[Polly] Canonicalize arrays according to base-ptr equivalence class

[grosser]

Summary

In case two arrays share base pointers in the same invariant load equivalence
class, we canonicalize all memory accesses to the first of these arrays
(according to their order in the equivalence class).

This enables us to optimize kernels such as boost::ublas by ensuring that
different references to the C array are interpreted as accesses to the same
array. Before this change the runtime alias check for ublas would fail, as it
would assume models of the C array with differing (but identically valued) base
pointers would reference distinct regions of memory whereas the referenced
memory regions were indeed identical.

As part of this change we remove most of the MemoryAccess::get*BaseAddr
interface. We removed already all references to get*BaseAddr in previous
commits to ensure that no code relies on matching base pointers between
memory accesses and scop arrays -- except for three remaining uses where we
need the original base pointer. We document for these situations that
MemoryAccess::getOriginalBaseAddr may return a base pointer that is distinct
to the base pointer of the scop array referenced by this memory access.

[etherzhhb]

testcase?

[grosser]

Add test case

[Meinersbur]

My suggestion is to modify getOrCreateScopArrayInfo which before creating a new ScopArrayInfo, looks up the canonical load from InvEquivClassVMap.

include/polly/ScopInfo.h

1840 ↗

(On Diff #83922)

incorrect may be not the correct word as there is no guarantee that two base pointers are different anyway. In that sense a program with two base ptrs are ony correct if AA says they are disjoint. This is why we have alias checks.

1842 ↗

(On Diff #83922)

I'd interpret the future tense (\will\) as something that is going to happen later in the pipeline. This patch, however, removes this possibility. Can you make it clearer that it is something that would happen without this step?

lib/Analysis/ScopInfo.cpp

3692 ↗

(On Diff #83922)

unify sounds like after this there will be only one indirect array.

I am also not sure whether indirect array is the correct term as there is only one array whose pointer happens to be loaded twice. (The assertion you commented out thinks it is as soon as there is a dynamic load)

Alternative name suggestion: canonicalizeDynamicBasePtrs

3693–3694 ↗

(On Diff #83922)

We might separate the analysis part and the transformation part of invariant load hoisting, such that unifyIndirectArrays can be activated independently of invariant load hoisting.

3702 ↗

(On Diff #83922)

Three possible alternatives:

for (auto Pair : enumerate(EqClass.InvariantAccesses))
  if (Pair.Index == 0)

bool IsFirst = true;
for (...) 
  if (IsFirst) {
    IsFirst = False;
  }

if (InvAccess == EqClass.InvariantAccesses.front())

3705–3709 ↗

(On Diff #83922)

Isn't there CanonicalAccess->getScopArrayInfo(). If it hasn't been computed yet, could we either call unifyIndirectArrays() after it has been computed or compute it earlier?

3716–3724 ↗

(On Diff #83922)

Duplication. Refactor-out?

3732 ↗

(On Diff #83922)

This marks the access relation as been replaced as if done by eg. JSONImporter, the original still being accessible. The code generator has a different code path if a new access relation has been set. Is this intended?

[grosser]

Hi Michael,

I updated this patch according to your comments and added some good test coverage. With r292213 this patch works as intended and it seems reasonable clean.

There are however two open points:

1. I did not yet check if the very same thing could be implemented better in getOrCreateScopArrayInfo()

2. I still want to check if we can set the original access function, instead of setting a new one. However, this will require a closer review of the basepointer handling in Polly.

@gareevroman : This patch should be good enough for your experiments, but it still needs some more thoughts before being able to be committed.

include/polly/ScopInfo.h

1840 ↗

(On Diff #83922)

I reformulated this and expanded the comment.

1842 ↗

(On Diff #83922)

Reformulated. Please see if this now reads better.

lib/Analysis/ScopInfo.cpp

3692 ↗

(On Diff #83922)

I like the new name -> changed.

3693–3694 ↗

(On Diff #83922)

Actually, this check is not needed. If invariant load hoisting is disabled, the InvariantEquivClasses array will be empty and consequently this function won't do anything. I dropped the check.

3702 ↗

(On Diff #83922)

Very nice. Thank you for these ideas. I especially like the first one. I changed my code to the first one, but then moved to even another solution: copying the list of accesses and dropping the first one explicitly. This has the minor cost of copying the full access list. However, this cost is likely very small and the resulting code looks very readable.

3705–3709 ↗

(On Diff #83922)

Not sure what you have in mind here. CanonicalSAI is not the ScopArrayInfo of the CanonicalAccess, but its the SAI which has as basepointer the load in CanonoicalSAI.

I introduced now a function getScopArrayInfoOrNull() similarly to the already existing getScopArrayInfo and just use this instead of the loop above.

3716–3724 ↗

(On Diff #83922)

I also moved this to getScopArrayInfoOrNull()

3732 ↗

(On Diff #83922)

This was intended.

If I just reset the original access relation, the following check starts
to fail:

getOriginalScopArrayInfo()->getBasePtr() == BaseAddr'

We should probably review this invariant, but there are several parts of Polly that rely on this behavior. I still need to look at all of them to understand if they behavior is correct:

lib/Analysis/ScopInfo.cpp:    auto *SAI = S.getOrCreateScopArrayInfo(Access->getBaseAddr(), ElementType,
lib/Analysis/ScopInfo.cpp:    PHINode *PHI = cast<PHINode>(Access->getBaseAddr());
lib/Analysis/ScopInfo.cpp:  auto *BaseAddr = SE->getSCEV(MA->getBaseAddr());
lib/Analysis/ScopInfo.cpp:  auto *BaseAddr = SE->getSCEV(MA->getBaseAddr());
lib/Analysis/ScopInfo.cpp:        HasWriteAccess.insert(MA->getBaseAddr());
lib/Analysis/ScopInfo.cpp:    Value *BaseAddr = Access->getBaseAddr();
lib/Analysis/ScopInfo.cpp:      auto &SAI = ScopArrayInfoMap[std::make_pair(Access->getBaseAddr(),
lib/CodeGen/IRBuilder.cpp:        BasePtrs.insert(MA->getBaseAddr());
lib/CodeGen/IslAst.cpp:          ", " + MA->getBaseAddr()->getName().str();
lib/CodeGen/BlockGenerators.cpp:    return getOrCreateScalarAlloca(Access.getBaseAddr());
lib/CodeGen/BlockGenerators.cpp:    return getOrCreatePHIAlloca(Access.getBaseAddr());
lib/CodeGen/BlockGenerators.cpp:    return getOrCreatePHIAlloca(Access.getBaseAddr());
lib/CodeGen/BlockGenerators.cpp:    return getOrCreateScalarAlloca(Access.getBaseAddr());
lib/CodeGen/BlockGenerators.cpp:    BBMap[MA->getBaseAddr()] =
lib/CodeGen/BlockGenerators.cpp:    VectorBlockMap[MA->getBaseAddr()] = VectorVal;
lib/CodeGen/IslNodeBuilder.cpp:      if (BasePtr == MA->getBaseAddr()) {

[grosser]

Addressed Michael's review comments.

[grosser]

Update to r294734.

We now also modify the original access relation rather than setting a new
access relation. To make this possible we committed a variety of changes that
removed Polly's dependence on MemoryAccess::getBaseAddr() in previous commits.

[Meinersbur]

Can you rebase to trunk? There is a use of BasePtr left in IslNodeBuilder.cpp that I don't know to resolve (And look like an adhoc-modification of the (Original)BasePtr, something you tried to avoid in this patch by using setAccessRelation)

Is it possible to remove getOriginalBaseAddr() as well? All remaining uses seem to be related to invariant load hoisting, i.e. should be internal to that algorithm, not public API.

lib/Analysis/ScopInfo.cpp

3701–3708 ↗

(On Diff #87976)

The loop seems to be mainly about finding a canonical ScopArrayInfo, but also modifies the Accesses array of elements that will be skipped afterwards anyway. I think there is no reason to do that:

• Execution time is worse because you need to copy the array first.
• More importantly, it makes the code less readable. Now we have two location that effectively do the same thing: Lines 3705 and 3719. It takes some time to understand that.
• Maintainability suffers as well as the two location need to stay in sync.
• The probability of bugs increases as well. There are two locations that need to be implemented correctly.

test/Isl/CodeGen/invariant_load_unify_arrays.ll

1 ↗

(On Diff #87976)

The file's name still contains unify

5 ↗

(On Diff #87976)

How does this check whether %baseA and %baseB have been canonicalized?

I would think we'd check whether both stores will access the canonical base pointer, %baseB.

test/ScopInfo/invariant_load_unify_arrays.ll

1 ↗

(On Diff #87976)

The IR looks identical to the one in CodeGen. I understand that one is testing -polly-scops -analyze , the other -polly-codegen -S. However, since they are both testing the same feature, and for the sake of maintainability, wouldn't it be better to put both into the same file?

[grosser]

Rebased and addressed some final comments.

[grosser]

Hi Michael, hi Roman,

this patch works cleanly on trunk. I believe I addressed most, but not all open comments. Michael had some last ideas regarding how some code could be improved stylewise. I thought for a while about it, but could not come up with good ideas immediately. Hence, I just rebased the patch to make sure it runs on trunk. This hopefully makes it easy to read over it again and play with ideas of how to improve readability. While I think the patch is already well readable, I am glad to incorporate good ideas to make it even more readable.

Thanks for your feedback,
Tobias

lib/Analysis/ScopInfo.cpp

3732 ↗

(On Diff #83922)

This has been changed. We now directly change the access relation.

3701–3708 ↗

(On Diff #87976)

I am not fully sure how to improve the code, given that we may not
always choose the very first load as canonical array. The cost of copying the arrays is likely minor, but readability and understandability are strong arguments. I wonder if -- after the refactoring -- you happen to have a good idea of how to simplify this code?

test/Isl/CodeGen/invariant_load_unify_arrays.ll

1 ↗

(On Diff #87976)

Renamed to invariant_load_canonicalize_array_baseptrs.ll

5 ↗

(On Diff #87976)

I added CHECK-NEXT lines.

test/ScopInfo/invariant_load_unify_arrays.ll

1 ↗

(On Diff #87976)

Right. The problem with just dropping this test case is that we then have -polly-scops failures reported in test/CodeGen. I think it is a lot nicer to see directly from failing test cases if something in scop modeling or in code generation broke. Obviously this comes at a price of redundant test inputs. It seems to be a question of preference / tradeoffs. I generally tried to follow the rule to run only passes with the name of the test directory in the directory. However, neither was I consistent and I think Johannes also followed a different approach.

Not sure what to do.

[Meinersbur]

Thanks for the hand-crafted test cases.

include/polly/ScopInfo.h

817–824 ↗

(On Diff #98133)

Is this change related?

lib/Analysis/ScopInfo.cpp

3809–3818 ↗

(On Diff #98133)

A comment about what this is supposed to do would be nice. I know it is related to test/ScopInfo/invariant_load_canonicalize_array_baseptrs_5.ll, but I think an explanation here would be even more important than in the test case.

3821 ↗

(On Diff #98133)

There are two local variables with the name Access.

3875 ↗

(On Diff #98133)

Prefer lookup. operator[] creates an entry every time this return Null.

3701–3708 ↗

(On Diff #87976)

Suggestion:

static const ScopArrayInfo *findCanonicalArray(Scop *S,
                                               MemoryAccessList &Accesses) {
  for (MemoryAccess *Access : Accesses) {
    const ScopArrayInfo *CanonicalArray = S->getScopArrayInfoOrNull(
        Access->getAccessInstruction(), MemoryKind::Array);
    if (CanonicalArray)
      return CanonicalArray;
  }
  return nullptr;
}

static bool isUsedForIndirectHoistedLoad(Scop *S, const ScopArrayInfo *Array) {
  for (InvariantEquivClassTy &EqClass2 : S->getInvariantAccesses())
    for (MemoryAccess *Access2 : EqClass2.InvariantAccesses)
      if (Access2->getScopArrayInfo() == Array)
        return true;
  return false;
}

static void replaceBasePtrArrays(Scop *S, const ScopArrayInfo *Old,
                                 const ScopArrayInfo *New) {
  for (ScopStmt &Stmt : *S)
    for (MemoryAccess *Access : Stmt) {
      if (Access->getLatestScopArrayInfo() != Old)
        continue;

      isl_id *Id = New->getBasePtrId();
      isl_map *Map = Access->getAccessRelation();
      Map = isl_map_set_tuple_id(Map, isl_dim_out, Id);
      Access->setAccessRelation(Map);
    }
}

void Scop::canonicalizeDynamicBasePtrs() {
  for (InvariantEquivClassTy &EqClass : InvariantEquivClasses) {
    MemoryAccessList &BasePtrAccesses = EqClass.InvariantAccesses;

    const ScopArrayInfo *CanonicalBasePtrSAI =
        findCanonicalArray(this, BasePtrAccesses);
    if (!CanonicalBasePtrSAI)
      continue;

    for (MemoryAccess *BasePtrAccess : BasePtrAccesses) {
      const ScopArrayInfo *BasePtrSAI = getScopArrayInfoOrNull(
          BasePtrAccess->getAccessInstruction(), MemoryKind::Array);
      if (!BasePtrSAI || BasePtrSAI == CanonicalBasePtrSAI ||
          !BasePtrSAI->isCompatibleWith(CanonicalBasePtrSAI))
        continue;

      if (isUsedForIndirectHoistedLoad(this, BasePtrSAI))
        continue;

      replaceBasePtrArrays(this, BasePtrSAI, CanonicalBasePtrSAI);
    }
  }
}

test/Isl/CodeGen/invariant_load_unify_arrays.ll

5 ↗

(On Diff #87976)

Where?

test/ScopInfo/invariant_load_canonicalize_array_baseptrs_4.ll

5 ↗

(On Diff #98133)

"coalesced" -> "canonicalized"?

test/ScopInfo/invariant_load_canonicalize_array_baseptrs_5.ll

6 ↗

(On Diff #98133)

unify -> canonicalize

7 ↗

(On Diff #98133)

Why only "probably"?

12 ↗

(On Diff #98133)

Could you mention that %ptr (a hoisted load, itself requiring that %baseA2 is hoisted) is the culprit here?

58–61 ↗

(On Diff #98133)

To ensure a use of %v0, %v1, would

store float* undef, float** %ptr
store float* undef, float** %baseA2

be enough? In that case, one might peel one * off the types as use

store float 0.0, float* %ptr
store float 0.0, float* %baseA2

65 ↗

(On Diff #98133)

Why is %baseB2 based on %A? Would eg. %baseA3 (or %baseA1, which seems to be missing) be a better name?

polly/trunk/include/polly/ScopInfo.h

public:
   static const ScopArrayInfo *getFromId(__isl_take isl_id *Id);
 
   /// Get the space of this array access.
   __isl_give isl_space *getSpace() const;
 
   /// If the array is read only
   bool isReadOnly();
 
+  /// Verify that @p Array is compatible to this ScopArrayInfo.
+  ///
+  /// Two arrays are compatible if their dimensionality, the sizes of their
+  /// dimensions, and their element sizes match.
+  ///
+  /// @param Array The array to compare against.
+  ///
+  /// @returns True, if the arrays are compatible, False otherwise.
+  bool isCompatibleWith(const ScopArrayInfo *Array) const;
+
 private:
   void addDerivedSAI(ScopArrayInfo *DerivedSAI) {
     DerivedSAIs.insert(DerivedSAI);
   }
 
   /// For indirect accesses this is the SAI of the BP origin.
   const ScopArrayInfo *BasePtrOriginSAI;
 
public:
   applyScheduleToAccessRelation(__isl_take isl_union_map *Schedule) const;
 
   /// Get an isl string representing the access function read from IR.
   std::string getOriginalAccessRelationStr() const;
 
   /// Get an isl string representing a new access function, if available.
   std::string getNewAccessRelationStr() const;
 
-  /// Get the base address of this access (e.g. A for A[i+j]) when
+  /// Get the original base address of this access (e.g. A for A[i+j]) when
   /// detected.
-  Value *getOriginalBaseAddr() const {
-    assert(!getOriginalScopArrayInfo() /* may noy yet be initialized */ ||
-           getOriginalScopArrayInfo()->getBasePtr() == BaseAddr);
-    return BaseAddr;
-  }
-
-  /// Get the base address of this access (e.g. A for A[i+j]) after a
-  /// potential change by setNewAccessRelation().
-  Value *getLatestBaseAddr() const {
-    return getLatestScopArrayInfo()->getBasePtr();
-  }
-
-  /// Old name for getOriginalBaseAddr().
-  Value *getBaseAddr() const { return getOriginalBaseAddr(); }
+  ///
+  /// This adress may differ from the base address referenced by the Original
+  /// ScopArrayInfo to which this array belongs, as this memory access may
+  /// have been unified to a ScopArray which has a different but identically
+  /// valued base pointer in case invariant load hoisting is enabled.
+  Value *getOriginalBaseAddr() const { return BaseAddr; }
 
   /// Get the detection-time base array isl_id for this access.
   __isl_give isl_id *getOriginalArrayId() const;
 
   /// Get the base array isl_id for this access, modifiable through
   /// setNewAccessRelation().
   __isl_give isl_id *getLatestArrayId() const;
 
private:
   ///   for (int j = 1; j < *LB[1]; j++)
   ///     A[i][j] += A[0][0] + (*V);
   ///
   /// Common inv. loads: V, A[0][0], LB[0], LB[1]
   /// Required inv. loads: LB[0], LB[1], (V, if it may alias with A or LB)
   ///
   void hoistInvariantLoads();
 
+  /// Canonicalize arrays with base pointers from the same equivalence class.
+  ///
+  /// Some context: in our normal model we assume that each base pointer is
+  /// related to a single specific memory region, where memory regions
+  /// associated with different base pointers are disjoint. Consequently we do
+  /// not need to compute additional data dependences that model possible
+  /// overlaps of these memory regions. To verify our assumption we compute
+  /// alias checks that verify that modeled arrays indeed do not overlap. In
+  /// case an overlap is detected the runtime check fails and we fall back to
+  /// the original code.
+  ///
+  /// In case of arrays where the base pointers are know to be identical,
+  /// because they are dynamically loaded by accesses that are in the same
+  /// invariant load equivalence class, such run-time alias check would always
+  /// be false.
+  ///
+  /// This function makes sure that we do not generate consistently failing
+  /// run-time checks for code that contains distinct arrays with known
+  /// equivalent base pointers. It identifies for each invariant load
+  /// equivalence class a single canonical array and canonicalizes all memory
+  /// accesses that reference arrays that have base pointers that are known to
+  /// be equal to the base pointer of such a canonical array to this canonical
+  /// array.
+  ///
+  /// We currently do not canonicalize arrays for which certain memory accesses
+  /// have been hoisted as loop invariant.
+  void canonicalizeDynamicBasePtrs();
+
   /// Add invariant loads listed in @p InvMAs with the domain of @p Stmt.
   void addInvariantLoads(ScopStmt &Stmt, InvariantAccessesTy &InvMAs);
 
   /// Create an id for @p Param and store it in the ParameterIds map.
   void createParameterId(const SCEV *Param);
 
   /// Build the Context of the Scop.
   void buildContext();
public:
   const ScopArrayInfo *createScopArrayInfo(Type *ElementType,
                                            const std::string &BaseName,
                                            const std::vector<unsigned> &Sizes);
 
   /// Return the cached ScopArrayInfo object for @p BasePtr.
   ///
   /// @param BasePtr   The base pointer the object has been stored for.
   /// @param Kind      The kind of array info object.
+  ///
+  /// @returns The ScopArrayInfo pointer or NULL if no such pointer is
+  ///          available.
+  const ScopArrayInfo *getScopArrayInfoOrNull(Value *BasePtr, MemoryKind Kind);
+
+  /// Return the cached ScopArrayInfo object for @p BasePtr.
+  ///
+  /// @param BasePtr   The base pointer the object has been stored for.
+  /// @param Kind      The kind of array info object.
+  ///
+  /// @returns The ScopArrayInfo pointer (may assert if no such pointer is
+  ///          available).
   const ScopArrayInfo *getScopArrayInfo(Value *BasePtr, MemoryKind Kind);
 
   /// Invalidate ScopArrayInfo object for base address.
   ///
   /// @param BasePtr The base pointer of the ScopArrayInfo object to invalidate.
   /// @param Kind    The Kind of the ScopArrayInfo object.
   void invalidateScopArrayInfo(Value *BasePtr, MemoryKind Kind) {
     auto It = ScopArrayInfoMap.find(std::make_pair(BasePtr, Kind));

polly/trunk/lib/Analysis/ScopBuilder.cpp

void ScopBuilder::buildScop(Region &R, AssumptionCache &AC) {
   // assumed/invalid context.
   scop->addRecordedAssumptions();
 
   scop->simplifyContexts();
   if (!scop->buildAliasChecks(AA))
     return;
 
   scop->hoistInvariantLoads();
+  scop->canonicalizeDynamicBasePtrs();
   scop->verifyInvariantLoads();
   scop->simplifySCoP(true);
 
   // Check late for a feasible runtime context because profitability did not
   // change.
   if (!scop->hasFeasibleRuntimeContext())
     return;
 

polly/trunk/lib/Analysis/ScopInfo.cpp

WriteSet = isl_union_set_intersect(
       WriteSet, isl_union_set_from_set(isl_set_universe(Space)));
 
   bool IsReadOnly = isl_union_set_is_empty(WriteSet);
   isl_union_set_free(WriteSet);
 
   return IsReadOnly;
 }
 
+bool ScopArrayInfo::isCompatibleWith(const ScopArrayInfo *Array) const {
+  if (Array->getElementType() != getElementType())
+    return false;
+
+  if (Array->getNumberOfDimensions() != getNumberOfDimensions())
+    return false;
+
+  for (unsigned i = 0; i < getNumberOfDimensions(); i++)
+    if (Array->getDimensionSize(i) != getDimensionSize(i))
+      return false;
+
+  return true;
+}
+
 void ScopArrayInfo::updateElementType(Type *NewElementType) {
   if (NewElementType == ElementType)
     return;
 
   auto OldElementSize = DL.getTypeAllocSizeInBits(ElementType);
   auto NewElementSize = DL.getTypeAllocSizeInBits(NewElementType);
 
   if (NewElementSize == OldElementSize || NewElementSize == 0)
for (ScopStmt &Stmt : *this) {
     // Transfer the memory access from the statement to the SCoP.
     for (auto InvMA : InvariantAccesses)
       Stmt.removeMemoryAccess(InvMA.MA);
     addInvariantLoads(Stmt, InvariantAccesses);
   }
   isl_union_map_free(Writes);
 }
 
+/// Find the canonical scop array info object for a set of invariant load
+/// hoisted loads. The canonical array is the one that corresponds to the
+/// first load in the list of accesses which is used as base pointer of a
+/// scop array.
+static const ScopArrayInfo *findCanonicalArray(Scop *S,
+                                               MemoryAccessList &Accesses) {
+  for (MemoryAccess *Access : Accesses) {
+    const ScopArrayInfo *CanonicalArray = S->getScopArrayInfoOrNull(
+        Access->getAccessInstruction(), MemoryKind::Array);
+    if (CanonicalArray)
+      return CanonicalArray;
+  }
+  return nullptr;
+}
+
+/// Check if @p Array severs as base array in an invariant load.
+static bool isUsedForIndirectHoistedLoad(Scop *S, const ScopArrayInfo *Array) {
+  for (InvariantEquivClassTy &EqClass2 : S->getInvariantAccesses())
+    for (MemoryAccess *Access2 : EqClass2.InvariantAccesses)
+      if (Access2->getScopArrayInfo() == Array)
+        return true;
+  return false;
+}
+
+/// Replace the base pointer arrays in all memory accesses referencing @p Old,
+/// with a reference to @p New.
+static void replaceBasePtrArrays(Scop *S, const ScopArrayInfo *Old,
+                                 const ScopArrayInfo *New) {
+  for (ScopStmt &Stmt : *S)
+    for (MemoryAccess *Access : Stmt) {
+      if (Access->getLatestScopArrayInfo() != Old)
+        continue;
+
+      isl_id *Id = New->getBasePtrId();
+      isl_map *Map = Access->getAccessRelation();
+      Map = isl_map_set_tuple_id(Map, isl_dim_out, Id);
+      Access->setAccessRelation(Map);
+    }
+}
+
+void Scop::canonicalizeDynamicBasePtrs() {
+  for (InvariantEquivClassTy &EqClass : InvariantEquivClasses) {
+    MemoryAccessList &BasePtrAccesses = EqClass.InvariantAccesses;
+
+    const ScopArrayInfo *CanonicalBasePtrSAI =
+        findCanonicalArray(this, BasePtrAccesses);
+
+    if (!CanonicalBasePtrSAI)
+      continue;
+
+    for (MemoryAccess *BasePtrAccess : BasePtrAccesses) {
+      const ScopArrayInfo *BasePtrSAI = getScopArrayInfoOrNull(
+          BasePtrAccess->getAccessInstruction(), MemoryKind::Array);
+      if (!BasePtrSAI || BasePtrSAI == CanonicalBasePtrSAI ||
+          !BasePtrSAI->isCompatibleWith(CanonicalBasePtrSAI))
+        continue;
+
+      // we currently do not canonicalize arrays where some accesses are
+      // hoisted as invariant loads. If we would, we need to update the access
+      // function of the invariant loads as well. However, as this is not a
+      // very common situation, we leave this for now to avoid further
+      // complexity increases.
+      if (isUsedForIndirectHoistedLoad(this, BasePtrSAI))
+        continue;
+
+      replaceBasePtrArrays(this, BasePtrSAI, CanonicalBasePtrSAI);
+    }
+  }
+}
+
 const ScopArrayInfo *
 Scop::getOrCreateScopArrayInfo(Value *BasePtr, Type *ElementType,
                                ArrayRef<const SCEV *> Sizes, MemoryKind Kind,
                                const char *BaseName) {
   assert((BasePtr || BaseName) &&
          "BasePtr and BaseName can not be nullptr at the same time.");
   assert(!(BasePtr && BaseName) && "BaseName is redundant.");
   auto &SAI = BasePtr ? ScopArrayInfoMap[std::make_pair(BasePtr, Kind)]
for (auto size : Sizes)
     else
       SCEVSizes.push_back(nullptr);
 
   auto *SAI = getOrCreateScopArrayInfo(nullptr, ElementType, SCEVSizes,
                                        MemoryKind::Array, BaseName.c_str());
   return SAI;
 }
 
-const ScopArrayInfo *Scop::getScopArrayInfo(Value *BasePtr, MemoryKind Kind) {
+const ScopArrayInfo *Scop::getScopArrayInfoOrNull(Value *BasePtr,
+                                                  MemoryKind Kind) {
   auto *SAI = ScopArrayInfoMap[std::make_pair(BasePtr, Kind)].get();
+  return SAI;
+}
+
+const ScopArrayInfo *Scop::getScopArrayInfo(Value *BasePtr, MemoryKind Kind) {
+  auto *SAI = getScopArrayInfoOrNull(BasePtr, Kind);
   assert(SAI && "No ScopArrayInfo available for this base pointer");
   return SAI;
 }
 
 std::string Scop::getContextStr() const { return stringFromIslObj(Context); }
 
 std::string Scop::getAssumedContextStr() const {
   assert(AssumedContext && "Assumed context not yet built");

polly/trunk/lib/CodeGen/IslNodeBuilder.cpp

bool IslNodeBuilder::preloadInvariantEquivClass(
   for (auto *DerivedSAI : SAI->getDerivedSAIs()) {
     Value *BasePtr = DerivedSAI->getBasePtr();
 
     for (const MemoryAccess *MA : MAs) {
       // As the derived SAI information is quite coarse, any load from the
       // current SAI could be the base pointer of the derived SAI, however we
       // should only change the base pointer of the derived SAI if we actually
       // preloaded it.
-      if (BasePtr == MA->getBaseAddr()) {
+      if (BasePtr == MA->getOriginalBaseAddr()) {
         assert(BasePtr->getType() == PreloadVal->getType());
         DerivedSAI->setBasePtr(PreloadVal);
       }
 
       // For scalar derived SAIs we remap the alloca used for the derived value.
       if (BasePtr == MA->getAccessInstruction())
         ScalarMap[DerivedSAI] = Alloca;
     }

polly/trunk/lib/Transform/ScheduleOptimizer.cpp

return isl::manage(isl_schedule_node_insert_partial_schedule(
       Node.take(), PartialScheduleMultiPwAff.take()));
 }
 } // namespace
 
 __isl_give isl_schedule_node *ScheduleTreeOptimizer::optimizeMatMulPattern(
     __isl_take isl_schedule_node *Node, const llvm::TargetTransformInfo *TTI,
     MatMulInfoTy &MMI) {
   assert(TTI && "The target transform info should be provided.");
-  Node = markInterIterationAliasFree(Node, MMI.WriteToC->getLatestBaseAddr());
+  Node = markInterIterationAliasFree(
+      Node, MMI.WriteToC->getLatestScopArrayInfo()->getBasePtr());
   int DimOutNum = isl_schedule_node_band_n_member(Node);
   assert(DimOutNum > 2 && "In case of the matrix multiplication the loop nest "
                           "and, consequently, the corresponding scheduling "
                           "functions have at least three dimensions.");
   Node = getBandNodeWithOriginDimOrder(isl::manage(Node)).take();
   Node = permuteBandNodeDimensions(Node, MMI.i, DimOutNum - 3);
   int NewJ = MMI.j == DimOutNum - 3 ? MMI.i : MMI.j;
   int NewK = MMI.k == DimOutNum - 3 ? MMI.i : MMI.k;

polly/trunk/test/Isl/CodeGen/invariant_load_canonicalize_array_baseptrs.ll

+; RUN: opt %loadPolly -polly-codegen -S < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; CHECK: %polly.access.A = getelementptr float*, float** %A, i64 0
+; CHECK: %polly.access.A.load = load float*, float** %polly.access.A
+; CHECK: store float 4.200000e+01, float* %polly.access.A.load
+; CHECK: store float 4.800000e+01, float* %polly.access.A.load
+
+define void @foo(float** %A) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseA = load float*, float** %A
+  store float 42.0, float* %baseA
+  br label %body2
+
+body2:
+  %baseB = load float*, float** %A
+  store float 48.0, float* %baseB
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; CHECK:      Stmt_body1
+; CHECK-NEXT:       Domain :=
+; CHECK-NEXT:           { Stmt_body1[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:       Schedule :=
+; CHECK-NEXT:           { Stmt_body1[i0] -> [i0, 0] };
+; CHECK-NEXT:       MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:          { Stmt_body1[i0] -> MemRef_baseB[0] };
+; CHECK-NEXT: Stmt_body2
+; CHECK-NEXT:       Domain :=
+; CHECK-NEXT:           { Stmt_body2[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:       Schedule :=
+; CHECK-NEXT:           { Stmt_body2[i0] -> [i0, 1] };
+; CHECK-NEXT:       MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:                { Stmt_body2[i0] -> MemRef_baseB[0] };
+
+define void @foo(float** %A) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseA = load float*, float** %A
+  store float 42.0, float* %baseA
+  br label %body2
+
+body2:
+  %baseB = load float*, float** %A
+  store float 42.0, float* %baseB
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs_2.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; Make sure we choose a canonical element that is not the first invariant load,
+; but the first that is an array base pointer.
+
+; CHECK:     Statements {
+; CHECK-NEXT:       Stmt_body0
+; CHECK-NEXT:             Domain :=
+; CHECK-NEXT:                 { Stmt_body0[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:             Schedule :=
+; CHECK-NEXT:                 { Stmt_body0[i0] -> [i0, 0] };
+; CHECK-NEXT:             MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:                 { Stmt_body0[i0] -> MemRef_X[0] };
+; CHECK-NEXT:       Stmt_body1
+; CHECK-NEXT:             Domain :=
+; CHECK-NEXT:                 { Stmt_body1[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:             Schedule :=
+; CHECK-NEXT:                 { Stmt_body1[i0] -> [i0, 1] };
+; CHECK-NEXT:             MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:                 { Stmt_body1[i0] -> MemRef_baseB[0] };
+; CHECK-NEXT:       Stmt_body2
+; CHECK-NEXT:             Domain :=
+; CHECK-NEXT:                 { Stmt_body2[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:             Schedule :=
+; CHECK-NEXT:                 { Stmt_body2[i0] -> [i0, 2] };
+; CHECK-NEXT:             MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:                 { Stmt_body2[i0] -> MemRef_X[0] };
+; CHECK-NEXT:             ReadAccess := [Reduction Type: NONE] [Scalar: 1]
+; CHECK-NEXT:                 { Stmt_body2[i0] -> MemRef_ptr[] };
+; CHECK-NEXT:       Stmt_body3
+; CHECK-NEXT:             Domain :=
+; CHECK-NEXT:                 { Stmt_body3[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:             Schedule :=
+; CHECK-NEXT:                 { Stmt_body3[i0] -> [i0, 3] };
+; CHECK-NEXT:             MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:                 { Stmt_body3[i0] -> MemRef_baseB[0] };
+; CHECK-NEXT:       Stmt_body4
+; CHECK-NEXT:             Domain :=
+; CHECK-NEXT:                 { Stmt_body4[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:             Schedule :=
+; CHECK-NEXT:                 { Stmt_body4[i0] -> [i0, 4] };
+; CHECK-NEXT:             MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:                 { Stmt_body4[i0] -> MemRef_X[0] };
+; CHECK-NEXT:             ReadAccess := [Reduction Type: NONE] [Scalar: 1]
+; CHECK-NEXT:                 { Stmt_body4[i0] -> MemRef_ptr[] };
+; CHECK-NEXT:     }
+
+define void @foo(float** %A, float** %X) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body0, label %exit
+
+body0:
+  %ptr = load float*, float** %A
+  store float* %ptr, float** %X
+  br label %body1
+
+body1:
+  %baseA = load float*, float** %A
+  store float 42.0, float* %baseA
+  br label %body2
+
+body2:
+  %ptr2 = load float*, float** %A
+  store float* %ptr, float** %X
+  br label %body3
+
+body3:
+  %baseB = load float*, float** %A
+  store float 42.0, float* %baseB
+  br label %body4
+
+body4:
+  %ptr3 = load float*, float** %A
+  store float* %ptr, float** %X
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs_3.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; Verify that we canonicalize accesses even tough one of the accesses (even
+; the canonical base) has a partial execution context. This is correct as
+; the combined execution context still coveres both accesses.
+
+; CHECK:      Invariant Accesses: {
+; CHECK-NEXT:         ReadAccess := [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body2[i0] -> MemRef_A[0] };
+; CHECK-NEXT:         Execution Context: {  :  }
+; CHECK-NEXT: }
+
+; CHECK:      Stmt_body1
+; CHECK-NEXT:   Domain :=
+; CHECK-NEXT:       { Stmt_body1[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:   Schedule :=
+; CHECK-NEXT:       { Stmt_body1[i0] -> [i0, 0] };
+; CHECK-NEXT:   MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:       { Stmt_body1[i0] -> MemRef_baseB[0] };
+; CHECK-NEXT: Stmt_body2
+; CHECK-NEXT:   Domain :=
+; CHECK-NEXT:       { Stmt_body2[i0] : 0 <= i0 <= 510 };
+; CHECK-NEXT:   Schedule :=
+; CHECK-NEXT:       { Stmt_body2[i0] -> [i0, 1] };
+; CHECK-NEXT:   MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:       { Stmt_body2[i0] -> MemRef_baseB[0] };
+
+
+define void @foo(float** %A) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseA = load float*, float** %A
+  store float 42.0, float* %baseA
+  %cmp = icmp slt i64 %indvar.next, 512
+  br i1 %cmp, label %body2, label %latch
+
+body2:
+  %baseB = load float*, float** %A
+  store float 42.0, float* %baseB
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs_4.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; Verify that a delinearized and a not delinearized access are not
+; canonizalized.
+
+; CHECK:      Stmt_body1
+; CHECK-NEXT:   Domain :=
+; CHECK-NEXT:       [n] -> { Stmt_body1[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:   Schedule :=
+; CHECK-NEXT:       [n] -> { Stmt_body1[i0] -> [i0, 0] };
+; CHECK-NEXT:   MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:       [n] -> { Stmt_body1[i0] -> MemRef_baseB[0] };
+; CHECK-NEXT: Stmt_body2
+; CHECK-NEXT:   Domain :=
+; CHECK-NEXT:       [n] -> { Stmt_body2[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:   Schedule :=
+; CHECK-NEXT:       [n] -> { Stmt_body2[i0] -> [i0, 1] };
+; CHECK-NEXT:   MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:       [n] -> { Stmt_body2[i0] -> MemRef_baseA[i0, i0] };
+; CHECK-NEXT: }
+
+
+define void @foo(float** %A, i64 %n, i64 %m) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseB = load float*, float** %A
+  store float 42.0, float* %baseB
+  br label %body2
+
+body2:
+  %baseA = load float*, float** %A
+  %offsetA = mul i64 %indvar, %n
+  %offsetA2 = add i64 %offsetA, %indvar
+  %ptrA = getelementptr float, float* %baseA, i64 %offsetA2
+  store float 42.0, float* %ptrA
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs_4b.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; Verify that two arrays delinearized with different sizes are not coalesced.
+
+; CHECK:      Stmt_body1
+; CHECK-NEXT:     Domain :=
+; CHECK-NEXT:         [m, n] -> { Stmt_body1[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:     Schedule :=
+; CHECK-NEXT:         [m, n] -> { Stmt_body1[i0] -> [i0, 0] };
+; CHECK-NEXT:     MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:         [m, n] -> { Stmt_body1[i0] -> MemRef_baseB[i0, i0] };
+; CHECK-NEXT: Stmt_body2
+; CHECK-NEXT:     Domain :=
+; CHECK-NEXT:         [m, n] -> { Stmt_body2[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:     Schedule :=
+; CHECK-NEXT:         [m, n] -> { Stmt_body2[i0] -> [i0, 1] };
+; CHECK-NEXT:     MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:         [m, n] -> { Stmt_body2[i0] -> MemRef_baseA[i0, i0] };
+; CHECK-NEXT: }
+
+define void @foo(float** %A, i64 %n, i64 %m) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseB = load float*, float** %A
+  %offsetB = mul i64 %indvar, %m
+  %offsetB2 = add i64 %offsetB, %indvar
+  %ptrB = getelementptr float, float* %baseB, i64 %offsetB2
+  store float 42.0, float* %ptrB
+  br label %body2
+
+body2:
+  %baseA = load float*, float** %A
+  %offsetA = mul i64 %indvar, %n
+  %offsetA2 = add i64 %offsetA, %indvar
+  %ptrA = getelementptr float, float* %baseA, i64 %offsetA2
+  store float 42.0, float* %ptrA
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs_4c.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; Verify that arrays with different element types are not coalesced.
+
+; CHECK:      Statements {
+; CHECK-NEXT:   Stmt_body1
+; CHECK-NEXT:         Domain :=
+; CHECK-NEXT:             { Stmt_body1[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:         Schedule :=
+; CHECK-NEXT:             { Stmt_body1[i0] -> [i0, 0] };
+; CHECK-NEXT:         MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body1[i0] -> MemRef_baseB[0] };
+; CHECK-NEXT:   Stmt_body2
+; CHECK-NEXT:         Domain :=
+; CHECK-NEXT:             { Stmt_body2[i0] : 0 <= i0 <= 1022 };
+; CHECK-NEXT:         Schedule :=
+; CHECK-NEXT:             { Stmt_body2[i0] -> [i0, 1] };
+; CHECK-NEXT:         MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body2[i0] -> MemRef_baseA[0] };
+; CHECK-NEXT: }
+
+define void @foo(float** %A, i64 %n, i64 %m) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [0, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseB = load float*, float** %A
+  store float 42.0, float* %baseB
+  br label %body2
+
+body2:
+  %baseA = load float*, float** %A
+  %ptrcast = bitcast float* %baseA to i64*
+  store i64 42, i64* %ptrcast
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}

polly/trunk/test/ScopInfo/invariant_load_canonicalize_array_baseptrs_5.ll

+; RUN: opt %loadPolly -polly-scops -analyze < %s \
+; RUN:  -polly-invariant-load-hoisting \
+; RUN:  | FileCheck %s
+
+; Verify that nested arrays with invariant base pointers are handled correctly.
+; Specifically, we currently do not canonicalize arrays where some accesses are
+; hoisted as invariant loads. If we would, we need to update the access function
+; of the invariant loads as well. However, as this is not a very common
+; situation, we leave this for now to avoid further complexity increases.
+;
+; In this test case the arrays baseA1 and baseA2 could be canonicalized to a
+; single array, but there is also an invariant access to baseA1[0] through
+; "%v0 = load float, float* %ptr" which prevents the canonicalization.
+
+; CHECK:      Invariant Accesses: {
+; CHECK-NEXT:         ReadAccess := [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body2[i0] -> MemRef_A[0] };
+; CHECK-NEXT:         Execution Context: {  :  }
+; CHECK-NEXT:         ReadAccess := [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body1[i0] -> MemRef_baseA1[0] };
+; CHECK-NEXT:         Execution Context: {  :  }
+; CHECK-NEXT: }
+
+; CHECK:      Statements {
+; CHECK-NEXT:   Stmt_body1
+; CHECK-NEXT:         Domain :=
+; CHECK-NEXT:             { Stmt_body1[i0] : 0 <= i0 <= 1021 };
+; CHECK-NEXT:         Schedule :=
+; CHECK-NEXT:             { Stmt_body1[i0] -> [i0, 0] };
+; CHECK-NEXT:         ReadAccess := [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body1[i0] -> MemRef_baseA1[1 + i0] };
+; CHECK-NEXT:         MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body1[i0] -> MemRef_B[0] };
+; CHECK-NEXT:         MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body1[i0] -> MemRef_B[0] };
+; CHECK-NEXT:   Stmt_body2
+; CHECK-NEXT:         Domain :=
+; CHECK-NEXT:             { Stmt_body2[i0] : 0 <= i0 <= 1021 };
+; CHECK-NEXT:         Schedule :=
+; CHECK-NEXT:             { Stmt_body2[i0] -> [i0, 1] };
+; CHECK-NEXT:         MustWriteAccess :=  [Reduction Type: NONE] [Scalar: 0]
+; CHECK-NEXT:             { Stmt_body2[i0] -> MemRef_baseA2[0] };
+; CHECK-NEXT: }
+
+define void @foo(float** %A, float* %B) {
+start:
+  br label %loop
+
+loop:
+  %indvar = phi i64 [1, %start], [%indvar.next, %latch]
+  %indvar.next = add nsw i64 %indvar, 1
+  %icmp = icmp slt i64 %indvar.next, 1024
+  br i1 %icmp, label %body1, label %exit
+
+body1:
+  %baseA1 = load float*, float** %A
+  %ptr = getelementptr inbounds float, float* %baseA1, i64 %indvar
+  %v0 = load float, float* %ptr
+  %v1 = load float, float* %baseA1
+  store float %v0, float* %B
+  store float %v1, float* %B
+  br label %body2
+
+body2:
+  %baseA2 = load float*, float** %A
+  store float undef, float* %baseA2
+  br label %body3
+
+body3:
+  br label %latch
+
+latch:
+  br label %loop
+
+exit:
+  ret void
+
+}