[MLIR] Support for ReturnOps in memref map layout normalization

[avarmapml]

Summary

• This commit handles the returnOp in memref map layout normalization.
• An initial filter is applied on FuncOps which helps us know which functions can be a suitable candidate for memref normalization which doesn't lead to invalid IR.
• Handles memref map normalization for external function assuming the external function is normalizable.

Signed-off-by: Abhishek Varma <[e-mail]>

[bondhugula]

mlir/lib/Transforms/NormalizeMemRefs.cpp

130–173

Nit: caller -> calling

157–158

MLIR doesn't have any overloading. The function names are unique.

mlir/lib/Transforms/Utils/Utils.cpp

282

You don't need the extra parentheses around isa.

[avarmapml]

Minor review changes

[bondhugula]

@AlexEichenberger Would you be able to review this - esp. for the part that's connected to what you wanted?

[AlexEichenberger]

The code looks good, and I like the addition of skipping the analysis for "extern" functions. Because dialect ops can in some ways also represent "future" external functions, a natural way of handling "not yet expanded" external functions would to add an interface query that ask if a given op is "external" also. Default would be false, and dialects that needs dome/all of their ops to be external would be able to refine the interface to provide the necessary functionality.

Second, the presence of "dim" currently prevent normalization when the dim act on a memref wit maps. It is my firm belief that "dim" should return the logical iterations, not the mapped ones. Would it be possible that when looking at a dim as below:

%d = dim %a, %c0 : memref<?x?x?xf32,  map>

the proper value is directly returned?

Its fine if this functionality is not part of this patch, I believe they will be important for many practical cases.

[bondhugula]

In D85226#2205325, @AlexEichenberger wrote:

The code looks good, and I like the addition of skipping the analysis for "extern" functions. Because dialect ops can in some ways also represent "future" external functions, a natural way of handling "not yet expanded" external functions would to add an interface query that ask if a given op is "external" also. Default would be false, and dialects that needs dome/all of their ops to be external would be able to refine the interface to provide the necessary functionality.

Second, the presence of "dim" currently prevent normalization when the dim act on a memref wit maps. It is my firm belief that "dim" should return the logical iterations, not the mapped ones. Would it be possible that when looking at a dim as below:

Hi Alex, dim does already return the extents of the logical dimensions, whatever you see in the shape signature of the memref (... x ... x ...), and not the physical ones. So, the dim is oblivious to the layout map.

%d = dim %a, %c0 : memref<?x?x?xf32,  map>

the proper value is directly returned?

Its fine if this functionality is not part of this patch, I believe they will be important for many practical cases.

[bondhugula]

Looks great. Some initial comments.

mlir/lib/Transforms/NormalizeMemRefs.cpp

132

Should this be renamed setCalleesCallersNonNormalizable - most accurate (plural) and as long.

156

Terminate with a full stop.

333

Comment here.

340–344

Drop the obvious "This function".

mlir/lib/Transforms/Utils/Utils.cpp

279–282

types -> ops

[AlexEichenberger]

I tried the patch and this simple code appears to disable memref normalization

#map0 = affine_map<(d0, d1) -> (d1, d0)>
module {
  func @test_simplification(%arg : memref<5x10xf32>) {
    %a = alloc() : memref<10x5xf32, #map0>
    %c1 = constant 1 :index
    %d = dim %arg, %c1 : memref<5x10xf32>
    dealloc %a : memref<10x5xf32, #map0>
    return 
  }
}

The dim is used on a memref that does not have a map, the presence of the dim for arg variable (no maps) seems to disable the normalization of the a variable (with map)

[bondhugula]

In D85226#2209870, @AlexEichenberger wrote:

I tried the patch and this simple code appears to disable memref normalization

#map0 = affine_map<(d0, d1) -> (d1, d0)>
module {
  func @test_simplification(%arg : memref<5x10xf32>) {
    %a = alloc() : memref<10x5xf32, #map0>
    %c1 = constant 1 :index
    %d = dim %arg, %c1 : memref<5x10xf32>
    dealloc %a : memref<10x5xf32, #map0>
    return 
  }
}

The dim is used on a memref that does not have a map, the presence of the dim for arg variable (no maps) seems to disable the normalization of the a variable (with map)

@AlexEichenberger The patch doesn't handle/treat dim specially at all - irrespective of its map; it's being treated as a non-dereferencing op and so is bailing out on such ops. For static shapes, the approach would be to just fold the dim op at the start or expect the input to have been canonicalized, which will fold it away. For dynamic shapes, it's quite involved and will have to be definitely dealt with separately.

[AlexEichenberger]

@bondhugula Static is easy. We are working on making it work for the dynamic shapes, currently in our code base but we could migrate it to the MLIR as part of another patch. Basically, we go back to the alloc responsible for the array, and parse the memref to pick either a constant or the right alloc parameter corresponding to the n th '?' in the memref of the alloc.

[avarmapml]

Addressed review changes.

[bondhugula]

In D85226#2212034, @AlexEichenberger wrote:

@bondhugula Static is easy. We are working on making it work for the dynamic shapes, currently in our code base but we could migrate it to the MLIR as part of another patch. Basically, we go back to the alloc responsible for the array, and parse the memref to pick either a constant or the right alloc parameter corresponding to the n th '?' in the memref of the alloc.

That would be great, thanks!

[bondhugula]

Looks good - thanks.

[bondhugula]

Please add a TODO somewhere on the dim op handling part.

[avarmapml]

Added TODO section for DimOp.

[AlexEichenberger]

Looking into extending this approach to handle dialect ops that will become calls to external functions. Specifically, I am looking for a way to express that an operation guarantees that (when it will be lowered to an external function call), the external function be aware of the data layout of the maps and thus it is safe to normalize the op memref parameters.

MLIR experts out there, what is the preferred way to do this? Adding a interface on the dialect? Adding an interface on the operation (like AffineReadOpInterface, e.g. ExpectNormalizedMemRefParameters)?

[AlexEichenberger]

Once this patch is in, I have a follow on patch that introduces a new trait, MemRefNormalizable to be used by operations (such as DeallocOp, CallOp, ReturnOp) as well as any ops, for example, such as operations of an dialect that 1) will be expanded to external calls at some later time and 2) are ok with having their memrefs normalized to get rid of their maps.

This trait can also be used to special case behavior for std.dim or other such operations

[bondhugula]

In D85226#2215776, @AlexEichenberger wrote:

Looking into extending this approach to handle dialect ops that will become calls to external functions. Specifically, I am looking for a way to express that an operation guarantees that (when it will be lowered to an external function call), the external function be aware of the data layout of the maps and thus it is safe to normalize the op memref parameters.

MLIR experts out there, what is the preferred way to do this? Adding a interface on the dialect? Adding an interface on the operation (like AffineReadOpInterface, e.g. ExpectNormalizedMemRefParameters)?

I missed these comments. This discussion is probably better taken on the discourse thread we already have? Having a trait like this sounds useful.

[bondhugula]

In D85226#2224667, @AlexEichenberger wrote:

Once this patch is in, I have a follow on patch that introduces a new trait, MemRefNormalizable to be used by operations (such as DeallocOp, CallOp, ReturnOp) as well as any ops, for example, such as operations of an dialect that 1) will be expanded to external calls at some later time and 2) are ok with having their memrefs normalized to get rid of their maps.

This trait can also be used to special case behavior for std.dim or other such operations

This patch is already in. We can take this discussion on the discourse thread.

mlir/lib/Transforms/NormalizeMemRefs.cpp

 // identity layout maps.
 //
 //===----------------------------------------------------------------------===//
 
 #include "PassDetail.h"
 #include "mlir/Dialect/Affine/IR/AffineOps.h"
 #include "mlir/Transforms/Passes.h"
 #include "mlir/Transforms/Utils.h"
+#include "llvm/ADT/SmallSet.h"
 
 #define DEBUG_TYPE "normalize-memrefs"
 
 using namespace mlir;
 
 namespace {
 
 /// All memrefs passed across functions with non-trivial layout maps are
 /// converted to ones with trivial identity layout ones.
-
-// Input :-
-// #tile = affine_map<(i) -> (i floordiv 4, i mod 4)>
-// func @matmul(%A: memref<16xf64, #tile>, %B: index, %C: memref<16xf64>) ->
-// (memref<16xf64, #tile>) {
-//   affine.for %arg3 = 0 to 16 {
-//         %a = affine.load %A[%arg3] : memref<16xf64, #tile>
-//         %p = mulf %a, %a : f64
-//         affine.store %p, %A[%arg3] : memref<16xf64, #tile>
-//   }
-//   %c = alloc() : memref<16xf64, #tile>
-//   %d = affine.load %c[0] : memref<16xf64, #tile>
-//   return %A: memref<16xf64, #tile>
-// }
-
-// Output :-
-//   func @matmul(%arg0: memref<4x4xf64>, %arg1: index, %arg2: memref<16xf64>)
-//   -> memref<4x4xf64> {
-//     affine.for %arg3 = 0 to 16 {
-//       %2 = affine.load %arg0[%arg3 floordiv 4, %arg3 mod 4] : memref<4x4xf64>
-//       %3 = mulf %2, %2 : f64
-//       affine.store %3, %arg0[%arg3 floordiv 4, %arg3 mod 4] : memref<4x4xf64>
-//     }
-//     %0 = alloc() : memref<16xf64, #map0>
-//     %1 = affine.load %0[0] : memref<16xf64, #map0>
-//     return %arg0 : memref<4x4xf64>
-//   }
-
+/// If all the memref types/uses in a function are normalizable, we treat
+/// such functions as normalizable. Also, if a normalizable function is known
+/// to call a non-normalizable function, we treat that function as
+/// non-normalizable as well. We assume external functions to be normalizable.
+///
+/// Input :-
+/// #tile = affine_map<(i) -> (i floordiv 4, i mod 4)>
+/// func @matmul(%A: memref<16xf64, #tile>, %B: index, %C: memref<16xf64>) ->
+/// (memref<16xf64, #tile>) {
+///   affine.for %arg3 = 0 to 16 {
+///         %a = affine.load %A[%arg3] : memref<16xf64, #tile>
+///         %p = mulf %a, %a : f64
+///         affine.store %p, %A[%arg3] : memref<16xf64, #tile>
+///   }
+///   %c = alloc() : memref<16xf64, #tile>
+///   %d = affine.load %c[0] : memref<16xf64, #tile>
+///   return %A: memref<16xf64, #tile>
+/// }
+///
+/// Output :-
+///   func @matmul(%arg0: memref<4x4xf64>, %arg1: index, %arg2: memref<16xf64>)
+///   -> memref<4x4xf64> {
+///     affine.for %arg3 = 0 to 16 {
+///       %2 = affine.load %arg0[%arg3 floordiv 4, %arg3 mod 4] :
+///       memref<4x4xf64> %3 = mulf %2, %2 : f64 affine.store %3, %arg0[%arg3
+///       floordiv 4, %arg3 mod 4] : memref<4x4xf64>
+///     }
+///     %0 = alloc() : memref<16xf64, #map0>
+///     %1 = affine.load %0[0] : memref<16xf64, #map0>
+///     return %arg0 : memref<4x4xf64>
+///   }
+///
 struct NormalizeMemRefs : public NormalizeMemRefsBase<NormalizeMemRefs> {
   void runOnOperation() override;
-  void runOnFunction(FuncOp funcOp);
+  void normalizeFuncOpMemRefs(FuncOp funcOp, ModuleOp moduleOp);
   bool areMemRefsNormalizable(FuncOp funcOp);
-  void updateFunctionSignature(FuncOp funcOp);
+  void updateFunctionSignature(FuncOp funcOp, ModuleOp moduleOp);
+  void setCalleesAndCallersNonNormalizable(FuncOp funcOp, ModuleOp moduleOp,
+                                           DenseSet<FuncOp> &normalizableFuncs);
 };
 
 } // end anonymous namespace
 
 std::unique_ptr<OperationPass<ModuleOp>> mlir::createNormalizeMemRefsPass() {
   return std::make_unique<NormalizeMemRefs>();
 }
 
 void NormalizeMemRefs::runOnOperation() {
   ModuleOp moduleOp = getOperation();
-  // We traverse each function within the module in order to normalize the
-  // memref type arguments.
-  // TODO: Handle external functions.
+  // We maintain all normalizable FuncOps in a DenseSet. It is initialized
+  // with all the functions within a module and then functions which are not
+  // normalizable are removed from this set.
+  // TODO: Change this to work on FuncLikeOp once there is an operation
+  // interface for it.
+  DenseSet<FuncOp> normalizableFuncs;
+  // Initialize `normalizableFuncs` with all the functions within a module.
+  moduleOp.walk([&](FuncOp funcOp) { normalizableFuncs.insert(funcOp); });
+
+  // Traverse through all the functions applying a filter which determines
+  // whether that function is normalizable or not. All callers/callees of
+  // a non-normalizable function will also become non-normalizable even if
+  // they aren't passing any or specific non-normalizable memrefs. So,
+  // functions which calls or get called by a non-normalizable becomes non-
+  // normalizable functions themselves.
   moduleOp.walk([&](FuncOp funcOp) {
-    if (areMemRefsNormalizable(funcOp))
-      runOnFunction(funcOp);
+    if (normalizableFuncs.contains(funcOp)) {
+      if (!areMemRefsNormalizable(funcOp)) {
+        // Since this function is not normalizable, we set all the caller
+        // functions and the callees of this function as not normalizable.
+        // TODO: Drop this conservative assumption in the future.
+        setCalleesAndCallersNonNormalizable(funcOp, moduleOp,
+                                            normalizableFuncs);
+      }
+    }
   });
+
+  // Those functions which can be normalized are subjected to normalization.
+  for (FuncOp &funcOp : normalizableFuncs)
+    normalizeFuncOpMemRefs(funcOp, moduleOp);
 }
 
-// Return true if this operation dereferences one or more memref's.
-// TODO: Temporary utility, will be replaced when this is modeled through
-// side-effects/op traits.
+/// Return true if this operation dereferences one or more memref's.
+/// TODO: Temporary utility, will be replaced when this is modeled through
+/// side-effects/op traits.
 static bool isMemRefDereferencingOp(Operation &op) {
   return isa<AffineReadOpInterface, AffineWriteOpInterface, AffineDmaStartOp,
              AffineDmaWaitOp>(op);
 }
 
-// Check whether all the uses of oldMemRef are either dereferencing uses or the
-// op is of type : DeallocOp, CallOp. Only if these constraints are satisfied
-// will the value become a candidate for replacement.
+/// Check whether all the uses of oldMemRef are either dereferencing uses or the
+/// op is of type : DeallocOp, CallOp or ReturnOp. Only if these constraints
+/// are satisfied will the value become a candidate for replacement.
 static bool isMemRefNormalizable(Value::user_range opUsers) {
   if (llvm::any_of(opUsers, [](Operation *op) {
         if (isMemRefDereferencingOp(*op))
           return false;
-        return !isa<DeallocOp, CallOp>(*op);
+        return !isa<DeallocOp, CallOp, ReturnOp>(*op);
       }))
     return false;
   return true;
 }
 
-// Check whether all the uses of AllocOps, CallOps and function arguments of a
-// function are either of dereferencing type or of type: DeallocOp, CallOp. Only
-// if these constraints are satisfied will the function become a candidate for
-// normalization.
+/// Set all the calling functions and the callees of the function as not
+/// normalizable.
+void NormalizeMemRefs::setCalleesAndCallersNonNormalizable(
+    FuncOp funcOp, ModuleOp moduleOp, DenseSet<FuncOp> &normalizableFuncs) {
+  if (!normalizableFuncs.contains(funcOp))
+    return;
+
+  normalizableFuncs.erase(funcOp);
+  // Caller of the function.
+  Optional<SymbolTable::UseRange> symbolUses = funcOp.getSymbolUses(moduleOp);
+  for (SymbolTable::SymbolUse symbolUse : *symbolUses) {
+    // TODO: Extend this for ops that are FunctionLike. This would require
+    // creating an OpInterface for FunctionLike ops.
+    FuncOp parentFuncOp = symbolUse.getUser()->getParentOfType<FuncOp>();
+    for (FuncOp &funcOp : normalizableFuncs) {
+      if (parentFuncOp == funcOp) {
+        setCalleesAndCallersNonNormalizable(funcOp, moduleOp,
+                                            normalizableFuncs);
+        break;
+      }
+    }
+  }
+
+  // Functions called by this function.
+  funcOp.walk([&](CallOp callOp) {
+    StringRef callee = callOp.getCallee();
+    for (FuncOp &funcOp : normalizableFuncs) {
+      // We compare FuncOp and callee's name.
+      if (callee == funcOp.getName()) {
+        setCalleesAndCallersNonNormalizable(funcOp, moduleOp,
+                                            normalizableFuncs);
+        break;
+      }
+    }
+  });
+}
+
+/// Check whether all the uses of AllocOps, CallOps and function arguments of a
+/// function are either of dereferencing type or are uses in: DeallocOp, CallOp
+/// or ReturnOp. Only if these constraints are satisfied will the function
+/// become a candidate for normalization. We follow a conservative approach here
+/// wherein even if the non-normalizable memref is not a part of the function's
+/// argument or return type, we still label the entire function as
+/// non-normalizable. We assume external functions to be normalizable.
 bool NormalizeMemRefs::areMemRefsNormalizable(FuncOp funcOp) {
+  // We assume external functions to be normalizable.
+  if (funcOp.isExternal())
+    return true;
+
   if (funcOp
           .walk([&](AllocOp allocOp) -> WalkResult {
             Value oldMemRef = allocOp.getResult();
             if (!isMemRefNormalizable(oldMemRef.getUsers()))
               return WalkResult::interrupt();
             return WalkResult::advance();
           })
           .wasInterrupted())
for (unsigned argIndex : llvm::seq<unsigned>(0, funcOp.getNumArguments())) {
     if (oldMemRef.getType().isa<MemRefType>())
       if (!isMemRefNormalizable(oldMemRef.getUsers()))
         return false;
   }
 
   return true;
 }
 
-// Fetch the updated argument list and result of the function and update the
-// function signature.
-void NormalizeMemRefs::updateFunctionSignature(FuncOp funcOp) {
+/// Fetch the updated argument list and result of the function and update the
+/// function signature. This updates the function's return type at the caller
+/// site and in case the return type is a normalized memref then it updates
+/// the calling function's signature.
+/// TODO: An update to the calling function signature is required only if the
+/// returned value is in turn used in ReturnOp of the calling function.
+void NormalizeMemRefs::updateFunctionSignature(FuncOp funcOp,
+                                               ModuleOp moduleOp) {
   FunctionType functionType = funcOp.getType();
-  SmallVector<Type, 8> argTypes;
   SmallVector<Type, 4> resultTypes;
+  FunctionType newFuncType;
+  resultTypes = llvm::to_vector<4>(functionType.getResults());
 
-  for (const auto &arg : llvm::enumerate(funcOp.getArguments()))
-    argTypes.push_back(arg.value().getType());
+  // External function's signature was already updated in
+  // 'normalizeFuncOpMemRefs()'.
+  if (!funcOp.isExternal()) {
+    SmallVector<Type, 8> argTypes;
+    for (const auto &argEn : llvm::enumerate(funcOp.getArguments()))
+      argTypes.push_back(argEn.value().getType());
+
+    // Traverse ReturnOps to check if an update to the return type in the
+    // function signature is required.
+    funcOp.walk([&](ReturnOp returnOp) {
+      for (const auto &operandEn : llvm::enumerate(returnOp.getOperands())) {
+        Type opType = operandEn.value().getType();
+        MemRefType memrefType = opType.dyn_cast<MemRefType>();
+        // If type is not memref or if the memref type is same as that in
+        // function's return signature then no update is required.
+        if (!memrefType || memrefType == resultTypes[operandEn.index()])
+          continue;
+        // Update function's return type signature.
+        // Return type gets normalized either as a result of function argument
+        // normalization, AllocOp normalization or an update made at CallOp.
+        // There can be many call flows inside a function and an update to a
+        // specific ReturnOp has not yet been made. So we check that the result
+        // memref type is normalized.
+        // TODO: When selective normalization is implemented, handle multiple
+        // results case where some are normalized, some aren't.
+        if (memrefType.getAffineMaps().empty())
+          resultTypes[operandEn.index()] = memrefType;
+      }
+    });
 
-  resultTypes = llvm::to_vector<4>(functionType.getResults());
     // We create a new function type and modify the function signature with this
     // new type.
-  FunctionType newFuncType = FunctionType::get(/*inputs=*/argTypes,
-                                               /*results=*/resultTypes,
-                                               /*context=*/&getContext());
+    newFuncType = FunctionType::get(/*inputs=*/argTypes,
+  }
 
-  // TODO: Handle ReturnOps to update function results the caller site.
+  // Since we update the function signature, it might affect the result types at
+  // the caller site. Since this result might even be used by the caller
+  // function in ReturnOps, the caller function's signature will also change.
+  // Hence we record the caller function in 'funcOpsToUpdate' to update their
+  // signature as well.
+  llvm::SmallDenseSet<FuncOp, 8> funcOpsToUpdate;
+  // We iterate over all symbolic uses of the function and update the return
+  // type at the caller site.
+  Optional<SymbolTable::UseRange> symbolUses = funcOp.getSymbolUses(moduleOp);
+  for (SymbolTable::SymbolUse symbolUse : *symbolUses) {
+    Operation *callOp = symbolUse.getUser();
+    OpBuilder builder(callOp);
+    StringRef callee = cast<CallOp>(callOp).getCallee();
+    Operation *newCallOp = builder.create<CallOp>(
+        callOp->getLoc(), resultTypes, builder.getSymbolRefAttr(callee),
+        callOp->getOperands());
+    bool replacingMemRefUsesFailed = false;
+    bool returnTypeChanged = false;
+    for (unsigned resIndex : llvm::seq<unsigned>(0, callOp->getNumResults())) {
+      OpResult oldResult = callOp->getResult(resIndex);
+      OpResult newResult = newCallOp->getResult(resIndex);
+      // This condition ensures that if the result is not of type memref or if
+      // the resulting memref was already having a trivial map layout then we
+      // need not perform any use replacement here.
+      if (oldResult.getType() == newResult.getType())
+        continue;
+      AffineMap layoutMap =
+          oldResult.getType().dyn_cast<MemRefType>().getAffineMaps().front();
+      if (failed(replaceAllMemRefUsesWith(oldResult, /*newMemRef=*/newResult,
+                                          /*extraIndices=*/{},
+                                          /*indexRemap=*/layoutMap,
+                                          /*extraOperands=*/{},
+                                          /*symbolOperands=*/{},
+                                          /*domInstFilter=*/nullptr,
+                                          /*postDomInstFilter=*/nullptr,
+                                          /*allowDereferencingOps=*/true,
+                                          /*replaceInDeallocOp=*/true))) {
+        // If it failed (due to escapes for example), bail out.
+        // It should never hit this part of the code because it is called by
+        // only those functions which are normalizable.
+        newCallOp->erase();
+        replacingMemRefUsesFailed = true;
+        break;
+      }
+      returnTypeChanged = true;
+    }
+    if (replacingMemRefUsesFailed)
+      continue;
+    // Replace all uses for other non-memref result types.
+    callOp->replaceAllUsesWith(newCallOp);
+    callOp->erase();
+    if (returnTypeChanged) {
+      // Since the return type changed it might lead to a change in function's
+      // signature.
+      // TODO: If funcOp doesn't return any memref type then no need to update
+      // signature.
+      // TODO: Further optimization - Check if the memref is indeed part of
+      // ReturnOp at the parentFuncOp and only then updation of signature is
+      // required.
+      // TODO: Extend this for ops that are FunctionLike. This would require
+      // creating an OpInterface for FunctionLike ops.
+      FuncOp parentFuncOp = newCallOp->getParentOfType<FuncOp>();
+      funcOpsToUpdate.insert(parentFuncOp);
+    }
+  }
+  // Because external function's signature is already updated in
+  // 'normalizeFuncOpMemRefs()', we don't need to update it here again.
+  if (!funcOp.isExternal())
     funcOp.setType(newFuncType);
+
+  // Updating the signature type of those functions which call the current
+  // function. Only if the return type of the current function has a normalized
+  // memref will the caller function become a candidate for signature update.
+  for (FuncOp parentFuncOp : funcOpsToUpdate)
+    updateFunctionSignature(parentFuncOp, moduleOp);
 }
 
-void NormalizeMemRefs::runOnFunction(FuncOp funcOp) {
+/// Normalizes the memrefs within a function which includes those arising as a
+/// result of AllocOps, CallOps and function's argument. The ModuleOp argument
+/// is used to help update function's signature after normalization.
+void NormalizeMemRefs::normalizeFuncOpMemRefs(FuncOp funcOp,
+                                              ModuleOp moduleOp) {
   // Turn memrefs' non-identity layouts maps into ones with identity. Collect
   // alloc ops first and then process since normalizeMemRef replaces/erases ops
   // during memref rewriting.
   SmallVector<AllocOp, 4> allocOps;
   funcOp.walk([&](AllocOp op) { allocOps.push_back(op); });
   for (AllocOp allocOp : allocOps)
     normalizeMemRef(allocOp);
 
   // We use this OpBuilder to create new memref layout later.
   OpBuilder b(funcOp);
 
+  FunctionType functionType = funcOp.getType();
+  SmallVector<Type, 8> inputTypes;
   // Walk over each argument of a function to perform memref normalization (if
-  // any).
-  for (unsigned argIndex : llvm::seq<unsigned>(0, funcOp.getNumArguments())) {
-    Type argType = funcOp.getArgument(argIndex).getType();
+  for (unsigned argIndex :
+       llvm::seq<unsigned>(0, functionType.getNumInputs())) {
+    Type argType = functionType.getInput(argIndex);
     MemRefType memrefType = argType.dyn_cast<MemRefType>();
     // Check whether argument is of MemRef type. Any other argument type can
     // simply be part of the final function signature.
-    if (!memrefType)
+    if (!memrefType) {
+      inputTypes.push_back(argType);
       continue;
+    }
     // Fetch a new memref type after normalizing the old memref to have an
     // identity map layout.
     MemRefType newMemRefType = normalizeMemRefType(memrefType, b,
                                                    /*numSymbolicOperands=*/0);
-    if (newMemRefType == memrefType) {
+    if (newMemRefType == memrefType || funcOp.isExternal()) {
       // Either memrefType already had an identity map or the map couldn't be
       // transformed to an identity map.
+      inputTypes.push_back(newMemRefType);
       continue;
     }
 
     // Insert a new temporary argument with the new memref type.
     BlockArgument newMemRef =
         funcOp.front().insertArgument(argIndex, newMemRefType);
     BlockArgument oldMemRef = funcOp.getArgument(argIndex + 1);
     AffineMap layoutMap = memrefType.getAffineMaps().front();
     // Replace all uses of the old memref.
     if (failed(replaceAllMemRefUsesWith(oldMemRef, /*newMemRef=*/newMemRef,
                                         /*extraIndices=*/{},
                                         /*indexRemap=*/layoutMap,
                                         /*extraOperands=*/{},
                                         /*symbolOperands=*/{},
                                         /*domInstFilter=*/nullptr,
                                         /*postDomInstFilter=*/nullptr,
                                         /*allowNonDereferencingOps=*/true,
-                                        /*handleDeallocOp=*/true))) {
+                                        /*replaceInDeallocOp=*/true))) {
       // If it failed (due to escapes for example), bail out. Removing the
       // temporary argument inserted previously.
       funcOp.front().eraseArgument(argIndex);
       continue;
     }
 
     // All uses for the argument with old memref type were replaced
     // successfully. So we remove the old argument now.
     funcOp.front().eraseArgument(argIndex + 1);
   }
 
-  updateFunctionSignature(funcOp);
+  // In a normal function, memrefs in the return type signature gets normalized
+  // as a result of normalization of functions arguments, AllocOps or CallOps'
+  // result types. Since an external function doesn't have a body, memrefs in
+  // the return type signature can only get normalized by iterating over the
+  // individual return types.
+  if (funcOp.isExternal()) {
+    SmallVector<Type, 4> resultTypes;
+    for (unsigned resIndex :
+         llvm::seq<unsigned>(0, functionType.getNumResults())) {
+      Type resType = functionType.getResult(resIndex);
+      MemRefType memrefType = resType.dyn_cast<MemRefType>();
+      // Check whether result is of MemRef type. Any other argument type can
+      // simply be part of the final function signature.
+      if (!memrefType) {
+        resultTypes.push_back(resType);
+        continue;
+      }
+      // Computing a new memref type after normalizing the old memref to have an
+      // identity map layout.
+      MemRefType newMemRefType = normalizeMemRefType(memrefType, b,
+                                                     /*numSymbolicOperands=*/0);
+      resultTypes.push_back(newMemRefType);
+      continue;
+    }
+
+    FunctionType newFuncType = FunctionType::get(/*inputs=*/inputTypes,
+                                                 /*results=*/resultTypes,
+                                                 /*context=*/&getContext());
+    // Setting the new function signature for this external function.
+    funcOp.setType(newFuncType);
+  }
+  updateFunctionSignature(funcOp, moduleOp);
 }

mlir/lib/Transforms/Utils/Utils.cpp

for (auto *op : oldMemRef.getUsers()) {
     // at other uses doesn't hurt these dealloc's.
     if (isa<DeallocOp>(op) && !replaceInDeallocOp)
       continue;
 
     // Check if the memref was used in a non-dereferencing context. It is fine
     // for the memref to be used in a non-dereferencing way outside of the
     // region where this replacement is happening.
     if (!isMemRefDereferencingOp(*op)) {
-      // Currently we support the following non-dereferencing types to be a
-      // candidate for replacement: Dealloc and CallOp.
-      // TODO: Add support for other kinds of ops.
       if (!allowNonDereferencingOps)
         return failure();
-      if (!(isa<DeallocOp, CallOp>(*op)))
+      // Currently we support the following non-dereferencing ops to be a
+      // candidate for replacement: Dealloc, CallOp and ReturnOp.
+      // TODO: Add support for other kinds of ops.
+      if (!isa<DeallocOp, CallOp, ReturnOp>(*op))
         return failure();
     }
 
     // We'll first collect and then replace --- since replacement erases the op
     // that has the use, and that op could be postDomFilter or domFilter itself!
     opsToReplace.insert(op);
   }
 

mlir/test/Transforms/normalize-memrefs.mlir

affine.for %j = 0 to 10 {
       // CHECK: affine.load %{{.*}}[%{{.*}} * 10 + %{{.*}}] : memref<100xf32>
       %1 = affine.load %A[%i, %j] : memref<10x10xf32, affine_map<(d0,d1)[s0] -> (10*d0 + d1)>>
       "prevent.dce"(%1) : (f32) -> ()
     }
   }
   return
 }
 
-// Memref escapes; no normalization.
-// CHECK-LABEL: func @escaping() -> memref<64xf32, #map{{[0-9]+}}>
-func @escaping() ->  memref<64xf32, affine_map<(d0) -> (d0 + 2)>> {
-  // CHECK: %{{.*}} = alloc() : memref<64xf32, #map{{[0-9]+}}>
-  %A = alloc() : memref<64xf32, affine_map<(d0) -> (d0 + 2)>>
-  return %A : memref<64xf32, affine_map<(d0) -> (d0 + 2)>>
-}
-
 // Semi-affine maps, normalization not implemented yet.
 // CHECK-LABEL: func @semi_affine_layout_map
 func @semi_affine_layout_map(%s0: index, %s1: index) {
   %A = alloc()[%s0, %s1] : memref<256x1024xf32, affine_map<(d0, d1)[s0, s1] -> (d0*s0 + d1*s1)>>
   affine.for %i = 0 to 256 {
     affine.for %j = 0 to 1024 {
       // CHECK: memref<256x1024xf32, #map{{[0-9]+}}>
       affine.load %A[%i, %j] : memref<256x1024xf32, affine_map<(d0, d1)[s0, s1] -> (d0*s0 + d1*s1)>>

 // Test case 3: Check function returning any other type except memref.
 // CHECK-LABEL: func @non_memref_ret
 // CHECK-SAME: (%[[C:arg[0-9]+]]: memref<2x4xf64>) -> i1
 func @non_memref_ret(%A: memref<8xf64, #tile>) -> i1 {
   %d = constant 1 : i1
   return %d : i1
 }
 
-// Test case 4: No normalization should take place because the function is returning the memref.
-// CHECK-LABEL: func @memref_used_in_return
-// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<8xf64, #map{{[0-9]+}}>) -> memref<8xf64, #map{{[0-9]+}}>
-func @memref_used_in_return(%A: memref<8xf64, #tile>) -> (memref<8xf64, #tile>) {
-  return %A : memref<8xf64, #tile>
+// Test cases here onwards deal with normalization of memref in function signature, caller site.
+
+// Test case 4: Check successful memref normalization in case of inter/intra-recursive calls.
+// CHECK-LABEL: func @ret_multiple_argument_type
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<4x4xf64>, %[[B:arg[0-9]+]]: f64, %[[C:arg[0-9]+]]: memref<2x4xf64>) -> (memref<2x4xf64>, f64)
+func @ret_multiple_argument_type(%A: memref<16xf64, #tile>, %B: f64, %C: memref<8xf64, #tile>) -> (memref<8xf64, #tile>, f64) {
+  %a = affine.load %A[0] : memref<16xf64, #tile>
+  %p = mulf %a, %a : f64
+  %cond = constant 1 : i1
+  cond_br %cond, ^bb1, ^bb2
+  ^bb1:
+    %res1, %res2 = call @ret_single_argument_type(%C) : (memref<8xf64, #tile>) -> (memref<16xf64, #tile>, memref<8xf64, #tile>)
+    return %res2, %p: memref<8xf64, #tile>, f64
+  ^bb2:
+    return %C, %p: memref<8xf64, #tile>, f64
+}
+
+// CHECK:   %[[a:[0-9]+]] = affine.load %[[A]][0, 0] : memref<4x4xf64>
+// CHECK:   %[[p:[0-9]+]] = mulf %[[a]], %[[a]] : f64
+// CHECK:   %true = constant true
+// CHECK:   cond_br %true, ^bb1, ^bb2
+// CHECK: ^bb1:  // pred: ^bb0
+// CHECK:   %[[res:[0-9]+]]:2 = call @ret_single_argument_type(%[[C]]) : (memref<2x4xf64>) -> (memref<4x4xf64>, memref<2x4xf64>)
+// CHECK:   return %[[res]]#1, %[[p]] : memref<2x4xf64>, f64
+// CHECK: ^bb2:  // pred: ^bb0
+// CHECK:   return %{{.*}}, %{{.*}} : memref<2x4xf64>, f64
+
+// CHECK-LABEL: func @ret_single_argument_type
+// CHECK-SAME: (%[[C:arg[0-9]+]]: memref<2x4xf64>) -> (memref<4x4xf64>, memref<2x4xf64>)
+func @ret_single_argument_type(%C: memref<8xf64, #tile>) -> (memref<16xf64, #tile>, memref<8xf64, #tile>){
+  %a = alloc() : memref<8xf64, #tile>
+  %b = alloc() : memref<16xf64, #tile>
+  %d = constant 23.0 : f64
+  call @ret_single_argument_type(%a) : (memref<8xf64, #tile>) -> (memref<16xf64, #tile>, memref<8xf64, #tile>)
+  call @ret_single_argument_type(%C) : (memref<8xf64, #tile>) -> (memref<16xf64, #tile>, memref<8xf64, #tile>)
+  %res1, %res2 = call @ret_multiple_argument_type(%b, %d, %a) : (memref<16xf64, #tile>, f64, memref<8xf64, #tile>) -> (memref<8xf64, #tile>, f64)
+  %res3, %res4 = call @ret_single_argument_type(%res1) : (memref<8xf64, #tile>) -> (memref<16xf64, #tile>, memref<8xf64, #tile>)
+  return %b, %a: memref<16xf64, #tile>, memref<8xf64, #tile>
+}
+
+// CHECK: %[[a:[0-9]+]] = alloc() : memref<2x4xf64>
+// CHECK: %[[b:[0-9]+]] = alloc() : memref<4x4xf64>
+// CHECK: %cst = constant 2.300000e+01 : f64
+// CHECK: %[[resA:[0-9]+]]:2 = call @ret_single_argument_type(%[[a]]) : (memref<2x4xf64>) -> (memref<4x4xf64>, memref<2x4xf64>)
+// CHECK: %[[resB:[0-9]+]]:2 = call @ret_single_argument_type(%[[C]]) : (memref<2x4xf64>) -> (memref<4x4xf64>, memref<2x4xf64>)
+// CHECK: %[[resC:[0-9]+]]:2 = call @ret_multiple_argument_type(%[[b]], %cst, %[[a]]) : (memref<4x4xf64>, f64, memref<2x4xf64>) -> (memref<2x4xf64>, f64)
+// CHECK: %[[resD:[0-9]+]]:2 = call @ret_single_argument_type(%[[resC]]#0) : (memref<2x4xf64>) -> (memref<4x4xf64>, memref<2x4xf64>)
+// CHECK: return %{{.*}}, %{{.*}} : memref<4x4xf64>, memref<2x4xf64>
+
+// Test case set #5: To check normalization in a chain of interconnected functions.
+// CHECK-LABEL: func @func_A
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<2x4xf64>)
+func @func_A(%A: memref<8xf64, #tile>) {
+  call @func_B(%A) : (memref<8xf64, #tile>) -> ()
+  return
+}
+// CHECK: call @func_B(%[[A]]) : (memref<2x4xf64>) -> ()
+
+// CHECK-LABEL: func @func_B
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<2x4xf64>)
+func @func_B(%A: memref<8xf64, #tile>) {
+  call @func_C(%A) : (memref<8xf64, #tile>) -> ()
+  return
+}
+// CHECK: call @func_C(%[[A]]) : (memref<2x4xf64>) -> ()
+
+// CHECK-LABEL: func @func_C
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<2x4xf64>)
+func @func_C(%A: memref<8xf64, #tile>) {
+  return
+}
+
+// Test case set #6: Checking if no normalization takes place in a scenario: A -> B -> C and B has an unsupported type.
+// CHECK-LABEL: func @some_func_A
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<8xf64, #map{{[0-9]+}}>)
+func @some_func_A(%A: memref<8xf64, #tile>) {
+  call @some_func_B(%A) : (memref<8xf64, #tile>) -> ()
+  return
+}
+// CHECK: call @some_func_B(%[[A]]) : (memref<8xf64, #map{{[0-9]+}}>) -> ()
+
+// CHECK-LABEL: func @some_func_B
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<8xf64, #map{{[0-9]+}}>)
+func @some_func_B(%A: memref<8xf64, #tile>) {
+  "test.test"(%A) : (memref<8xf64, #tile>) -> ()
+  call @some_func_C(%A) : (memref<8xf64, #tile>) -> ()
+  return
+}
+// CHECK: call @some_func_C(%[[A]]) : (memref<8xf64, #map{{[0-9]+}}>) -> ()
+
+// CHECK-LABEL: func @some_func_C
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<8xf64, #map{{[0-9]+}}>)
+func @some_func_C(%A: memref<8xf64, #tile>) {
+  return
+}
+
+// Test case set #7: Check normalization in case of external functions.
+// CHECK-LABEL: func @external_func_A
+// CHECK-SAME: (memref<4x4xf64>)
+func @external_func_A(memref<16xf64, #tile>) -> ()
+
+// CHECK-LABEL: func @external_func_B
+// CHECK-SAME: (memref<4x4xf64>, f64) -> memref<2x4xf64>
+func @external_func_B(memref<16xf64, #tile>, f64) -> (memref<8xf64, #tile>)
+
+// CHECK-LABEL: func @simply_call_external()
+func @simply_call_external() {
+  %a = alloc() : memref<16xf64, #tile>
+  call @external_func_A(%a) : (memref<16xf64, #tile>) -> ()
+  return
+}
+// CHECK: %[[a:[0-9]+]] = alloc() : memref<4x4xf64>
+// CHECK: call @external_func_A(%[[a]]) : (memref<4x4xf64>) -> ()
+
+// CHECK-LABEL: func @use_value_of_external
+// CHECK-SAME: (%[[A:arg[0-9]+]]: memref<4x4xf64>, %[[B:arg[0-9]+]]: f64) -> memref<2x4xf64>
+func @use_value_of_external(%A: memref<16xf64, #tile>, %B: f64) -> (memref<8xf64, #tile>) {
+  %res = call @external_func_B(%A, %B) : (memref<16xf64, #tile>, f64) -> (memref<8xf64, #tile>)
+  return %res : memref<8xf64, #tile>
 }
+// CHECK: %[[res:[0-9]+]] = call @external_func_B(%[[A]], %[[B]]) : (memref<4x4xf64>, f64) -> memref<2x4xf64>
+// CHECK: return %{{.*}} : memref<2x4xf64>