.
+    // Logical binary ops preserve the number of sign bits at the worst.
+    Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+    if (Tmp != 1) {
+      Tmp2 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
+      FirstAnswer = std::min(Tmp, Tmp2);
+      // We computed what we know about the sign bits as our first
+      // answer. Now proceed to the generic code that uses
+      // computeKnownBits, and pick whichever answer is better.
+    }
+    break;
+
+  case Instruction::Select: {
+    // If we have a clamp pattern, we know that the number of sign bits will be
+    // the minimum of the clamp min/max range.
+    const Value *X;
+    const APInt *CLow, *CHigh;
+    if (isSignedMinMaxClamp(U, X, CLow, CHigh))
+      return std::min(CLow->getNumSignBits(), CHigh->getNumSignBits());
+
+    Tmp = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
+    if (Tmp == 1) break;
+    Tmp2 = ComputeNumSignBits(U->getOperand(2), Depth + 1, Q);
+    return std::min(Tmp, Tmp2);
+  }
+
+  case Instruction::Add:
+    // Add can have at most one carry bit.  Thus we know that the output
+    // is, at worst, one more bit than the inputs.
+    Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+    if (Tmp == 1) break;
+
+    // Special case decrementing a value (ADD X, -1):
+    if (const auto *CRHS = dyn_cast<Constant>(U->getOperand(1)))
+      if (CRHS->isAllOnesValue()) {
+        KnownBits Known(TyBits);
+        computeKnownBits(U->getOperand(0), Known, Depth + 1, Q);
+
+        // If the input is known to be 0 or 1, the output is 0/-1, which is all
+        // sign bits set.
+        if ((Known.Zero | 1).isAllOnesValue())
+          return TyBits;
+
+        // If we are subtracting one from a positive number, there is no carry
+        // out of the result.
+        if (Known.isNonNegative())
+          return Tmp;
+      }
+
+    Tmp2 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
+    if (Tmp2 == 1) break;
+    return std::min(Tmp, Tmp2)-1;
+
+  case Instruction::Sub:
+    Tmp2 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
+    if (Tmp2 == 1) break;
+
+    // Handle NEG.
+    if (const auto *CLHS = dyn_cast<Constant>(U->getOperand(0)))
+      if (CLHS->isNullValue()) {
+        KnownBits Known(TyBits);
+        computeKnownBits(U->getOperand(1), Known, Depth + 1, Q);
+        // If the input is known to be 0 or 1, the output is 0/-1, which is all
+        // sign bits set.
+        if ((Known.Zero | 1).isAllOnesValue())
+          return TyBits;
+
+        // If the input is known to be positive (the sign bit is known clear),
+        // the output of the NEG has the same number of sign bits as the input.
+        if (Known.isNonNegative())
+          return Tmp2;
+
+        // Otherwise, we treat this like a SUB.
+      }
+
+    // Sub can have at most one carry bit.  Thus we know that the output
+    // is, at worst, one more bit than the inputs.
+    Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+    if (Tmp == 1) break;
+    return std::min(Tmp, Tmp2)-1;
+
+  case Instruction::Mul: {
+    // The output of the Mul can be at most twice the valid bits in the inputs.
+    unsigned SignBitsOp0 = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+    if (SignBitsOp0 == 1) break;
+    unsigned SignBitsOp1 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
+    if (SignBitsOp1 == 1) break;
+    unsigned OutValidBits =
+        (TyBits - SignBitsOp0 + 1) + (TyBits - SignBitsOp1 + 1);
+    return OutValidBits > TyBits ? 1 : TyBits - OutValidBits + 1;
+  }
+
+  case Instruction::PHI: {
+    const PHINode *PN = cast<PHINode>(U);
+    unsigned NumIncomingValues = PN->getNumIncomingValues();
+    // Don't analyze large in-degree PHIs.
+    if (NumIncomingValues > 4) break;
+    // Unreachable blocks may have zero-operand PHI nodes.
+    if (NumIncomingValues == 0) break;
+
+    // Take the minimum of all incoming values.  This can't infinitely loop
+    // because of our depth threshold.
+    Tmp = ComputeNumSignBits(PN->getIncomingValue(0), Depth + 1, Q);
+    for (unsigned i = 1, e = NumIncomingValues; i != e; ++i) {
+      if (Tmp == 1) return Tmp;
+      Tmp = std::min(
+          Tmp, ComputeNumSignBits(PN->getIncomingValue(i), Depth + 1, Q));
+    }
+    return Tmp;
+  }
+
+  case Instruction::Trunc:
+    // FIXME: it's tricky to do anything useful for this, but it is an important
+    // case for targets like X86.
+    break;
+
+  case Instruction::ExtractElement:
+    // Look through extract element. At the moment we keep this simple and skip
+    // tracking the specific element. But at least we might find information
+    // valid for all elements of the vector (for example if vector is sign
+    // extended, shifted, etc).
+    return ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+
+  case Instruction::ShuffleVector: {
+    // TODO: This is copied almost directly from the SelectionDAG version of
+    //       ComputeNumSignBits. It would be better if we could share common
+    //       code. If not, make sure that changes are translated to the DAG.
+
+    // Collect the minimum number of sign bits that are shared by every vector
+    // element referenced by the shuffle.
+    auto *Shuf = cast<ShuffleVectorInst>(U);
+    int NumElts = Shuf->getOperand(0)->getType()->getVectorNumElements();
+    int NumMaskElts = Shuf->getMask()->getType()->getVectorNumElements();
+    APInt DemandedLHS(NumElts, 0), DemandedRHS(NumElts, 0);
+    for (int i = 0; i != NumMaskElts; ++i) {
+      int M = Shuf->getMaskValue(i);
+      assert(M < NumElts * 2 && "Invalid shuffle mask constant");
+      // For undef elements, we don't know anything about the common state of
+      // the shuffle result.
+      if (M == -1)
+        return 1;
+      if (M < NumElts)
+        DemandedLHS.setBit(M % NumElts);
+      else
+        DemandedRHS.setBit(M % NumElts);
+    }
+    Tmp = std::numeric_limits<unsigned>::max();
+    if (!!DemandedLHS)
+      Tmp = ComputeNumSignBits(Shuf->getOperand(0), Depth + 1, Q);
+    if (!!DemandedRHS) {
+      Tmp2 = ComputeNumSignBits(Shuf->getOperand(1), Depth + 1, Q);
+      Tmp = std::min(Tmp, Tmp2);
+    }
+    // If we don't know anything, early out and try computeKnownBits fall-back.
+    if (Tmp == 1)
+      break;
+    assert(Tmp <= V->getType()->getScalarSizeInBits() &&
+           "Failed to determine minimum sign bits");
+    return Tmp;
+  }
+  }
+
+  // Finally, if we can prove that the top bits of the result are 0's or 1's,
+  // use this information.
+
+  // If we can examine all elements of a vector constant successfully, we're
+  // done (we can't do any better than that). If not, keep trying.
+  if (unsigned VecSignBits = computeNumSignBitsVectorConstant(V, TyBits))
+    return VecSignBits;
+
+  KnownBits Known(TyBits);
+  computeKnownBits(V, Known, Depth, Q);
+
+  // If we know that the sign bit is either zero or one, determine the number of
+  // identical bits in the top of the input value.
+  return std::max(FirstAnswer, Known.countMinSignBits());
+}
+
+/// This function computes the integer multiple of Base that equals V.
+/// If successful, it returns true and returns the multiple in
+/// Multiple. If unsuccessful, it returns false. It looks
+/// through SExt instructions only if LookThroughSExt is true.
+bool llvm::ComputeMultiple(Value *V, unsigned Base, Value *&Multiple,
+                           bool LookThroughSExt, unsigned Depth) {
+  const unsigned MaxDepth = 6;
+
+  assert(V && "No Value?");
+  assert(Depth <= MaxDepth && "Limit Search Depth");
+  assert(V->getType()->isIntegerTy() && "Not integer or pointer type!");
+
+  Type *T = V->getType();
+
+  ConstantInt *CI = dyn_cast<ConstantInt>(V);
+
+  if (Base == 0)
+    return false;
+
+  if (Base == 1) {
+    Multiple = V;
+    return true;
+  }
+
+  ConstantExpr *CO = dyn_cast<ConstantExpr>(V);
+  Constant *BaseVal = ConstantInt::get(T, Base);
+  if (CO && CO == BaseVal) {
+    // Multiple is 1.
+    Multiple = ConstantInt::get(T, 1);
+    return true;
+  }
+
+  if (CI && CI->getZExtValue() % Base == 0) {
+    Multiple = ConstantInt::get(T, CI->getZExtValue() / Base);
+    return true;
+  }
+
+  if (Depth == MaxDepth) return false;  // Limit search depth.
+
+  Operator *I = dyn_cast<Operator>(V);
+  if (!I) return false;
+
+  switch (I->getOpcode()) {
+  default: break;
+  case Instruction::SExt:
+    if (!LookThroughSExt) return false;
+    // otherwise fall through to ZExt
+    LLVM_FALLTHROUGH;
+  case Instruction::ZExt:
+    return ComputeMultiple(I->getOperand(0), Base, Multiple,
+                           LookThroughSExt, Depth+1);
+  case Instruction::Shl:
+  case Instruction::Mul: {
+    Value *Op0 = I->getOperand(0);
+    Value *Op1 = I->getOperand(1);
+
+    if (I->getOpcode() == Instruction::Shl) {
+      ConstantInt *Op1CI = dyn_cast<ConstantInt>(Op1);
+      if (!Op1CI) return false;
+      // Turn Op0 << Op1 into Op0 * 2^Op1
+      APInt Op1Int = Op1CI->getValue();
+      uint64_t BitToSet = Op1Int.getLimitedValue(Op1Int.getBitWidth() - 1);
+      APInt API(Op1Int.getBitWidth(), 0);
+      API.setBit(BitToSet);
+      Op1 = ConstantInt::get(V->getContext(), API);
+    }
+
+    Value *Mul0 = nullptr;
+    if (ComputeMultiple(Op0, Base, Mul0, LookThroughSExt, Depth+1)) {
+      if (Constant *Op1C = dyn_cast<Constant>(Op1))
+        if (Constant *MulC = dyn_cast<Constant>(Mul0)) {
+          if (Op1C->getType()->getPrimitiveSizeInBits() <
+              MulC->getType()->getPrimitiveSizeInBits())
+            Op1C = ConstantExpr::getZExt(Op1C, MulC->getType());
+          if (Op1C->getType()->getPrimitiveSizeInBits() >
+              MulC->getType()->getPrimitiveSizeInBits())
+            MulC = ConstantExpr::getZExt(MulC, Op1C->getType());
+
+          // V == Base * (Mul0 * Op1), so return (Mul0 * Op1)
+          Multiple = ConstantExpr::getMul(MulC, Op1C);
+          return true;
+        }
+
+      if (ConstantInt *Mul0CI = dyn_cast<ConstantInt>(Mul0))
+        if (Mul0CI->getValue() == 1) {
+          // V == Base * Op1, so return Op1
+          Multiple = Op1;
+          return true;
+        }
+    }
+
+    Value *Mul1 = nullptr;
+    if (ComputeMultiple(Op1, Base, Mul1, LookThroughSExt, Depth+1)) {
+      if (Constant *Op0C = dyn_cast<Constant>(Op0))
+        if (Constant *MulC = dyn_cast<Constant>(Mul1)) {
+          if (Op0C->getType()->getPrimitiveSizeInBits() <
+              MulC->getType()->getPrimitiveSizeInBits())
+            Op0C = ConstantExpr::getZExt(Op0C, MulC->getType());
+          if (Op0C->getType()->getPrimitiveSizeInBits() >
+              MulC->getType()->getPrimitiveSizeInBits())
+            MulC = ConstantExpr::getZExt(MulC, Op0C->getType());
+
+          // V == Base * (Mul1 * Op0), so return (Mul1 * Op0)
+          Multiple = ConstantExpr::getMul(MulC, Op0C);
+          return true;
+        }
+
+      if (ConstantInt *Mul1CI = dyn_cast<ConstantInt>(Mul1))
+        if (Mul1CI->getValue() == 1) {
+          // V == Base * Op0, so return Op0
+          Multiple = Op0;
+          return true;
+        }
+    }
+  }
+  }
+
+  // We could not determine if V is a multiple of Base.
+  return false;
+}
+
+Intrinsic::ID llvm::getIntrinsicForCallSite(ImmutableCallSite ICS,
+                                            const TargetLibraryInfo *TLI) {
+  const Function *F = ICS.getCalledFunction();
+  if (!F)
+    return Intrinsic::not_intrinsic;
+
+  if (F->isIntrinsic())
+    return F->getIntrinsicID();
+
+  if (!TLI)
+    return Intrinsic::not_intrinsic;
+
+  LibFunc Func;
+  // We're going to make assumptions on the semantics of the functions, check
+  // that the target knows that it's available in this environment and it does
+  // not have local linkage.
+  if (!F || F->hasLocalLinkage() || !TLI->getLibFunc(*F, Func))
+    return Intrinsic::not_intrinsic;
+
+  if (!ICS.onlyReadsMemory())
+    return Intrinsic::not_intrinsic;
+
+  // Otherwise check if we have a call to a function that can be turned into a
+  // vector intrinsic.
+  switch (Func) {
+  default:
+    break;
+  case LibFunc_sin:
+  case LibFunc_sinf:
+  case LibFunc_sinl:
+    return Intrinsic::sin;
+  case LibFunc_cos:
+  case LibFunc_cosf:
+  case LibFunc_cosl:
+    return Intrinsic::cos;
+  case LibFunc_exp:
+  case LibFunc_expf:
+  case LibFunc_expl:
+    return Intrinsic::exp;
+  case LibFunc_exp2:
+  case LibFunc_exp2f:
+  case LibFunc_exp2l:
+    return Intrinsic::exp2;
+  case LibFunc_log:
+  case LibFunc_logf:
+  case LibFunc_logl:
+    return Intrinsic::log;
+  case LibFunc_log10:
+  case LibFunc_log10f:
+  case LibFunc_log10l:
+    return Intrinsic::log10;
+  case LibFunc_log2:
+  case LibFunc_log2f:
+  case LibFunc_log2l:
+    return Intrinsic::log2;
+  case LibFunc_fabs:
+  case LibFunc_fabsf:
+  case LibFunc_fabsl:
+    return Intrinsic::fabs;
+  case LibFunc_fmin:
+  case LibFunc_fminf:
+  case LibFunc_fminl:
+    return Intrinsic::minnum;
+  case LibFunc_fmax:
+  case LibFunc_fmaxf:
+  case LibFunc_fmaxl:
+    return Intrinsic::maxnum;
+  case LibFunc_copysign:
+  case LibFunc_copysignf:
+  case LibFunc_copysignl:
+    return Intrinsic::copysign;
+  case LibFunc_floor:
+  case LibFunc_floorf:
+  case LibFunc_floorl:
+    return Intrinsic::floor;
+  case LibFunc_ceil:
+  case LibFunc_ceilf:
+  case LibFunc_ceill:
+    return Intrinsic::ceil;
+  case LibFunc_trunc:
+  case LibFunc_truncf:
+  case LibFunc_truncl:
+    return Intrinsic::trunc;
+  case LibFunc_rint:
+  case LibFunc_rintf:
+  case LibFunc_rintl:
+    return Intrinsic::rint;
+  case LibFunc_nearbyint:
+  case LibFunc_nearbyintf:
+  case LibFunc_nearbyintl:
+    return Intrinsic::nearbyint;
+  case LibFunc_round:
+  case LibFunc_roundf:
+  case LibFunc_roundl:
+    return Intrinsic::round;
+  case LibFunc_pow:
+  case LibFunc_powf:
+  case LibFunc_powl:
+    return Intrinsic::pow;
+  case LibFunc_sqrt:
+  case LibFunc_sqrtf:
+  case LibFunc_sqrtl:
+    return Intrinsic::sqrt;
+  }
+
+  return Intrinsic::not_intrinsic;
+}
+
+/// Return true if we can prove that the specified FP value is never equal to
+/// -0.0.
+///
+/// NOTE: this function will need to be revisited when we support non-default
+/// rounding modes!
+bool llvm::CannotBeNegativeZero(const Value *V, const TargetLibraryInfo *TLI,
+                                unsigned Depth) {
+  if (auto *CFP = dyn_cast<ConstantFP>(V))
+    return !CFP->getValueAPF().isNegZero();
+
+  // Limit search depth.
+  if (Depth == MaxDepth)
+    return false;
+
+  auto *Op = dyn_cast<Operator>(V);
+  if (!Op)
+    return false;
+
+  // Check if the nsz fast-math flag is set.
+  if (auto *FPO = dyn_cast<FPMathOperator>(Op))
+    if (FPO->hasNoSignedZeros())
+      return true;
+
+  // (fadd x, 0.0) is guaranteed to return +0.0, not -0.0.
+  if (match(Op, m_FAdd(m_Value(), m_PosZeroFP())))
+    return true;
+
+  // sitofp and uitofp turn into +0.0 for zero.
+  if (isa<SIToFPInst>(Op) || isa<UIToFPInst>(Op))
+    return true;
+
+  if (auto *Call = dyn_cast<CallInst>(Op)) {
+    Intrinsic::ID IID = getIntrinsicForCallSite(Call, TLI);
+    switch (IID) {
+    default:
+      break;
+    // sqrt(-0.0) = -0.0, no other negative results are possible.
+    case Intrinsic::sqrt:
+    case Intrinsic::canonicalize:
+      return CannotBeNegativeZero(Call->getArgOperand(0), TLI, Depth + 1);
+    // fabs(x) != -0.0
+    case Intrinsic::fabs:
+      return true;
+    }
+  }
+
+  return false;
+}
+
+/// If \p SignBitOnly is true, test for a known 0 sign bit rather than a
+/// standard ordered compare. e.g. make -0.0 olt 0.0 be true because of the sign
+/// bit despite comparing equal.
+static bool cannotBeOrderedLessThanZeroImpl(const Value *V,
+                                            const TargetLibraryInfo *TLI,
+                                            bool SignBitOnly,
+                                            unsigned Depth) {
+  // TODO: This function does not do the right thing when SignBitOnly is true
+  // and we're lowering to a hypothetical IEEE 754-compliant-but-evil platform
+  // which flips the sign bits of NaNs.  See
+  // https://llvm.org/bugs/show_bug.cgi?id=31702.
+
+  if (const ConstantFP *CFP = dyn_cast<ConstantFP>(V)) {
+    return !CFP->getValueAPF().isNegative() ||
+           (!SignBitOnly && CFP->getValueAPF().isZero());
+  }
+
+  // Handle vector of constants.
+  if (auto *CV = dyn_cast<Constant>(V)) {
+    if (CV->getType()->isVectorTy()) {
+      unsigned NumElts = CV->getType()->getVectorNumElements();
+      for (unsigned i = 0; i != NumElts; ++i) {
+        auto *CFP = dyn_cast_or_null<ConstantFP>(CV->getAggregateElement(i));
+        if (!CFP)
+          return false;
+        if (CFP->getValueAPF().isNegative() &&
+            (SignBitOnly || !CFP->getValueAPF().isZero()))
+          return false;
+      }
+
+      // All non-negative ConstantFPs.
+      return true;
+    }
+  }
+
+  if (Depth == MaxDepth)
+    return false; // Limit search depth.
+
+  const Operator *I = dyn_cast<Operator>(V);
+  if (!I)
+    return false;
+
+  switch (I->getOpcode()) {
+  default:
+    break;
+  // Unsigned integers are always nonnegative.
+  case Instruction::UIToFP:
+    return true;
+  case Instruction::FMul:
+    // x*x is always non-negative or a NaN.
+    if (I->getOperand(0) == I->getOperand(1) &&
+        (!SignBitOnly || cast<FPMathOperator>(I)->hasNoNaNs()))
+      return true;
+
+    LLVM_FALLTHROUGH;
+  case Instruction::FAdd:
+  case Instruction::FDiv:
+  case Instruction::FRem:
+    return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
+                                           Depth + 1) &&
+           cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
+                                           Depth + 1);
+  case Instruction::Select:
+    return cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
+                                           Depth + 1) &&
+           cannotBeOrderedLessThanZeroImpl(I->getOperand(2), TLI, SignBitOnly,
+                                           Depth + 1);
+  case Instruction::FPExt:
+  case Instruction::FPTrunc:
+    // Widening/narrowing never change sign.
+    return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
+                                           Depth + 1);
+  case Instruction::ExtractElement:
+    // Look through extract element. At the moment we keep this simple and skip
+    // tracking the specific element. But at least we might find information
+    // valid for all elements of the vector.
+    return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
+                                           Depth + 1);
+  case Instruction::Call:
+    const auto *CI = cast<CallInst>(I);
+    Intrinsic::ID IID = getIntrinsicForCallSite(CI, TLI);
+    switch (IID) {
+    default:
+      break;
+    case Intrinsic::maxnum:
+      return (isKnownNeverNaN(I->getOperand(0), TLI) &&
+              cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI,
+                                              SignBitOnly, Depth + 1)) ||
+            (isKnownNeverNaN(I->getOperand(1), TLI) &&
+              cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI,
+                                              SignBitOnly, Depth + 1));
+
+    case Intrinsic::maximum:
+      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
+                                             Depth + 1) ||
+             cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
+                                             Depth + 1);
+    case Intrinsic::minnum:
+    case Intrinsic::minimum:
+      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
+                                             Depth + 1) &&
+             cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
+                                             Depth + 1);
+    case Intrinsic::exp:
+    case Intrinsic::exp2:
+    case Intrinsic::fabs:
+      return true;
+
+    case Intrinsic::sqrt:
+      // sqrt(x) is always >= -0 or NaN.  Moreover, sqrt(x) == -0 iff x == -0.
+      if (!SignBitOnly)
+        return true;
+      return CI->hasNoNaNs() && (CI->hasNoSignedZeros() ||
+                                 CannotBeNegativeZero(CI->getOperand(0), TLI));
+
+    case Intrinsic::powi:
+      if (ConstantInt *Exponent = dyn_cast<ConstantInt>(I->getOperand(1))) {
+        // powi(x,n) is non-negative if n is even.
+        if (Exponent->getBitWidth() <= 64 && Exponent->getSExtValue() % 2u == 0)
+          return true;
+      }
+      // TODO: This is not correct.  Given that exp is an integer, here are the
+      // ways that pow can return a negative value:
+      //
+      //   pow(x, exp)    --> negative if exp is odd and x is negative.
+      //   pow(-0, exp)   --> -inf if exp is negative odd.
+      //   pow(-0, exp)   --> -0 if exp is positive odd.
+      //   pow(-inf, exp) --> -0 if exp is negative odd.
+      //   pow(-inf, exp) --> -inf if exp is positive odd.
+      //
+      // Therefore, if !SignBitOnly, we can return true if x >= +0 or x is NaN,
+      // but we must return false if x == -0.  Unfortunately we do not currently
+      // have a way of expressing this constraint.  See details in
+      // https://llvm.org/bugs/show_bug.cgi?id=31702.
+      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
+                                             Depth + 1);
+
+    case Intrinsic::fma:
+    case Intrinsic::fmuladd:
+      // x*x+y is non-negative if y is non-negative.
+      return I->getOperand(0) == I->getOperand(1) &&
+             (!SignBitOnly || cast<FPMathOperator>(I)->hasNoNaNs()) &&
+             cannotBeOrderedLessThanZeroImpl(I->getOperand(2), TLI, SignBitOnly,
+                                             Depth + 1);
+    }
+    break;
+  }
+  return false;
+}
+
+bool llvm::CannotBeOrderedLessThanZero(const Value *V,
+                                       const TargetLibraryInfo *TLI) {
+  return cannotBeOrderedLessThanZeroImpl(V, TLI, false, 0);
+}
+
+bool llvm::SignBitMustBeZero(const Value *V, const TargetLibraryInfo *TLI) {
+  return cannotBeOrderedLessThanZeroImpl(V, TLI, true, 0);
+}
+
+bool llvm::isKnownNeverNaN(const Value *V, const TargetLibraryInfo *TLI,
+                           unsigned Depth) {
+  assert(V->getType()->isFPOrFPVectorTy() && "Querying for NaN on non-FP type");
+
+  // If we're told that NaNs won't happen, assume they won't.
+  if (auto *FPMathOp = dyn_cast<FPMathOperator>(V))
+    if (FPMathOp->hasNoNaNs())
+      return true;
+
+  // Handle scalar constants.
+  if (auto *CFP = dyn_cast<ConstantFP>(V))
+    return !CFP->isNaN();
+
+  if (Depth == MaxDepth)
+    return false;
+
+  if (auto *Inst = dyn_cast<Instruction>(V)) {
+    switch (Inst->getOpcode()) {
+    case Instruction::FAdd:
+    case Instruction::FMul:
+    case Instruction::FSub:
+    case Instruction::FDiv:
+    case Instruction::FRem: {
+      // TODO: Need isKnownNeverInfinity
+      return false;
+    }
+    case Instruction::Select: {
+      return isKnownNeverNaN(Inst->getOperand(1), TLI, Depth + 1) &&
+             isKnownNeverNaN(Inst->getOperand(2), TLI, Depth + 1);
+    }
+    case Instruction::SIToFP:
+    case Instruction::UIToFP:
+      return true;
+    case Instruction::FPTrunc:
+    case Instruction::FPExt:
+      return isKnownNeverNaN(Inst->getOperand(0), TLI, Depth + 1);
+    default:
+      break;
+    }
+  }
+
+  if (const auto *II = dyn_cast<IntrinsicInst>(V)) {
+    switch (II->getIntrinsicID()) {
+    case Intrinsic::canonicalize:
+    case Intrinsic::fabs:
+    case Intrinsic::copysign:
+    case Intrinsic::exp:
+    case Intrinsic::exp2:
+    case Intrinsic::floor:
+    case Intrinsic::ceil:
+    case Intrinsic::trunc:
+    case Intrinsic::rint:
+    case Intrinsic::nearbyint:
+    case Intrinsic::round:
+      return isKnownNeverNaN(II->getArgOperand(0), TLI, Depth + 1);
+    case Intrinsic::sqrt:
+      return isKnownNeverNaN(II->getArgOperand(0), TLI, Depth + 1) &&
+             CannotBeOrderedLessThanZero(II->getArgOperand(0), TLI);
+    case Intrinsic::minnum:
+    case Intrinsic::maxnum:
+      // If either operand is not NaN, the result is not NaN.
+      return isKnownNeverNaN(II->getArgOperand(0), TLI, Depth + 1) ||
+             isKnownNeverNaN(II->getArgOperand(1), TLI, Depth + 1);
+    default:
+      return false;
+    }
+  }
+
+  // Bail out for constant expressions, but try to handle vector constants.
+  if (!V->getType()->isVectorTy() || !isa<Constant>(V))
+    return false;
+
+  // For vectors, verify that each element is not NaN.
+  unsigned NumElts = V->getType()->getVectorNumElements();
+  for (unsigned i = 0; i != NumElts; ++i) {
+    Constant *Elt = cast<Constant>(V)->getAggregateElement(i);
+    if (!Elt)
+      return false;
+    if (isa<UndefValue>(Elt))
+      continue;
+    auto *CElt = dyn_cast<ConstantFP>(Elt);
+    if (!CElt || CElt->isNaN())
+      return false;
+  }
+  // All elements were confirmed not-NaN or undefined.
+  return true;
+}
+
+Value *llvm::isBytewiseValue(Value *V, const DataLayout &DL) {
+
+  // All byte-wide stores are splatable, even of arbitrary variables.
+  if (V->getType()->isIntegerTy(8))
+    return V;
+
+  LLVMContext &Ctx = V->getContext();
+
+  // Undef don't care.
+  auto *UndefInt8 = UndefValue::get(Type::getInt8Ty(Ctx));
+  if (isa<UndefValue>(V))
+    return UndefInt8;
+
+  const uint64_t Size = DL.getTypeStoreSize(V->getType());
+  if (!Size)
+    return UndefInt8;
+
+  Constant *C = dyn_cast<Constant>(V);
+  if (!C) {
+    // Conceptually, we could handle things like:
+    //   %a = zext i8 %X to i16
+    //   %b = shl i16 %a, 8
+    //   %c = or i16 %a, %b
+    // but until there is an example that actually needs this, it doesn't seem
+    // worth worrying about.
+    return nullptr;
+  }
+
+  // Handle 'null' ConstantArrayZero etc.
+  if (C->isNullValue())
+    return Constant::getNullValue(Type::getInt8Ty(Ctx));
+
+  // Constant floating-point values can be handled as integer values if the
+  // corresponding integer value is "byteable".  An important case is 0.0.
+  if (ConstantFP *CFP = dyn_cast<ConstantFP>(C)) {
+    Type *Ty = nullptr;
+    if (CFP->getType()->isHalfTy())
+      Ty = Type::getInt16Ty(Ctx);
+    else if (CFP->getType()->isFloatTy())
+      Ty = Type::getInt32Ty(Ctx);
+    else if (CFP->getType()->isDoubleTy())
+      Ty = Type::getInt64Ty(Ctx);
+    // Don't handle long double formats, which have strange constraints.
+    return Ty ? isBytewiseValue(ConstantExpr::getBitCast(CFP, Ty), DL)
+              : nullptr;
+  }
+
+  // We can handle constant integers that are multiple of 8 bits.
+  if (ConstantInt *CI = dyn_cast<ConstantInt>(C)) {
+    if (CI->getBitWidth() % 8 == 0) {
+      assert(CI->getBitWidth() > 8 && "8 bits should be handled above!");
+      if (!CI->getValue().isSplat(8))
+        return nullptr;
+      return ConstantInt::get(Ctx, CI->getValue().trunc(8));
+    }
+  }
+
+  if (auto *CE = dyn_cast<ConstantExpr>(C)) {
+    if (CE->getOpcode() == Instruction::IntToPtr) {
+      auto PS = DL.getPointerSizeInBits(
+          cast<PointerType>(CE->getType())->getAddressSpace());
+      return isBytewiseValue(
+          ConstantExpr::getIntegerCast(CE->getOperand(0),
+                                       Type::getIntNTy(Ctx, PS), false),
+          DL);
+    }
+  }
+
+  auto Merge = [&](Value *LHS, Value *RHS) -> Value * {
+    if (LHS == RHS)
+      return LHS;
+    if (!LHS || !RHS)
+      return nullptr;
+    if (LHS == UndefInt8)
+      return RHS;
+    if (RHS == UndefInt8)
+      return LHS;
+    return nullptr;
+  };
+
+  if (ConstantDataSequential *CA = dyn_cast<ConstantDataSequential>(C)) {
+    Value *Val = UndefInt8;
+    for (unsigned I = 0, E = CA->getNumElements(); I != E; ++I)
+      if (!(Val = Merge(Val, isBytewiseValue(CA->getElementAsConstant(I), DL))))
+        return nullptr;
+    return Val;
+  }
+
+  if (isa<ConstantAggregate>(C)) {
+    Value *Val = UndefInt8;
+    for (unsigned I = 0, E = C->getNumOperands(); I != E; ++I)
+      if (!(Val = Merge(Val, isBytewiseValue(C->getOperand(I), DL))))
+        return nullptr;
+    return Val;
+  }
+
+  // Don't try to handle the handful of other constants.
+  return nullptr;
+}
+
+// This is the recursive version of BuildSubAggregate. It takes a few different
+// arguments. Idxs is the index within the nested struct From that we are
+// looking at now (which is of type IndexedType). IdxSkip is the number of
+// indices from Idxs that should be left out when inserting into the resulting
+// struct. To is the result struct built so far, new insertvalue instructions
+// build on that.
+static Value *BuildSubAggregate(Value *From, Value* To, Type *IndexedType,
+                                SmallVectorImpl<unsigned> &Idxs,
+                                unsigned IdxSkip,
+                                Instruction *InsertBefore) {
+  StructType *STy = dyn_cast<StructType>(IndexedType);
+  if (STy) {
+    // Save the original To argument so we can modify it
+    Value *OrigTo = To;
+    // General case, the type indexed by Idxs is a struct
+    for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i) {
+      // Process each struct element recursively
+      Idxs.push_back(i);
+      Value *PrevTo = To;
+      To = BuildSubAggregate(From, To, STy->getElementType(i), Idxs, IdxSkip,
+                             InsertBefore);
+      Idxs.pop_back();
+      if (!To) {
+        // Couldn't find any inserted value for this index? Cleanup
+        while (PrevTo != OrigTo) {
+          InsertValueInst* Del = cast<InsertValueInst>(PrevTo);
+          PrevTo = Del->getAggregateOperand();
+          Del->eraseFromParent();
+        }
+        // Stop processing elements
+        break;
+      }
+    }
+    // If we successfully found a value for each of our subaggregates
+    if (To)
+      return To;
+  }
+  // Base case, the type indexed by SourceIdxs is not a struct, or not all of
+  // the struct's elements had a value that was inserted directly. In the latter
+  // case, perhaps we can't determine each of the subelements individually, but
+  // we might be able to find the complete struct somewhere.
+
+  // Find the value that is at that particular spot
+  Value *V = FindInsertedValue(From, Idxs);
+
+  if (!V)
+    return nullptr;
+
+  // Insert the value in the new (sub) aggregate
+  return InsertValueInst::Create(To, V, makeArrayRef(Idxs).slice(IdxSkip),
+                                 "tmp", InsertBefore);
+}
+
+// This helper takes a nested struct and extracts a part of it (which is again a
+// struct) into a new value. For example, given the struct:
+// { a, { b, { c, d }, e } }
+// and the indices "1, 1" this returns
+// { c, d }.
+//
+// It does this by inserting an insertvalue for each element in the resulting
+// struct, as opposed to just inserting a single struct. This will only work if
+// each of the elements of the substruct are known (ie, inserted into From by an
+// insertvalue instruction somewhere).
+//
+// All inserted insertvalue instructions are inserted before InsertBefore
+static Value *BuildSubAggregate(Value *From, ArrayRef<unsigned> idx_range,
+                                Instruction *InsertBefore) {
+  assert(InsertBefore && "Must have someplace to insert!");
+  Type *IndexedType = ExtractValueInst::getIndexedType(From->getType(),
+                                                             idx_range);
+  Value *To = UndefValue::get(IndexedType);
+  SmallVector<unsigned, 10> Idxs(idx_range.begin(), idx_range.end());
+  unsigned IdxSkip = Idxs.size();
+
+  return BuildSubAggregate(From, To, IndexedType, Idxs, IdxSkip, InsertBefore);
+}
+
+/// Given an aggregate and a sequence of indices, see if the scalar value
+/// indexed is already around as a register, for example if it was inserted
+/// directly into the aggregate.
+///
+/// If InsertBefore is not null, this function will duplicate (modified)
+/// insertvalues when a part of a nested struct is extracted.
+Value *llvm::FindInsertedValue(Value *V, ArrayRef<unsigned> idx_range,
+                               Instruction *InsertBefore) {
+  // Nothing to index? Just return V then (this is useful at the end of our
+  // recursion).
+  if (idx_range.empty())
+    return V;
+  // We have indices, so V should have an indexable type.
+  assert((V->getType()->isStructTy() || V->getType()->isArrayTy()) &&
+         "Not looking at a struct or array?");
+  assert(ExtractValueInst::getIndexedType(V->getType(), idx_range) &&
+         "Invalid indices for type?");
+
+  if (Constant *C = dyn_cast<Constant>(V)) {
+    C = C->getAggregateElement(idx_range[0]);
+    if (!C) return nullptr;
+    return FindInsertedValue(C, idx_range.slice(1), InsertBefore);
+  }
+
+  if (InsertValueInst *I = dyn_cast<InsertValueInst>(V)) {
+    // Loop the indices for the insertvalue instruction in parallel with the
+    // requested indices
+    const unsigned *req_idx = idx_range.begin();
+    for (const unsigned *i = I->idx_begin(), *e = I->idx_end();
+         i != e; ++i, ++req_idx) {
+      if (req_idx == idx_range.end()) {
+        // We can't handle this without inserting insertvalues
+        if (!InsertBefore)
+          return nullptr;
+
+        // The requested index identifies a part of a nested aggregate. Handle
+        // this specially. For example,
+        // %A = insertvalue { i32, {i32, i32 } } undef, i32 10, 1, 0
+        // %B = insertvalue { i32, {i32, i32 } } %A, i32 11, 1, 1
+        // %C = extractvalue {i32, { i32, i32 } } %B, 1
+        // This can be changed into
+        // %A = insertvalue {i32, i32 } undef, i32 10, 0
+        // %C = insertvalue {i32, i32 } %A, i32 11, 1
+        // which allows the unused 0,0 element from the nested struct to be
+        // removed.
+        return BuildSubAggregate(V, makeArrayRef(idx_range.begin(), req_idx),
+                                 InsertBefore);
+      }
+
+      // This insert value inserts something else than what we are looking for.
+      // See if the (aggregate) value inserted into has the value we are
+      // looking for, then.
+      if (*req_idx != *i)
+        return FindInsertedValue(I->getAggregateOperand(), idx_range,
+                                 InsertBefore);
+    }
+    // If we end up here, the indices of the insertvalue match with those
+    // requested (though possibly only partially). Now we recursively look at
+    // the inserted value, passing any remaining indices.
+    return FindInsertedValue(I->getInsertedValueOperand(),
+                             makeArrayRef(req_idx, idx_range.end()),
+                             InsertBefore);
+  }
+
+  if (ExtractValueInst *I = dyn_cast<ExtractValueInst>(V)) {
+    // If we're extracting a value from an aggregate that was extracted from
+    // something else, we can extract from that something else directly instead.
+    // However, we will need to chain I's indices with the requested indices.
+
+    // Calculate the number of indices required
+    unsigned size = I->getNumIndices() + idx_range.size();
+    // Allocate some space to put the new indices in
+    SmallVector<unsigned, 5> Idxs;
+    Idxs.reserve(size);
+    // Add indices from the extract value instruction
+    Idxs.append(I->idx_begin(), I->idx_end());
+
+    // Add requested indices
+    Idxs.append(idx_range.begin(), idx_range.end());
+
+    assert(Idxs.size() == size
+           && "Number of indices added not correct?");
+
+    return FindInsertedValue(I->getAggregateOperand(), Idxs, InsertBefore);
+  }
+  // Otherwise, we don't know (such as, extracting from a function return value
+  // or load instruction)
+  return nullptr;
+}
+
+bool llvm::isGEPBasedOnPointerToString(const GEPOperator *GEP,
+                                       unsigned CharSize) {
+  // Make sure the GEP has exactly three arguments.
+  if (GEP->getNumOperands() != 3)
+    return false;
+
+  // Make sure the index-ee is a pointer to array of \p CharSize integers.
+  // CharSize.
+  ArrayType *AT = dyn_cast<ArrayType>(GEP->getSourceElementType());
+  if (!AT || !AT->getElementType()->isIntegerTy(CharSize))
+    return false;
+
+  // Check to make sure that the first operand of the GEP is an integer and
+  // has value 0 so that we are sure we're indexing into the initializer.
+  const ConstantInt *FirstIdx = dyn_cast<ConstantInt>(GEP->getOperand(1));
+  if (!FirstIdx || !FirstIdx->isZero())
+    return false;
+
+  return true;
+}
+
+bool llvm::getConstantDataArrayInfo(const Value *V,
+                                    ConstantDataArraySlice &Slice,
+                                    unsigned ElementSize, uint64_t Offset) {
+  assert(V);
+
+  // Look through bitcast instructions and geps.
+  V = V->stripPointerCasts();
+
+  // If the value is a GEP instruction or constant expression, treat it as an
+  // offset.
+  if (const GEPOperator *GEP = dyn_cast<GEPOperator>(V)) {
+    // The GEP operator should be based on a pointer to string constant, and is
+    // indexing into the string constant.
+    if (!isGEPBasedOnPointerToString(GEP, ElementSize))
+      return false;
+
+    // If the second index isn't a ConstantInt, then this is a variable index
+    // into the array.  If this occurs, we can't say anything meaningful about
+    // the string.
+    uint64_t StartIdx = 0;
+    if (const ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(2)))
+      StartIdx = CI->getZExtValue();
+    else
+      return false;
+    return getConstantDataArrayInfo(GEP->getOperand(0), Slice, ElementSize,
+                                    StartIdx + Offset);
+  }
+
+  // The GEP instruction, constant or instruction, must reference a global
+  // variable that is a constant and is initialized. The referenced constant
+  // initializer is the array that we'll use for optimization.
+  const GlobalVariable *GV = dyn_cast<GlobalVariable>(V);
+  if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer())
+    return false;
+
+  const ConstantDataArray *Array;
+  ArrayType *ArrayTy;
+  if (GV->getInitializer()->isNullValue()) {
+    Type *GVTy = GV->getValueType();
+    if ( (ArrayTy = dyn_cast<ArrayType>(GVTy)) ) {
+      // A zeroinitializer for the array; there is no ConstantDataArray.
+      Array = nullptr;
+    } else {
+      const DataLayout &DL = GV->getParent()->getDataLayout();
+      uint64_t SizeInBytes = DL.getTypeStoreSize(GVTy);
+      uint64_t Length = SizeInBytes / (ElementSize / 8);
+      if (Length <= Offset)
+        return false;
+
+      Slice.Array = nullptr;
+      Slice.Offset = 0;
+      Slice.Length = Length - Offset;
+      return true;
+    }
+  } else {
+    // This must be a ConstantDataArray.
+    Array = dyn_cast<ConstantDataArray>(GV->getInitializer());
+    if (!Array)
+      return false;
+    ArrayTy = Array->getType();
+  }
+  if (!ArrayTy->getElementType()->isIntegerTy(ElementSize))
+    return false;
+
+  uint64_t NumElts = ArrayTy->getArrayNumElements();
+  if (Offset > NumElts)
+    return false;
+
+  Slice.Array = Array;
+  Slice.Offset = Offset;
+  Slice.Length = NumElts - Offset;
+  return true;
+}
+
+/// This function computes the length of a null-terminated C string pointed to
+/// by V. If successful, it returns true and returns the string in Str.
+/// If unsuccessful, it returns false.
+bool llvm::getConstantStringInfo(const Value *V, StringRef &Str,
+                                 uint64_t Offset, bool TrimAtNul) {
+  ConstantDataArraySlice Slice;
+  if (!getConstantDataArrayInfo(V, Slice, 8, Offset))
+    return false;
+
+  if (Slice.Array == nullptr) {
+    if (TrimAtNul) {
+      Str = StringRef();
+      return true;
+    }
+    if (Slice.Length == 1) {
+      Str = StringRef("", 1);
+      return true;
+    }
+    // We cannot instantiate a StringRef as we do not have an appropriate string
+    // of 0s at hand.
+    return false;
+  }
+
+  // Start out with the entire array in the StringRef.
+  Str = Slice.Array->getAsString();
+  // Skip over 'offset' bytes.
+  Str = Str.substr(Slice.Offset);
+
+  if (TrimAtNul) {
+    // Trim off the \0 and anything after it.  If the array is not nul
+    // terminated, we just return the whole end of string.  The client may know
+    // some other way that the string is length-bound.
+    Str = Str.substr(0, Str.find('\0'));
+  }
+  return true;
+}
+
+// These next two are very similar to the above, but also look through PHI
+// nodes.
+// TODO: See if we can integrate these two together.
+
+/// If we can compute the length of the string pointed to by
+/// the specified pointer, return 'len+1'.  If we can't, return 0.
+static uint64_t GetStringLengthH(const Value *V,
+                                 SmallPtrSetImpl<const PHINode*> &PHIs,
+                                 unsigned CharSize) {
+  // Look through noop bitcast instructions.
+  V = V->stripPointerCasts();
+
+  // If this is a PHI node, there are two cases: either we have already seen it
+  // or we haven't.
+  if (const PHINode *PN = dyn_cast<PHINode>(V)) {
+    if (!PHIs.insert(PN).second)
+      return ~0ULL;  // already in the set.
+
+    // If it was new, see if all the input strings are the same length.
+    uint64_t LenSoFar = ~0ULL;
+    for (Value *IncValue : PN->incoming_values()) {
+      uint64_t Len = GetStringLengthH(IncValue, PHIs, CharSize);
+      if (Len == 0) return 0; // Unknown length -> unknown.
+
+      if (Len == ~0ULL) continue;
+
+      if (Len != LenSoFar && LenSoFar != ~0ULL)
+        return 0;    // Disagree -> unknown.
+      LenSoFar = Len;
+    }
+
+    // Success, all agree.
+    return LenSoFar;
+  }
+
+  // strlen(select(c,x,y)) -> strlen(x) ^ strlen(y)
+  if (const SelectInst *SI = dyn_cast<SelectInst>(V)) {
+    uint64_t Len1 = GetStringLengthH(SI->getTrueValue(), PHIs, CharSize);
+    if (Len1 == 0) return 0;
+    uint64_t Len2 = GetStringLengthH(SI->getFalseValue(), PHIs, CharSize);
+    if (Len2 == 0) return 0;
+    if (Len1 == ~0ULL) return Len2;
+    if (Len2 == ~0ULL) return Len1;
+    if (Len1 != Len2) return 0;
+    return Len1;
+  }
+
+  // Otherwise, see if we can read the string.
+  ConstantDataArraySlice Slice;
+  if (!getConstantDataArrayInfo(V, Slice, CharSize))
+    return 0;
+
+  if (Slice.Array == nullptr)
+    return 1;
+
+  // Search for nul characters
+  unsigned NullIndex = 0;
+  for (unsigned E = Slice.Length; NullIndex < E; ++NullIndex) {
+    if (Slice.Array->getElementAsInteger(Slice.Offset + NullIndex) == 0)
+      break;
+  }
+
+  return NullIndex + 1;
+}
+
+/// If we can compute the length of the string pointed to by
+/// the specified pointer, return 'len+1'.  If we can't, return 0.
+uint64_t llvm::GetStringLength(const Value *V, unsigned CharSize) {
+  if (!V->getType()->isPointerTy())
+    return 0;
+
+  SmallPtrSet<const PHINode*, 32> PHIs;
+  uint64_t Len = GetStringLengthH(V, PHIs, CharSize);
+  // If Len is ~0ULL, we had an infinite phi cycle: this is dead code, so return
+  // an empty string as a length.
+  return Len == ~0ULL ? 1 : Len;
+}
+
+const Value *llvm::getArgumentAliasingToReturnedPointer(const CallBase *Call) {
+  assert(Call &&
+         "getArgumentAliasingToReturnedPointer only works on nonnull calls");
+  if (const Value *RV = Call->getReturnedArgOperand())
+    return RV;
+  // This can be used only as a aliasing property.
+  if (isIntrinsicReturningPointerAliasingArgumentWithoutCapturing(Call))
+    return Call->getArgOperand(0);
+  return nullptr;
+}
+
+bool llvm::isIntrinsicReturningPointerAliasingArgumentWithoutCapturing(
+    const CallBase *Call) {
+  return Call->getIntrinsicID() == Intrinsic::launder_invariant_group ||
+         Call->getIntrinsicID() == Intrinsic::strip_invariant_group ||
+         Call->getIntrinsicID() == Intrinsic::aarch64_irg ||
+         Call->getIntrinsicID() == Intrinsic::aarch64_tagp;
+}
+
+/// \p PN defines a loop-variant pointer to an object.  Check if the
+/// previous iteration of the loop was referring to the same object as \p PN.
+static bool isSameUnderlyingObjectInLoop(const PHINode *PN,
+                                         const LoopInfo *LI) {
+  // Find the loop-defined value.
+  Loop *L = LI->getLoopFor(PN->getParent());
+  if (PN->getNumIncomingValues() != 2)
+    return true;
+
+  // Find the value from previous iteration.
+  auto *PrevValue = dyn_cast<Instruction>(PN->getIncomingValue(0));
+  if (!PrevValue || LI->getLoopFor(PrevValue->getParent()) != L)
+    PrevValue = dyn_cast<Instruction>(PN->getIncomingValue(1));
+  if (!PrevValue || LI->getLoopFor(PrevValue->getParent()) != L)
+    return true;
+
+  // If a new pointer is loaded in the loop, the pointer references a different
+  // object in every iteration.  E.g.:
+  //    for (i)
+  //       int *p = a[i];
+  //       ...
+  if (auto *Load = dyn_cast<LoadInst>(PrevValue))
+    if (!L->isLoopInvariant(Load->getPointerOperand()))
+      return false;
+  return true;
+}
+
+Value *llvm::GetUnderlyingObject(Value *V, const DataLayout &DL,
+                                 unsigned MaxLookup) {
+  if (!V->getType()->isPointerTy())
+    return V;
+  for (unsigned Count = 0; MaxLookup == 0 || Count < MaxLookup; ++Count) {
+    if (GEPOperator *GEP = dyn_cast<GEPOperator>(V)) {
+      V = GEP->getPointerOperand();
+    } else if (Operator::getOpcode(V) == Instruction::BitCast ||
+               Operator::getOpcode(V) == Instruction::AddrSpaceCast) {
+      V = cast<Operator>(V)->getOperand(0);
+    } else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
+      if (GA->isInterposable())
+        return V;
+      V = GA->getAliasee();
+    } else if (isa<AllocaInst>(V)) {
+      // An alloca can't be further simplified.
+      return V;
+    } else {
+      if (auto *Call = dyn_cast<CallBase>(V)) {
+        // CaptureTracking can know about special capturing properties of some
+        // intrinsics like launder.invariant.group, that can't be expressed with
+        // the attributes, but have properties like returning aliasing pointer.
+        // Because some analysis may assume that nocaptured pointer is not
+        // returned from some special intrinsic (because function would have to
+        // be marked with returns attribute), it is crucial to use this function
+        // because it should be in sync with CaptureTracking. Not using it may
+        // cause weird miscompilations where 2 aliasing pointers are assumed to
+        // noalias.
+        if (auto *RP = getArgumentAliasingToReturnedPointer(Call)) {
+          V = RP;
+          continue;
+        }
+      }
+
+      // See if InstructionSimplify knows any relevant tricks.
+      if (Instruction *I = dyn_cast<Instruction>(V))
+        // TODO: Acquire a DominatorTree and AssumptionCache and use them.
+        if (Value *Simplified = SimplifyInstruction(I, {DL, I})) {
+          V = Simplified;
+          continue;
+        }
+
+      return V;
+    }
+    assert(V->getType()->isPointerTy() && "Unexpected operand type!");
+  }
+  return V;
+}
+
+void llvm::GetUnderlyingObjects(const Value *V,
+                                SmallVectorImpl<const Value *> &Objects,
+                                const DataLayout &DL, LoopInfo *LI,
+                                unsigned MaxLookup) {
+  SmallPtrSet<const Value *, 4> Visited;
+  SmallVector<const Value *, 4> Worklist;
+  Worklist.push_back(V);
+  do {
+    const Value *P = Worklist.pop_back_val();
+    P = GetUnderlyingObject(P, DL, MaxLookup);
+
+    if (!Visited.insert(P).second)
+      continue;
+
+    if (auto *SI = dyn_cast<SelectInst>(P)) {
+      Worklist.push_back(SI->getTrueValue());
+      Worklist.push_back(SI->getFalseValue());
+      continue;
+    }
+
+    if (auto *PN = dyn_cast<PHINode>(P)) {
+      // If this PHI changes the underlying object in every iteration of the
+      // loop, don't look through it.  Consider:
+      //   int **A;
+      //   for (i) {
+      //     Prev = Curr;     // Prev = PHI (Prev_0, Curr)
+      //     Curr = A[i];
+      //     *Prev, *Curr;
+      //
+      // Prev is tracking Curr one iteration behind so they refer to different
+      // underlying objects.
+      if (!LI || !LI->isLoopHeader(PN->getParent()) ||
+          isSameUnderlyingObjectInLoop(PN, LI))
+        for (Value *IncValue : PN->incoming_values())
+          Worklist.push_back(IncValue);
+      continue;
+    }
+
+    Objects.push_back(P);
+  } while (!Worklist.empty());
+}
+
+/// This is the function that does the work of looking through basic
+/// ptrtoint+arithmetic+inttoptr sequences.
+static const Value *getUnderlyingObjectFromInt(const Value *V) {
+  do {
+    if (const Operator *U = dyn_cast<Operator>(V)) {
+      // If we find a ptrtoint, we can transfer control back to the
+      // regular getUnderlyingObjectFromInt.
+      if (U->getOpcode() == Instruction::PtrToInt)
+        return U->getOperand(0);
+      // If we find an add of a constant, a multiplied value, or a phi, it's
+      // likely that the other operand will lead us to the base
+      // object. We don't have to worry about the case where the
+      // object address is somehow being computed by the multiply,
+      // because our callers only care when the result is an
+      // identifiable object.
+      if (U->getOpcode() != Instruction::Add ||
+          (!isa<ConstantInt>(U->getOperand(1)) &&
+           Operator::getOpcode(U->getOperand(1)) != Instruction::Mul &&
+           !isa<PHINode>(U->getOperand(1))))
+        return V;
+      V = U->getOperand(0);
+    } else {
+      return V;
+    }
+    assert(V->getType()->isIntegerTy() && "Unexpected operand type!");
+  } while (true);
+}
+
+/// This is a wrapper around GetUnderlyingObjects and adds support for basic
+/// ptrtoint+arithmetic+inttoptr sequences.
+/// It returns false if unidentified object is found in GetUnderlyingObjects.
+bool llvm::getUnderlyingObjectsForCodeGen(const Value *V,
+                          SmallVectorImpl<Value *> &Objects,
+                          const DataLayout &DL) {
+  SmallPtrSet<const Value *, 16> Visited;
+  SmallVector<const Value *, 4> Working(1, V);
+  do {
+    V = Working.pop_back_val();
+
+    SmallVector<const Value *, 4> Objs;
+    GetUnderlyingObjects(V, Objs, DL);
+
+    for (const Value *V : Objs) {
+      if (!Visited.insert(V).second)
+        continue;
+      if (Operator::getOpcode(V) == Instruction::IntToPtr) {
+        const Value *O =
+          getUnderlyingObjectFromInt(cast<User>(V)->getOperand(0));
+        if (O->getType()->isPointerTy()) {
+          Working.push_back(O);
+          continue;
+        }
+      }
+      // If GetUnderlyingObjects fails to find an identifiable object,
+      // getUnderlyingObjectsForCodeGen also fails for safety.
+      if (!isIdentifiedObject(V)) {
+        Objects.clear();
+        return false;
+      }
+      Objects.push_back(const_cast<Value *>(V));
+    }
+  } while (!Working.empty());
+  return true;
+}
+
+/// Return true if the only users of this pointer are lifetime markers.
+bool llvm::onlyUsedByLifetimeMarkers(const Value *V) {
+  for (const User *U : V->users()) {
+    const IntrinsicInst *II = dyn_cast<IntrinsicInst>(U);
+    if (!II) return false;
+
+    if (!II->isLifetimeStartOrEnd())
+      return false;
+  }
+  return true;
+}
+
+bool llvm::isSafeToSpeculativelyExecute(const Value *V,
+                                        const Instruction *CtxI,
+                                        const DominatorTree *DT) {
+  const Operator *Inst = dyn_cast<Operator>(V);
+  if (!Inst)
+    return false;
+
+  for (unsigned i = 0, e = Inst->getNumOperands(); i != e; ++i)
+    if (Constant *C = dyn_cast<Constant>(Inst->getOperand(i)))
+      if (C->canTrap())
+        return false;
+
+  switch (Inst->getOpcode()) {
+  default:
+    return true;
+  case Instruction::UDiv:
+  case Instruction::URem: {
+    // x / y is undefined if y == 0.
+    const APInt *V;
+    if (match(Inst->getOperand(1), m_APInt(V)))
+      return *V != 0;
+    return false;
+  }
+  case Instruction::SDiv:
+  case Instruction::SRem: {
+    // x / y is undefined if y == 0 or x == INT_MIN and y == -1
+    const APInt *Numerator, *Denominator;
+    if (!match(Inst->getOperand(1), m_APInt(Denominator)))
+      return false;
+    // We cannot hoist this division if the denominator is 0.
+    if (*Denominator == 0)
+      return false;
+    // It's safe to hoist if the denominator is not 0 or -1.
+    if (*Denominator != -1)
+      return true;
+    // At this point we know that the denominator is -1.  It is safe to hoist as
+    // long we know that the numerator is not INT_MIN.
+    if (match(Inst->getOperand(0), m_APInt(Numerator)))
+      return !Numerator->isMinSignedValue();
+    // The numerator *might* be MinSignedValue.
+    return false;
+  }
+  case Instruction::Load: {
+    const LoadInst *LI = cast<LoadInst>(Inst);
+    if (!LI->isUnordered() ||
+        // Speculative load may create a race that did not exist in the source.
+        LI->getFunction()->hasFnAttribute(Attribute::SanitizeThread) ||
+        // Speculative load may load data from dirty regions.
+        LI->getFunction()->hasFnAttribute(Attribute::SanitizeAddress) ||
+        LI->getFunction()->hasFnAttribute(Attribute::SanitizeHWAddress))
+      return false;
+    const DataLayout &DL = LI->getModule()->getDataLayout();
+    return isDereferenceableAndAlignedPointer(LI->getPointerOperand(),
+                                              LI->getType(), LI->getAlignment(),
+                                              DL, CtxI, DT);
+  }
+  case Instruction::Call: {
+    auto *CI = cast<const CallInst>(Inst);
+    const Function *Callee = CI->getCalledFunction();
+
+    // The called function could have undefined behavior or side-effects, even
+    // if marked readnone nounwind.
+    return Callee && Callee->isSpeculatable();
+  }
+  case Instruction::VAArg:
+  case Instruction::Alloca:
+  case Instruction::Invoke:
+  case Instruction::CallBr:
+  case Instruction::PHI:
+  case Instruction::Store:
+  case Instruction::Ret:
+  case Instruction::Br:
+  case Instruction::IndirectBr:
+  case Instruction::Switch:
+  case Instruction::Unreachable:
+  case Instruction::Fence:
+  case Instruction::AtomicRMW:
+  case Instruction::AtomicCmpXchg:
+  case Instruction::LandingPad:
+  case Instruction::Resume:
+  case Instruction::CatchSwitch:
+  case Instruction::CatchPad:
+  case Instruction::CatchRet:
+  case Instruction::CleanupPad:
+  case Instruction::CleanupRet:
+    return false; // Misc instructions which have effects
+  }
+}
+
+bool llvm::mayBeMemoryDependent(const Instruction &I) {
+  return I.mayReadOrWriteMemory() || !isSafeToSpeculativelyExecute(&I);
+}
+
+/// Convert ConstantRange OverflowResult into ValueTracking OverflowResult.
+static OverflowResult mapOverflowResult(ConstantRange::OverflowResult OR) {
+  switch (OR) {
+    case ConstantRange::OverflowResult::MayOverflow:
+      return OverflowResult::MayOverflow;
+    case ConstantRange::OverflowResult::AlwaysOverflowsLow:
+      return OverflowResult::AlwaysOverflowsLow;
+    case ConstantRange::OverflowResult::AlwaysOverflowsHigh:
+      return OverflowResult::AlwaysOverflowsHigh;
+    case ConstantRange::OverflowResult::NeverOverflows:
+      return OverflowResult::NeverOverflows;
+  }
+  llvm_unreachable("Unknown OverflowResult");
+}
+
+/// Combine constant ranges from computeConstantRange() and computeKnownBits().
+static ConstantRange computeConstantRangeIncludingKnownBits(
+    const Value *V, bool ForSigned, const DataLayout &DL, unsigned Depth,
+    AssumptionCache *AC, const Instruction *CxtI, const DominatorTree *DT,
+    OptimizationRemarkEmitter *ORE = nullptr, bool UseInstrInfo = true) {
+  KnownBits Known = computeKnownBits(
+      V, DL, Depth, AC, CxtI, DT, ORE, UseInstrInfo);
+  ConstantRange CR1 = ConstantRange::fromKnownBits(Known, ForSigned);
+  ConstantRange CR2 = computeConstantRange(V, UseInstrInfo);
+  ConstantRange::PreferredRangeType RangeType =
+      ForSigned ? ConstantRange::Signed : ConstantRange::Unsigned;
+  return CR1.intersectWith(CR2, RangeType);
+}
+
+OverflowResult llvm::computeOverflowForUnsignedMul(
+    const Value *LHS, const Value *RHS, const DataLayout &DL,
+    AssumptionCache *AC, const Instruction *CxtI, const DominatorTree *DT,
+    bool UseInstrInfo) {
+  KnownBits LHSKnown = computeKnownBits(LHS, DL, /*Depth=*/0, AC, CxtI, DT,
+                                        nullptr, UseInstrInfo);
+  KnownBits RHSKnown = computeKnownBits(RHS, DL, /*Depth=*/0, AC, CxtI, DT,
+                                        nullptr, UseInstrInfo);
+  ConstantRange LHSRange = ConstantRange::fromKnownBits(LHSKnown, false);
+  ConstantRange RHSRange = ConstantRange::fromKnownBits(RHSKnown, false);
+  return mapOverflowResult(LHSRange.unsignedMulMayOverflow(RHSRange));
+}
+
+OverflowResult
+llvm::computeOverflowForSignedMul(const Value *LHS, const Value *RHS,
+                                  const DataLayout &DL, AssumptionCache *AC,
+                                  const Instruction *CxtI,
+                                  const DominatorTree *DT, bool UseInstrInfo) {
+  // Multiplying n * m significant bits yields a result of n + m significant
+  // bits. If the total number of significant bits does not exceed the
+  // result bit width (minus 1), there is no overflow.
+  // This means if we have enough leading sign bits in the operands
+  // we can guarantee that the result does not overflow.
+  // Ref: "Hacker's Delight" by Henry Warren
+  unsigned BitWidth = LHS->getType()->getScalarSizeInBits();
+
+  // Note that underestimating the number of sign bits gives a more
+  // conservative answer.
+  unsigned SignBits = ComputeNumSignBits(LHS, DL, 0, AC, CxtI, DT) +
+                      ComputeNumSignBits(RHS, DL, 0, AC, CxtI, DT);
+
+  // First handle the easy case: if we have enough sign bits there's
+  // definitely no overflow.
+  if (SignBits > BitWidth + 1)
+    return OverflowResult::NeverOverflows;
+
+  // There are two ambiguous cases where there can be no overflow:
+  //   SignBits == BitWidth + 1    and
+  //   SignBits == BitWidth
+  // The second case is difficult to check, therefore we only handle the
+  // first case.
+  if (SignBits == BitWidth + 1) {
+    // It overflows only when both arguments are negative and the true
+    // product is exactly the minimum negative number.
+    // E.g. mul i16 with 17 sign bits: 0xff00 * 0xff80 = 0x8000
+    // For simplicity we just check if at least one side is not negative.
+    KnownBits LHSKnown = computeKnownBits(LHS, DL, /*Depth=*/0, AC, CxtI, DT,
+                                          nullptr, UseInstrInfo);
+    KnownBits RHSKnown = computeKnownBits(RHS, DL, /*Depth=*/0, AC, CxtI, DT,
+                                          nullptr, UseInstrInfo);
+    if (LHSKnown.isNonNegative() || RHSKnown.isNonNegative())
+      return OverflowResult::NeverOverflows;
+  }
+  return OverflowResult::MayOverflow;
+}
+
+OverflowResult llvm::computeOverflowForUnsignedAdd(
+    const Value *LHS, const Value *RHS, const DataLayout &DL,
+    AssumptionCache *AC, const Instruction *CxtI, const DominatorTree *DT,
+    bool UseInstrInfo) {
+  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
+      LHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT,
+      nullptr, UseInstrInfo);
+  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
+      RHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT,
+      nullptr, UseInstrInfo);
+  return mapOverflowResult(LHSRange.unsignedAddMayOverflow(RHSRange));
+}
+
+static OverflowResult computeOverflowForSignedAdd(const Value *LHS,
+                                                  const Value *RHS,
+                                                  const AddOperator *Add,
+                                                  const DataLayout &DL,
+                                                  AssumptionCache *AC,
+                                                  const Instruction *CxtI,
+                                                  const DominatorTree *DT) {
+  if (Add && Add->hasNoSignedWrap()) {
+    return OverflowResult::NeverOverflows;
+  }
+
+  // If LHS and RHS each have at least two sign bits, the addition will look
+  // like
+  //
+  // XX..... +
+  // YY.....
+  //
+  // If the carry into the most significant position is 0, X and Y can't both
+  // be 1 and therefore the carry out of the addition is also 0.
+  //
+  // If the carry into the most significant position is 1, X and Y can't both
+  // be 0 and therefore the carry out of the addition is also 1.
+  //
+  // Since the carry into the most significant position is always equal to
+  // the carry out of the addition, there is no signed overflow.
+  if (ComputeNumSignBits(LHS, DL, 0, AC, CxtI, DT) > 1 &&
+      ComputeNumSignBits(RHS, DL, 0, AC, CxtI, DT) > 1)
+    return OverflowResult::NeverOverflows;
+
+  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
+      LHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
+  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
+      RHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
+  OverflowResult OR =
+      mapOverflowResult(LHSRange.signedAddMayOverflow(RHSRange));
+  if (OR != OverflowResult::MayOverflow)
+    return OR;
+
+  // The remaining code needs Add to be available. Early returns if not so.
+  if (!Add)
+    return OverflowResult::MayOverflow;
+
+  // If the sign of Add is the same as at least one of the operands, this add
+  // CANNOT overflow. If this can be determined from the known bits of the
+  // operands the above signedAddMayOverflow() check will have already done so.
+  // The only other way to improve on the known bits is from an assumption, so
+  // call computeKnownBitsFromAssume() directly.
+  bool LHSOrRHSKnownNonNegative =
+      (LHSRange.isAllNonNegative() || RHSRange.isAllNonNegative());
+  bool LHSOrRHSKnownNegative =
+      (LHSRange.isAllNegative() || RHSRange.isAllNegative());
+  if (LHSOrRHSKnownNonNegative || LHSOrRHSKnownNegative) {
+    KnownBits AddKnown(LHSRange.getBitWidth());
+    computeKnownBitsFromAssume(
+        Add, AddKnown, /*Depth=*/0, Query(DL, AC, CxtI, DT, true));
+    if ((AddKnown.isNonNegative() && LHSOrRHSKnownNonNegative) ||
+        (AddKnown.isNegative() && LHSOrRHSKnownNegative))
+      return OverflowResult::NeverOverflows;
+  }
+
+  return OverflowResult::MayOverflow;
+}
+
+OverflowResult llvm::computeOverflowForUnsignedSub(const Value *LHS,
+                                                   const Value *RHS,
+                                                   const DataLayout &DL,
+                                                   AssumptionCache *AC,
+                                                   const Instruction *CxtI,
+                                                   const DominatorTree *DT) {
+  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
+      LHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT);
+  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
+      RHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT);
+  return mapOverflowResult(LHSRange.unsignedSubMayOverflow(RHSRange));
+}
+
+OverflowResult llvm::computeOverflowForSignedSub(const Value *LHS,
+                                                 const Value *RHS,
+                                                 const DataLayout &DL,
+                                                 AssumptionCache *AC,
+                                                 const Instruction *CxtI,
+                                                 const DominatorTree *DT) {
+  // If LHS and RHS each have at least two sign bits, the subtraction
+  // cannot overflow.
+  if (ComputeNumSignBits(LHS, DL, 0, AC, CxtI, DT) > 1 &&
+      ComputeNumSignBits(RHS, DL, 0, AC, CxtI, DT) > 1)
+    return OverflowResult::NeverOverflows;
+
+  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
+      LHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
+  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
+      RHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
+  return mapOverflowResult(LHSRange.signedSubMayOverflow(RHSRange));
+}
+
+bool llvm::isOverflowIntrinsicNoWrap(const WithOverflowInst *WO,
+                                     const DominatorTree &DT) {
+  SmallVector<const BranchInst *, 2> GuardingBranches;
+  SmallVector<const ExtractValueInst *, 2> Results;
+
+  for (const User *U : WO->users()) {
+    if (const auto *EVI = dyn_cast<ExtractValueInst>(U)) {
+      assert(EVI->getNumIndices() == 1 && "Obvious from CI's type");
+
+      if (EVI->getIndices()[0] == 0)
+        Results.push_back(EVI);
+      else {
+        assert(EVI->getIndices()[0] == 1 && "Obvious from CI's type");
+
+        for (const auto *U : EVI->users())
+          if (const auto *B = dyn_cast<BranchInst>(U)) {
+            assert(B->isConditional() && "How else is it using an i1?");
+            GuardingBranches.push_back(B);
+          }
+      }
+    } else {
+      // We are using the aggregate directly in a way we don't want to analyze
+      // here (storing it to a global, say).
+      return false;
+    }
+  }
+
+  auto AllUsesGuardedByBranch = [&](const BranchInst *BI) {
+    BasicBlockEdge NoWrapEdge(BI->getParent(), BI->getSuccessor(1));
+    if (!NoWrapEdge.isSingleEdge())
+      return false;
+
+    // Check if all users of the add are provably no-wrap.
+    for (const auto *Result : Results) {
+      // If the extractvalue itself is not executed on overflow, the we don't
+      // need to check each use separately, since domination is transitive.
+      if (DT.dominates(NoWrapEdge, Result->getParent()))
+        continue;
+
+      for (auto &RU : Result->uses())
+        if (!DT.dominates(NoWrapEdge, RU))
+          return false;
+    }
+
+    return true;
+  };
+
+  return llvm::any_of(GuardingBranches, AllUsesGuardedByBranch);
+}
+
+
+OverflowResult llvm::computeOverflowForSignedAdd(const AddOperator *Add,
+                                                 const DataLayout &DL,
+                                                 AssumptionCache *AC,
+                                                 const Instruction *CxtI,
+                                                 const DominatorTree *DT) {
+  return ::computeOverflowForSignedAdd(Add->getOperand(0), Add->getOperand(1),
+                                       Add, DL, AC, CxtI, DT);
+}
+
+OverflowResult llvm::computeOverflowForSignedAdd(const Value *LHS,
+                                                 const Value *RHS,
+                                                 const DataLayout &DL,
+                                                 AssumptionCache *AC,
+                                                 const Instruction *CxtI,
+                                                 const DominatorTree *DT) {
+  return ::computeOverflowForSignedAdd(LHS, RHS, nullptr, DL, AC, CxtI, DT);
+}
+
+bool llvm::isGuaranteedToTransferExecutionToSuccessor(const Instruction *I) {
+  // A memory operation returns normally if it isn't volatile. A volatile
+  // operation is allowed to trap.
+  //
+  // An atomic operation isn't guaranteed to return in a reasonable amount of
+  // time because it's possible for another thread to interfere with it for an
+  // arbitrary length of time, but programs aren't allowed to rely on that.
+  if (const LoadInst *LI = dyn_cast<LoadInst>(I))
+    return !LI->isVolatile();
+  if (const StoreInst *SI = dyn_cast<StoreInst>(I))
+    return !SI->isVolatile();
+  if (const AtomicCmpXchgInst *CXI = dyn_cast<AtomicCmpXchgInst>(I))
+    return !CXI->isVolatile();
+  if (const AtomicRMWInst *RMWI = dyn_cast<AtomicRMWInst>(I))
+    return !RMWI->isVolatile();
+  if (const MemIntrinsic *MII = dyn_cast<MemIntrinsic>(I))
+    return !MII->isVolatile();
+
+  // If there is no successor, then execution can't transfer to it.
+  if (const auto *CRI = dyn_cast<CleanupReturnInst>(I))
+    return !CRI->unwindsToCaller();
+  if (const auto *CatchSwitch = dyn_cast<CatchSwitchInst>(I))
+    return !CatchSwitch->unwindsToCaller();
+  if (isa<ResumeInst>(I))
+    return false;
+  if (isa<ReturnInst>(I))
+    return false;
+  if (isa<UnreachableInst>(I))
+    return false;
+
+  // Calls can throw, or contain an infinite loop, or kill the process.
+  if (auto CS = ImmutableCallSite(I)) {
+    // Call sites that throw have implicit non-local control flow.
+    if (!CS.doesNotThrow())
+      return false;
+
+    // A function which doens't throw and has "willreturn" attribute will
+    // always return.
+    if (CS.hasFnAttr(Attribute::WillReturn))
+      return true;
+
+    // Non-throwing call sites can loop infinitely, call exit/pthread_exit
+    // etc. and thus not return.  However, LLVM already assumes that
+    //
+    //  - Thread exiting actions are modeled as writes to memory invisible to
+    //    the program.
+    //
+    //  - Loops that don't have side effects (side effects are volatile/atomic
+    //    stores and IO) always terminate (see http://llvm.org/PR965).
+    //    Furthermore IO itself is also modeled as writes to memory invisible to
+    //    the program.
+    //
+    // We rely on those assumptions here, and use the memory effects of the call
+    // target as a proxy for checking that it always returns.
+
+    // FIXME: This isn't aggressive enough; a call which only writes to a global
+    // is guaranteed to return.
+    return CS.onlyReadsMemory() || CS.onlyAccessesArgMemory() ||
+           match(I, m_Intrinsic<Intrinsic::assume>()) ||
+           match(I, m_Intrinsic<Intrinsic::sideeffect>()) ||
+           match(I, m_Intrinsic<Intrinsic::experimental_widenable_condition>());
+  }
+
+  // Other instructions return normally.
+  return true;
+}
+
+bool llvm::isGuaranteedToTransferExecutionToSuccessor(const BasicBlock *BB) {
+  // TODO: This is slightly conservative for invoke instruction since exiting
+  // via an exception *is* normal control for them.
+  for (auto I = BB->begin(), E = BB->end(); I != E; ++I)
+    if (!isGuaranteedToTransferExecutionToSuccessor(&*I))
+      return false;
+  return true;
+}
+
+bool llvm::isGuaranteedToExecuteForEveryIteration(const Instruction *I,
+                                                  const Loop *L) {
+  // The loop header is guaranteed to be executed for every iteration.
+  //
+  // FIXME: Relax this constraint to cover all basic blocks that are
+  // guaranteed to be executed at every iteration.
+  if (I->getParent() != L->getHeader()) return false;
+
+  for (const Instruction &LI : *L->getHeader()) {
+    if (&LI == I) return true;
+    if (!isGuaranteedToTransferExecutionToSuccessor(&LI)) return false;
+  }
+  llvm_unreachable("Instruction not contained in its own parent basic block.");
+}
+
+bool llvm::propagatesFullPoison(const Instruction *I) {
+  // TODO: This should include all instructions apart from phis, selects and
+  // call-like instructions.
+  switch (I->getOpcode()) {
+  case Instruction::Add:
+  case Instruction::Sub:
+  case Instruction::Xor:
+  case Instruction::Trunc:
+  case Instruction::BitCast:
+  case Instruction::AddrSpaceCast:
+  case Instruction::Mul:
+  case Instruction::Shl:
+  case Instruction::GetElementPtr:
+    // These operations all propagate poison unconditionally. Note that poison
+    // is not any particular value, so xor or subtraction of poison with
+    // itself still yields poison, not zero.
+    return true;
+
+  case Instruction::AShr:
+  case Instruction::SExt:
+    // For these operations, one bit of the input is replicated across
+    // multiple output bits. A replicated poison bit is still poison.
+    return true;
+
+  case Instruction::ICmp:
+    // Comparing poison with any value yields poison.  This is why, for
+    // instance, x s< (x +nsw 1) can be folded to true.
+    return true;
+
+  default:
+    return false;
+  }
+}
+
+const Value *llvm::getGuaranteedNonFullPoisonOp(const Instruction *I) {
+  switch (I->getOpcode()) {
+    case Instruction::Store:
+      return cast<StoreInst>(I)->getPointerOperand();
+
+    case Instruction::Load:
+      return cast<LoadInst>(I)->getPointerOperand();
+
+    case Instruction::AtomicCmpXchg:
+      return cast<AtomicCmpXchgInst>(I)->getPointerOperand();
+
+    case Instruction::AtomicRMW:
+      return cast<AtomicRMWInst>(I)->getPointerOperand();
+
+    case Instruction::UDiv:
+    case Instruction::SDiv:
+    case Instruction::URem:
+    case Instruction::SRem:
+      return I->getOperand(1);
+
+    default:
+      // Note: It's really tempting to think that a conditional branch or
+      // switch should be listed here, but that's incorrect.  It's not
+      // branching off of poison which is UB, it is executing a side effecting
+      // instruction which follows the branch.
+      return nullptr;
+  }
+}
+
+bool llvm::mustTriggerUB(const Instruction *I,
+                         const SmallSet<const Value *, 16>& KnownPoison) {
+  auto *NotPoison = getGuaranteedNonFullPoisonOp(I);
+  return (NotPoison && KnownPoison.count(NotPoison));
+}
+
+
+bool llvm::programUndefinedIfFullPoison(const Instruction *PoisonI) {
+  // We currently only look for uses of poison values within the same basic
+  // block, as that makes it easier to guarantee that the uses will be
+  // executed given that PoisonI is executed.
+  //
+  // FIXME: Expand this to consider uses beyond the same basic block. To do
+  // this, look out for the distinction between post-dominance and strong
+  // post-dominance.
+  const BasicBlock *BB = PoisonI->getParent();
+
+  // Set of instructions that we have proved will yield poison if PoisonI
+  // does.
+  SmallSet<const Value *, 16> YieldsPoison;
+  SmallSet<const BasicBlock *, 4> Visited;
+  YieldsPoison.insert(PoisonI);
+  Visited.insert(PoisonI->getParent());
+
+  BasicBlock::const_iterator Begin = PoisonI->getIterator(), End = BB->end();
+
+  unsigned Iter = 0;
+  while (Iter++ < MaxDepth) {
+    for (auto &I : make_range(Begin, End)) {
+      if (&I != PoisonI) {
+        if (mustTriggerUB(&I, YieldsPoison))
+          return true;
+        if (!isGuaranteedToTransferExecutionToSuccessor(&I))
+          return false;
+      }
+
+      // Mark poison that propagates from I through uses of I.
+      if (YieldsPoison.count(&I)) {
+        for (const User *User : I.users()) {
+          const Instruction *UserI = cast<Instruction>(User);
+          if (propagatesFullPoison(UserI))
+            YieldsPoison.insert(User);
+        }
+      }
+    }
+
+    if (auto *NextBB = BB->getSingleSuccessor()) {
+      if (Visited.insert(NextBB).second) {
+        BB = NextBB;
+        Begin = BB->getFirstNonPHI()->getIterator();
+        End = BB->end();
+        continue;
+      }
+    }
+
+    break;
+  }
+  return false;
+}
+
+static bool isKnownNonNaN(const Value *V, FastMathFlags FMF) {
+  if (FMF.noNaNs())
+    return true;
+
+  if (auto *C = dyn_cast<ConstantFP>(V))
+    return !C->isNaN();
+
+  if (auto *C = dyn_cast<ConstantDataVector>(V)) {
+    if (!C->getElementType()->isFloatingPointTy())
+      return false;
+    for (unsigned I = 0, E = C->getNumElements(); I < E; ++I) {
+      if (C->getElementAsAPFloat(I).isNaN())
+        return false;
+    }
+    return true;
+  }
+
+  return false;
+}
+
+static bool isKnownNonZero(const Value *V) {
+  if (auto *C = dyn_cast<ConstantFP>(V))
+    return !C->isZero();
+
+  if (auto *C = dyn_cast<ConstantDataVector>(V)) {
+    if (!C->getElementType()->isFloatingPointTy())
+      return false;
+    for (unsigned I = 0, E = C->getNumElements(); I < E; ++I) {
+      if (C->getElementAsAPFloat(I).isZero())
+        return false;
+    }
+    return true;
+  }
+
+  return false;
+}
+
+/// Match clamp pattern for float types without care about NaNs or signed zeros.
+/// Given non-min/max outer cmp/select from the clamp pattern this
+/// function recognizes if it can be substitued by a "canonical" min/max
+/// pattern.
+static SelectPatternResult matchFastFloatClamp(CmpInst::Predicate Pred,
+                                               Value *CmpLHS, Value *CmpRHS,
+                                               Value *TrueVal, Value *FalseVal,
+                                               Value *&LHS, Value *&RHS) {
+  // Try to match
+  //   X < C1 ? C1 : Min(X, C2) --> Max(C1, Min(X, C2))
+  //   X > C1 ? C1 : Max(X, C2) --> Min(C1, Max(X, C2))
+  // and return description of the outer Max/Min.
+
+  // First, check if select has inverse order:
+  if (CmpRHS == FalseVal) {
+    std::swap(TrueVal, FalseVal);
+    Pred = CmpInst::getInversePredicate(Pred);
+  }
+
+  // Assume success now. If there's no match, callers should not use these anyway.
+  LHS = TrueVal;
+  RHS = FalseVal;
+
+  const APFloat *FC1;
+  if (CmpRHS != TrueVal || !match(CmpRHS, m_APFloat(FC1)) || !FC1->isFinite())
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  const APFloat *FC2;
+  switch (Pred) {
+  case CmpInst::FCMP_OLT:
+  case CmpInst::FCMP_OLE:
+  case CmpInst::FCMP_ULT:
+  case CmpInst::FCMP_ULE:
+    if (match(FalseVal,
+              m_CombineOr(m_OrdFMin(m_Specific(CmpLHS), m_APFloat(FC2)),
+                          m_UnordFMin(m_Specific(CmpLHS), m_APFloat(FC2)))) &&
+        FC1->compare(*FC2) == APFloat::cmpResult::cmpLessThan)
+      return {SPF_FMAXNUM, SPNB_RETURNS_ANY, false};
+    break;
+  case CmpInst::FCMP_OGT:
+  case CmpInst::FCMP_OGE:
+  case CmpInst::FCMP_UGT:
+  case CmpInst::FCMP_UGE:
+    if (match(FalseVal,
+              m_CombineOr(m_OrdFMax(m_Specific(CmpLHS), m_APFloat(FC2)),
+                          m_UnordFMax(m_Specific(CmpLHS), m_APFloat(FC2)))) &&
+        FC1->compare(*FC2) == APFloat::cmpResult::cmpGreaterThan)
+      return {SPF_FMINNUM, SPNB_RETURNS_ANY, false};
+    break;
+  default:
+    break;
+  }
+
+  return {SPF_UNKNOWN, SPNB_NA, false};
+}
+
+/// Recognize variations of:
+///   CLAMP(v,l,h) ==> ((v) < (l) ? (l) : ((v) > (h) ? (h) : (v)))
+static SelectPatternResult matchClamp(CmpInst::Predicate Pred,
+                                      Value *CmpLHS, Value *CmpRHS,
+                                      Value *TrueVal, Value *FalseVal) {
+  // Swap the select operands and predicate to match the patterns below.
+  if (CmpRHS != TrueVal) {
+    Pred = ICmpInst::getSwappedPredicate(Pred);
+    std::swap(TrueVal, FalseVal);
+  }
+  const APInt *C1;
+  if (CmpRHS == TrueVal && match(CmpRHS, m_APInt(C1))) {
+    const APInt *C2;
+    // (X <s C1) ? C1 : SMIN(X, C2) ==> SMAX(SMIN(X, C2), C1)
+    if (match(FalseVal, m_SMin(m_Specific(CmpLHS), m_APInt(C2))) &&
+        C1->slt(*C2) && Pred == CmpInst::ICMP_SLT)
+      return {SPF_SMAX, SPNB_NA, false};
+
+    // (X >s C1) ? C1 : SMAX(X, C2) ==> SMIN(SMAX(X, C2), C1)
+    if (match(FalseVal, m_SMax(m_Specific(CmpLHS), m_APInt(C2))) &&
+        C1->sgt(*C2) && Pred == CmpInst::ICMP_SGT)
+      return {SPF_SMIN, SPNB_NA, false};
+
+    // (X <u C1) ? C1 : UMIN(X, C2) ==> UMAX(UMIN(X, C2), C1)
+    if (match(FalseVal, m_UMin(m_Specific(CmpLHS), m_APInt(C2))) &&
+        C1->ult(*C2) && Pred == CmpInst::ICMP_ULT)
+      return {SPF_UMAX, SPNB_NA, false};
+
+    // (X >u C1) ? C1 : UMAX(X, C2) ==> UMIN(UMAX(X, C2), C1)
+    if (match(FalseVal, m_UMax(m_Specific(CmpLHS), m_APInt(C2))) &&
+        C1->ugt(*C2) && Pred == CmpInst::ICMP_UGT)
+      return {SPF_UMIN, SPNB_NA, false};
+  }
+  return {SPF_UNKNOWN, SPNB_NA, false};
+}
+
+/// Recognize variations of:
+///   a < c ? min(a,b) : min(b,c) ==> min(min(a,b),min(b,c))
+static SelectPatternResult matchMinMaxOfMinMax(CmpInst::Predicate Pred,
+                                               Value *CmpLHS, Value *CmpRHS,
+                                               Value *TVal, Value *FVal,
+                                               unsigned Depth) {
+  // TODO: Allow FP min/max with nnan/nsz.
+  assert(CmpInst::isIntPredicate(Pred) && "Expected integer comparison");
+
+  Value *A, *B;
+  SelectPatternResult L = matchSelectPattern(TVal, A, B, nullptr, Depth + 1);
+  if (!SelectPatternResult::isMinOrMax(L.Flavor))
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  Value *C, *D;
+  SelectPatternResult R = matchSelectPattern(FVal, C, D, nullptr, Depth + 1);
+  if (L.Flavor != R.Flavor)
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  // We have something like: x Pred y ? min(a, b) : min(c, d).
+  // Try to match the compare to the min/max operations of the select operands.
+  // First, make sure we have the right compare predicate.
+  switch (L.Flavor) {
+  case SPF_SMIN:
+    if (Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE) {
+      Pred = ICmpInst::getSwappedPredicate(Pred);
+      std::swap(CmpLHS, CmpRHS);
+    }
+    if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE)
+      break;
+    return {SPF_UNKNOWN, SPNB_NA, false};
+  case SPF_SMAX:
+    if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE) {
+      Pred = ICmpInst::getSwappedPredicate(Pred);
+      std::swap(CmpLHS, CmpRHS);
+    }
+    if (Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE)
+      break;
+    return {SPF_UNKNOWN, SPNB_NA, false};
+  case SPF_UMIN:
+    if (Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE) {
+      Pred = ICmpInst::getSwappedPredicate(Pred);
+      std::swap(CmpLHS, CmpRHS);
+    }
+    if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_ULE)
+      break;
+    return {SPF_UNKNOWN, SPNB_NA, false};
+  case SPF_UMAX:
+    if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_ULE) {
+      Pred = ICmpInst::getSwappedPredicate(Pred);
+      std::swap(CmpLHS, CmpRHS);
+    }
+    if (Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE)
+      break;
+    return {SPF_UNKNOWN, SPNB_NA, false};
+  default:
+    return {SPF_UNKNOWN, SPNB_NA, false};
+  }
+
+  // If there is a common operand in the already matched min/max and the other
+  // min/max operands match the compare operands (either directly or inverted),
+  // then this is min/max of the same flavor.
+
+  // a pred c ? m(a, b) : m(c, b) --> m(m(a, b), m(c, b))
+  // ~c pred ~a ? m(a, b) : m(c, b) --> m(m(a, b), m(c, b))
+  if (D == B) {
+    if ((CmpLHS == A && CmpRHS == C) || (match(C, m_Not(m_Specific(CmpLHS))) &&
+                                         match(A, m_Not(m_Specific(CmpRHS)))))
+      return {L.Flavor, SPNB_NA, false};
+  }
+  // a pred d ? m(a, b) : m(b, d) --> m(m(a, b), m(b, d))
+  // ~d pred ~a ? m(a, b) : m(b, d) --> m(m(a, b), m(b, d))
+  if (C == B) {
+    if ((CmpLHS == A && CmpRHS == D) || (match(D, m_Not(m_Specific(CmpLHS))) &&
+                                         match(A, m_Not(m_Specific(CmpRHS)))))
+      return {L.Flavor, SPNB_NA, false};
+  }
+  // b pred c ? m(a, b) : m(c, a) --> m(m(a, b), m(c, a))
+  // ~c pred ~b ? m(a, b) : m(c, a) --> m(m(a, b), m(c, a))
+  if (D == A) {
+    if ((CmpLHS == B && CmpRHS == C) || (match(C, m_Not(m_Specific(CmpLHS))) &&
+                                         match(B, m_Not(m_Specific(CmpRHS)))))
+      return {L.Flavor, SPNB_NA, false};
+  }
+  // b pred d ? m(a, b) : m(a, d) --> m(m(a, b), m(a, d))
+  // ~d pred ~b ? m(a, b) : m(a, d) --> m(m(a, b), m(a, d))
+  if (C == A) {
+    if ((CmpLHS == B && CmpRHS == D) || (match(D, m_Not(m_Specific(CmpLHS))) &&
+                                         match(B, m_Not(m_Specific(CmpRHS)))))
+      return {L.Flavor, SPNB_NA, false};
+  }
+
+  return {SPF_UNKNOWN, SPNB_NA, false};
+}
+
+/// Match non-obvious integer minimum and maximum sequences.
+static SelectPatternResult matchMinMax(CmpInst::Predicate Pred,
+                                       Value *CmpLHS, Value *CmpRHS,
+                                       Value *TrueVal, Value *FalseVal,
+                                       Value *&LHS, Value *&RHS,
+                                       unsigned Depth) {
+  // Assume success. If there's no match, callers should not use these anyway.
+  LHS = TrueVal;
+  RHS = FalseVal;
+
+  SelectPatternResult SPR = matchClamp(Pred, CmpLHS, CmpRHS, TrueVal, FalseVal);
+  if (SPR.Flavor != SelectPatternFlavor::SPF_UNKNOWN)
+    return SPR;
+
+  SPR = matchMinMaxOfMinMax(Pred, CmpLHS, CmpRHS, TrueVal, FalseVal, Depth);
+  if (SPR.Flavor != SelectPatternFlavor::SPF_UNKNOWN)
+    return SPR;
+
+  if (Pred != CmpInst::ICMP_SGT && Pred != CmpInst::ICMP_SLT)
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  // Z = X -nsw Y
+  // (X >s Y) ? 0 : Z ==> (Z >s 0) ? 0 : Z ==> SMIN(Z, 0)
+  // (X <s Y) ? 0 : Z ==> (Z <s 0) ? 0 : Z ==> SMAX(Z, 0)
+  if (match(TrueVal, m_Zero()) &&
+      match(FalseVal, m_NSWSub(m_Specific(CmpLHS), m_Specific(CmpRHS))))
+    return {Pred == CmpInst::ICMP_SGT ? SPF_SMIN : SPF_SMAX, SPNB_NA, false};
+
+  // Z = X -nsw Y
+  // (X >s Y) ? Z : 0 ==> (Z >s 0) ? Z : 0 ==> SMAX(Z, 0)
+  // (X <s Y) ? Z : 0 ==> (Z <s 0) ? Z : 0 ==> SMIN(Z, 0)
+  if (match(FalseVal, m_Zero()) &&
+      match(TrueVal, m_NSWSub(m_Specific(CmpLHS), m_Specific(CmpRHS))))
+    return {Pred == CmpInst::ICMP_SGT ? SPF_SMAX : SPF_SMIN, SPNB_NA, false};
+
+  const APInt *C1;
+  if (!match(CmpRHS, m_APInt(C1)))
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  // An unsigned min/max can be written with a signed compare.
+  const APInt *C2;
+  if ((CmpLHS == TrueVal && match(FalseVal, m_APInt(C2))) ||
+      (CmpLHS == FalseVal && match(TrueVal, m_APInt(C2)))) {
+    // Is the sign bit set?
+    // (X <s 0) ? X : MAXVAL ==> (X >u MAXVAL) ? X : MAXVAL ==> UMAX
+    // (X <s 0) ? MAXVAL : X ==> (X >u MAXVAL) ? MAXVAL : X ==> UMIN
+    if (Pred == CmpInst::ICMP_SLT && C1->isNullValue() &&
+        C2->isMaxSignedValue())
+      return {CmpLHS == TrueVal ? SPF_UMAX : SPF_UMIN, SPNB_NA, false};
+
+    // Is the sign bit clear?
+    // (X >s -1) ? MINVAL : X ==> (X <u MINVAL) ? MINVAL : X ==> UMAX
+    // (X >s -1) ? X : MINVAL ==> (X <u MINVAL) ? X : MINVAL ==> UMIN
+    if (Pred == CmpInst::ICMP_SGT && C1->isAllOnesValue() &&
+        C2->isMinSignedValue())
+      return {CmpLHS == FalseVal ? SPF_UMAX : SPF_UMIN, SPNB_NA, false};
+  }
+
+  // Look through 'not' ops to find disguised signed min/max.
+  // (X >s C) ? ~X : ~C ==> (~X <s ~C) ? ~X : ~C ==> SMIN(~X, ~C)
+  // (X <s C) ? ~X : ~C ==> (~X >s ~C) ? ~X : ~C ==> SMAX(~X, ~C)
+  if (match(TrueVal, m_Not(m_Specific(CmpLHS))) &&
+      match(FalseVal, m_APInt(C2)) && ~(*C1) == *C2)
+    return {Pred == CmpInst::ICMP_SGT ? SPF_SMIN : SPF_SMAX, SPNB_NA, false};
+
+  // (X >s C) ? ~C : ~X ==> (~X <s ~C) ? ~C : ~X ==> SMAX(~C, ~X)
+  // (X <s C) ? ~C : ~X ==> (~X >s ~C) ? ~C : ~X ==> SMIN(~C, ~X)
+  if (match(FalseVal, m_Not(m_Specific(CmpLHS))) &&
+      match(TrueVal, m_APInt(C2)) && ~(*C1) == *C2)
+    return {Pred == CmpInst::ICMP_SGT ? SPF_SMAX : SPF_SMIN, SPNB_NA, false};
+
+  return {SPF_UNKNOWN, SPNB_NA, false};
+}
+
+bool llvm::isKnownNegation(const Value *X, const Value *Y, bool NeedNSW) {
+  assert(X && Y && "Invalid operand");
+
+  // X = sub (0, Y) || X = sub nsw (0, Y)
+  if ((!NeedNSW && match(X, m_Sub(m_ZeroInt(), m_Specific(Y)))) ||
+      (NeedNSW && match(X, m_NSWSub(m_ZeroInt(), m_Specific(Y)))))
+    return true;
+
+  // Y = sub (0, X) || Y = sub nsw (0, X)
+  if ((!NeedNSW && match(Y, m_Sub(m_ZeroInt(), m_Specific(X)))) ||
+      (NeedNSW && match(Y, m_NSWSub(m_ZeroInt(), m_Specific(X)))))
+    return true;
+
+  // X = sub (A, B), Y = sub (B, A) || X = sub nsw (A, B), Y = sub nsw (B, A)
+  Value *A, *B;
+  return (!NeedNSW && (match(X, m_Sub(m_Value(A), m_Value(B))) &&
+                        match(Y, m_Sub(m_Specific(B), m_Specific(A))))) ||
+         (NeedNSW && (match(X, m_NSWSub(m_Value(A), m_Value(B))) &&
+                       match(Y, m_NSWSub(m_Specific(B), m_Specific(A)))));
+}
+
+static SelectPatternResult matchSelectPattern(CmpInst::Predicate Pred,
+                                              FastMathFlags FMF,
+                                              Value *CmpLHS, Value *CmpRHS,
+                                              Value *TrueVal, Value *FalseVal,
+                                              Value *&LHS, Value *&RHS,
+                                              unsigned Depth) {
+  if (CmpInst::isFPPredicate(Pred)) {
+    // IEEE-754 ignores the sign of 0.0 in comparisons. So if the select has one
+    // 0.0 operand, set the compare's 0.0 operands to that same value for the
+    // purpose of identifying min/max. Disregard vector constants with undefined
+    // elements because those can not be back-propagated for analysis.
+    Value *OutputZeroVal = nullptr;
+    if (match(TrueVal, m_AnyZeroFP()) && !match(FalseVal, m_AnyZeroFP()) &&
+        !cast<Constant>(TrueVal)->containsUndefElement())
+      OutputZeroVal = TrueVal;
+    else if (match(FalseVal, m_AnyZeroFP()) && !match(TrueVal, m_AnyZeroFP()) &&
+             !cast<Constant>(FalseVal)->containsUndefElement())
+      OutputZeroVal = FalseVal;
+
+    if (OutputZeroVal) {
+      if (match(CmpLHS, m_AnyZeroFP()))
+        CmpLHS = OutputZeroVal;
+      if (match(CmpRHS, m_AnyZeroFP()))
+        CmpRHS = OutputZeroVal;
+    }
+  }
+
+  LHS = CmpLHS;
+  RHS = CmpRHS;
+
+  // Signed zero may return inconsistent results between implementations.
+  //  (0.0 <= -0.0) ? 0.0 : -0.0 // Returns 0.0
+  //  minNum(0.0, -0.0)          // May return -0.0 or 0.0 (IEEE 754-2008 5.3.1)
+  // Therefore, we behave conservatively and only proceed if at least one of the
+  // operands is known to not be zero or if we don't care about signed zero.
+  switch (Pred) {
+  default: break;
+  // FIXME: Include OGT/OLT/UGT/ULT.
+  case CmpInst::FCMP_OGE: case CmpInst::FCMP_OLE:
+  case CmpInst::FCMP_UGE: case CmpInst::FCMP_ULE:
+    if (!FMF.noSignedZeros() && !isKnownNonZero(CmpLHS) &&
+        !isKnownNonZero(CmpRHS))
+      return {SPF_UNKNOWN, SPNB_NA, false};
+  }
+
+  SelectPatternNaNBehavior NaNBehavior = SPNB_NA;
+  bool Ordered = false;
+
+  // When given one NaN and one non-NaN input:
+  //   - maxnum/minnum (C99 fmaxf()/fminf()) return the non-NaN input.
+  //   - A simple C99 (a < b ? a : b) construction will return 'b' (as the
+  //     ordered comparison fails), which could be NaN or non-NaN.
+  // so here we discover exactly what NaN behavior is required/accepted.
+  if (CmpInst::isFPPredicate(Pred)) {
+    bool LHSSafe = isKnownNonNaN(CmpLHS, FMF);
+    bool RHSSafe = isKnownNonNaN(CmpRHS, FMF);
+
+    if (LHSSafe && RHSSafe) {
+      // Both operands are known non-NaN.
+      NaNBehavior = SPNB_RETURNS_ANY;
+    } else if (CmpInst::isOrdered(Pred)) {
+      // An ordered comparison will return false when given a NaN, so it
+      // returns the RHS.
+      Ordered = true;
+      if (LHSSafe)
+        // LHS is non-NaN, so if RHS is NaN then NaN will be returned.
+        NaNBehavior = SPNB_RETURNS_NAN;
+      else if (RHSSafe)
+        NaNBehavior = SPNB_RETURNS_OTHER;
+      else
+        // Completely unsafe.
+        return {SPF_UNKNOWN, SPNB_NA, false};
+    } else {
+      Ordered = false;
+      // An unordered comparison will return true when given a NaN, so it
+      // returns the LHS.
+      if (LHSSafe)
+        // LHS is non-NaN, so if RHS is NaN then non-NaN will be returned.
+        NaNBehavior = SPNB_RETURNS_OTHER;
+      else if (RHSSafe)
+        NaNBehavior = SPNB_RETURNS_NAN;
+      else
+        // Completely unsafe.
+        return {SPF_UNKNOWN, SPNB_NA, false};
+    }
+  }
+
+  if (TrueVal == CmpRHS && FalseVal == CmpLHS) {
+    std::swap(CmpLHS, CmpRHS);
+    Pred = CmpInst::getSwappedPredicate(Pred);
+    if (NaNBehavior == SPNB_RETURNS_NAN)
+      NaNBehavior = SPNB_RETURNS_OTHER;
+    else if (NaNBehavior == SPNB_RETURNS_OTHER)
+      NaNBehavior = SPNB_RETURNS_NAN;
+    Ordered = !Ordered;
+  }
+
+  // ([if]cmp X, Y) ? X : Y
+  if (TrueVal == CmpLHS && FalseVal == CmpRHS) {
+    switch (Pred) {
+    default: return {SPF_UNKNOWN, SPNB_NA, false}; // Equality.
+    case ICmpInst::ICMP_UGT:
+    case ICmpInst::ICMP_UGE: return {SPF_UMAX, SPNB_NA, false};
+    case ICmpInst::ICMP_SGT:
+    case ICmpInst::ICMP_SGE: return {SPF_SMAX, SPNB_NA, false};
+    case ICmpInst::ICMP_ULT:
+    case ICmpInst::ICMP_ULE: return {SPF_UMIN, SPNB_NA, false};
+    case ICmpInst::ICMP_SLT:
+    case ICmpInst::ICMP_SLE: return {SPF_SMIN, SPNB_NA, false};
+    case FCmpInst::FCMP_UGT:
+    case FCmpInst::FCMP_UGE:
+    case FCmpInst::FCMP_OGT:
+    case FCmpInst::FCMP_OGE: return {SPF_FMAXNUM, NaNBehavior, Ordered};
+    case FCmpInst::FCMP_ULT:
+    case FCmpInst::FCMP_ULE:
+    case FCmpInst::FCMP_OLT:
+    case FCmpInst::FCMP_OLE: return {SPF_FMINNUM, NaNBehavior, Ordered};
+    }
+  }
+
+  if (isKnownNegation(TrueVal, FalseVal)) {
+    // Sign-extending LHS does not change its sign, so TrueVal/FalseVal can
+    // match against either LHS or sext(LHS).
+    auto MaybeSExtCmpLHS =
+        m_CombineOr(m_Specific(CmpLHS), m_SExt(m_Specific(CmpLHS)));
+    auto ZeroOrAllOnes = m_CombineOr(m_ZeroInt(), m_AllOnes());
+    auto ZeroOrOne = m_CombineOr(m_ZeroInt(), m_One());
+    if (match(TrueVal, MaybeSExtCmpLHS)) {
+      // Set the return values. If the compare uses the negated value (-X >s 0),
+      // swap the return values because the negated value is always 'RHS'.
+      LHS = TrueVal;
+      RHS = FalseVal;
+      if (match(CmpLHS, m_Neg(m_Specific(FalseVal))))
+        std::swap(LHS, RHS);
+
+      // (X >s 0) ? X : -X or (X >s -1) ? X : -X --> ABS(X)
+      // (-X >s 0) ? -X : X or (-X >s -1) ? -X : X --> ABS(X)
+      if (Pred == ICmpInst::ICMP_SGT && match(CmpRHS, ZeroOrAllOnes))
+        return {SPF_ABS, SPNB_NA, false};
+
+      // (X >=s 0) ? X : -X or (X >=s 1) ? X : -X --> ABS(X)
+      if (Pred == ICmpInst::ICMP_SGE && match(CmpRHS, ZeroOrOne))
+        return {SPF_ABS, SPNB_NA, false};
+
+      // (X <s 0) ? X : -X or (X <s 1) ? X : -X --> NABS(X)
+      // (-X <s 0) ? -X : X or (-X <s 1) ? -X : X --> NABS(X)
+      if (Pred == ICmpInst::ICMP_SLT && match(CmpRHS, ZeroOrOne))
+        return {SPF_NABS, SPNB_NA, false};
+    }
+    else if (match(FalseVal, MaybeSExtCmpLHS)) {
+      // Set the return values. If the compare uses the negated value (-X >s 0),
+      // swap the return values because the negated value is always 'RHS'.
+      LHS = FalseVal;
+      RHS = TrueVal;
+      if (match(CmpLHS, m_Neg(m_Specific(TrueVal))))
+        std::swap(LHS, RHS);
+
+      // (X >s 0) ? -X : X or (X >s -1) ? -X : X --> NABS(X)
+      // (-X >s 0) ? X : -X or (-X >s -1) ? X : -X --> NABS(X)
+      if (Pred == ICmpInst::ICMP_SGT && match(CmpRHS, ZeroOrAllOnes))
+        return {SPF_NABS, SPNB_NA, false};
+
+      // (X <s 0) ? -X : X or (X <s 1) ? -X : X --> ABS(X)
+      // (-X <s 0) ? X : -X or (-X <s 1) ? X : -X --> ABS(X)
+      if (Pred == ICmpInst::ICMP_SLT && match(CmpRHS, ZeroOrOne))
+        return {SPF_ABS, SPNB_NA, false};
+    }
+  }
+
+  if (CmpInst::isIntPredicate(Pred))
+    return matchMinMax(Pred, CmpLHS, CmpRHS, TrueVal, FalseVal, LHS, RHS, Depth);
+
+  // According to (IEEE 754-2008 5.3.1), minNum(0.0, -0.0) and similar
+  // may return either -0.0 or 0.0, so fcmp/select pair has stricter
+  // semantics than minNum. Be conservative in such case.
+  if (NaNBehavior != SPNB_RETURNS_ANY ||
+      (!FMF.noSignedZeros() && !isKnownNonZero(CmpLHS) &&
+       !isKnownNonZero(CmpRHS)))
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  return matchFastFloatClamp(Pred, CmpLHS, CmpRHS, TrueVal, FalseVal, LHS, RHS);
+}
+
+/// Helps to match a select pattern in case of a type mismatch.
+///
+/// The function processes the case when type of true and false values of a
+/// select instruction differs from type of the cmp instruction operands because
+/// of a cast instruction. The function checks if it is legal to move the cast
+/// operation after "select". If yes, it returns the new second value of
+/// "select" (with the assumption that cast is moved):
+/// 1. As operand of cast instruction when both values of "select" are same cast
+/// instructions.
+/// 2. As restored constant (by applying reverse cast operation) when the first
+/// value of the "select" is a cast operation and the second value is a
+/// constant.
+/// NOTE: We return only the new second value because the first value could be
+/// accessed as operand of cast instruction.
+static Value *lookThroughCast(CmpInst *CmpI, Value *V1, Value *V2,
+                              Instruction::CastOps *CastOp) {
+  auto *Cast1 = dyn_cast<CastInst>(V1);
+  if (!Cast1)
+    return nullptr;
+
+  *CastOp = Cast1->getOpcode();
+  Type *SrcTy = Cast1->getSrcTy();
+  if (auto *Cast2 = dyn_cast<CastInst>(V2)) {
+    // If V1 and V2 are both the same cast from the same type, look through V1.
+    if (*CastOp == Cast2->getOpcode() && SrcTy == Cast2->getSrcTy())
+      return Cast2->getOperand(0);
+    return nullptr;
+  }
+
+  auto *C = dyn_cast<Constant>(V2);
+  if (!C)
+    return nullptr;
+
+  Constant *CastedTo = nullptr;
+  switch (*CastOp) {
+  case Instruction::ZExt:
+    if (CmpI->isUnsigned())
+      CastedTo = ConstantExpr::getTrunc(C, SrcTy);
+    break;
+  case Instruction::SExt:
+    if (CmpI->isSigned())
+      CastedTo = ConstantExpr::getTrunc(C, SrcTy, true);
+    break;
+  case Instruction::Trunc:
+    Constant *CmpConst;
+    if (match(CmpI->getOperand(1), m_Constant(CmpConst)) &&
+        CmpConst->getType() == SrcTy) {
+      // Here we have the following case:
+      //
+      //   %cond = cmp iN %x, CmpConst
+      //   %tr = trunc iN %x to iK
+      //   %narrowsel = select i1 %cond, iK %t, iK C
+      //
+      // We can always move trunc after select operation:
+      //
+      //   %cond = cmp iN %x, CmpConst
+      //   %widesel = select i1 %cond, iN %x, iN CmpConst
+      //   %tr = trunc iN %widesel to iK
+      //
+      // Note that C could be extended in any way because we don't care about
+      // upper bits after truncation. It can't be abs pattern, because it would
+      // look like:
+      //
+      //   select i1 %cond, x, -x.
+      //
+      // So only min/max pattern could be matched. Such match requires widened C
+      // == CmpConst. That is why set widened C = CmpConst, condition trunc
+      // CmpConst == C is checked below.
+      CastedTo = CmpConst;
+    } else {
+      CastedTo = ConstantExpr::getIntegerCast(C, SrcTy, CmpI->isSigned());
+    }
+    break;
+  case Instruction::FPTrunc:
+    CastedTo = ConstantExpr::getFPExtend(C, SrcTy, true);
+    break;
+  case Instruction::FPExt:
+    CastedTo = ConstantExpr::getFPTrunc(C, SrcTy, true);
+    break;
+  case Instruction::FPToUI:
+    CastedTo = ConstantExpr::getUIToFP(C, SrcTy, true);
+    break;
+  case Instruction::FPToSI:
+    CastedTo = ConstantExpr::getSIToFP(C, SrcTy, true);
+    break;
+  case Instruction::UIToFP:
+    CastedTo = ConstantExpr::getFPToUI(C, SrcTy, true);
+    break;
+  case Instruction::SIToFP:
+    CastedTo = ConstantExpr::getFPToSI(C, SrcTy, true);
+    break;
+  default:
+    break;
+  }
+
+  if (!CastedTo)
+    return nullptr;
+
+  // Make sure the cast doesn't lose any information.
+  Constant *CastedBack =
+      ConstantExpr::getCast(*CastOp, CastedTo, C->getType(), true);
+  if (CastedBack != C)
+    return nullptr;
+
+  return CastedTo;
+}
+
+SelectPatternResult llvm::matchSelectPattern(Value *V, Value *&LHS, Value *&RHS,
+                                             Instruction::CastOps *CastOp,
+                                             unsigned Depth) {
+  if (Depth >= MaxDepth)
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  SelectInst *SI = dyn_cast<SelectInst>(V);
+  if (!SI) return {SPF_UNKNOWN, SPNB_NA, false};
+
+  CmpInst *CmpI = dyn_cast<CmpInst>(SI->getCondition());
+  if (!CmpI) return {SPF_UNKNOWN, SPNB_NA, false};
+
+  Value *TrueVal = SI->getTrueValue();
+  Value *FalseVal = SI->getFalseValue();
+
+  return llvm::matchDecomposedSelectPattern(CmpI, TrueVal, FalseVal, LHS, RHS,
+                                            CastOp, Depth);
+}
+
+SelectPatternResult llvm::matchDecomposedSelectPattern(
+    CmpInst *CmpI, Value *TrueVal, Value *FalseVal, Value *&LHS, Value *&RHS,
+    Instruction::CastOps *CastOp, unsigned Depth) {
+  CmpInst::Predicate Pred = CmpI->getPredicate();
+  Value *CmpLHS = CmpI->getOperand(0);
+  Value *CmpRHS = CmpI->getOperand(1);
+  FastMathFlags FMF;
+  if (isa<FPMathOperator>(CmpI))
+    FMF = CmpI->getFastMathFlags();
+
+  // Bail out early.
+  if (CmpI->isEquality())
+    return {SPF_UNKNOWN, SPNB_NA, false};
+
+  // Deal with type mismatches.
+  if (CastOp && CmpLHS->getType() != TrueVal->getType()) {
+    if (Value *C = lookThroughCast(CmpI, TrueVal, FalseVal, CastOp)) {
+      // If this is a potential fmin/fmax with a cast to integer, then ignore
+      // -0.0 because there is no corresponding integer value.
+      if (*CastOp == Instruction::FPToSI || *CastOp == Instruction::FPToUI)
+        FMF.setNoSignedZeros();
+      return ::matchSelectPattern(Pred, FMF, CmpLHS, CmpRHS,
+                                  cast<CastInst>(TrueVal)->getOperand(0), C,
+                                  LHS, RHS, Depth);
+    }
+    if (Value *C = lookThroughCast(CmpI, FalseVal, TrueVal, CastOp)) {
+      // If this is a potential fmin/fmax with a cast to integer, then ignore
+      // -0.0 because there is no corresponding integer value.
+      if (*CastOp == Instruction::FPToSI || *CastOp == Instruction::FPToUI)
+        FMF.setNoSignedZeros();
+      return ::matchSelectPattern(Pred, FMF, CmpLHS, CmpRHS,
+                                  C, cast<CastInst>(FalseVal)->getOperand(0),
+                                  LHS, RHS, Depth);
+    }
+  }
+  return ::matchSelectPattern(Pred, FMF, CmpLHS, CmpRHS, TrueVal, FalseVal,
+                              LHS, RHS, Depth);
+}
+
+CmpInst::Predicate llvm::getMinMaxPred(SelectPatternFlavor SPF, bool Ordered) {
+  if (SPF == SPF_SMIN) return ICmpInst::ICMP_SLT;
+  if (SPF == SPF_UMIN) return ICmpInst::ICMP_ULT;
+  if (SPF == SPF_SMAX) return ICmpInst::ICMP_SGT;
+  if (SPF == SPF_UMAX) return ICmpInst::ICMP_UGT;
+  if (SPF == SPF_FMINNUM)
+    return Ordered ? FCmpInst::FCMP_OLT : FCmpInst::FCMP_ULT;
+  if (SPF == SPF_FMAXNUM)
+    return Ordered ? FCmpInst::FCMP_OGT : FCmpInst::FCMP_UGT;
+  llvm_unreachable("unhandled!");
+}
+
+SelectPatternFlavor llvm::getInverseMinMaxFlavor(SelectPatternFlavor SPF) {
+  if (SPF == SPF_SMIN) return SPF_SMAX;
+  if (SPF == SPF_UMIN) return SPF_UMAX;
+  if (SPF == SPF_SMAX) return SPF_SMIN;
+  if (SPF == SPF_UMAX) return SPF_UMIN;
+  llvm_unreachable("unhandled!");
+}
+
+CmpInst::Predicate llvm::getInverseMinMaxPred(SelectPatternFlavor SPF) {
+  return getMinMaxPred(getInverseMinMaxFlavor(SPF));
+}
+
+/// Return true if "icmp Pred LHS RHS" is always true.
+static bool isTruePredicate(CmpInst::Predicate Pred, const Value *LHS,
+                            const Value *RHS, const DataLayout &DL,
+                            unsigned Depth) {
+  assert(!LHS->getType()->isVectorTy() && "TODO: extend to handle vectors!");
+  if (ICmpInst::isTrueWhenEqual(Pred) && LHS == RHS)
+    return true;
+
+  switch (Pred) {
+  default:
+    return false;
+
+  case CmpInst::ICMP_SLE: {
+    const APInt *C;
+
+    // LHS s<= LHS +_{nsw} C   if C >= 0
+    if (match(RHS, m_NSWAdd(m_Specific(LHS), m_APInt(C))))
+      return !C->isNegative();
+    return false;
+  }
+
+  case CmpInst::ICMP_ULE: {
+    const APInt *C;
+
+    // LHS u<= LHS +_{nuw} C   for any C
+    if (match(RHS, m_NUWAdd(m_Specific(LHS), m_APInt(C))))
+      return true;
+
+    // Match A to (X +_{nuw} CA) and B to (X +_{nuw} CB)
+    auto MatchNUWAddsToSameValue = [&](const Value *A, const Value *B,
+                                       const Value *&X,
+                                       const APInt *&CA, const APInt *&CB) {
+      if (match(A, m_NUWAdd(m_Value(X), m_APInt(CA))) &&
+          match(B, m_NUWAdd(m_Specific(X), m_APInt(CB))))
+        return true;
+
+      // If X & C == 0 then (X | C) == X +_{nuw} C
+      if (match(A, m_Or(m_Value(X), m_APInt(CA))) &&
+          match(B, m_Or(m_Specific(X), m_APInt(CB)))) {
+        KnownBits Known(CA->getBitWidth());
+        computeKnownBits(X, Known, DL, Depth + 1, /*AC*/ nullptr,
+                         /*CxtI*/ nullptr, /*DT*/ nullptr);
+        if (CA->isSubsetOf(Known.Zero) && CB->isSubsetOf(Known.Zero))
+          return true;
+      }
+
+      return false;
+    };
+
+    const Value *X;
+    const APInt *CLHS, *CRHS;
+    if (MatchNUWAddsToSameValue(LHS, RHS, X, CLHS, CRHS))
+      return CLHS->ule(*CRHS);
+
+    return false;
+  }
+  }
+}
+
+/// Return true if "icmp Pred BLHS BRHS" is true whenever "icmp Pred
+/// ALHS ARHS" is true.  Otherwise, return None.
+static Optional<bool>
+isImpliedCondOperands(CmpInst::Predicate Pred, const Value *ALHS,
+                      const Value *ARHS, const Value *BLHS, const Value *BRHS,
+                      const DataLayout &DL, unsigned Depth) {
+  switch (Pred) {
+  default:
+    return None;
+
+  case CmpInst::ICMP_SLT:
+  case CmpInst::ICMP_SLE:
+    if (isTruePredicate(CmpInst::ICMP_SLE, BLHS, ALHS, DL, Depth) &&
+        isTruePredicate(CmpInst::ICMP_SLE, ARHS, BRHS, DL, Depth))
+      return true;
+    return None;
+
+  case CmpInst::ICMP_ULT:
+  case CmpInst::ICMP_ULE:
+    if (isTruePredicate(CmpInst::ICMP_ULE, BLHS, ALHS, DL, Depth) &&
+        isTruePredicate(CmpInst::ICMP_ULE, ARHS, BRHS, DL, Depth))
+      return true;
+    return None;
+  }
+}
+
+/// Return true if the operands of the two compares match.  IsSwappedOps is true
+/// when the operands match, but are swapped.
+static bool isMatchingOps(const Value *ALHS, const Value *ARHS,
+                          const Value *BLHS, const Value *BRHS,
+                          bool &IsSwappedOps) {
+
+  bool IsMatchingOps = (ALHS == BLHS && ARHS == BRHS);
+  IsSwappedOps = (ALHS == BRHS && ARHS == BLHS);
+  return IsMatchingOps || IsSwappedOps;
+}
+
+/// Return true if "icmp1 APred X, Y" implies "icmp2 BPred X, Y" is true.
+/// Return false if "icmp1 APred X, Y" implies "icmp2 BPred X, Y" is false.
+/// Otherwise, return None if we can't infer anything.
+static Optional<bool> isImpliedCondMatchingOperands(CmpInst::Predicate APred,
+                                                    CmpInst::Predicate BPred,
+                                                    bool AreSwappedOps) {
+  // Canonicalize the predicate as if the operands were not commuted.
+  if (AreSwappedOps)
+    BPred = ICmpInst::getSwappedPredicate(BPred);
+
+  if (CmpInst::isImpliedTrueByMatchingCmp(APred, BPred))
+    return true;
+  if (CmpInst::isImpliedFalseByMatchingCmp(APred, BPred))
+    return false;
+
+  return None;
+}
+
+/// Return true if "icmp APred X, C1" implies "icmp BPred X, C2" is true.
+/// Return false if "icmp APred X, C1" implies "icmp BPred X, C2" is false.
+/// Otherwise, return None if we can't infer anything.
+static Optional<bool>
+isImpliedCondMatchingImmOperands(CmpInst::Predicate APred,
+                                 const ConstantInt *C1,
+                                 CmpInst::Predicate BPred,
+                                 const ConstantInt *C2) {
+  ConstantRange DomCR =
+      ConstantRange::makeExactICmpRegion(APred, C1->getValue());
+  ConstantRange CR =
+      ConstantRange::makeAllowedICmpRegion(BPred, C2->getValue());
+  ConstantRange Intersection = DomCR.intersectWith(CR);
+  ConstantRange Difference = DomCR.difference(CR);
+  if (Intersection.isEmptySet())
+    return false;
+  if (Difference.isEmptySet())
+    return true;
+  return None;
+}
+
+/// Return true if LHS implies RHS is true.  Return false if LHS implies RHS is
+/// false.  Otherwise, return None if we can't infer anything.
+static Optional<bool> isImpliedCondICmps(const ICmpInst *LHS,
+                                         const ICmpInst *RHS,
+                                         const DataLayout &DL, bool LHSIsTrue,
+                                         unsigned Depth) {
+  Value *ALHS = LHS->getOperand(0);
+  Value *ARHS = LHS->getOperand(1);
+  // The rest of the logic assumes the LHS condition is true.  If that's not the
+  // case, invert the predicate to make it so.
+  ICmpInst::Predicate APred =
+      LHSIsTrue ? LHS->getPredicate() : LHS->getInversePredicate();
+
+  Value *BLHS = RHS->getOperand(0);
+  Value *BRHS = RHS->getOperand(1);
+  ICmpInst::Predicate BPred = RHS->getPredicate();
+
+  // Can we infer anything when the two compares have matching operands?
+  bool AreSwappedOps;
+  if (isMatchingOps(ALHS, ARHS, BLHS, BRHS, AreSwappedOps)) {
+    if (Optional<bool> Implication = isImpliedCondMatchingOperands(
+            APred, BPred, AreSwappedOps))
+      return Implication;
+    // No amount of additional analysis will infer the second condition, so
+    // early exit.
+    return None;
+  }
+
+  // Can we infer anything when the LHS operands match and the RHS operands are
+  // constants (not necessarily matching)?
+  if (ALHS == BLHS && isa<ConstantInt>(ARHS) && isa<ConstantInt>(BRHS)) {
+    if (Optional<bool> Implication = isImpliedCondMatchingImmOperands(
+            APred, cast<ConstantInt>(ARHS), BPred, cast<ConstantInt>(BRHS)))
+      return Implication;
+    // No amount of additional analysis will infer the second condition, so
+    // early exit.
+    return None;
+  }
+
+  if (APred == BPred)
+    return isImpliedCondOperands(APred, ALHS, ARHS, BLHS, BRHS, DL, Depth);
+  return None;
+}
+
+/// Return true if LHS implies RHS is true.  Return false if LHS implies RHS is
+/// false.  Otherwise, return None if we can't infer anything.  We expect the
+/// RHS to be an icmp and the LHS to be an 'and' or an 'or' instruction.
+static Optional<bool> isImpliedCondAndOr(const BinaryOperator *LHS,
+                                         const ICmpInst *RHS,
+                                         const DataLayout &DL, bool LHSIsTrue,
+                                         unsigned Depth) {
+  // The LHS must be an 'or' or an 'and' instruction.
+  assert((LHS->getOpcode() == Instruction::And ||
+          LHS->getOpcode() == Instruction::Or) &&
+         "Expected LHS to be 'and' or 'or'.");
+
+  assert(Depth <= MaxDepth && "Hit recursion limit");
+
+  // If the result of an 'or' is false, then we know both legs of the 'or' are
+  // false.  Similarly, if the result of an 'and' is true, then we know both
+  // legs of the 'and' are true.
+  Value *ALHS, *ARHS;
+  if ((!LHSIsTrue && match(LHS, m_Or(m_Value(ALHS), m_Value(ARHS)))) ||
+      (LHSIsTrue && match(LHS, m_And(m_Value(ALHS), m_Value(ARHS))))) {
+    // FIXME: Make this non-recursion.
+    if (Optional<bool> Implication =
+            isImpliedCondition(ALHS, RHS, DL, LHSIsTrue, Depth + 1))
+      return Implication;
+    if (Optional<bool> Implication =
+            isImpliedCondition(ARHS, RHS, DL, LHSIsTrue, Depth + 1))
+      return Implication;
+    return None;
+  }
+  return None;
+}
+
+Optional<bool> llvm::isImpliedCondition(const Value *LHS, const Value *RHS,
+                                        const DataLayout &DL, bool LHSIsTrue,
+                                        unsigned Depth) {
+  // Bail out when we hit the limit.
+  if (Depth == MaxDepth)
+    return None;
+
+  // A mismatch occurs when we compare a scalar cmp to a vector cmp, for
+  // example.
+  if (LHS->getType() != RHS->getType())
+    return None;
+
+  Type *OpTy = LHS->getType();
+  assert(OpTy->isIntOrIntVectorTy(1) && "Expected integer type only!");
+
+  // LHS ==> RHS by definition
+  if (LHS == RHS)
+    return LHSIsTrue;
+
+  // FIXME: Extending the code below to handle vectors.
+  if (OpTy->isVectorTy())
+    return None;
+
+  assert(OpTy->isIntegerTy(1) && "implied by above");
+
+  // Both LHS and RHS are icmps.
+  const ICmpInst *LHSCmp = dyn_cast<ICmpInst>(LHS);
+  const ICmpInst *RHSCmp = dyn_cast<ICmpInst>(RHS);
+  if (LHSCmp && RHSCmp)
+    return isImpliedCondICmps(LHSCmp, RHSCmp, DL, LHSIsTrue, Depth);
+
+  // The LHS should be an 'or' or an 'and' instruction.  We expect the RHS to be
+  // an icmp. FIXME: Add support for and/or on the RHS.
+  const BinaryOperator *LHSBO = dyn_cast<BinaryOperator>(LHS);
+  if (LHSBO && RHSCmp) {
+    if ((LHSBO->getOpcode() == Instruction::And ||
+         LHSBO->getOpcode() == Instruction::Or))
+      return isImpliedCondAndOr(LHSBO, RHSCmp, DL, LHSIsTrue, Depth);
+  }
+  return None;
+}
+
+Optional<bool> llvm::isImpliedByDomCondition(const Value *Cond,
+                                             const Instruction *ContextI,
+                                             const DataLayout &DL) {
+  assert(Cond->getType()->isIntOrIntVectorTy(1) && "Condition must be bool");
+  if (!ContextI || !ContextI->getParent())
+    return None;
+
+  // TODO: This is a poor/cheap way to determine dominance. Should we use a
+  // dominator tree (eg, from a SimplifyQuery) instead?
+  const BasicBlock *ContextBB = ContextI->getParent();
+  const BasicBlock *PredBB = ContextBB->getSinglePredecessor();
+  if (!PredBB)
+    return None;
+
+  // We need a conditional branch in the predecessor.
+  Value *PredCond;
+  BasicBlock *TrueBB, *FalseBB;
+  if (!match(PredBB->getTerminator(), m_Br(m_Value(PredCond), TrueBB, FalseBB)))
+    return None;
+
+  // The branch should get simplified. Don't bother simplifying this condition.
+  if (TrueBB == FalseBB)
+    return None;
+
+  assert((TrueBB == ContextBB || FalseBB == ContextBB) &&
+         "Predecessor block does not point to successor?");
+
+  // Is this condition implied by the predecessor condition?
+  bool CondIsTrue = TrueBB == ContextBB;
+  return isImpliedCondition(PredCond, Cond, DL, CondIsTrue);
+}
+
+static void setLimitsForBinOp(const BinaryOperator &BO, APInt &Lower,
+                              APInt &Upper, const InstrInfoQuery &IIQ) {
+  unsigned Width = Lower.getBitWidth();
+  const APInt *C;
+  switch (BO.getOpcode()) {
+  case Instruction::Add:
+    if (match(BO.getOperand(1), m_APInt(C)) && !C->isNullValue()) {
+      // FIXME: If we have both nuw and nsw, we should reduce the range further.
+      if (IIQ.hasNoUnsignedWrap(cast<OverflowingBinaryOperator>(&BO))) {
+        // 'add nuw x, C' produces [C, UINT_MAX].
+        Lower = *C;
+      } else if (IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(&BO))) {
+        if (C->isNegative()) {
+          // 'add nsw x, -C' produces [SINT_MIN, SINT_MAX - C].
+          Lower = APInt::getSignedMinValue(Width);
+          Upper = APInt::getSignedMaxValue(Width) + *C + 1;
+        } else {
+          // 'add nsw x, +C' produces [SINT_MIN + C, SINT_MAX].
+          Lower = APInt::getSignedMinValue(Width) + *C;
+          Upper = APInt::getSignedMaxValue(Width) + 1;
+        }
+      }
+    }
+    break;
+
+  case Instruction::And:
+    if (match(BO.getOperand(1), m_APInt(C)))
+      // 'and x, C' produces [0, C].
+      Upper = *C + 1;
+    break;
+
+  case Instruction::Or:
+    if (match(BO.getOperand(1), m_APInt(C)))
+      // 'or x, C' produces [C, UINT_MAX].
+      Lower = *C;
+    break;
+
+  case Instruction::AShr:
+    if (match(BO.getOperand(1), m_APInt(C)) && C->ult(Width)) {
+      // 'ashr x, C' produces [INT_MIN >> C, INT_MAX >> C].
+      Lower = APInt::getSignedMinValue(Width).ashr(*C);
+      Upper = APInt::getSignedMaxValue(Width).ashr(*C) + 1;
+    } else if (match(BO.getOperand(0), m_APInt(C))) {
+      unsigned ShiftAmount = Width - 1;
+      if (!C->isNullValue() && IIQ.isExact(&BO))
+        ShiftAmount = C->countTrailingZeros();
+      if (C->isNegative()) {
+        // 'ashr C, x' produces [C, C >> (Width-1)]
+        Lower = *C;
+        Upper = C->ashr(ShiftAmount) + 1;
+      } else {
+        // 'ashr C, x' produces [C >> (Width-1), C]
+        Lower = C->ashr(ShiftAmount);
+        Upper = *C + 1;
+      }
+    }
+    break;
+
+  case Instruction::LShr:
+    if (match(BO.getOperand(1), m_APInt(C)) && C->ult(Width)) {
+      // 'lshr x, C' produces [0, UINT_MAX >> C].
+      Upper = APInt::getAllOnesValue(Width).lshr(*C) + 1;
+    } else if (match(BO.getOperand(0), m_APInt(C))) {
+      // 'lshr C, x' produces [C >> (Width-1), C].
+      unsigned ShiftAmount = Width - 1;
+      if (!C->isNullValue() && IIQ.isExact(&BO))
+        ShiftAmount = C->countTrailingZeros();
+      Lower = C->lshr(ShiftAmount);
+      Upper = *C + 1;
+    }
+    break;
+
+  case Instruction::Shl:
+    if (match(BO.getOperand(0), m_APInt(C))) {
+      if (IIQ.hasNoUnsignedWrap(&BO)) {
+        // 'shl nuw C, x' produces [C, C << CLZ(C)]
+        Lower = *C;
+        Upper = Lower.shl(Lower.countLeadingZeros()) + 1;
+      } else if (BO.hasNoSignedWrap()) { // TODO: What if both nuw+nsw?
+        if (C->isNegative()) {
+          // 'shl nsw C, x' produces [C << CLO(C)-1, C]
+          unsigned ShiftAmount = C->countLeadingOnes() - 1;
+          Lower = C->shl(ShiftAmount);
+          Upper = *C + 1;
+        } else {
+          // 'shl nsw C, x' produces [C, C << CLZ(C)-1]
+          unsigned ShiftAmount = C->countLeadingZeros() - 1;
+          Lower = *C;
+          Upper = C->shl(ShiftAmount) + 1;
+        }
+      }
+    }
+    break;
+
+  case Instruction::SDiv:
+    if (match(BO.getOperand(1), m_APInt(C))) {
+      APInt IntMin = APInt::getSignedMinValue(Width);
+      APInt IntMax = APInt::getSignedMaxValue(Width);
+      if (C->isAllOnesValue()) {
+        // 'sdiv x, -1' produces [INT_MIN + 1, INT_MAX]
+        //    where C != -1 and C != 0 and C != 1
+        Lower = IntMin + 1;
+        Upper = IntMax + 1;
+      } else if (C->countLeadingZeros() < Width - 1) {
+        // 'sdiv x, C' produces [INT_MIN / C, INT_MAX / C]
+        //    where C != -1 and C != 0 and C != 1
+        Lower = IntMin.sdiv(*C);
+        Upper = IntMax.sdiv(*C);
+        if (Lower.sgt(Upper))
+          std::swap(Lower, Upper);
+        Upper = Upper + 1;
+        assert(Upper != Lower && "Upper part of range has wrapped!");
+      }
+    } else if (match(BO.getOperand(0), m_APInt(C))) {
+      if (C->isMinSignedValue()) {
+        // 'sdiv INT_MIN, x' produces [INT_MIN, INT_MIN / -2].
+        Lower = *C;
+        Upper = Lower.lshr(1) + 1;
+      } else {
+        // 'sdiv C, x' produces [-|C|, |C|].
+        Upper = C->abs() + 1;
+        Lower = (-Upper) + 1;
+      }
+    }
+    break;
+
+  case Instruction::UDiv:
+    if (match(BO.getOperand(1), m_APInt(C)) && !C->isNullValue()) {
+      // 'udiv x, C' produces [0, UINT_MAX / C].
+      Upper = APInt::getMaxValue(Width).udiv(*C) + 1;
+    } else if (match(BO.getOperand(0), m_APInt(C))) {
+      // 'udiv C, x' produces [0, C].
+      Upper = *C + 1;
+    }
+    break;
+
+  case Instruction::SRem:
+    if (match(BO.getOperand(1), m_APInt(C))) {
+      // 'srem x, C' produces (-|C|, |C|).
+      Upper = C->abs();
+      Lower = (-Upper) + 1;
+    }
+    break;
+
+  case Instruction::URem:
+    if (match(BO.getOperand(1), m_APInt(C)))
+      // 'urem x, C' produces [0, C).
+      Upper = *C;
+    break;
+
+  default:
+    break;
+  }
+}
+
+static void setLimitsForIntrinsic(const IntrinsicInst &II, APInt &Lower,
+                                  APInt &Upper) {
+  unsigned Width = Lower.getBitWidth();
+  const APInt *C;
+  switch (II.getIntrinsicID()) {
+  case Intrinsic::uadd_sat:
+    // uadd.sat(x, C) produces [C, UINT_MAX].
+    if (match(II.getOperand(0), m_APInt(C)) ||
+        match(II.getOperand(1), m_APInt(C)))
+      Lower = *C;
+    break;
+  case Intrinsic::sadd_sat:
+    if (match(II.getOperand(0), m_APInt(C)) ||
+        match(II.getOperand(1), m_APInt(C))) {
+      if (C->isNegative()) {
+        // sadd.sat(x, -C) produces [SINT_MIN, SINT_MAX + (-C)].
+        Lower = APInt::getSignedMinValue(Width);
+        Upper = APInt::getSignedMaxValue(Width) + *C + 1;
+      } else {
+        // sadd.sat(x, +C) produces [SINT_MIN + C, SINT_MAX].
+        Lower = APInt::getSignedMinValue(Width) + *C;
+        Upper = APInt::getSignedMaxValue(Width) + 1;
+      }
+    }
+    break;
+  case Intrinsic::usub_sat:
+    // usub.sat(C, x) produces [0, C].
+    if (match(II.getOperand(0), m_APInt(C)))
+      Upper = *C + 1;
+    // usub.sat(x, C) produces [0, UINT_MAX - C].
+    else if (match(II.getOperand(1), m_APInt(C)))
+      Upper = APInt::getMaxValue(Width) - *C + 1;
+    break;
+  case Intrinsic::ssub_sat:
+    if (match(II.getOperand(0), m_APInt(C))) {
+      if (C->isNegative()) {
+        // ssub.sat(-C, x) produces [SINT_MIN, -SINT_MIN + (-C)].
+        Lower = APInt::getSignedMinValue(Width);
+        Upper = *C - APInt::getSignedMinValue(Width) + 1;
+      } else {
+        // ssub.sat(+C, x) produces [-SINT_MAX + C, SINT_MAX].
+        Lower = *C - APInt::getSignedMaxValue(Width);
+        Upper = APInt::getSignedMaxValue(Width) + 1;
+      }
+    } else if (match(II.getOperand(1), m_APInt(C))) {
+      if (C->isNegative()) {
+        // ssub.sat(x, -C) produces [SINT_MIN - (-C), SINT_MAX]:
+        Lower = APInt::getSignedMinValue(Width) - *C;
+        Upper = APInt::getSignedMaxValue(Width) + 1;
+      } else {
+        // ssub.sat(x, +C) produces [SINT_MIN, SINT_MAX - C].
+        Lower = APInt::getSignedMinValue(Width);
+        Upper = APInt::getSignedMaxValue(Width) - *C + 1;
+      }
+    }
+    break;
+  default:
+    break;
+  }
+}
+
+static void setLimitsForSelectPattern(const SelectInst &SI, APInt &Lower,
+                                      APInt &Upper) {
+  const Value *LHS, *RHS;
+  SelectPatternResult R = matchSelectPattern(&SI, LHS, RHS);
+  if (R.Flavor == SPF_UNKNOWN)
+    return;
+
+  unsigned BitWidth = SI.getType()->getScalarSizeInBits();
+
+  if (R.Flavor == SelectPatternFlavor::SPF_ABS) {
+    // If the negation part of the abs (in RHS) has the NSW flag,
+    // then the result of abs(X) is [0..SIGNED_MAX],
+    // otherwise it is [0..SIGNED_MIN], as -SIGNED_MIN == SIGNED_MIN.
+    Lower = APInt::getNullValue(BitWidth);
+    if (cast<Instruction>(RHS)->hasNoSignedWrap())
+      Upper = APInt::getSignedMaxValue(BitWidth) + 1;
+    else
+      Upper = APInt::getSignedMinValue(BitWidth) + 1;
+    return;
+  }
+
+  if (R.Flavor == SelectPatternFlavor::SPF_NABS) {
+    // The result of -abs(X) is <= 0.
+    Lower = APInt::getSignedMinValue(BitWidth);
+    Upper = APInt(BitWidth, 1);
+    return;
+  }
+
+  const APInt *C;
+  if (!match(LHS, m_APInt(C)) && !match(RHS, m_APInt(C)))
+    return;
+
+  switch (R.Flavor) {
+    case SPF_UMIN:
+      Upper = *C + 1;
+      break;
+    case SPF_UMAX:
+      Lower = *C;
+      break;
+    case SPF_SMIN:
+      Lower = APInt::getSignedMinValue(BitWidth);
+      Upper = *C + 1;
+      break;
+    case SPF_SMAX:
+      Lower = *C;
+      Upper = APInt::getSignedMaxValue(BitWidth) + 1;
+      break;
+    default:
+      break;
+  }
+}
+
+ConstantRange llvm::computeConstantRange(const Value *V, bool UseInstrInfo) {
+  assert(V->getType()->isIntOrIntVectorTy() && "Expected integer instruction");
+
+  const APInt *C;
+  if (match(V, m_APInt(C)))
+    return ConstantRange(*C);
+
+  InstrInfoQuery IIQ(UseInstrInfo);
+  unsigned BitWidth = V->getType()->getScalarSizeInBits();
+  APInt Lower = APInt(BitWidth, 0);
+  APInt Upper = APInt(BitWidth, 0);
+  if (auto *BO = dyn_cast<BinaryOperator>(V))
+    setLimitsForBinOp(*BO, Lower, Upper, IIQ);
+  else if (auto *II = dyn_cast<IntrinsicInst>(V))
+    setLimitsForIntrinsic(*II, Lower, Upper);
+  else if (auto *SI = dyn_cast<SelectInst>(V))
+    setLimitsForSelectPattern(*SI, Lower, Upper);
+
+  ConstantRange CR = ConstantRange::getNonEmpty(Lower, Upper);
+
+  if (auto *I = dyn_cast<Instruction>(V))
+    if (auto *Range = IIQ.getMetadata(I, LLVMContext::MD_range))
+      CR = CR.intersectWith(getConstantRangeFromMetadata(*Range));
+
+  return CR;
+}