Loop vectorization with induction variable with non-constant step.

[delena]

Summary

One of vectorization limitation today is non-const step of induction variable.
In this patch, I allow vectorization when the step is a loop-invariant variable.
This is the loop example that was vectorized after my patch:
int int_inc;
int bar(int init, int *restrict A, int N) {

int x = init;
 for (int i=0;i<N;i++){
   A[i] = x;
   x += int_inc;
 }
 return x;

}
In this case "x" is an induction variable with"init_inc" step. Loop exit count is calculated from another induction variable "i".
The following loop remains scalar right now:

for (int i=0; i<N; i+=int_inc) {
  A[i] = i;
}

In this case the vectorizer can't calculate the exit count.

[delena]

Ping.

[hfinkel]

../lib/Transforms/Utils/LoopUtils.cpp

754–755

I don't think this is a good way to handle this, because we'll run into all kinds of non-trivial situations where SCEV has computed an expression for the step that does not exactly correspond to a pre-existing IR value. We won't handle those cases, and it will be nearly impossible for a user to understand why.

Instead, convert StepValue in InductionDescriptor to a const SCEV *, and then when we need the Value* when generating IR, get one from the SCEVBuilder. It will reuse an existing Value* should one exist.

[delena]

../lib/Transforms/Utils/LoopUtils.cpp

754–755

I can't find a way to build a Value from SCEV. If the Step is "SCEVAddRecExpr", how do I get Value* from it?

[mssimpso]

../lib/Transforms/Utils/LoopUtils.cpp

754–755

Elena,

I think Hal was suggesting you use a SCEVExpander to build a Value from a SCEV expression. SCEVExpander's are used elsewhere in the loop vectorizer.

[hfinkel]

../lib/Transforms/Utils/LoopUtils.cpp

754–755

Yes, exactly. SCEVExpander will reuse an existing value if an appropriate one is known, or otherwise materialize some appropriate IR value.

[delena]

Following Hal's and Matthew comments, I keep Step as a SCEV inside InductionDescriptor. It allows to vectorize loop with induction variable with any *loop-invariant* step.
Again, we are talking about a "secondary" induction variable, which is being updated inside loop, but does not participate in trip count calculation.

I added one more example, where the step is a SCEV from outer loop:

for (int j = 0; j < M; j++) {
  for (int i=0; i<N; i++){
    A[i] = x;
    x += j; // loop-invariant step
  }
}

[hfinkel]

../lib/Transforms/Utils/LoopUtils.cpp

661

Comments should be complete sentences and end with a period.

669

See above.

702

The logic here is now repeating things that SCEVExpander should already know how to do (plus SCEV might know about even more simplification rules). Try calculating the expression using SCEV and then expand that. This seems to be computing Start + Index*Step, so we can generate:

const SCEV *S = SE->getAddExpr(SE->getSCEV(Start), SE->getMulExpr(SE->getSCEV(Index), Step);
return Exp.expandCodeFor(S, StartValue->getType(), &*B.GetInsertPoint());

If you use StartValue->getType() as I did above, this might just work for the pointer inductions too.

[delena]

../lib/Transforms/Utils/LoopUtils.cpp

702

I tried to apply your proposal. The generated code is right but not always match the original. Some tests fail due to this replacement. It happens because getAddExpr() tries to combine all addends recursively. In some cases the result is better. But I saw one case at least, where the code became less optimal.

[delena]

I added SCEV calculation where it was possible without changing the existing tests.
I also changed some comments.

[delena]

Hi Hal,

I checked again. SE->getAddExpr(SE->getSCEV(A), SE->getSCEV(B)) does not always give better results than just createAdd(A, B).
It happens when we mix getAddExpr on SCEVs and ADD/SUB operations. As a result, we receive redundant intermediate values being calculated in different ways and Instcombine is unable to reduce them all.

Could you, please, continue reviewing this patch. Thank you.

[hfinkel]

../lib/Transforms/Utils/LoopUtils.cpp

702

Okay. That's unfortunate. Please add a FIXME comment here explaining the situation. Otherwise, this LGTM.

[delena]

Thanks a lot for the review! I added a comment about SCEV expressions.

../include/llvm/Transforms/Utils/LoopUtils.h

enum InductionKind {
     IK_NoInduction,  ///< Not an induction variable.
     IK_IntInduction, ///< Integer induction variable. Step = C.
     IK_PtrInduction  ///< Pointer induction var. Step = C / sizeof(elem).
   };
 
 public:
   /// Default constructor - creates an invalid induction.
   InductionDescriptor()
-    : StartValue(nullptr), IK(IK_NoInduction), StepValue(nullptr) {}
+    : StartValue(nullptr), IK(IK_NoInduction), Step(nullptr) {}
 
   /// Get the consecutive direction. Returns:
   ///   0 - unknown or non-consecutive.
   ///   1 - consecutive and increasing.
   ///  -1 - consecutive and decreasing.
   int getConsecutiveDirection() const;
 
   /// Compute the transformed value of Index at offset StartValue using step
   /// StepValue.
   /// For integer induction, returns StartValue + Index * StepValue.
   /// For pointer induction, returns StartValue[Index * StepValue].
   /// FIXME: The newly created binary instructions should contain nsw/nuw
   /// flags, which can be found from the original scalar operations.
-  Value *transform(IRBuilder<> &B, Value *Index) const;
+  Value *transform(IRBuilder<> &B, Value *Index, ScalarEvolution *SE,
+                   const DataLayout& DL) const;
 
   Value *getStartValue() const { return StartValue; }
   InductionKind getKind() const { return IK; }
-  ConstantInt *getStepValue() const { return StepValue; }
+  const SCEV *getStep() const { return Step; }
+  ConstantInt *getConstIntStepValue() const;
 
   static bool isInductionPHI(PHINode *Phi, ScalarEvolution *SE,
                              InductionDescriptor &D);
 
 private:
   /// Private constructor - used by \c isInductionPHI.
-  InductionDescriptor(Value *Start, InductionKind K, ConstantInt *Step);
+  InductionDescriptor(Value *Start, InductionKind K, const SCEV *Step);
 
   /// Start value.
   TrackingVH<Value> StartValue;
   /// Induction kind.
   InductionKind IK;
   /// Step value.
-  ConstantInt *StepValue;
+  const SCEV *Step;
 };
 
 BasicBlock *InsertPreheaderForLoop(Loop *L, DominatorTree *DT, LoopInfo *LI,
                                    bool PreserveLCSSA);
 
 /// \brief Simplify each loop in a loop nest recursively.
 ///
 /// This takes a potentially un-simplified loop L (and its children) and turns

../lib/Transforms/Utils/LoopUtils.cpp

 //
 //===----------------------------------------------------------------------===//
 
 #include "llvm/Analysis/AliasAnalysis.h"
 #include "llvm/Analysis/BasicAliasAnalysis.h"
 #include "llvm/Analysis/LoopInfo.h"
 #include "llvm/Analysis/GlobalsModRef.h"
 #include "llvm/Analysis/ScalarEvolution.h"
+#include "llvm/Analysis/ScalarEvolutionExpander.h"
 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
 #include "llvm/Analysis/ScalarEvolutionAliasAnalysis.h"
 #include "llvm/IR/Dominators.h"
 #include "llvm/IR/Instructions.h"
 #include "llvm/IR/Module.h"
 #include "llvm/IR/PatternMatch.h"
 #include "llvm/IR/ValueHandle.h"
 #include "llvm/Pass.h"
Value *RecurrenceDescriptor::createMinMaxOp(IRBuilder<> &Builder,
   else
     Cmp = Builder.CreateICmp(P, Left, Right, "rdx.minmax.cmp");
 
   Value *Select = Builder.CreateSelect(Cmp, Left, Right, "rdx.minmax.select");
   return Select;
 }
 
 InductionDescriptor::InductionDescriptor(Value *Start, InductionKind K,
-                                         ConstantInt *Step)
-  : StartValue(Start), IK(K), StepValue(Step) {
+                                         const SCEV *Step)
+  : StartValue(Start), IK(K), Step(Step) {
   assert(IK != IK_NoInduction && "Not an induction");
+
+  // Start value type should match the induction kind and the value
+  // itself should not be null.
   assert(StartValue && "StartValue is null");
-  assert(StepValue && !StepValue->isZero() && "StepValue is zero");
   assert((IK != IK_PtrInduction || StartValue->getType()->isPointerTy()) &&
          "StartValue is not a pointer for pointer induction");
   assert((IK != IK_IntInduction || StartValue->getType()->isIntegerTy()) &&
          "StartValue is not an integer for integer induction");
-  assert(StepValue->getType()->isIntegerTy() &&
-         "StepValue is not an integer");
+
+  // Check the Step Value. It should be non-zero integer value.
+  assert((!getConstIntStepValue() || !getConstIntStepValue()->isZero()) &&
+         "Step value is zero");
+
+  assert((IK != IK_PtrInduction || getConstIntStepValue()) &&
+         "Step value should be constant for pointer induction");
+  assert(Step->getType()->isIntegerTy() && "StepValue is not an integer");
 }
 
 int InductionDescriptor::getConsecutiveDirection() const {
-  if (StepValue && (StepValue->isOne() || StepValue->isMinusOne()))
-    return StepValue->getSExtValue();
+  ConstantInt *ConstStep = getConstIntStepValue();
+  if (ConstStep && (ConstStep->isOne() || ConstStep->isMinusOne()))
+    return ConstStep->getSExtValue();
   return 0;
 }
 
-Value *InductionDescriptor::transform(IRBuilder<> &B, Value *Index) const {
+ConstantInt *InductionDescriptor::getConstIntStepValue() const {
+  if (isa<SCEVConstant>(Step))
+    return dyn_cast<ConstantInt>(cast<SCEVConstant>(Step)->getValue());
+  return nullptr;
+}
+
+Value *InductionDescriptor::transform(IRBuilder<> &B, Value *Index,
+                                      ScalarEvolution *SE,
+                                      const DataLayout& DL) const {
+
+  SCEVExpander Exp(*SE, DL, "induction");
   switch (IK) {
-  case IK_IntInduction:
+  case IK_IntInduction: {
     assert(Index->getType() == StartValue->getType() &&
            "Index type does not match StartValue type");
-    if (StepValue->isMinusOne())
+    if (getConstIntStepValue() &&
+        getConstIntStepValue()->isMinusOne())
       return B.CreateSub(StartValue, Index);
-    if (!StepValue->isOne())
-      Index = B.CreateMul(Index, StepValue);
+    if (getConstIntStepValue() &&
+        getConstIntStepValue()->isOne())
       return B.CreateAdd(StartValue, Index);
-
-  case IK_PtrInduction:
-    assert(Index->getType() == StepValue->getType() &&
+    const SCEV *S = SE->getAddExpr(SE->getSCEV(StartValue),
+                                   SE->getMulExpr(Step, SE->getSCEV(Index)));
+    return Exp.expandCodeFor(S, StartValue->getType(), &*B.GetInsertPoint());
+  }
+  case IK_PtrInduction: {
+    assert(Index->getType() == Step->getType() &&
            "Index type does not match StepValue type");
-    if (StepValue->isMinusOne())
-      Index = B.CreateNeg(Index);
-    else if (!StepValue->isOne())
-      Index = B.CreateMul(Index, StepValue);
+    assert(isa<SCEVConstant>(Step) &&
+           "Expected constant step for pointer induction");
+    const SCEV *S = SE->getMulExpr(SE->getSCEV(Index), Step);
+    Index = Exp.expandCodeFor(S, Index->getType(), &*B.GetInsertPoint());
     return B.CreateGEP(nullptr, StartValue, Index);
-
+  }
   case IK_NoInduction:
     return nullptr;
   }
   llvm_unreachable("invalid enum");
 }
 
 bool InductionDescriptor::isInductionPHI(PHINode *Phi, ScalarEvolution *SE,
                                          InductionDescriptor &D) {
bool InductionDescriptor::isInductionPHI(PHINode *Phi, ScalarEvolution *SE,
   }
 
   assert(AR->getLoop()->getHeader() == Phi->getParent() &&
          "PHI is an AddRec for a different loop?!");
   Value *StartValue =
     Phi->getIncomingValueForBlock(AR->getLoop()->getLoopPreheader());
   const SCEV *Step = AR->getStepRecurrence(*SE);
   // Calculate the pointer stride and check if it is consecutive.
-  const SCEVConstant *C = dyn_cast<SCEVConstant>(Step);
-  if (!C)
+  // The stride may be a constant or a loop invariant integer value.
+  const SCEVConstant *ConstStep = dyn_cast<SCEVConstant>(Step);
+  if (!ConstStep && !SE->isLoopInvariant(Step, AR->getLoop()))
     return false;
 
-  ConstantInt *CV = C->getValue();
   if (PhiTy->isIntegerTy()) {
-    D = InductionDescriptor(StartValue, IK_IntInduction, CV);
+    D = InductionDescriptor(StartValue, IK_IntInduction, Step);
     return true;
   }
 
   assert(PhiTy->isPointerTy() && "The PHI must be a pointer");
+  // Pointer induction should be a constant.
+  if (!ConstStep)
+    return false;
+
+  ConstantInt *CV = ConstStep->getValue();
   Type *PointerElementType = PhiTy->getPointerElementType();
   // The pointer stride cannot be determined if the pointer element type is not
   // sized.
   if (!PointerElementType->isSized())
     return false;
 
   const DataLayout &DL = Phi->getModule()->getDataLayout();
   int64_t Size = static_cast<int64_t>(DL.getTypeAllocSize(PointerElementType));
   if (!Size)
     return false;
 
   int64_t CVSize = CV->getSExtValue();
   if (CVSize % Size)
     return false;
-  auto *StepValue = ConstantInt::getSigned(CV->getType(), CVSize / Size);
-
+  auto *StepValue = SE->getConstant(CV->getType(), CVSize / Size,
+                                    true /* signed */);
   D = InductionDescriptor(StartValue, IK_PtrInduction, StepValue);
   return true;
 }
 
 /// \brief Returns the instructions that use values defined in the loop.
 SmallVector<Instruction *, 8> llvm::findDefsUsedOutsideOfLoop(Loop *L) {
   SmallVector<Instruction *, 8> UsedOutside;
 

../lib/Transforms/Vectorize/LoopVectorize.cpp

protected:
   /// this is needed because each iteration in the loop corresponds to a SIMD
   /// element.
   virtual Value *getBroadcastInstrs(Value *V);
 
   /// This function adds (StartIdx, StartIdx + Step, StartIdx + 2*Step, ...)
   /// to each vector element of Val. The sequence starts at StartIndex.
   virtual Value *getStepVector(Value *Val, int StartIdx, Value *Step);
 
+  /// This function adds (StartIdx, StartIdx + Step, StartIdx + 2*Step, ...)
+  /// to each vector element of Val. The sequence starts at StartIndex.
+  /// Step is a SCEV. In order to get StepValue it takes the existing value
+  /// from SCEV or creates a new using SCEVExpander.
+  virtual Value *getStepVector(Value *Val, int StartIdx, const SCEV *Step);
+
   /// When we go over instructions in the basic block we rely on previous
   /// values within the current basic block or on loop invariant values.
   /// When we widen (vectorize) values we place them in the map. If the values
   /// are not within the map, they have to be loop invariant, so we simply
   /// broadcast them into a vector.
   VectorParts &getVectorValue(Value *V);
 
   /// Try to vectorize the interleaved access group that \p Instr belongs to.
InnerLoopUnroller(Loop *OrigLoop, PredicatedScalarEvolution &PSE,
                             UnrollFactor) {}
 
 private:
   void scalarizeInstruction(Instruction *Instr,
                             bool IfPredicateStore = false) override;
   void vectorizeMemoryInstruction(Instruction *Instr) override;
   Value *getBroadcastInstrs(Value *V) override;
   Value *getStepVector(Value *Val, int StartIdx, Value *Step) override;
+  Value *getStepVector(Value *Val, int StartIdx, const SCEV *StepSCEV) override;
   Value *reverseVector(Value *Vec) override;
 };
 
 /// \brief Look for a meaningful debug location on the instruction or it's
 /// operands.
 static Instruction *getDebugLocFromInstOrOperands(Instruction *I) {
   if (!I)
     return I;
Value *InnerLoopVectorizer::getBroadcastInstrs(Value *V) {
 
   // Broadcast the scalar into all locations in the vector.
   Value *Shuf = Builder.CreateVectorSplat(VF, V, "broadcast");
 
   return Shuf;
 }
 
 Value *InnerLoopVectorizer::getStepVector(Value *Val, int StartIdx,
+                                          const SCEV *StepSCEV) {
+  const DataLayout &DL = OrigLoop->getHeader()->getModule()->getDataLayout();
+  SCEVExpander Exp(*PSE.getSE(), DL, "induction");
+  Value *StepValue = Exp.expandCodeFor(StepSCEV, StepSCEV->getType(),
+                                       &*Builder.GetInsertPoint());
+  return getStepVector(Val, StartIdx, StepValue);
+}
+
+Value *InnerLoopVectorizer::getStepVector(Value *Val, int StartIdx,
                                           Value *Step) {
   assert(Val->getType()->isVectorTy() && "Must be a vector");
   assert(Val->getType()->getScalarType()->isIntegerTy() &&
          "Elem must be an integer");
   assert(Step->getType() == Val->getType()->getScalarType() &&
          "Step has wrong type");
   // Create the types.
   Type *ITy = Val->getType()->getScalarType();
PHINode *BCResumeVal = PHINode::Create(OrigPhi->getType(), 3,
                                            ScalarPH->getTerminator());
     Value *EndValue;
     if (OrigPhi == OldInduction) {
       // We know what the end value is.
       EndValue = CountRoundDown;
     } else {
       IRBuilder<> B(LoopBypassBlocks.back()->getTerminator());
       Value *CRD = B.CreateSExtOrTrunc(CountRoundDown,
-                                       II.getStepValue()->getType(),
+                                       II.getStep()->getType(),
                                        "cast.crd");
-      EndValue = II.transform(B, CRD);
+      const DataLayout &DL = OrigLoop->getHeader()->getModule()->getDataLayout();
+      EndValue = II.transform(B, CRD, PSE.getSE(), DL);
       EndValue->setName("ind.end");
     }
 
     // The new PHI merges the original incoming value, in case of a bypass,
     // or the value at the end of the vectorized loop.
     BCResumeVal->addIncoming(EndValue, MiddleBlock);
 
     // Fix the scalar body counter (PHI node).
void InnerLoopVectorizer::widenPHIInstruction(
   }
 
   // This PHINode must be an induction variable.
   // Make sure that we know about it.
   assert(Legal->getInductionVars()->count(P) &&
          "Not an induction variable");
 
   InductionDescriptor II = Legal->getInductionVars()->lookup(P);
+  const DataLayout &DL = OrigLoop->getHeader()->getModule()->getDataLayout();
 
   // FIXME: The newly created binary instructions should contain nsw/nuw flags,
   // which can be found from the original scalar operations.
   switch (II.getKind()) {
     case InductionDescriptor::IK_NoInduction:
       llvm_unreachable("Unknown induction");
     case InductionDescriptor::IK_IntInduction: {
       assert(P->getType() == II.getStartValue()->getType() &&
              "Types must match");
       // Handle other induction variables that are now based on the
       // canonical one.
       Value *V = Induction;
       if (P != OldInduction) {
         V = Builder.CreateSExtOrTrunc(Induction, P->getType());
-        V = II.transform(Builder, V);
+        V = II.transform(Builder, V, PSE.getSE(), DL);
         V->setName("offset.idx");
       }
       Value *Broadcasted = getBroadcastInstrs(V);
       // After broadcasting the induction variable we need to make the vector
       // consecutive by adding 0, 1, 2, etc.
       for (unsigned part = 0; part < UF; ++part)
-        Entry[part] = getStepVector(Broadcasted, VF * part, II.getStepValue());
+        Entry[part] = getStepVector(Broadcasted, VF * part, II.getStep());
       return;
     }
     case InductionDescriptor::IK_PtrInduction:
       // Handle the pointer induction variable case.
       assert(P->getType()->isPointerTy() && "Unexpected type.");
       // This is the normalized GEP that starts counting at zero.
       Value *PtrInd = Induction;
-      PtrInd = Builder.CreateSExtOrTrunc(PtrInd, II.getStepValue()->getType());
+      PtrInd = Builder.CreateSExtOrTrunc(PtrInd, II.getStep()->getType());
       // This is the vector of results. Notice that we don't generate
       // vector geps because scalar geps result in better code.
       for (unsigned part = 0; part < UF; ++part) {
         if (VF == 1) {
           int EltIndex = part;
           Constant *Idx = ConstantInt::get(PtrInd->getType(), EltIndex);
           Value *GlobalIdx = Builder.CreateAdd(PtrInd, Idx);
-          Value *SclrGep = II.transform(Builder, GlobalIdx);
+          Value *SclrGep = II.transform(Builder, GlobalIdx, PSE.getSE(), DL);
           SclrGep->setName("next.gep");
           Entry[part] = SclrGep;
           continue;
         }
 
         Value *VecVal = UndefValue::get(VectorType::get(P->getType(), VF));
         for (unsigned int i = 0; i < VF; ++i) {
           int EltIndex = i + part * VF;
           Constant *Idx = ConstantInt::get(PtrInd->getType(), EltIndex);
           Value *GlobalIdx = Builder.CreateAdd(PtrInd, Idx);
-          Value *SclrGep = II.transform(Builder, GlobalIdx);
+          Value *SclrGep = II.transform(Builder, GlobalIdx, PSE.getSE(), DL);
           SclrGep->setName("next.gep");
           VecVal = Builder.CreateInsertElement(VecVal, SclrGep,
                                                Builder.getInt32(i),
                                                "insert.gep");
         }
         Entry[part] = VecVal;
       }
       return;
for (BasicBlock::iterator it = BB->begin(), e = BB->end(); it != e; ++it) {
     case Instruction::IntToPtr:
     case Instruction::SIToFP:
     case Instruction::UIToFP:
     case Instruction::Trunc:
     case Instruction::FPTrunc:
     case Instruction::BitCast: {
       CastInst *CI = dyn_cast<CastInst>(it);
       setDebugLocFromInst(Builder, &*it);
-      /// Optimize the special case where the source is the induction
-      /// variable. Notice that we can only optimize the 'trunc' case
+      /// Optimize the special case where the source is a constant integer
+      /// induction variable. Notice that we can only optimize the 'trunc' case
       /// because: a. FP conversions lose precision, b. sext/zext may wrap,
       /// c. other casts depend on pointer size.
+
       if (CI->getOperand(0) == OldInduction &&
           it->getOpcode() == Instruction::Trunc) {
+        InductionDescriptor II =
+          Legal->getInductionVars()->lookup(OldInduction);
+        if (auto StepValue = II.getConstIntStepValue()) {
+          StepValue = ConstantInt::getSigned(cast<IntegerType>(CI->getType()),
+                                             StepValue->getSExtValue());
           Value *ScalarCast = Builder.CreateCast(CI->getOpcode(), Induction,
                                                  CI->getType());
           Value *Broadcasted = getBroadcastInstrs(ScalarCast);
-        InductionDescriptor II =
-            Legal->getInductionVars()->lookup(OldInduction);
-        Constant *Step = ConstantInt::getSigned(
-            CI->getType(), II.getStepValue()->getSExtValue());
           for (unsigned Part = 0; Part < UF; ++Part)
-          Entry[Part] = getStepVector(Broadcasted, VF * Part, Step);
+            Entry[Part] = getStepVector(Broadcasted, VF * Part, StepValue);
           addMetadata(Entry, &*it);
           break;
         }
+      }
       /// Vectorize casts.
       Type *DestTy = (VF == 1) ? CI->getType() :
                                  VectorType::get(CI->getType(), VF);
 
       VectorParts &A = getVectorValue(it->getOperand(0));
       for (unsigned Part = 0; Part < UF; ++Part)
         Entry[Part] = Builder.CreateCast(CI->getOpcode(), A[Part], DestTy);
       addMetadata(Entry, &*it);
for (BasicBlock::iterator it = (*bb)->begin(), e = (*bb)->end(); it != e;
           // Get the widest type.
           if (!WidestIndTy)
             WidestIndTy = convertPointerToIntegerType(DL, PhiTy);
           else
             WidestIndTy = getWiderType(DL, PhiTy, WidestIndTy);
 
           // Int inductions are special because we only allow one IV.
           if (ID.getKind() == InductionDescriptor::IK_IntInduction &&
-              ID.getStepValue()->isOne() &&
+              ID.getConstIntStepValue() &&
+              ID.getConstIntStepValue()->isOne() &&
               isa<Constant>(ID.getStartValue()) &&
                 cast<Constant>(ID.getStartValue())->isNullValue()) {
             // Use the phi node with the widest type as induction. Use the last
             // one if there are multiple (no good reason for doing this other
             // than it is expedient). We've checked that it begins at zero and
             // steps by one, so this is a canonical induction variable.
             if (!Induction || PhiTy == WidestIndTy)
               Induction = Phi;

 Value *InnerLoopUnroller::reverseVector(Value *Vec) {
   return Vec;
 }
 
 Value *InnerLoopUnroller::getBroadcastInstrs(Value *V) {
   return V;
 }
 
+Value *InnerLoopUnroller::getStepVector(Value *Val, int StartIdx,
+                                        const SCEV *StepSCEV) {
+  const DataLayout &DL = OrigLoop->getHeader()->getModule()->getDataLayout();
+  SCEVExpander Exp(*PSE.getSE(), DL, "induction");
+  Value *StepValue = Exp.expandCodeFor(StepSCEV, StepSCEV->getType(),
+                                       &*Builder.GetInsertPoint());
+  return getStepVector(Val, StartIdx, StepValue);
+}
+
 Value *InnerLoopUnroller::getStepVector(Value *Val, int StartIdx, Value *Step) {
   // When unrolling and the VF is 1, we only need to add a simple scalar.
   Type *ITy = Val->getType();
   assert(!ITy->isVectorTy() && "Val must be a scalar");
   Constant *C = ConstantInt::get(ITy, StartIdx);
   return Builder.CreateAdd(Val, Builder.CreateMul(C, Step), "induction");
 }

../test/Transforms/LoopVectorize/induction-step.ll

+; RUN: opt < %s -loop-vectorize -force-vector-interleave=1 -force-vector-width=8 -S | FileCheck %s
+
+; int int_inc;
+;
+;int induction_with_global(int init, int *restrict A, int N) {
+;  int x = init;
+;  for (int i=0;i<N;i++){
+;    A[i] = x;
+;    x += int_inc;
+;  }
+;  return x;
+;}
+
+; CHECK-LABEL: @induction_with_global(
+; CHECK: %[[INT_INC:.*]] = load i32, i32* @int_inc, align 4
+; CHECK: vector.body:
+; CHECK:  %[[VAR1:.*]] = insertelement <8 x i32> undef, i32 %[[INT_INC]], i32 0
+; CHECK:  %[[VAR2:.*]] = shufflevector <8 x i32> %[[VAR1]], <8 x i32> undef, <8 x i32> zeroinitializer
+; CHECK:  mul <8 x i32> <i32 0, i32 1, i32 2, i32 3, i32 4, i32 5, i32 6, i32 7>, %[[VAR2]]
+
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+
+
+@int_inc = common global i32 0, align 4
+
+define i32 @induction_with_global(i32 %init, i32* noalias nocapture %A, i32 %N) {
+entry:
+  %cmp4 = icmp sgt i32 %N, 0
+  br i1 %cmp4, label %for.body.lr.ph, label %for.end
+
+for.body.lr.ph:                                   ; preds = %entry
+  %0 = load i32, i32* @int_inc, align 4
+  %1 = mul i32 %0, %N
+  br label %for.body
+
+for.body:                                         ; preds = %for.body, %for.body.lr.ph
+  %indvars.iv = phi i64 [ 0, %for.body.lr.ph ], [ %indvars.iv.next, %for.body ]
+  %x.05 = phi i32 [ %init, %for.body.lr.ph ], [ %add, %for.body ]
+  %arrayidx = getelementptr inbounds i32, i32* %A, i64 %indvars.iv
+  store i32 %x.05, i32* %arrayidx, align 4
+  %add = add nsw i32 %0, %x.05
+  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
+  %lftr.wideiv = trunc i64 %indvars.iv.next to i32
+  %exitcond = icmp eq i32 %lftr.wideiv, %N
+  br i1 %exitcond, label %for.end.loopexit, label %for.body
+
+for.end.loopexit:                                 ; preds = %for.body
+  %2 = add i32 %1, %init
+  br label %for.end
+
+for.end:                                          ; preds = %for.end.loopexit, %entry
+  %x.0.lcssa = phi i32 [ %init, %entry ], [ %2, %for.end.loopexit ]
+  ret i32 %x.0.lcssa
+}
+
+
+;int induction_with_loop_inv(int init, int *restrict A, int N, int M) {
+;  int x = init;
+;  for (int j = 0; j < M; j++) {
+;    for (int i=0; i<N; i++){
+;      A[i] = x;
+;      x += j; // induction step is a loop invariant variable
+;    }
+;  }
+;  return x;
+;}
+
+; CHECK-LABEL: @induction_with_loop_inv(
+; CHECK: for.cond1.preheader:                            
+; CHECK: %[[INDVAR0:.*]] = phi i32 [ 0,
+; CHECK: %[[INDVAR1:.*]] = phi i32 [ 0,
+; CHECK: vector.body:
+; CHECK:  %[[VAR1:.*]] = insertelement <8 x i32> undef, i32 %[[INDVAR1]], i32 0
+; CHECK:  %[[VAR2:.*]] = shufflevector <8 x i32> %[[VAR1]], <8 x i32> undef, <8 x i32> zeroinitializer
+; CHECK:  mul <8 x i32> <i32 0, i32 1, i32 2, i32 3, i32 4, i32 5, i32 6, i32 7>, %[[VAR2]]
+
+define i32 @induction_with_loop_inv(i32 %init, i32* noalias nocapture %A, i32 %N, i32 %M) {
+entry:
+  %cmp10 = icmp sgt i32 %M, 0
+  br i1 %cmp10, label %for.cond1.preheader.lr.ph, label %for.end6
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  %cmp27 = icmp sgt i32 %N, 0
+  br label %for.cond1.preheader
+
+for.cond1.preheader:                              ; preds = %for.inc4, %for.cond1.preheader.lr.ph
+  %indvars.iv15 = phi i32 [ 0, %for.cond1.preheader.lr.ph ], [ %indvars.iv.next16, %for.inc4 ]
+  %j.012 = phi i32 [ 0, %for.cond1.preheader.lr.ph ], [ %inc5, %for.inc4 ]
+  %x.011 = phi i32 [ %init, %for.cond1.preheader.lr.ph ], [ %x.1.lcssa, %for.inc4 ]
+  br i1 %cmp27, label %for.body3.preheader, label %for.inc4
+
+for.body3.preheader:                              ; preds = %for.cond1.preheader
+  br label %for.body3
+
+for.body3:                                        ; preds = %for.body3.preheader, %for.body3
+  %indvars.iv = phi i64 [ %indvars.iv.next, %for.body3 ], [ 0, %for.body3.preheader ]
+  %x.18 = phi i32 [ %add, %for.body3 ], [ %x.011, %for.body3.preheader ]
+  %arrayidx = getelementptr inbounds i32, i32* %A, i64 %indvars.iv
+  store i32 %x.18, i32* %arrayidx, align 4
+  %add = add nsw i32 %x.18, %j.012
+  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
+  %lftr.wideiv = trunc i64 %indvars.iv.next to i32
+  %exitcond = icmp eq i32 %lftr.wideiv, %N
+  br i1 %exitcond, label %for.inc4.loopexit, label %for.body3
+
+for.inc4.loopexit:                                ; preds = %for.body3
+  %0 = add i32 %x.011, %indvars.iv15
+  br label %for.inc4
+
+for.inc4:                                         ; preds = %for.inc4.loopexit, %for.cond1.preheader
+  %x.1.lcssa = phi i32 [ %x.011, %for.cond1.preheader ], [ %0, %for.inc4.loopexit ]
+  %inc5 = add nuw nsw i32 %j.012, 1
+  %indvars.iv.next16 = add i32 %indvars.iv15, %N
+  %exitcond17 = icmp eq i32 %inc5, %M
+  br i1 %exitcond17, label %for.end6.loopexit, label %for.cond1.preheader
+
+for.end6.loopexit:                                ; preds = %for.inc4
+  %x.1.lcssa.lcssa = phi i32 [ %x.1.lcssa, %for.inc4 ]
+  br label %for.end6
+
+for.end6:                                         ; preds = %for.end6.loopexit, %entry
+  %x.0.lcssa = phi i32 [ %init, %entry ], [ %x.1.lcssa.lcssa, %for.end6.loopexit ]
+  ret i32 %x.0.lcssa
+}