[mlir][Linalg] Introduce a BufferizationAliasInfo (6/n)

[nicolasvasilache]

Summary

This revision adds a BufferizationAliasInfo which maintains and updates information about which tensors will alias once bufferized, which bufferized tensors are equivalent to others and how to handle clobbers.

Bufferization greedily tries to bufferize inplace by:

1. first trying to bufferize SubTensorInsertOp inplace, in reverse order (these are deemed the most expensives).
2. then trying to bufferize all non SubTensorOp / SubTensorInsertOp, in reverse order.
3. lastly trying to bufferize all SubTensorOp in reverse order.

Reverse order is a heuristic that seems to work nicely because structured tensor codegen very often proceeds by:

1. take a subset of a tensor
2. compute on that subset
3. insert the result subset into the full tensor and yield a new tensor.

BufferizationAliasInfo + equivalence sets + clobber analysis allows bufferizing nested
subtensor/compute/subtensor_insert sequences inplace to a certain extent.
To fully realize inplace bufferization, additional container-containee analysis will be necessary and is left for a subsequent commit.

[nicolasvasilache]

Drop spurious test file.

[nicolasvasilache]

This still requires a bit more work and tests but should already be reviewable.

[rriddle]

Thanks! Starting working through, mostly stylistic nits while digesting the design.

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

133

Does the printer for BlockArgument add a newline? I don't think it should if it does.

164

Was this supposed to be debug logging?

364–367

379

nit: Drop the llvm:: here.

(This also applies quite a bit in this revision, many of these classes are re-exported in the mlir:: namespace).

384

417

Can you spell out auto here?

431

443

Same here.

456–457

Same comment here as above.

822

There is a mismatch of commenting style in this file, a lot of //.

843

Why the inline here?

864–865

Unfinished comment?

1497–1498

nit: Spell out auto here.

1517–1520

Should this be removed? Looks like a TODO.

1550–1559

[nicolasvasilache]

Finish the implementation and make tests green again.

[nicolasvasilache]

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

133

see https://reviews.llvm.org/D104368

[nicolasvasilache]

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

456–457

Can't seem to match this comment to a previous one, the code was cleaned up a bunch in the meantime, tentatively marking as resolved.

822

Made a general cleanup of /// for methods and classes in the meantime, I think this comment was referring to those?
Tentatively marking as done.

[nicolasvasilache]

Address River's comments.

[nicolasvasilache]

Avoid DenseMap update-while-iterating, which hopfully will fix Windows.
Add constness to relevant places in the analysis following-up on update-while-iterating issue.
Fix one test in comprehensive-func-bufferize which did not consider ReturnOp to read and resulted in a spurious clobber.

[ftynse]

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

168

Could we store the result of lookupOrNull in a variable and avoid double lookup here?

297

ReturnOp has no results so it will also be caught by the second alternative below.

363–364

This looks unnecessary and can be treated as "other ops" in the default clause.

487

Nit: explicit

490–491

I couldn't match the documentation with the function name. The documentation says "would bufferize to a write to a buffer", but the function is named "aliasesNonWritableBuffer". How can it be non-writable if there is a write to it?

493–494

Looks like copy-pasta form the above.

497

1013

Leftover debug

1175

1532

Looks like leftover (excessive) debug

1554

Most places in this file use just TensorType but this, and a couple of others, a more specific RankedTensorType. Is this intentional?

1633–1636

Nit: return mlir::failure(result.wasInterrupted())

[nicolasvasilache]

Address Alex's comments.

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

497

I thought the function/method comment style guide was to use infinitive rather than 3rd person ?
I've tried to be consistent with use of infinitive.

1554

Yes, there are some differences that will appear more clearly with unranked tensors (e.g. calls to external functions are supported but alloc of unranked buffer for out-of-place unranked tensor is not).
Good parts of this code are ported from an external prototype where unranked tensors are supported to some extent; I'll be able to tighten all uses when I get to adding the right functionality
In this particular case it seems TensorType is more permissive and is the right call.

[nicolasvasilache]

Revert spuriously commented line.

[ftynse]

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

497

This was (and still is) saying "Merge <...> and iterates" <...>", which is grammatically incorrect regardless of your preference for the comment style. I don't care beyond local consistency.

[nicolasvasilache]

Pass bufferAliasInfo to bufferize functions to fix subtensor_insert bufferization impl. that does not match the description.

[nicolasvasilache]

Rebase.

[nicolasvasilache]

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

497

Fixed.

mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp

 //===- ComprehensiveBufferize.cpp - Single pass bufferization -------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 //
 // Perform inplace bufferization within function boundaries.
 // This is a specialized pass that supports inplace analysis for a fixed subset
 // of ops that have well-defined inplace semantics.
 // This pass caters to high-performance codegen where buffer reuse is deemed
-// necessary: the pass should fail if the bufferized form of the function needs
+// critical: the pass should fail if the bufferized form of the function needs
 // to return any buffer.
 // Generic control-flow and branching are unsupported.
 // Composability with extensible set of ops is not a first-class concern.
 //
 // Bufferization occurs by:
 //  a. performing an inPlace analysis `inPlaceAnalysisFuncOpInternals`
 //     which marks each operation within the function with the
 //     `kInPlaceResultsAttrName` attribute.
 //  b. traversing each operation in the function and rewriting it in
 //     buffer form and keeping a BlockAndValueMapping mapping of the
 //     rewrites. New allocations are introduced during this step.
 //     TODO: Allocation + depending op hoisting to outermost enclosing
 //     sequential scope.
-//  c. at the end of this bufferization, 2 cases may occur:
-//     * inplaceable function arguments may be reused in place after the
-//       function itself has been bufferized. This is encoded by IR resembling:
+//  c. at the end of this bufferization, 3 cases may occur:
+//     i. inplaceable function arguments may be reused in place after the
+//        function itself has been bufferized. This is encoded by IR resembling:
 //
-// ```
-//   #map = affine_map<(d0)[s0, s1] -> (d0 * s1 + s0)>
-//   func @foo(%A: tensor<?xf32> {linalg.inplaceable = true}) -> tensor<?xf32> {
-//     %0 = memref.buffer_cast %A : memref<?xf32, #map>
-//     // ... uses of %0
-//     %res = memref.tensor_load %0 : memref<?xf32, #map>
-//     return %res : tensor<?xf32>
-//   }
-// ```
+//        ```
+//          #map = affine_map<(d0)[s0, s1] -> (d0 * s1 + s0)>
+//           func @foo(%A: tensor<?xf32> {linalg.inplaceable = true})
+//              -> tensor<?xf32> {
+//            %0 = memref.buffer_cast %A : memref<?xf32, #map>
+//            // ... uses of %0
+//            %res = memref.tensor_load %0 : memref<?xf32, #map>
+//            return %res : tensor<?xf32>
+//          }
+//        ```
 //
-//       this is the cue for the bufferization of the function foo (and calls to
-//       it) may bufferize to `func @foo(%A: memref<?xf32, some_layout>)`.
-//       To fully achieve bufferization, an additional analysis is needed to
-//       determine whether function argument/operand pairs bufferize to a single
-//       inplace buffer argument (i.e. functions may return tensors in arbitrary
-//       order that may not match argument numbers).
-//     * results that don't map to an inplaceable function argument must be
-//       allocated. Since memref semantics wrt ownership of the underlying
-//       memory region are not well-defined, comprehensive bufferization chooses
-//       to perform allocations in a scoped fashion: returning memrefs is always
-//       considered illegal. Such scenarios are encoded by IR resembling:
+//        this is the cue for the bufferization of the function foo (and calls
+//        to it) may bufferize to `func @foo(%A: memref<?xf32, some_layout>)`.
+//        To fully achieve bufferization, an additional analysis is needed to
+//        determine whether function argument/operand pairs bufferize to a
+//        single inplace buffer argument (i.e. functions may return tensors in
+//        arbitrary order that may not match argument numbers).
+//
+//    ii. results that don't map to an inplaceable function argument are
+//        generally allocated. Since memref semantics wrt ownership of the
+//        underlying memory region are not well-defined, comprehensive
+//        bufferization chooses to perform allocations in a scoped fashion:
+//        returning memrefs is always considered illegal.
+//        Such scenarios are encoded by IR resembling:
 //
-// ```
-//   #map = affine_map<(d0)[s0, s1] -> (d0 * s1 + s0)>
-//   func @foo(%A: tensor<?xf32> {linalg.inplaceable = true}) -> tensor<?xf32> {
-//     %0 = memref.buffer_cast %A : memref<?xf32, #map>
-//     %1 = memref.dim %0, %c0 : memref<?xf32, #map>
-//     %2 = memref.alloc(%1) : memref<?xf32>
-//     %3 = memref.cast %2 : memref<?xf32> to memref<?xf32, #map>
-//     // ... uses of %3
-//     memref.dealloc %2 : memref<?xf32, #map>
-//     %res = memref.tensor_load %3 : memref<?xf32, #map>
-//     return %res : tensor<?xf32>
-//   }
-// ```
+//        ```
+//          #map = affine_map<(d0)[s0, s1] -> (d0 * s1 + s0)>
+//          func @foo(%A: tensor<?xf32> {linalg.inplaceable = true})
+//              -> tensor<?xf32> {
+//            %0 = memref.buffer_cast %A : memref<?xf32, #map>
+//            %1 = memref.dim %0, %c0 : memref<?xf32, #map>
+//            %2 = memref.alloc(%1) : memref<?xf32>
+//            %3 = memref.cast %2 : memref<?xf32> to memref<?xf32, #map>
+//            // ... uses of %3
+//            memref.dealloc %2 : memref<?xf32, #map>
+//            %res = memref.tensor_load %3 : memref<?xf32, #map>
+//            return %res : tensor<?xf32>
+//          }
+//       ```
 //
-//       this is the cue for the bufferization of the function foo (and calls to
-//       it) that it must bufferize to
-//       `func @foo(%A: memref<?xf32, some_layout>,
-//                  %B: memref<?xf32, some_layout>)` (i.e. make a cloned
-//       allocation of the result tensor)
-//       To fully achieve bufferization, the alloc/dealloc pair must be lifted
-//       out of the function at each call site.
+//        this is the cue for the bufferization of the function foo (and calls
+//        to it) that it must bufferize to `func @foo(%A: memref<?xf32,
+//        some_layout>,
+//                   %B: memref<?xf32, some_layout>)` (i.e. make a cloned
+//        allocation of the result tensor)
+//        To fully achieve bufferization, the alloc/dealloc pair must be lifted
+//        out of the function at each call site.
 //
+//   iii. as an optimization over ii., it may be possible to reuse an argument
+//        and only want to return a subtensor.
+//        This may forego allocation by letting *all* callers decide whether to
+//        pass a new *aliasing* memref function argument (i.e. a subview).
+//        Without loss of generality, callers may agree to allocate a new buffer
+//        to avoid this aliasing. Such scenarios are encoded by IR resembling:
+//
+//        ```
+//          #map = affine_map<(d0)[s0, s1] -> (d0 * s1 + s0)>
+//          func @foo(%arg0: tensor<?xf32> {linalg.inplaceable = true})
+//              -> tensor<4xf32> {
+//            %0 = memref.buffer_cast %arg0 : memref<?xf32, #map>
+//            %1 = memref.subview %0[0] [4] [1] : memref<?xf32, #map> to
+//                                                memref<4xf32, #map>
+//            // ... inplace computes into %1
+//            %3 = memref.tensor_load %1 : memref<4xf32, #map>
+//            return %3 : tensor<4xf32>
+//          }
+//        ```
+//
+//  Note: In the future, it may be worthwhile to design special bufferization
+//  ops to encode the desired semantics at function boundaries for i., ii. and
+//  iii.
+//
 //  Lastly, note that layout map chosen to bufferize is the most dynamic
 //  canonical strided layout of the proper rank. This ensures compatibility with
 //  expected layouts after transformations. Combinations of memref.cast +
 //  canonicalization are responsible for clean ups.
 
 #include "PassDetail.h"
-#include "mlir/Analysis/SliceAnalysis.h"
 #include "mlir/Dialect/Linalg/IR/LinalgOps.h"
 #include "mlir/Dialect/Linalg/Passes.h"
 #include "mlir/Dialect/MemRef/IR/MemRef.h"
 #include "mlir/Dialect/Vector/VectorOps.h"
 #include "mlir/IR/Operation.h"
 #include "mlir/Pass/Pass.h"
 #include "mlir/Transforms/BufferUtils.h"
 
+#include "llvm/ADT/DenseSet.h"
+#include "llvm/ADT/EquivalenceClasses.h"
 #include "llvm/ADT/ScopeExit.h"
+#include "llvm/ADT/SetOperations.h"
 #include "llvm/ADT/SetVector.h"
 #include "llvm/ADT/TypeSwitch.h"
 
 #define DEBUG_TYPE "comprehensive-func-bufferize"
 
 using namespace mlir;
 using namespace linalg;
 using namespace tensor;
 
 #define DBGS() (llvm::dbgs() << '[' << DEBUG_TYPE << "] ")
+#define LDBG(X) LLVM_DEBUG(DBGS() << X)
 
 //===----------------------------------------------------------------------===//
-// Op-specific semantics helper to retrieve matching inplaceable result.
+// Bufferization-specific BlockAndValueMapping support with debugging.
 //===----------------------------------------------------------------------===//
 
-/// Return the OpResult that matches an operand.
-/// Return null if no such result exists.
-OpResult getMatchingOpResult(LinalgOp linalgOp, OpOperand &opOperand) {
-  if (!opOperand.get().getType().isa<RankedTensorType>())
-    return OpResult();
-  // For now assume inputs are never inplaceable.
-  // TODO: refine this.
-  if (opOperand.getOperandNumber() < linalgOp.getNumInputs())
-    return OpResult();
-  // For now assume if the operand appears twice, it is not inplaceable.
-  // TODO: refine this.
-  for (auto &opOperand2 : linalgOp->getOpOperands()) {
-    if (opOperand.getOperandNumber() == opOperand2.getOperandNumber())
-      continue;
-    if (opOperand.get() == opOperand2.get())
-      return OpResult();
-  }
-  int64_t outputOperandIndex =
-      opOperand.getOperandNumber() - linalgOp.getNumInputs();
-  int64_t numOutputBuffers = 0;
-  for (unsigned idx = 0; idx < outputOperandIndex; ++idx)
-    if (!linalgOp.getOutputOperand(idx)->get().getType().isa<TensorType>())
-      ++numOutputBuffers;
-  return linalgOp->getResult(outputOperandIndex - numOutputBuffers);
+/// Wrapper for better debugging.
+static void map(BlockAndValueMapping &bvm, ValueRange keys, ValueRange values) {
+  assert(!keys.empty() && "Unexpected empty keys");
+  LDBG("Map: " << keys.front() << " to " << values.front() << '\n');
+  return bvm.map(keys, values);
 }
 
-/// Return the OpResult that matches an operand.
-/// Return null if no such result exists.
-OpResult getMatchingOpResult(VectorTransferOpInterface op,
-                             OpOperand &opOperand) {
-  if (opOperand.get() != op.source() ||
-      !op.source().getType().isa<TensorType>())
-    return OpResult();
-  return op->getResult(0);
+/// Wrapper for better debugging.
+static void map(BlockAndValueMapping &bvm, Value key, Value value) {
+  LDBG("Map: " << key << " to " << value << '\n');
+  return bvm.map(key, value);
 }
 
-/// Return the OpResult that matches an operand.
-/// Return null if no such result exists.
-OpResult getMatchingOpResult(SubTensorInsertOp op, OpOperand &opOperand) {
-  if (opOperand.get() != op.dest())
-    return OpResult();
-  return op->getResult(0);
-}
+/// Wrapper for better debugging.
+static Value lookup(BlockAndValueMapping &bvm, Value key) {
+  // TODO: if key comes from bbArg, forward.
+  assert(key.getType().isa<TensorType>());
+  Value v = bvm.lookupOrNull(key);
+  if (v)
+    return v;
 
-/// Determine which results may be reused inplace by the bufferization
-/// patterns of `bufferizeFuncOpInternals`.
-/// The inplace analysis uses this information along with interfering read
-/// analysis to determine which op results reuse the same buffer as some
-/// operand.
-OpResult getMatchingOpResult(OpOperand &opOperand) {
-  return llvm::TypeSwitch<Operation *, OpResult>(opOperand.getOwner())
-      // clang-format off
-        // Ops that perform destructive updates on operand(s) to produce
-        // result(s).
-        .Case<LinalgOp,
-              SubTensorInsertOp,
-              VectorTransferOpInterface>(
-            [&](auto op) { return getMatchingOpResult(op, opOperand); })
-        // Other ops.
-        .Case<SubTensorOp>([&](auto op) { return OpResult(); })
-        .Default([&](Operation *op) { return OpResult(); });
-  // clang-format on
+  Operation *parentOp;
+  if (auto bbArg = key.dyn_cast<BlockArgument>()) {
+    if (isa<FuncOp>(key.getParentBlock()->getParentOp()))
+      parentOp = key.getParentBlock()->getParentOp();
+    else
+      parentOp = key.getParentBlock()->getParentOp()->getParentOfType<FuncOp>();
+  } else {
+    parentOp = key.getDefiningOp()->getParentOfType<FuncOp>();
+  }
+  LDBG("In func:\n" << *parentOp << "NO VALUE FOR KEY: " << key << '\n');
+  return Value();
 }
 
 //===----------------------------------------------------------------------===//
 // Bufferization-specific attribute manipulation.
+// These could be simplified with helper structs on the side, for now attributes
+// allow simple embedding in the IR which simplifies testing.
+// This could also be folded in BufferizationAliasInfo or a Bufferizer class
+// that uses BufferizationAliasInfo.
 //===----------------------------------------------------------------------===//
 
 /// Attribute marker to specify op results that can be bufferized inPlace.
 constexpr StringLiteral kInPlaceResultsAttrName = "__inplace_results_attr__";
 
 // TODO: proper enum.
 enum class InPlaceSpec {
   False,
static void setInPlaceOpResult(OpResult opResult,
   Operation *op = opResult.getOwner();
   auto attr =
       op->getAttr(kInPlaceResultsAttrName).dyn_cast_or_null<ArrayAttr>();
   SmallVector<StringRef> inPlaceVector =
       attr ? SmallVector<StringRef>(
                  llvm::to_vector<4>(attr.getAsValueRange<StringAttr>()))
            : SmallVector<StringRef>(op->getNumResults(),
                                     stringify(InPlaceSpec::None));
-  LLVM_DEBUG(DBGS() << "Set inPlace=" << stringify(inPlace) << ": " << *op
-                    << " @idx=" << opResult.getResultNumber() << "\n");
+  LDBG("->set inPlace=" << stringify(inPlace) << ": " << *op
+                        << " @idx=" << opResult.getResultNumber() << '\n');
   inPlaceVector[opResult.getResultNumber()] = stringify(inPlace);
   op->setAttr(kInPlaceResultsAttrName,
               OpBuilder(op).getStrArrayAttr(inPlaceVector));
 }
 
 /// Get the InPlaceSpec attribute entry `kInPlaceResultsAttrName` for
 /// `opResult`. If the result is `InPlaceSpec::True`, the use-def chain analysis
 /// has guaranteed that no subsequent read of the tensor value occurs and the
if (!funcOp)
     return InPlaceSpec::False;
   auto attr = funcOp.getArgAttrOfType<BoolAttr>(
       bbArg.getArgNumber(), LinalgDialect::kInplaceableAttrName);
   if (!attr)
     return InPlaceSpec::None;
   return attr.getValue() ? InPlaceSpec::True : InPlaceSpec::False;
 }
 
+static InPlaceSpec getInPlace(Value v) {
+  if (auto bbArg = v.dyn_cast<BlockArgument>())
+    return getInPlace(bbArg);
+  return getInPlace(v.cast<OpResult>());
+}
+
 //===----------------------------------------------------------------------===//
-// Bufferization-specific BlockAndValueMapping support with debugging.
+// Op-specific semantics helper to retrieve matching inplaceable result.
+// These should become proper interfaces interfaces when the time is right.
+// Modulo better naming, these helpers / interfaces comprise information on:
+//   1. Whether an op has a known bufferization behavior (i.e. an instance of
+//      BufferizableOpInterface).
+//   2. Whether an op, when bufferized inplace, can guarantee an
+//      (OpOperand, OpResult) pair bufferizes to equivalent (i.e. the same)
+//      buffers in memory.
+//   3. Whether an op operand, when bufferized inplace, aliases a return value.
+//   4. Whether an op return value, when bufferized inplace, aliases an operand.
+//   5. Wheher an op bufferizes to a memory read.
+//   6. Wheher an op bufferizes to a memory write.
+// These interfaces are necessary to distinguish between various cases and allow
+// special inplace behavior for (SubTensorOp, SubTensorInsertOp) pairs.
 //===----------------------------------------------------------------------===//
 
-/// Wrapper for better debugging.
-static void map(BlockAndValueMapping &bvm, ValueRange keys, ValueRange values) {
-  assert(!keys.empty() && "Unexpected empty keys");
-  LLVM_DEBUG(DBGS() << "Map: " << keys.front() << " to " << values.front()
-                    << "\n");
-  return bvm.map(keys, values);
+/// Return `true` if the op is explicitly supported by bufferization or if it
+/// has no result tensors.
+/// Other cases must be conservative.
+static bool hasKnownBufferizationAliasingBehavior(Operation *op) {
+  return
+      // clang-format off
+      isa<LinalgOp,
+          ReturnOp,
+          SubTensorOp,
+          SubTensorInsertOp,
+          VectorTransferOpInterface>(op)
+      // clang-format on
+      || (none_of(op->getResultTypes(),
+                  [](Type t) { return t.isa<TensorType>(); }) &&
+          none_of(op->getOperandTypes(),
+                  [](Type t) { return t.isa<TensorType>(); }));
 }
 
-/// Wrapper for better debugging.
-static void map(BlockAndValueMapping &bvm, Value key, Value value) {
-  LLVM_DEBUG(DBGS() << "Map: " << key << " to " << value << "\n");
-  return bvm.map(key, value);
+/// Return the OpResult that may bufferize into the same buffer as `opOperand`
+/// when the op is bufferized inplace.
+/// Return null if no such result exists.
+static OpResult getInplaceableOpResult(LinalgOp linalgOp,
+                                       OpOperand &opOperand) {
+  if (!opOperand.get().getType().isa<RankedTensorType>())
+    return OpResult();
+  // For now assume inputs are never inplaceable.
+  // TODO: refine this.
+  if (opOperand.getOperandNumber() < linalgOp.getNumInputs())
+    return OpResult();
+  int64_t outputOperandIndex =
+      opOperand.getOperandNumber() - linalgOp.getNumInputs();
+  int64_t numOutputBuffers = 0;
+  for (unsigned idx = 0; idx < outputOperandIndex; ++idx)
+    if (!linalgOp.getOutputOperand(idx)->get().getType().isa<TensorType>())
+      ++numOutputBuffers;
+  return linalgOp->getResult(outputOperandIndex - numOutputBuffers);
 }
 
-/// Wrapper for better debugging.
-static Value lookup(BlockAndValueMapping &bvm, Value key) {
-  // TODO: if key comes from bbArg, forward.
-  assert(key.getType().isa<TensorType>());
-  if (!bvm.lookupOrNull(key)) {
-    if (auto bbArg = key.dyn_cast<BlockArgument>()) {
-      if (isa<FuncOp>(key.getParentBlock()->getParentOp()))
-        key.getParentBlock()->getParentOp()->dump();
-      else
-        key.getParentBlock()->getParentOp()->getParentOfType<FuncOp>()->dump();
-      bbArg.getOwner()->getParentOp()->dump();
-    } else {
-      key.getDefiningOp()->getParentOfType<FuncOp>()->dump();
+/// Return the OpResult that may bufferize into the same buffer as `opOperand`
+/// when the op is bufferized inplace.
+/// Return null if no such result exists.
+static OpResult getInplaceableOpResult(VectorTransferOpInterface op,
+                                       OpOperand &opOperand) {
+  if (opOperand.get() != op.source() ||
+      !op.source().getType().isa<TensorType>())
+    return OpResult();
+  return op->getResult(0);
+}
+
+/// Return the OpResult that may bufferize into the same buffer as `opOperand`
+/// when the op is bufferized inplace.
+/// Return null if no such result exists.
+static OpResult getInplaceableOpResult(SubTensorInsertOp op,
+                                       OpOperand &opOperand) {
+  if (opOperand.get() != op.dest())
+    return OpResult();
+  return op->getResult(0);
+}
+
+/// Return the OpResult that may bufferize into the same buffer as `opOperand`
+/// when the op is bufferized inplace.
+/// The inplace analysis uses this information along with interfering read
+/// analysis to determine which op results reuse the same buffer as some
+/// operand.
+static OpResult getInplaceableOpResult(OpOperand &opOperand) {
+  return TypeSwitch<Operation *, OpResult>(opOperand.getOwner())
+      // clang-format off
+        // Ops that perform destructive updates on operand(s) to produce
+        // result(s).
+        .Case<LinalgOp,
+              SubTensorInsertOp,
+              VectorTransferOpInterface>(
+            [&](auto op) { return getInplaceableOpResult(op, opOperand); })
+        // SubTensorOp is special, when bufferized inplace it just returns an
+        // alias to its operand. Its result is never inplaceable on its operand.
+        .Case([&](SubTensorOp op) { return OpResult(); })
+        // Other ops.
+        .Default([&](Operation *op) { return OpResult(); });
+  // clang-format on
+}
+
+/// Determine which OpResult will alias with `opOperand` if the op is bufferized
+/// in place. This is a superset of `getInplaceableOpResult`.
+/// Return None if the owner of `opOperand` does not have known
+/// bufferization aliasing behavior, which indicates that the op must allocate
+/// all of its tensor results.
+/// TODO: in the future this may need to evolve towards a list of OpResult.
+static Optional<OpResult> getAliasingOpResult(OpOperand &opOperand) {
+  if (!hasKnownBufferizationAliasingBehavior(opOperand.getOwner()))
+    return None;
+  return TypeSwitch<Operation *, OpResult>(opOperand.getOwner())
+      // ReturnOp has no result.
+      .Case([&](ReturnOp op) { return OpResult(); })
+      // SubTensorOp is different: its result is not inplaceable on op.source
+      // but when bufferized inplace, the result is an aliasing subregion of
+      // op.source.
+      .Case([&](SubTensorOp op) { return op->getResult(0); })
+      .Default(
+          [&](Operation *op) { return getInplaceableOpResult(opOperand); });
+}
+
+/// Return true if `opOperand` bufferizes to a memory read.
+static bool bufferizesToMemoryRead(OpOperand &opOperand) {
+  Optional<OpResult> maybeOpResult = getAliasingOpResult(opOperand);
+  // Unknown op that returns a tensor. The inplace analysis does not support
+  // it. Conservatively return true.
+  if (!maybeOpResult)
+    return true;
+  // SubTensorOp alone doesn't bufferize to a memory read, one of its uses may.
+  if (isa<SubTensorOp>(opOperand.getOwner()))
+    return false;
+  if (auto linalgOp = dyn_cast<LinalgOp>(opOperand.getOwner()))
+    return linalgOp.isInputTensor(&opOperand) ||
+           linalgOp.isInitTensor(&opOperand);
+  // All other cases are considered to bufferize to memory reads.
+  // In particular, terminators are often the last use and need to be considered
+  // as reads to return the proper value and avoid WAW clobbers.
+  return true;
+}
+
+/// Return true if `opOperand` bufferizes to a memory write.
+/// If inPlaceSpec is different from InPlaceSpec::None, additionally require the
+/// write to match the inplace specification.
+static bool
+bufferizesToMemoryWrite(OpOperand &opOperand,
+                        InPlaceSpec inPlaceSpec = InPlaceSpec::None) {
+  Optional<OpResult> maybeOpResult = getAliasingOpResult(opOperand);
+  // Unknown op that returns a tensor. The inplace analysis does not support
+  // it. Conservatively return true.
+  if (!maybeOpResult)
+    return true;
+  // Supported op without a matching result for opOperand (e.g. ReturnOp).
+  // This does not bufferize to a write.
+  if (!*maybeOpResult)
+    return false;
+  // A ReturnOp is not a write.
+  if (isa<ReturnOp>(opOperand.getOwner()))
+    return false;
+  // SubTensorOp alone doesn't bufferize to a memory write, one of its uses may.
+  if (maybeOpResult->getDefiningOp<SubTensorOp>())
+    return false;
+  // If we have a matching OpResult, this is a write.
+  // Additionally allow to restrict to only inPlace write, if so specified.
+  return inPlaceSpec == InPlaceSpec::None ||
+         getInPlace(*maybeOpResult) == inPlaceSpec;
+}
+
+//===----------------------------------------------------------------------===//
+// Bufferization-specific alias analysis.
+//===----------------------------------------------------------------------===//
+
+namespace {
+
+/// The BufferizationAliasInfo class maintains a list of buffer aliases and
+/// equivalence classes to support bufferization.
+/// SubTensorOps have special behavior, they act as a level of indirection for
+/// bufferization. They don't create reads or writes themselves and analysis
+/// needs to look through their uses.
+/// SubTensorOp + SubTensorInsertOp have special joint behavior: they may
+/// bufferize to the same buffer (i.e. subview), which is what introduces the
+/// need for bufferization classes.
+/// Some of these functionalities could be refactored in a Bufferizer class that
+/// uses BufferizationAliasInfo.
+class BufferizationAliasInfo {
+public:
+  /// Specify fine-grain relationship between buffers to enable more analysis.
+  enum class BufferRelation {
+    None,
+    // TODO: ResultContainsOperand,
+    // TODO: OperandContainsResult,
+    Equivalent
+  };
+
+  explicit BufferizationAliasInfo(FuncOp funcOp);
+
+  /// Return true if the buffer to which `operand` would bufferize aliases a
+  /// buffer that is known to not be writeable. This implies that the matching
+  /// OpResult cannot be bufferized inplace.
+  bool aliasesNonWriteableBuffer(OpOperand &operand) const;
+
+  /// Return true if the buffer to which `operand` would bufferize is equivalent
+  /// to some use that would bufferize to a write to a buffer.
+  bool aliasesInPlaceWrite(SubTensorOp subTensorOp) const;
+
+  /// Merge result's and operand's aliasing sets and iterate to a fixed point.
+  void bufferizeInPlace(OpResult result, OpOperand &operand,
+                        BufferRelation bufferRelation = BufferRelation::None);
+
+  /// Return true if it is possible to find an inplace write W among the uses of
+  /// aliasInfo[rootWrite], and a read R among the uses of aliasInfo[rootRead],
+  /// such that W and R interfere.
+  /// Such a (W, R) pair is an interference to the inplace bufferization of
+  /// rootWrite when:
+  ///   1. R is not known properly dominate W (i.e. the effects of the write may
+  ///      be visible from R).
+  ///   2. one cannot find an intermediate clobbering write `C` to W, such that
+  ///      C interleaved between W and R (i.e. W -> C -> R where -> denotes
+  ///      dominance).
+  bool
+  wouldCreateReadAfterWriteInterference(Value rootWrite, Value rootRead,
+                                        Operation *opToBufferize,
+                                        const DominanceInfo &domInfo) const;
+
+  /// Return true if we find any read to opOperand.get() or any of its aliases,
+  /// that does not dominate opOperand.getOwner().
+  bool existsNonDominatingRead(OpOperand &opOperand,
+                               const DominanceInfo &domInfo) const;
+
+  /// Return true if the source of a `subTensorInsertOp` bufferizes to an
+  /// equivalent SubTensorOp.
+  bool isSourceEquivalentToAMatchingSubTensorOp(
+      SubTensorInsertOp subTensorInsertOp) const;
+
+  /// Print to `os`.
+  void print(raw_ostream &os) const;
+
+  /// Print to `errs()`.
+  void dump() const { print(llvm::errs()); }
+
+private:
+  /// Check aliasInfo for `v` exists and return a reference to it.
+  DenseSet<Value> &getAliasInfoRef(Value v);
+  const DenseSet<Value> &getAliasInfoRef(Value v) const {
+    return const_cast<BufferizationAliasInfo *>(this)->getAliasInfoRef(v);
+  }
+
+  /// Union all the aliasing sets of all aliases of v1 and v2.
+  bool mergeAliases(Value v1, Value v2);
+
+  /// Iteratively merge alias sets until a fixed-point.
+  void mergeAliasesToFixedPoint();
+
+  /// Return true if the (SubTensorOp, SubTensorInsertOp) pair match (i.e.
+  /// equivalent operand / result and same offset/sizes/strides specification).
+  ///
+  /// This is one particular type of relationship between ops on tensors that
+  /// reduce to an equivalence on buffers. This should be generalized and
+  /// exposed as interfaces on the proper types.
+  bool areEquivalentSubTensorOps(SubTensorOp st, SubTensorInsertOp sti) const;
+
+  /// Return true if there is a `candidateOp` that would write to memory after
+  /// bufferization and such that:
+  ///   1. The written buffer is equivalent to either `aliasingRead` or
+  ///      `aliasingWrite` under the inPlace bufferization decisions taken
+  ///      so far.
+  ///   2. `aliasingWrite` properly dominates `candidateOp`.
+  ///   3. `candidateOp` properly dominates `aliasingReadOp`.
+  // TODO: richer clobbering analysis with container-containee relationship
+  // instead of equivalence.
+  bool existsInterleavedValueClobber(OpOperand &aliasingRead,
+                                     OpOperand &aliasingWrite,
+                                     const DominanceInfo &domInfo) const;
+
+  /// Return true if there is a write that:
+  ///   1. Properly dominates aliasingReadOp.
+  ///   2. Is properly dominated by aliasingWriteOp.
+  ///   3. Clobbers the write that would be interfering with the read.
+  ///
+  /// Case discussion:
+  /// ================
+  /// Case 1: rootRead is produced by opToBufferize,
+  /// Case 2: rootWrite is produced by opToBufferize,
+  /// Common case:
+  ///   - aliasingReadOp is a read to an alias of rootRead.
+  ///   - aliasingWriteOp is an inplace write to an alias of rootWrite.
+  ///   - aliasingWriteOp dominates aliasingReadOp.
+  ///
+  /// ```
+  ///    // Either case 1:
+  ///    %rootRead = opToBufferize(%rootWrite)
+  ///    aliasingWriteOp(%aliasingWrite = alias(%rootWrite)) // inplace
+  ///     aliasingReadOp( %aliasingRead = alias(%rootRead))
+  /// ```
+  ///
+  /// ```
+  ///    // Or case 2:
+  ///    %rootWrite = opToBufferize(%rootRead)
+  ///    aliasingWriteOp(%aliasingWrite = alias(%rootWrite)) // inplace
+  ///     aliasingReadOp( %aliasingRead = alias(%rootRead))
+  /// ```
+  ///
+  /// Capture possible cases where `aliasingWriteOp(alias(%rootWrite))` has no
+  /// visible effect on `aliasingReadOp(alias(%rootRead))`.
+  bool isClobberedWriteBeforeRead(Operation *opToBufferize, Value rootRead,
+                                  Value rootWrite, OpOperand &aliasingRead,
+                                  OpOperand &aliasingWrite,
+                                  const DominanceInfo &domInfo) const;
+
+  /// EquivalenceClasses wants comparable elements because it uses std::set.
+  /// ValueWrapper wraps Value and uses pointer comparison on the defining op.
+  /// This is a poor man's comparison but it's not like UnionFind needs ordering
+  /// anyway ..
+  struct ValueWrapper {
+    ValueWrapper(Value val) : v(val) {}
+    operator Value() const { return v; }
+    bool operator<(const ValueWrapper &wrap) const {
+      return v.getImpl() < wrap.v.getImpl();
+    }
+    bool operator==(const ValueWrapper &wrap) const { return v == wrap.v; }
+    Value v;
+  };
+
+  /// Auxiliary structure to store all the values a given value aliases with.
+  /// These are the conservative cases that can further decompose into
+  /// "equivalent" buffer relationships.
+  DenseMap<Value, DenseSet<Value>> aliasInfo;
+
+  /// Auxiliary structure to store all the equivalent buffer classes.
+  llvm::EquivalenceClasses<ValueWrapper> equivalentInfo;
+};
+} // namespace
+
+BufferizationAliasInfo::BufferizationAliasInfo(FuncOp funcOp) {
+  for (auto bbArg : funcOp.getArguments()) {
+    if (!bbArg.getType().isa<TensorType>())
+      continue;
+    DenseSet<Value> selfSet;
+    selfSet.insert(bbArg);
+    aliasInfo.try_emplace(bbArg, selfSet);
+    equivalentInfo.insert(bbArg);
+  }
+  funcOp.walk([&](Operation *op) {
+    for (Value v : op->getResults()) {
+      if (!v.getType().isa<TensorType>())
+        continue;
+      assert(getInPlace(v) == InPlaceSpec::None &&
+             "unexpected inplace in analysis.");
+      DenseSet<Value> selfSet;
+      selfSet.insert(v);
+      aliasInfo.try_emplace(v, selfSet);
+      equivalentInfo.insert(v);
+    }
+  });
+}
+
+/// Return true if the buffer to which `operand` would bufferize aliases a
+/// buffer that is known to not be writeable. This implies that the matching
+/// OpResult cannot be bufferized inplace.
+bool BufferizationAliasInfo::aliasesNonWriteableBuffer(
+    OpOperand &operand) const {
+  LDBG("----Start aliasesNonWriteableBuffer\n");
+  LDBG("-------for operand #" << operand.getOperandNumber() << ": "
+                              << *(operand.getOwner()) << '\n');
+  for (Value v : getAliasInfoRef(operand.get())) {
+    LDBG("-----------examine: " << v << '\n');
+    if (auto bbArg = v.dyn_cast<BlockArgument>()) {
+      // Uses of function arguments that may be written-to can be skipped.
+      if (isa<FuncOp>(bbArg.getOwner()->getParentOp()) &&
+          getInPlace(bbArg) == InPlaceSpec::True) {
+        LDBG("-----------bbArg is writeable -> skip: " << bbArg << '\n');
+        continue;
+      }
+      // Conservatively dump any other block argument for now.
+      LDBG("-----------notWriteable: " << v << '\n');
+      return true;
+    }
+
+    if (Operation *op = v.getDefiningOp()) {
+      if (isa<ConstantOp>(op) || !hasKnownBufferizationAliasingBehavior(op)) {
+        LDBG("-----------notWriteable: " << v << '\n');
+        return true;
+      }
+    }
+  }
+  LDBG("---->operand is writeable\n");
+  return false;
+}
+
+/// Return true if the buffer to which `operand` would bufferize is equivalent
+/// to some use that would bufferize to a write to a buffer.
+bool BufferizationAliasInfo::aliasesInPlaceWrite(
+    SubTensorOp subTensorOp) const {
+  LDBG("----Start aliasesInPlaceWrite\n");
+  LDBG("-------for op: " << *subTensorOp.getOperation() << '\n');
+  for (Value v : getAliasInfoRef(subTensorOp.result())) {
+    for (auto &use : v.getUses()) {
+      if (bufferizesToMemoryWrite(use, InPlaceSpec::True)) {
+        LDBG("-----------wants to bufferize to inPlace write: "
+             << *use.getOwner() << '\n');
+        return true;
+      }
+    }
+  }
+  LDBG("----------->subtensor does not alias an inplace write");
+  return false;
+}
+
+/// Merge result's and operand's aliasing sets and iterates to a fixed point.
+void BufferizationAliasInfo::bufferizeInPlace(OpResult result,
+                                              OpOperand &operand,
+                                              BufferRelation bufferRelation) {
+  if (mergeAliases(result, operand.get()))
+    mergeAliasesToFixedPoint();
+  if (bufferRelation == BufferRelation::Equivalent)
+    equivalentInfo.unionSets(result, operand.get());
+}
+
+/// Return true if merging the alias sets of `rootWrite` and `rootRead` would
+/// result in a semantic change in the program (i.e. RAW violation).
+///
+/// This is the case when one can find an inplace write W among the aliases
+/// `rootWrite`, that may become an interference if W were to be bufferized
+/// inplace. A potential interference would be with respect to a read R among
+/// the aliases of `rootRead`.
+///
+/// Such a (W, R) pair is an interference to the inplace bufferization of
+/// rootWrite when R does not properly dominate W (i.e. W may come before R
+/// along some control-flow path).
+bool BufferizationAliasInfo::wouldCreateReadAfterWriteInterference(
+    Value rootWrite, Value rootRead, Operation *opToBufferize,
+    const DominanceInfo &domInfo) const {
+  LDBG("----Start wouldCreateReadAfterWriteInterference\n");
+
+  // Collect all the inplace write uses of some alias of `rootWrite`.
+  DenseSet<OpOperand *> usesWrite;
+  auto &aliasListWrite = getAliasInfoRef(rootWrite);
+  for (Value vWrite : aliasListWrite) {
+    for (auto &uWrite : vWrite.getUses()) {
+      if (!bufferizesToMemoryWrite(uWrite, InPlaceSpec::True))
+        continue;
+      usesWrite.insert(&uWrite);
+    }
+  }
+
+  // Collect all the read uses of some alias of `rootRead`.
+  DenseSet<OpOperand *> usesRead;
+  auto &aliasListRead = getAliasInfoRef(rootRead);
+  for (Value vRead : aliasListRead) {
+    for (auto &uRead : vRead.getUses()) {
+      if (!bufferizesToMemoryRead(uRead))
+        continue;
+      usesRead.insert(&uRead);
+    }
+  }
+
+  for (OpOperand *uRead : usesRead) {
+    Operation *aliasingReadOp = uRead->getOwner();
+    LDBG("----++++aliasRead  #" << uRead->getOperandNumber()
+                                << " in: " << *aliasingReadOp << '\n');
+    for (OpOperand *uWrite : usesWrite) {
+      // Don't consider self-use of the same operand.
+      // Uses within the same op is fine though.
+      if (uWrite == uRead)
+        continue;
+      Operation *aliasingWriteOp = uWrite->getOwner();
+      LDBG("----    aliasWrite #" << uWrite->getOperandNumber()
+                                  << " in: " << *aliasingWriteOp << '\n');
+      // If read and written value already alias, no interference would be added
+      // by bufferizing inplace.
+      if (getAliasInfoRef(uRead->get()).contains(uWrite->get()))
+        continue;
+      // If aliasingReadOp properly dominates aliasingWriteOp, the read cannot
+      // be affected by the write: there is no interference.
+      if (domInfo.properlyDominates(aliasingReadOp, aliasingWriteOp))
+        continue;
+      // At this point, aliasingWriteOp properly dominates aliasingReadOp or
+      // there is no clear dominance and we need to be conservative.
+      LDBG("---->found RaW interference\n");
+      LDBG("     Interfering  read (op #" << uRead->getOperandNumber()
+                                          << "): " << *aliasingReadOp << '\n');
+      LDBG("     Interfering write (op #" << uWrite->getOperandNumber()
+                                          << "): " << *aliasingWriteOp << '\n');
+      LDBG("         aliases rootRead: " << rootRead << '\n');
+      LDBG("         aliases rootWrite: " << rootWrite << '\n');
+      LDBG("---->opportunity to clobber RaW interference\n");
+      if (isClobberedWriteBeforeRead(opToBufferize, rootRead, rootWrite, *uRead,
+                                     *uWrite, domInfo)) {
+
+        LDBG("---->clobbered! -> skip\n");
+        continue;
+      }
+
+      LDBG("---->not clobbered -> found an interference\n");
+      return true;
+    }
+  }
+  LDBG("----No interference found\n");
+  return false;
+}
+
+/// Return true if we find any read to opOperand.get() or any of its aliases,
+/// that does not dominate opOperand.getOwner().
+bool BufferizationAliasInfo::existsNonDominatingRead(
+    OpOperand &opOperand, const DominanceInfo &domInfo) const {
+  LDBG("----Start existsNonDominatingRead\n");
+  Operation *op = opOperand.getOwner();
+  for (Value alias : getAliasInfoRef(opOperand.get())) {
+    for (OpOperand &wantReadUse : alias.getUses()) {
+      LDBG("--------current operand #" << wantReadUse.getOperandNumber() << ": "
+                                       << *(wantReadUse.getOwner()) << '\n');
+      if (!bufferizesToMemoryRead(wantReadUse)) {
+        LDBG("------------not a read -> skip\n");
+        continue;
+      }
+      if (&wantReadUse == &opOperand) {
+        LDBG("------------self-read is not an interference -> skip\n");
+        continue;
+      }
+      if (domInfo.properlyDominates(wantReadUse.getOwner(), op)) {
+        LDBG("------------read properly dominates -> skip\n");
+        continue;
+      }
+      LDBG("----found interfering read of " << wantReadUse.get() << '\n');
+      return true;
+    }
+  }
+  return false;
+}
+
+/// Return true if the source of a `subTensorInsertOp` bufferizes to an
+/// equivalent SubTensorOp.
+bool BufferizationAliasInfo::isSourceEquivalentToAMatchingSubTensorOp(
+    SubTensorInsertOp subTensorInsertOp) const {
+  auto leaderIt = equivalentInfo.findLeader(subTensorInsertOp.source());
+  for (auto mit = leaderIt, meit = equivalentInfo.member_end(); mit != meit;
+       ++mit) {
+    if (areEquivalentSubTensorOps(
+            dyn_cast_or_null<SubTensorOp>(mit->v.getDefiningOp()),
+            subTensorInsertOp))
+      return true;
+  }
+  return false;
+}
+
+void BufferizationAliasInfo::print(raw_ostream &os) const {
+  os << "\n/========================== AliasInfo "
+        "==========================\n";
+  for (auto it : aliasInfo) {
+    os << "|\n| -- source: " << it.getFirst() << '\n';
+    for (auto v : it.getSecond())
+      os << "| ---- target: " << v << '\n';
+  }
+  os << "|\n\\====================== End AliasInfo "
+        "======================\n\n";
+  os << "\n/********************* Equivalent Buffers *********************\n";
+  for (auto it = equivalentInfo.begin(), eit = equivalentInfo.end(); it != eit;
+       ++it) {
+    if (!it->isLeader())
+      continue;
+    Value leader = it->getData();
+    os << "|\n| -- leader: " << leader << '\n';
+    for (auto mit = equivalentInfo.member_begin(it),
+              meit = equivalentInfo.member_end();
+         mit != meit; ++mit) {
+      Value v = static_cast<Value>(*mit);
+      os << "| ---- equivalent member: " << v << '\n';
+    }
+  }
+  os << "|\n\\***************** End Equivalent Buffers *****************\n\n";
+}
+
+DenseSet<Value> &BufferizationAliasInfo::getAliasInfoRef(Value v) {
+  auto it = aliasInfo.find(v);
+  if (it == aliasInfo.end())
+    llvm_unreachable("Missing alias");
+  return it->getSecond();
+}
+
+/// Union all the aliasing sets of all aliases of v1 and v2.
+bool BufferizationAliasInfo::mergeAliases(Value v1, Value v2) {
+  // Avoid invalidation of iterators by pre unioning the aliases for v1 and v2.
+  bool changed = set_union(getAliasInfoRef(v1), getAliasInfoRef(v2)) ||
+                 set_union(getAliasInfoRef(v2), getAliasInfoRef(v1));
+  for (auto v : getAliasInfoRef(v1))
+    if (v != v1)
+      changed |= set_union(getAliasInfoRef(v), getAliasInfoRef(v2));
+  for (auto v : getAliasInfoRef(v2))
+    if (v != v2)
+      changed |= set_union(getAliasInfoRef(v), getAliasInfoRef(v1));
+  return changed;
+}
+
+/// Iteratively merge alias sets until a fixed-point.
+void BufferizationAliasInfo::mergeAliasesToFixedPoint() {
+  while (true) {
+    bool changed = false;
+    for (auto it : aliasInfo)
+      for (auto v : it.getSecond())
+        changed |= mergeAliases(it.getFirst(), v);
+    if (!changed)
+      break;
+  }
+}
+
+/// This is one particular type of relationship between ops on tensors that
+/// reduce to an equivalence on buffers. This should be generalized and exposed
+/// as interfaces on the proper types.
+bool BufferizationAliasInfo::areEquivalentSubTensorOps(
+    SubTensorOp st, SubTensorInsertOp sti) const {
+  if (!st || !sti)
+    return false;
+  if (!equivalentInfo.isEquivalent(st.source(), sti.dest()))
+    return false;
+  if (!sameOffsetsSizesAndStrides(st, sti, isEqualConstantIntOrValue))
+    return false;
+  if (!equivalentInfo.isEquivalent(st.result(), sti.source()))
+    return false;
+  return true;
+}
+
+/// Return true if there is a `candidateOp` that would write to memory after
+/// bufferization and such that:
+///   1. The written buffer is equivalent to either `aliasingRead` or
+///      `aliasingWrite` under the inPlace bufferization decisions taken
+///      so far.
+///   2. `aliasingWrite` properly dominates `candidateOp`.
+///   3. `candidateOp` properly dominates `aliasingReadOp`.
+// TODO: richer clobbering analysis with container-containee relationship
+// instead of equivalence.
+bool BufferizationAliasInfo::existsInterleavedValueClobber(
+    OpOperand &aliasingRead, OpOperand &aliasingWrite,
+    const DominanceInfo &domInfo) const {
+  Operation *aliasingReadOp = aliasingRead.getOwner();
+  Operation *aliasingWriteOp = aliasingWrite.getOwner();
+  assert(!domInfo.properlyDominates(aliasingReadOp, aliasingWriteOp) &&
+         "Unexpected aliasingReadOp properly dominates aliasingWriteOp");
+
+  for (Value valueToClobber : {aliasingRead.get(), aliasingWrite.get()}) {
+    auto leaderIt = equivalentInfo.findLeader(valueToClobber);
+    for (auto mit = leaderIt, meit = equivalentInfo.member_end(); mit != meit;
+         ++mit) {
+      /// Note: the "would write to memory after bufferization" condition is
+      /// verified by `candidateOp` since it would produce a value that
+      /// bufferizes to an equivalent buffer.
+      Operation *candidateOp = mit->v.getDefiningOp();
+      if (!candidateOp)
+        continue;
+      LDBG("---->clobbering candidate: " << *candidateOp << '\n');
+      if (domInfo.properlyDominates(aliasingWriteOp, candidateOp) &&
+          domInfo.properlyDominates(candidateOp, aliasingReadOp))
+        return true;
+    }
+  }
+  return false;
+}
+
+/// Return true if there is a write that:
+///   1. Properly dominates aliasingReadOp.
+///   2. Is properly dominated by aliasingWriteOp.
+///   3. Clobbers the write that would be interfering with the read.
+///
+bool BufferizationAliasInfo::isClobberedWriteBeforeRead(
+    Operation *opToBufferize, Value rootRead, Value rootWrite,
+    OpOperand &aliasingRead, OpOperand &aliasingWrite,
+    const DominanceInfo &domInfo) const {
+  Operation *aliasingReadOp = aliasingRead.getOwner();
+  Operation *aliasingWriteOp = aliasingWrite.getOwner();
+  assert(!domInfo.properlyDominates(aliasingReadOp, aliasingWriteOp) &&
+         "Unexpected aliasingReadOp properly dominates aliasingWriteOp");
+
+  bool opProducesRootRead =
+      rootRead.isa<OpResult>() && rootRead.getDefiningOp() == opToBufferize;
+  bool opProducesRootWrite =
+      rootWrite.isa<OpResult>() && rootWrite.getDefiningOp() == opToBufferize;
+  assert((opProducesRootRead || opProducesRootWrite) &&
+         "Expected rootRead or rootWrite to be produced by opToBufferize");
+
+  // Bail if the write does not dominate the read: it may clobber but only on
+  // a strict subset of paths, which is not enough for safety.
+  if (!domInfo.dominates(aliasingWriteOp, aliasingReadOp)) {
+    LDBG("---->no clobbering: write does not dominate read\n");
+    return false;
+  }
+
+  // The case `opToBufferize` isa SubTensorOp is important enough that we look
+  // for it specifically. The key information to discover is whether the
+  // aliasing read or write come from a matching SubTensorInsertOp.
+  // Such a pattern is introduced by tiling and is the key inplace condition
+  // not to miss.
+  if (auto subTensorOp = dyn_cast<SubTensorOp>(opToBufferize)) {
+    if (auto subTensorInsertOp = dyn_cast<SubTensorInsertOp>(aliasingReadOp)) {
+      // %1 = subtensor %0[%offset_sizes_and_strides_1]
+      //
+      // ... // 0 or more of inplace compute that reduces to: %X is an
+      //     // aliasingWrite equivalent to %1.
+      // %W = inplace_write(%1)
+      //
+      // // aliasingRead %Y in subtensor_insert
+      // ... = subtensor_insert %W into %R[%offset_sizes_and_strides_1]
+      if (aliasingRead.get() == subTensorInsertOp.dest() &&
+          // TODO: This is currently too restrictive and misses clobberings.
+          // When available, use container-containee analysis: the condition
+          // should be that the `aliasingWrite` is contained within
+          // `subTensorInsertOp.source()`.
+          equivalentInfo.isEquivalent(aliasingWrite.get(),
+                                      subTensorInsertOp.source()) &&
+          areEquivalentSubTensorOps(subTensorOp, subTensorInsertOp)) {
+        LDBG("---->clobbering matching subtensor/subtensor_insert\n");
+        return true;
+      }
+      // %1 = subtensor %0[%offset_sizes_and_strides_1]
+      //
+      // ... // bunch of inplace ops that reduce to %X, equivalent to %1.
+      // %X = inplace_write(%1)
+      //
+      // // aliasingRead %X in subtensor_insert
+      // // aliasingWrite %Y in subtensor_insert
+      // ... = subtensor_insert %X into %Y[%offset_sizes_and_strides_1]
+      if (aliasingReadOp == aliasingWriteOp) {
+        assert(aliasingRead.get() == subTensorInsertOp.source() &&
+               "expected read to source of subtensor_insert");
+        assert(aliasingWrite.get() == subTensorInsertOp.dest() &&
+               "expected write to dest of subtensor_insert");
+        if (areEquivalentSubTensorOps(subTensorOp, subTensorInsertOp)) {
+          LDBG("---->clobbering matching subtensor/subtensor_insert\n");
+          return true;
         }
-    llvm::errs() << "NO VALUE FOR KEY: " << key << "\n";
-    return Value();
       }
-  return bvm.lookup(key);
+    }
+  }
+
+  // General case: look for a properly interleaved clobber of either exactly
+  // `aliasingRead` or `aliasingWrite`.
+  // TODO: Relax this to inclusion instead of double inclusion (a.k.a
+  // equivalence). We will need to compute container-containee relationship.
+  return existsInterleavedValueClobber(aliasingRead, aliasingWrite, domInfo);
 }
 
 //===----------------------------------------------------------------------===//
 // Bufferization-specific MemRefType support.
 //===----------------------------------------------------------------------===//
 
-/// Return a contiguous MemRefType (i.e. with canonical/empty layout map) with
-/// the same shape as `shapedType` and specified `layout` and `addressSpace`.
+/// Return a contiguous MemRefType (i.e. with canonical/empty layout map)
+/// with the same shape as `shapedType` and specified `layout` and
+/// `addressSpace`.
 static MemRefType getContiguousMemRefType(ShapedType shapedType,
                                           ArrayRef<AffineMap> layout = {},
                                           unsigned addressSpace = 0) {
   if (RankedTensorType tensorType = shapedType.dyn_cast<RankedTensorType>())
     return MemRefType::get(tensorType.getShape(), tensorType.getElementType(),
                            layout, addressSpace);
   MemRefType memrefType = shapedType.cast<MemRefType>();
   return MemRefType::get(memrefType.getShape(), memrefType.getElementType(),
                          layout, addressSpace);
 }
 
-/// Return a contiguous MemRefType (i.e. with canonical/empty layout map) with
-/// the same shape as `shapedType` and specified `layout` and `addressSpace` or
-/// an UnrankedMemRefType otherwise.
+/// Return a contiguous MemRefType (i.e. with canonical/empty layout map)
+/// with the same shape as `shapedType` and specified `layout` and
+/// `addressSpace` or an UnrankedMemRefType otherwise.
 static Type getContiguousOrUnrankedMemRefType(Type type,
                                               ArrayRef<AffineMap> layout = {},
                                               unsigned addressSpace = 0) {
   if (type.isa<RankedTensorType, MemRefType>())
     return getContiguousMemRefType(type.cast<ShapedType>(), layout,
                                    addressSpace);
   assert(layout.empty() && "expected empty layout with UnrankedMemRefType");
   return UnrankedMemRefType::get(getElementTypeOrSelf(type), addressSpace);
return MemRefType::get(tensorType.getShape(), tensorType.getElementType(),
                          stridedLayout, addressSpace);
 }
 
 //===----------------------------------------------------------------------===//
 // Bufferization-specific scoped alloc/dealloc insertion support.
 //===----------------------------------------------------------------------===//
 
 /// Create an Allocop/DeAllocOp pair, where the AllocOp is after
-/// `shapedValue.getDefiningOp` (or at the top of the block in case of a bbArg)
-/// and the DeallocOp is at the end of the block.
-static Value createNewAllocDeallocPairForShapedValue(
-    OpBuilder &b, Location loc, Value shapedValue,
-    SmallVector<Value, 4> dynOperands = {}) {
+/// `shapedValue.getDefiningOp` (or at the top of the block in case of a
+/// bbArg) and the DeallocOp is at the end of the block.
+static Value createNewAllocDeallocPairForShapedValue(OpBuilder &b, Location loc,
+                                                     Value shapedValue) {
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
 
   // TODO: non-zero address space.
   // TODO: layout information if relevant.
   // Cannot allocate an unranked memref so just always go for the contiguous
   // form.
   MemRefType allocMemRefType =
       getContiguousMemRefType(shapedValue.getType().cast<ShapedType>());
   assert(shapedValue.getType().isa<ShapedType>());
   MemRefType memRefType = shapedValue.getType().dyn_cast<MemRefType>();
   memRefType = memRefType ? memRefType : allocMemRefType;
 
   if (auto bbArg = shapedValue.dyn_cast<BlockArgument>()) {
     b.setInsertionPointToStart(bbArg.getOwner());
     loc = bbArg.getOwner()->getParentOp()->getLoc();
   } else {
     b.setInsertionPointAfter(shapedValue.getDefiningOp());
     loc = shapedValue.getDefiningOp()->getLoc();
   }
 
-  // If the dynOperands are not passed explicity, copmpute them.
-  // This circumvents currently missing dim(init_tensor) canonicalizations.
-  // TODO: dim(init_tensor) canonicalization.
-  if (dynOperands.empty()) {
-    for (auto dim : llvm::enumerate(memRefType.getShape()))
-      if (dim.value() == ShapedType::kDynamicSize)
-        dynOperands.push_back(
-            b.create<memref::DimOp>(loc, shapedValue, dim.index()));
-  }
+  // Compute the dynamic part of the shape.
+  SmallVector<Value> dynShape;
+  for (auto dim : enumerate(memRefType.getShape()))
+      dynShape.push_back(
 
-  Value allocated =
-      b.create<memref::AllocOp>(loc, allocMemRefType, dynOperands);
+  Value allocated = b.create<memref::AllocOp>(loc, allocMemRefType, dynShape);
   Value casted = allocated;
   if (memRefType != allocMemRefType)
     casted = b.create<memref::CastOp>(loc, memRefType, allocated);
   b.setInsertionPoint(allocated.getParentBlock()->getTerminator());
   b.create<memref::DeallocOp>(loc, allocated);
   return casted;
 }
 
 //===----------------------------------------------------------------------===//
 // Bufferization as simple BlockAndValueMapping rewrites.
 //===----------------------------------------------------------------------===//
 
 /// Helper function for LinalgOp bufferization.
-/// Operate on mixed tensor + buffer Linalg ops for progressive bufferization.
-/// Allocate the output buffers for the remaining tensor output operands of
-/// the Linalg op. If the tensor is an "init" tensor (i.e. its value is
-/// actually used in the payload region), we additionally copy the original
-/// value into the newly allocated buffer.
+/// Examines each result and determines whether it bufferizes inplace on an
+/// operand.
+/// If the opResult bufferizes inplace, just reuse the existing buffer.
+/// Otherwise allocate a new buffer to hold the result.
+/// When allocating a new buffer, analyze whether `op` want to read form that
+/// buffer. In such a case, insert a copy to ensure the newly allocated buffer
+/// is properly initialiazed.
 static LogicalResult
 allocateBuffersForResults(OpBuilder &b, Location loc, LinalgOp op,
                           SmallVectorImpl<Value> &resultBuffers,
                           BlockAndValueMapping &bvm) {
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
 
-  // Lazily compute loopRanges.
-  SmallVector<Range, 4> loopRanges;
-
-  // Linalg invariant: output tensors and result match 1-1.
-  assert(op.getOutputTensorOperands().size() == op->getNumResults());
+  // TODO: provide the proper interface to iterate on OpResults and get the
+  // matching OpOperands.
   for (OpOperand *opOperand : op.getOutputOperands()) {
     Value output = opOperand->get();
-    if (output.getType().isa<MemRefType>()) {
-      resultBuffers.push_back(output);
-      continue;
-    }
+    assert(output.getType().isa<TensorType>() && "expected tensor type");
 
     // If output tensor is marked inPlace, just use the buffer.
-    // The following uses internal knowledge of the position of tied operand /
-    // results.
-    OpResult tiedResult = getMatchingOpResult(op, *opOperand);
-    if (getInPlace(tiedResult) == InPlaceSpec::True) {
+    // The following uses internal knowledge of the position of inplaceable
+    // operand / results.
+    OpResult opResult = getInplaceableOpResult(*opOperand);
+    if (getInPlace(opResult) == InPlaceSpec::True) {
       Value v = lookup(bvm, output);
       if (!v)
         return failure();
       resultBuffers.push_back(v);
       continue;
     }
 
+    // Otherwise, `op` is not inplaceable and we need to allocate its result.
     Value dimTensor = bvm.lookupOrDefault(output);
     Value alloc = createNewAllocDeallocPairForShapedValue(b, loc, dimTensor);
     b.setInsertionPointAfter(alloc.getDefiningOp());
     resultBuffers.push_back(alloc);
 
     // Additionally, if the output buffer is used, clone its value for now.
     if (op.payloadUsesValueFromOperand(opOperand)) {
-      Value v = lookup(bvm, output);
-      if (!v)
-        return failure();
+      if (Value v = lookup(bvm, output))
         b.create<CopyOp>(loc, v, alloc);
+      else
+        return failure();
     }
   }
+
   if (op->getNumResults())
     map(bvm, op->getResults(), resultBuffers);
 
   return success();
 }
 
-static void finalizeBufferAllocation(OpBuilder &b, LinalgOp op,
-                                     ValueRange inputs, ValueRange outputs,
-                                     BlockAndValueMapping &bvm) {
-  SmallVector<Value, 8> newOperands = inputs;
-  newOperands.append(outputs.begin(), outputs.end());
-  auto otherOperands = op.getAssumedNonShapedOperands();
-  newOperands.append(otherOperands.begin(), otherOperands.end());
-  Location loc = op.getLoc();
-  op.clone(b, loc, /*resultTypes=*/TypeRange{}, newOperands);
-
-  // Replace the results of the old op with the new output buffers.
-  if (op->getNumResults())
-    map(bvm, op->getResults(), outputs);
-  if (!op.hasTensorSemantics())
-    op->erase();
-}
-
-/// Generic conversion for any LinalgOp.
-/// Operate on mixed tensor + buffer Linalg ops for progressive bufferization.
+/// Generic conversion for any LinalgOp on tensors.
 static LogicalResult bufferize(OpBuilder &b, LinalgOp op,
-                               BlockAndValueMapping &bvm) {
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
 
-  if (op.hasBufferSemantics())
+  // Ensure op has only tensors. Allow mixed tensor-buffer mode on a per-need
+  // basis.
+  if (!op.hasTensorSemantics())
     return failure();
 
-  LLVM_DEBUG(DBGS() << "bufferize: " << *op << "\n");
+  LDBG("bufferize: " << *op << '\n');
 
   b.setInsertionPoint(op);
   Location loc = op.getLoc();
-  SmallVector<Value> newInputs;
-  newInputs.reserve(op.getNumInputs());
+  SmallVector<Value> newInputBuffers;
+  newInputBuffers.reserve(op.getNumInputs());
   for (OpOperand *opOperand : op.getInputOperands()) {
     if (op.isScalar(opOperand)) {
-      newInputs.push_back(opOperand->get());
+      newInputBuffers.push_back(opOperand->get());
       continue;
     }
-    newInputs.push_back(lookup(bvm, opOperand->get()));
-    if (!newInputs.back())
+    newInputBuffers.push_back(lookup(bvm, opOperand->get()));
+    if (!newInputBuffers.back())
       return failure();
   }
   SmallVector<Value> newOutputBuffers;
+  // Try to allocate new buffers depending on op's inplace semantics.
   if (failed(allocateBuffersForResults(b, loc, op, newOutputBuffers, bvm)))
     return failure();
-  finalizeBufferAllocation(b, op, newInputs, newOutputBuffers, bvm);
+
+  // Clone the newly bufferized op.
+  SmallVector<Value> newOperands = newInputBuffers;
+  newOperands.append(newOutputBuffers.begin(), newOutputBuffers.end());
+  auto otherOperands = op.getAssumedNonShapedOperands();
+  newOperands.append(otherOperands.begin(), otherOperands.end());
+  op.clone(b, loc, /*resultTypes=*/TypeRange{}, newOperands);
+
+  // Replace the results of the old op with the new output buffers.
+  if (op->getNumResults())
+    map(bvm, op->getResults(), newOutputBuffers);
+
+  // The original op will be DCE'd away later.
+
   return success();
 }
 
-/// DimOp tensor operand is modified inplace. This allows leaving dead tensors
-/// behind that will get DCE'd.
+/// DimOp tensor operand is modified inplace. This allows leaving dead
+/// tensors behind that will get DCE'd.
 static LogicalResult bufferize(OpBuilder &b, memref::DimOp dimOp,
-                               BlockAndValueMapping &bvm) {
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
   if (dimOp.memrefOrTensor().getType().isa<RankedTensorType>()) {
     Value v = lookup(bvm, dimOp.memrefOrTensor());
     if (!v)
       return failure();
     dimOp.memrefOrTensorMutable().assign(v);
   }
   return success();
 }
 
 /// FuncOp always creates TensorToMemRef ops.
 static LogicalResult bufferize(OpBuilder &b, FuncOp funcOp,
-                               BlockAndValueMapping &bvm) {
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
   b.setInsertionPointToStart(&funcOp.body().front());
   for (auto bbArg : funcOp.getArguments()) {
     auto tensorType = bbArg.getType().dyn_cast<TensorType>();
     if (!tensorType)
       continue;
     auto rankedTensorType = tensorType.dyn_cast<RankedTensorType>();
     // Cast the tensor to the most dynamic buffer possible. Further
     // canonicalizations will clean up.
     Type memRefType = rankedTensorType
                           ? getDynamicMemRefType(rankedTensorType)
                           : getContiguousOrUnrankedMemRefType(tensorType);
     Value tensorToMemref =
         b.create<memref::BufferCastOp>(funcOp.getLoc(), memRefType, bbArg);
     map(bvm, bbArg, tensorToMemref);
   }
   return success();
 }
 
 /// ReturnOp always creates memref::TensorLoadOp.
 static LogicalResult bufferize(OpBuilder &b, ReturnOp returnOp,
-                               BlockAndValueMapping &bvm) {
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
   b.setInsertionPoint(returnOp);
 
   assert(isa<FuncOp>(returnOp->getParentOp()) &&
          "only support FuncOp parent for ReturnOp");
   for (OpOperand &operand : returnOp->getOpOperands()) {
     auto tensorType = operand.get().getType().dyn_cast<TensorType>();
     if (!tensorType)
       continue;
     Value v = lookup(bvm, operand.get());
     if (!v)
       return failure();
     operand.set(b.create<memref::TensorLoadOp>(returnOp.getLoc(), v));
   }
   return success();
 }
 
 /// Bufferize SubTensorOp to subview with optional alloc + copy depending on
 /// whether or not it is marked inplaceable.
-/// Note that `getMatchingOpResult` on a SubTensorOp always returns null.
-/// As consequence a SubTensorOp always alloc + copy when taken in isolation.
+/// Note that `getInplaceableOpResult` on a SubTensorOp always returns null.
+/// As consequence a SubTensorOp always alloc + copy when taken in
+/// isolation.
 static LogicalResult bufferize(OpBuilder &b, SubTensorOp subTensorOp,
-                               BlockAndValueMapping &bvm) {
-  LLVM_DEBUG(DBGS() << "bufferize: " << *subTensorOp << "\n");
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
+  LDBG("bufferize: " << *subTensorOp << '\n');
 
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
   b.setInsertionPoint(subTensorOp);
 
   Location loc = subTensorOp.getLoc();
   // Bail if source was not bufferized.
   Value srcMemref = lookup(bvm, subTensorOp.source());
static LogicalResult bufferize(OpBuilder &b, SubTensorOp subTensorOp,
   }
 
   map(bvm, subTensorOp.result(), subView);
   return success();
 }
 
 static LogicalResult bufferize(OpBuilder &b,
                                SubTensorInsertOp subTensorInsertOp,
-                               BlockAndValueMapping &bvm) {
-  LLVM_DEBUG(DBGS() << "bufferize: " << *subTensorInsertOp << "\n");
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
+  LDBG("bufferize: " << *subTensorInsertOp << '\n');
 
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
   b.setInsertionPoint(subTensorInsertOp);
   Location loc = subTensorInsertOp.getLoc();
 
   Value dstMemref = lookup(bvm, subTensorInsertOp.dest());
   if (!dstMemref)
     return failure();
   auto inPlace = getInPlace(subTensorInsertOp->getResult(0));
   if (inPlace != InPlaceSpec::True) {
-    // Since subtensor_insert arise from tiling and introducing loops, this case
-    // is generally a deal breaker. When used with loops, this ends up cloning
-    // the whole tensor on every single iteration and is a symptom of a
-    // catastrophically bad scheduling decision.
+    // Since subtensor_insert arise from tiling and introducing loops, this
+    // case is generally a deal breaker. When used with loops, this ends up
+    // cloning the whole tensor on every single iteration and is a symptom
+    // of a catastrophically bad scheduling decision.
     // TODO: be very loud about it or even consider failing the pass.
     Value newDstMemref = createNewAllocDeallocPairForShapedValue(
         b, loc, subTensorInsertOp.result());
     b.setInsertionPointAfter(newDstMemref.getDefiningOp());
     b.create<CopyOp>(subTensorInsertOp.getLoc(), dstMemref, newDstMemref);
     dstMemref = newDstMemref;
   }
   auto dstMemrefType = dstMemref.getType().cast<MemRefType>();
auto subviewMemRefType =
           .cast<MemRefType>();
 
   // A copy of the source buffer is needed if either:
   //   - The producer of `source` is not inplace. This is the case where a
   //     subtensor is computed out of place into the inplace full tensor.
   //   - The result is not inplace. This is the case where the whole tensor is
   //     cloned and the clone needs to be updated.
   Value source = subTensorInsertOp.source();
-  InPlaceSpec inPlaceProducer = InPlaceSpec::None;
-  if (auto opResult = source.dyn_cast<OpResult>())
-    inPlaceProducer = getInPlace(opResult);
-  else
-    inPlaceProducer = getInPlace(source.cast<BlockArgument>());
-  if (inPlaceProducer != InPlaceSpec::True) {
-    LLVM_DEBUG(DBGS() << "subtensor_insert needs extra source copy: " << source
-                      << " -> copy\n");
+  if (!aliasInfo.isSourceEquivalentToAMatchingSubTensorOp(subTensorInsertOp) ||
+      inPlace != InPlaceSpec::True) {
+    LDBG("subtensor_insert needs extra source copy: "
+         << subTensorInsertOp.source() << " -> copy\n");
     // Take a subview of the dst.
     Value subView = b.create<memref::SubViewOp>(
         loc, subviewMemRefType, dstMemref, subTensorInsertOp.getMixedOffsets(),
         subTensorInsertOp.getMixedSizes(), subTensorInsertOp.getMixedStrides());
     b.create<CopyOp>(subTensorInsertOp.getLoc(), srcMemref, subView);
   }
 
   map(bvm, subTensorInsertOp.result(), dstMemref);
 
   return success();
 }
 
 static LogicalResult bufferize(OpBuilder &b, VectorTransferOpInterface op,
-                               BlockAndValueMapping &bvm) {
+                               BlockAndValueMapping &bvm,
+                               const BufferizationAliasInfo &aliasInfo) {
   // Take a guard before anything else.
   OpBuilder::InsertionGuard g(b);
   b.setInsertionPoint(op);
   Location loc = op.getLoc();
 
   if (op.getShapedType().isa<MemRefType>())
     return failure();
 
-  LLVM_DEBUG(DBGS() << "bufferize: " << *op << "\n");
+  LDBG("bufferize: " << *op << '\n');
 
-  /// transfer_read from buffer always reads from the bufferized op.source().
+  /// transfer_read from buffer always reads from the bufferized
+  /// op.source().
   if (auto readOp = dyn_cast<vector::TransferReadOp>(op.getOperation())) {
     Value v = lookup(bvm, op.source());
     if (!v)
       return failure();
     readOp.sourceMutable().assign(v);
     return success();
   }
 
b.create<vector::TransferWriteOp>(
       writeOp.in_bounds() ? *writeOp.in_bounds() : ArrayAttr());
 
   map(bvm, op->getResult(0), newInputBuffer);
 
   return success();
 }
 
 //===----------------------------------------------------------------------===//
-// Functions and calls bufferization support.
+// Bufferization analyses.
 //===----------------------------------------------------------------------===//
 
-/// Determine whether any subsequent read of the tensor `opOperand` may occur.
-/// For now, this assumes any use is a read. If any use of the tensor does not
-/// properly dominate `opOperand.getOwner()`, then the tensor cannot be
-/// bufferized inPlace.
-// TODO: For now, this assumes any use is a read. Refine this.
-bool hasInterferingTensorRead(OpOperand &opOperand,
+///
+/// Rationale for bufferizing `%1 = subtensor %0[...]` inplace.
+/// ===========================================================
+///
+/// When bufferized out of place, a SubTensorOp lowers to alloc + copy. This
+/// cannot change the flow of information for either the source or the
+/// result buffers.
+///
+/// When bufferized inplace, a SubTensorOp does not by itself create any read or
+/// write from memory. Instead, it has the effect of merging the alias sets of
+/// the source and the result buffers.
+///
+/// An analysis is required to ensure inplace bufferization would not result in
+/// RaW dependence violations.
+static void bufferizableInPlaceAnalysis(SubTensorOp subTensorOp,
+                                        BufferizationAliasInfo &aliasInfo,
                                         const DominanceInfo &domInfo) {
-  if (!opOperand.get().getType().isa<RankedTensorType>())
-    return false;
-  for (auto &use : opOperand.get().getUses()) {
-    Operation *user = use.getOwner();
-    // If properly dominate, there  is a clear sequence point and we can dismiss
-    // read.
-    if (domInfo.properlyDominates(user, opOperand.getOwner()))
-      continue;
-    // Otherwise, we need to analyze self-dependencies, for now just let it go.
-    // TODO: proper self-dependence analysis.
-    if (domInfo.dominates(user, opOperand.getOwner()))
-      continue;
-    if (user == opOperand.getOwner() &&
-        use.getOperandNumber() == opOperand.getOperandNumber())
-      continue;
-    LLVM_DEBUG(DBGS() << "found interfering read operand #"
-                      << opOperand.getOperandNumber()
-                      << " in op: " << *opOperand.getOwner() << "\n");
-    return true;
-  }
-  LLVM_DEBUG(DBGS() << "no interfering read\n");
-  return false;
-}
+  LDBG('\n');
+  LDBG("Try to bufferize subtensor inplace: " << *subTensorOp << '\n');
 
-/// Return false if either:
-/// 1. `opOperand` is produced by a constant op. For now this is assumed to be
-///    bufferized to a GlobalMemrefOp that cannot be written. Generalize in the
-///    future.
-/// 2.`opOperand` is a BlockArgument of a FuncOp that is not known to be
-///    bufferizable inplace.
-/// Return true otherwise.
-static bool bufferizeToWriteable(OpOperand &opOperand) {
-  // Constant tensors are deemed not bufferizable for now.
-  if (auto constantOp =
-          dyn_cast_or_null<ConstantOp>(opOperand.get().getDefiningOp()))
-    return !constantOp.getResult().getType().isa<RankedTensorType>();
-  if (auto bbArg = opOperand.get().dyn_cast<BlockArgument>()) {
-    // Uses of function arguments that may not be written-to need to be copied.
-    // If the function argument itself is not inplaceable, early return false.
-    // If is is inplaceable, interfering tensor read need to be checked.
-    //
-    // TODO: better propagate the fact that we want a single clone inside the
-    // function. Atm every user that wants to write inplace will create its own
-    // alloc, irrespective of whether or not interfering reads occur.
-    if (isa<FuncOp>(bbArg.getOwner()->getParentOp())) {
-      if (getInPlace(bbArg) != InPlaceSpec::True)
-        return false;
-    } else {
-      // Conservatively dump any other block argument for now.
-      return false;
-    }
-  }
-  return true;
+  // If `subTensorOp` were to be bufferized inplace, it cannot end up
+  // aliasing a write into a non-writeable buffer.
+  bool wouldCreateAliasingWriteToNonWriteableBuffer =
+      aliasInfo.aliasesInPlaceWrite(subTensorOp) &&
+      aliasInfo.aliasesNonWriteableBuffer(subTensorOp->getOpOperand(0));
+
+  if (wouldCreateAliasingWriteToNonWriteableBuffer)
+    LDBG("->the corresponding buffer is not writeable\n");
+  LDBG("->bufferizes to writeable inplace buffer\n");
+
+  // In any of subTensorOp.result's aliases, can we find 2 such that we hit
+  // an interfering write?
+  Value s = subTensorOp.source(), r = subTensorOp.result();
+  bool foundInterference = wouldCreateAliasingWriteToNonWriteableBuffer ||
+                           // Do not consider (s, s) and (r, r) as all the
+                           // aliasings already exist by construction; we are
+                           // interested in new interfering aliases only.
+                           aliasInfo.wouldCreateReadAfterWriteInterference(
+                               s, r, subTensorOp, domInfo) ||
+                           aliasInfo.wouldCreateReadAfterWriteInterference(
+                               r, s, subTensorOp, domInfo);
+  if (foundInterference) {
+    setInPlaceOpResult(subTensorOp->getResult(0), InPlaceSpec::False);
+    setInPlaceOpResult(subTensorOp->getResult(0), InPlaceSpec::True);
+    aliasInfo.bufferizeInPlace(subTensorOp->getResult(0),
+                               subTensorOp->getOpOperand(0));
+  }
+  LDBG("Done bufferizing subtensor\n");
 }
 
-/// Return false if either:
-/// 1. `opOperand` is produced by a constant op. For now this is assumed to be
-///    bufferized to a GlobalMemrefOp that cannot be written. Generalize in the
-///    future.
-/// 2.`opOperand` is a BlockArgument of a FuncOp that is not known to be
-///    bufferizable inplace.
-/// 3.`opOperand` has an interfering tensor read.
-/// Return true otherwise.
-static bool isBufferizableInPlace(OpOperand &opOperand,
+/// Analyze the (opOperand, result) pair to determine whether the result can
+/// be bufferized inPlace. If successful, InPlaceSpec::True is set for
+/// `result`. Otherwise, InPlaceSpec::False is set for `result`.
+static void bufferizableInPlaceAnalysis(OpOperand &operand, OpResult result,
+                                        BufferizationAliasInfo &aliasInfo,
                                         const DominanceInfo &domInfo) {
-  return bufferizeToWriteable(opOperand) &&
-         !hasInterferingTensorRead(opOperand, domInfo);
-}
+  Operation *op = result.getDefiningOp();
+  assert(result && !isa<SubTensorOp>(op) &&
+         "expected OpResult not coming from a SubTensorOp");
+
+  int64_t operandNumber = operand.getOperandNumber();
+  int64_t resultNumber = result.getResultNumber();
+  LDBG('\n');
+  LDBG("Try to bufferize inplace result #" << resultNumber << " (operand #"
+                                           << operandNumber << ") in " << result
+                                           << '\n');
+
+  // `result` must bufferize to a writeable buffer to be a candidate.
+  // This means the use->def chain not backpropagate to a function that is
+  // not inplaceable or to a constant op to be considered.
+  bool wouldCreateAliasingWriteToNonWriteableBuffer =
+      aliasInfo.aliasesNonWriteableBuffer(operand);
+  if (wouldCreateAliasingWriteToNonWriteableBuffer)
+    LDBG("->the corresponding buffer is not writeable\n");
+  LDBG("->bufferizes to writeable inplace buffer\n");
+
+  Value s = operand.get(), r = result;
+  bool foundInterference =
+      wouldCreateAliasingWriteToNonWriteableBuffer ||
+      aliasInfo.existsNonDominatingRead(operand, domInfo) ||
+      // Do not consider (s, s) and (r, r) as all the aliasings already
+      // exist by construction; we are interested in new interfering aliases
+      // only.
+      aliasInfo.wouldCreateReadAfterWriteInterference(s, r, op, domInfo) ||
+      aliasInfo.wouldCreateReadAfterWriteInterference(r, s, op, domInfo);
 
-/// Return true if `operand` bufferizes to a buffer that is known to never be
-/// written.
-static bool bufferizeToReadOnly(OpOperand &operand) {
-  return llvm::TypeSwitch<Operation *, bool>(operand.getOwner())
-      .Case([&](LinalgOp linalgOp) { return linalgOp.isInputTensor(&operand); })
-      .Default([&](Operation *op) { return false; });
-}
-
-/// Assume operand is a use of a `subTensorOp`.
-/// Return true if this use bufferizes to a buffer that is known to never be
-/// written.
-/// Note: This function takes into consideration uses of subTensorOp and whether
-/// the owner of those uses is inplaceable. This needs to be run in postorder to
-/// provide the most accurate analysis; otherwise it is conservative.
-static bool subTensorUseBufferizesToReadOnly(OpOperand &operand) {
-  assert(operand.get().getDefiningOp<SubTensorOp>() && "expected subtensor op");
-  if (auto subTensorInsertOp =
-          dyn_cast<SubTensorInsertOp>(operand.getOwner())) {
-    return operand.getOperandNumber() == 0 /* source of the subTensorInsert*/ &&
-           // If the subTensorInsertOp is not inplace, there is no possible
-           // internal aliasing with subTensorOp, which is inplaceable.
-           getInPlace(subTensorInsertOp->getResult(0)) != InPlaceSpec::True;
-  }
-  return bufferizeToReadOnly(operand);
-}
-
-/// Return true if `dominator.getOwner()` dominates all other uses of
-/// `dominator.get()`.
-static bool dominatesAllOtherUses(OpOperand &dominator,
-                                  const DominanceInfo &domInfo) {
-  for (OpOperand &use : dominator.get().getUses()) {
-    // Same use.
-    if (use.getOwner() == dominator.getOwner() &&
-        use.getOperandNumber() == dominator.getOperandNumber())
-      continue;
-    if (!domInfo.properlyDominates(dominator.getOwner(), use.getOwner()))
-      return false;
+  if (foundInterference) {
+    setInPlaceOpResult(result, InPlaceSpec::False);
+  } else {
+    setInPlaceOpResult(result, InPlaceSpec::True);
+    // TODO: Atm, all inplace bufferizations yield equivalent tensors. Support
+    // more cases on a per-need basis.
+    aliasInfo.bufferizeInPlace(
+        result, operand, BufferizationAliasInfo::BufferRelation::Equivalent);
   }
-  return true;
+  LDBG("Done bufferizing result #" << resultNumber << '\n');
 }
 
-/// SubTensorOp introduces potential aliasing and a combination of things need
-/// to occur to determine whether it is inplaceable.
-static void analyzeInPlaceSubTensor(SubTensorOp subTensorOp,
-                                    const DominanceInfo &domInfo) {
-  // Case 1:
-  //   a. All uses are known to bufferize to readonly buffers.
-  //   b. The source has no use that is not dominated by subTensorOp.
-  // This can skip bufferizeToWriteable analysis / function boundary annotation.
-  if (llvm::all_of(subTensorOp.result().getUses(),
-                   subTensorUseBufferizesToReadOnly) &&
-      dominatesAllOtherUses(subTensorOp->getOpOperand(0), domInfo))
-    return setInPlaceOpResult(subTensorOp->getResult(0), InPlaceSpec::True);
-
-  // TODO: Implement more advanced use cases.There is a notion of transitivity
-  // and interference sets lurking.
-}
-
-/// Analyze the internals of a FuncOp to determine inplaceable ops.
+/// Analyze the `funcOp` body to determine which OpResults are inplaceable.
 static void inPlaceAnalysisFuncOpInternals(FuncOp funcOp,
+                                           BufferizationAliasInfo &aliasInfo,
                                            const DominanceInfo &domInfo) {
+  LLVM_DEBUG(llvm::dbgs() << "\n\n");
+  LDBG("Begin InPlaceAnalysisFuncOpInternals:\n" << funcOp << '\n');
   assert(funcOp && funcOp->getNumRegions() > 0 && !funcOp.body().empty() &&
          "expected a funcOp definition with a body");
 
+  // Collect ops so we can build our own traversal.
+  SmallVector<SubTensorOp> subTensorOps;
+  SmallVector<SubTensorInsertOp> subTensorInsertOps;
+  SmallVector<Operation *> nonSubTensorOps;
   funcOp.walk([&](Operation *op) {
-    // Skip SubTensorOp in a first pass.
     if (auto subTensorOp = dyn_cast<SubTensorOp>(op))
-      return analyzeInPlaceSubTensor(subTensorOp, domInfo);
-
-    // All other ops are checked for `isBufferizableInPlace`.
-    for (OpOperand &opOperand : op->getOpOperands()) {
-      OpResult result = getMatchingOpResult(opOperand);
-      if (result && isBufferizableInPlace(opOperand, domInfo)) {
-        LLVM_DEBUG(DBGS() << "bufferizable inplace operand #"
-                          << opOperand.getOperandNumber() << " in " << *op);
-        setInPlaceOpResult(result);
-      }
-    }
+      return subTensorOps.push_back(subTensorOp);
+    if (auto subTensorInsertOp = dyn_cast<SubTensorInsertOp>(op))
+      return subTensorInsertOps.push_back(subTensorInsertOp);
+    auto isaTensor = [](Type t) { return t.isa<TensorType>(); };
+    // No tensors => no buffers.
+    if (none_of(op->getOperandTypes(), isaTensor) &&
+        none_of(op->getResultTypes(), isaTensor))
+      return;
+    nonSubTensorOps.push_back(op);
   });
+
+  // Bufferize SubTensorInsertOp greedily: we almost never want to bufferize
+  // the tensor "inserted into" to become out-of-place. This implementation
+  // does not distinguish between different SubTensorInsertOps. If we want
+  // finer-grained behavior, we could order the SubTensorInsertOps with some
+  // metric.
+  // Walk SubTensorInsertOps in reverse for better interference behavior.
+  for (SubTensorInsertOp subTensorInsertOp : reverse(subTensorInsertOps)) {
+    OpOperand &destOpOperand = subTensorInsertOp->getOpOperand(1);
+    bufferizableInPlaceAnalysis(destOpOperand,
+                                getInplaceableOpResult(destOpOperand),
+                                aliasInfo, domInfo);
+  }
+
+  // Bufferize all ops except SubTensorOp and SubTensorInsertOp which are
+  // handled separately.
+  // Walk other ops in reverse for better interference behavior.
+  for (Operation *op : reverse(nonSubTensorOps))
+    for (OpOperand &opOperand : op->getOpOperands())
+      if (OpResult result = getInplaceableOpResult(opOperand))
+        bufferizableInPlaceAnalysis(opOperand, result, aliasInfo, domInfo);
+
+  // Finally, bufferize SubTensorOp.
+  // Walk SubTensorOps in reverse for better clobbering behavior: it is easier
+  // to detect clobbers of smaller subtensors before larger ones.
+  for (SubTensorOp subTensorOp : reverse(subTensorOps))
+    bufferizableInPlaceAnalysis(subTensorOp, aliasInfo, domInfo);
+
+  LDBG("End InPlaceAnalysisFuncOpInternals:\n" << funcOp << '\n');
 }
 
-static LogicalResult bufferizeFuncOpInternals(
-    FuncOp funcOp, BlockAndValueMapping &bvm,
-    const DenseMap<FuncOp, SmallVector<int64_t>> &tiedResultsMap) {
+//===----------------------------------------------------------------------===//
+// Bufferization entry-point.
+//===----------------------------------------------------------------------===//
+
+static LogicalResult
+bufferizeFuncOpInternals(FuncOp funcOp, BlockAndValueMapping &bvm,
+                         const BufferizationAliasInfo &aliasInfo) {
+  LLVM_DEBUG(llvm::dbgs() << "\n\n");
+  LDBG("Begin BufferizeFuncOpInternals:\n" << funcOp << '\n');
   OpBuilder b(funcOp->getContext());
   /// Start by bufferizing `funcOp` arguments.
-  if (failed(bufferize(b, funcOp, bvm)))
+  if (failed(bufferize(b, funcOp, bvm, aliasInfo)))
     return failure();
   WalkResult result = funcOp.walk<WalkOrder::PostOrder>([&](Operation *op) {
     LogicalResult status =
-        llvm::TypeSwitch<Operation *, LogicalResult>(op)
+        TypeSwitch<Operation *, LogicalResult>(op)
             // Skip BufferCast and TensorLoad ops.
             // clang-format off
             .Case<memref::BufferCastOp,
                   memref::TensorLoadOp>(
                 [&](auto) { return success(); })
             .Case<memref::DimOp,
                   LinalgOp,
                   ReturnOp,
                   SubTensorOp,
                   SubTensorInsertOp,
                   VectorTransferOpInterface>(
-                [&](auto op) { return bufferize(b, op, bvm); })
+                [&](auto op) { return bufferize(b, op, bvm, aliasInfo); })
             // clang-format on
             .Default([&](Operation *op) {
               auto isaTensor = [](Type t) { return t.isa<TensorType>(); };
-              if (llvm::any_of(op->getOperandTypes(), isaTensor) ||
-                  llvm::any_of(op->getResultTypes(), isaTensor))
+              if (any_of(op->getOperandTypes(), isaTensor) ||
+                  any_of(op->getResultTypes(), isaTensor))
                 return failure();
               return success();
             });
     if (failed(status)) {
       op->emitError("Failed bufferization");
       return WalkResult::interrupt();
     }
     return WalkResult::advance();
   });
-  if (result.wasInterrupted())
-    return failure();
-  return success();
+  LDBG("End BufferizeFuncOpInternals:\n" << funcOp << '\n');
+
+  return failure(result.wasInterrupted());
 }
 
 namespace {
 struct LinalgComprehensiveFuncBufferize
     : public LinalgComprehensiveFuncBufferizeBase<
           LinalgComprehensiveFuncBufferize> {
   void runOnFunction() override;
 
   void getDependentDialects(DialectRegistry &registry) const override {
     registry.insert<linalg::LinalgDialect, memref::MemRefDialect>();
   }
 };
 } // end namespace
 
 void LinalgComprehensiveFuncBufferize::runOnFunction() {
   auto funcOp = getFunction();
+
+  // Analysis phase.
   DominanceInfo domInfo(funcOp);
-  BlockAndValueMapping bvm;
-  DenseMap<FuncOp, SmallVector<int64_t>> tiedResultsMap;
-  LLVM_DEBUG(llvm::dbgs() << "\n\n");
-  LLVM_DEBUG(DBGS() << "Begin InPlaceAnalysisFuncOpInternals:\n"
-                    << funcOp << "\n");
-  inPlaceAnalysisFuncOpInternals(funcOp, domInfo);
-  LLVM_DEBUG(DBGS() << "End InPlaceAnalysisFuncOpInternals:\n"
-                    << funcOp << "\n");
+  BufferizationAliasInfo aliasInfo(funcOp);
+  inPlaceAnalysisFuncOpInternals(funcOp, aliasInfo, domInfo);
 
   if (testAnalysisOnly)
     return;
 
-  LLVM_DEBUG(llvm::dbgs() << "\n\n");
-  LLVM_DEBUG(DBGS() << "Begin BufferizeFuncOpInternals:\n" << funcOp << "\n");
-  auto guard = llvm::make_scope_exit([&] {
-    funcOp.walk(
-        [&](Operation *op) { op->removeAttr(kInPlaceResultsAttrName); });
-    LLVM_DEBUG(DBGS() << "End BufferizeFuncOpInternals:\n" << funcOp << "\n");
-  });
-  if (failed(bufferizeFuncOpInternals(funcOp, bvm, tiedResultsMap)))
+  // Bufferization phase.
+  BlockAndValueMapping bvm;
+  if (failed(bufferizeFuncOpInternals(funcOp, bvm, aliasInfo)))
     signalPassFailure();
+
+  // Post-pass cleanup of inplaceable attributes.
+  funcOp.walk([&](Operation *op) { op->removeAttr(kInPlaceResultsAttrName); });
 }
 
 std::unique_ptr<Pass> mlir::createLinalgComprehensiveFuncBufferizePass() {
   return std::make_unique<LinalgComprehensiveFuncBufferize>();
 }

mlir/test/Dialect/Linalg/comprehensive-func-bufferize-analysis.mlir

+// RUN: mlir-opt %s -linalg-comprehensive-func-bufferize=test-analysis-only -split-input-file | FileCheck %s
+
+//===----------------------------------------------------------------------===//
+// Simple cases
+//===----------------------------------------------------------------------===//
+
+// -----
+
+// CHECK-LABEL: func @subtensor_fun
+func @subtensor_fun(%A : tensor<?xf32>, %B : tensor<?xf32> {linalg.inplaceable = true})
+  -> (tensor<4xf32>, tensor<8xf32>)
+{
+  // subtensor is not used in a write, it is not compelled to bufferize out of
+  // place. Let callers decide whether they want to create aliasing subviews at
+  // all call sites or whether they allocate.
+  // This is true irrespective of whether the function argument is inplaceable.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r1 = subtensor %B[0][8][1] : tensor<?xf32> to tensor<8xf32>
+
+  return %r0, %r1: tensor<4xf32>, tensor<8xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @subtensor_insert_fun
+func @subtensor_insert_fun(
+    %A : tensor<?xf32>,
+    %B : tensor<?xf32> {linalg.inplaceable = true},
+    %C : tensor<4xf32>)
+  -> (tensor<?xf32>, tensor<?xf32>)
+{
+  // must bufferize out of place.
+  //     CHECK: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %r0 = subtensor_insert %C into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  // bufferizes inplace.
+  //     CHECK: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r1 = subtensor_insert %C into %B[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  return %r0, %r1: tensor<?xf32>, tensor<?xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @conflict_on_B
+func @conflict_on_B(
+    %A : tensor<4x4xf32> {linalg.inplaceable = true},
+    %B : tensor<4x4xf32> {linalg.inplaceable = true})
+  -> (tensor<4x4xf32>, tensor<4x4xf32>, tensor<4x4xf32>)
+{
+  // matmul output operand interferes with input operand.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %C = linalg.matmul  ins(%A, %B: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%B: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  // matmul output operand interferes with input operand.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %D = linalg.matmul  ins(%B, %A: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%B: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  // matmul output operand does not interferes with input operand.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %E = linalg.matmul  ins(%A, %A: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%B: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  return %C, %D, %E: tensor<4x4xf32>, tensor<4x4xf32>, tensor<4x4xf32>
+}
+
+//===----------------------------------------------------------------------===//
+// Length-1 producer-consumer cases.
+//===----------------------------------------------------------------------===//
+
+// -----
+
+// CHECK-LABEL: func @subtensor_subtensor
+func @subtensor_subtensor(
+    %A : tensor<?xf32> {linalg.inplaceable = true}, %B : tensor<?xf32>)
+  -> (tensor<2xf32>, tensor<2xf32>)
+{
+  // subtensor is not used in a write, it is not compelled to bufferize out of
+  // place. Let callers decide whether they want to create aliasing subviews at
+  // all call sites or whether they allocate.
+  // This is true irrespective of whether the function argument is inplaceable.
+  // CHECK: {__inplace_results_attr__ = ["true"]}
+  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  // CHECK: {__inplace_results_attr__ = ["true"]}
+  %r1 = subtensor %r0[0][2][1] : tensor<4xf32> to tensor<2xf32>
+
+  // CHECK: {__inplace_results_attr__ = ["true"]}
+  %r2 = subtensor %B[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  // CHECK: {__inplace_results_attr__ = ["true"]}
+  %r3 = subtensor %r2[0][2][1] : tensor<4xf32> to tensor<2xf32>
+
+  return %r1, %r3: tensor<2xf32>, tensor<2xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @subtensor_insert_subtensor_insert
+func @subtensor_insert_subtensor_insert(
+    %A : tensor<?xf32> {linalg.inplaceable = true},
+    %A2 : tensor<4xf32> {linalg.inplaceable = true},
+    %A3 : tensor<2xf32> {linalg.inplaceable = true},
+    %B : tensor<?xf32>, %B2 : tensor<4xf32>, %B3 : tensor<2xf32>)
+  -> (tensor<?xf32>, tensor<?xf32>)
+{
+  // CHECK: {__inplace_results_attr__ = ["true"]}
+  %r0 = subtensor_insert %A3 into %A2[0][2][1] : tensor<2xf32> into tensor<4xf32>
+
+  // CHECK: {__inplace_results_attr__ = ["true"]}
+  %r1 = subtensor_insert %r0 into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  // CHECK: {__inplace_results_attr__ = ["false"]}
+  %r2 = subtensor_insert %B3 into %B2[0][2][1] : tensor<2xf32> into tensor<4xf32>
+
+  // CHECK: {__inplace_results_attr__ = ["false"]}
+  %r3 = subtensor_insert %r2 into %B[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  return %r1, %r3: tensor<?xf32>, tensor<?xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @subtensor_nonmatching_subtensor_insert
+func @subtensor_nonmatching_subtensor_insert(
+    %A : tensor<?xf32> {linalg.inplaceable = true},
+    %B : tensor<?xf32>, %idx: index)
+  -> (tensor<?xf32>, tensor<?xf32>)
+{
+  // %r1 bufferizes inplace because %A is inplaceable.
+  // %r0 is an overlapping subtensor that does not match, it must be out of place.
+  //      CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  // %r1 can bufferize inplace fine.
+  //      CHECK: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r1 = subtensor_insert %r0 into %A[%idx][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  // %r3 does bufferizes inplace because %B is not inplaceable.
+  // %r0 is an overlapping subtensor that does not match, but does not alias with
+  // the buffer coming from %r3 so it can actually bufferize inplace.
+  //      CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r2 = subtensor %B[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  // %r3 cannot bufferize inplace since %B is not inplaceable.
+  //      CHECK: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %r3 = subtensor_insert %r2 into %B[%idx][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  return %r1, %r3: tensor<?xf32>, tensor<?xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @subtensor_matching_subtensor_insert
+func @subtensor_matching_subtensor_insert(
+    %A : tensor<?xf32> {linalg.inplaceable = true},
+    %B : tensor<?xf32>)
+  -> (tensor<?xf32>, tensor<?xf32>)
+{
+  // %r1 bufferizes inplace because %A is inplaceable.
+  // %r0 is a subtensor that matches, it can also be bufferized inplace.
+  //      CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  //      CHECK: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r1 = subtensor_insert %r0 into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  // %r2 is a subtensor that matches %r3, it can be bufferized inplace.
+  //      CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %r2 = subtensor %B[0][4][1] : tensor<?xf32> to tensor<4xf32>
+
+  // subtensor_insert cannot bufferize inplace.
+  // This should have been captured by a canonicalization pattern and it would
+  // be unproductive to have special logic in bufferization to encode matching
+  // subtensor_insert(subtensor(A), A).
+  //      CHECK: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %r3 = subtensor_insert %r2 into %B[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  return %r1, %r3: tensor<?xf32>, tensor<?xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @subtensor_linalg_readonly_use
+func @subtensor_linalg_readonly_use(
+    %A : tensor<?x?xf32>,
+    %B : tensor<4x4xf32>,
+    %C : tensor<4x4xf32> {linalg.inplaceable = true})
+  ->  (tensor<4x4xf32>, tensor<4x4xf32>)
+{
+  // subtensor is only used as a read, no interference irrespective of user's
+  // inplace status.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %sA = subtensor %A[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+
+  // matmul output operand is not inplaceable at the function boundary.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %D = linalg.matmul  ins(%sA, %B: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%B: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  // matmul output operand is inplaceable at the function boundary.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %E = linalg.matmul  ins(%sA, %B: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%C: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  return %D, %E: tensor<4x4xf32>, tensor<4x4xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @subtensor_to_linalg_write_use
+func @subtensor_to_linalg_write_use(
+    %A : tensor<4x4xf32>,
+    %B : tensor<?x?xf32>,
+    %C : tensor<?x?xf32> {linalg.inplaceable = true})
+  ->  (tensor<4x4xf32>, tensor<4x4xf32>)
+{
+  // Step 3. %sB forward propagates to a write in %D but it is not inplace.
+  // So this is only ever read and can bufferize inplace.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %sB = subtensor %B[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+
+  // Step 2. %sB has a read interference in %E, it does not bufferize inplace.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %D = linalg.matmul  ins(%B, %C: tensor<?x?xf32>, tensor<?x?xf32>)
+                     outs(%sB: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  // Step 4. %sC forward propagates to an inplace write in %E.
+  // %sC backward propagates to %C which is inplaceable.
+  // As a consequence this is bufferized inplace.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %sC = subtensor %C[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+
+  // Step 1. %sC backprops to the subtensor producer which is not considered an
+  // interference. This bufferizes inplace.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %E = linalg.matmul  ins(%A, %sB: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%sC: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  return %D, %E: tensor<4x4xf32>, tensor<4x4xf32>
+}
+
+//===----------------------------------------------------------------------===//
+// Transitive cases
+//===----------------------------------------------------------------------===//
+
+// -----
+
+// CHECK-LABEL: func @subtensor_to_linalg_write_use
+func @subtensor_to_linalg_write_use(
+    %A : tensor<4x4xf32>,
+    %B : tensor<?x?xf32>,
+    %C : tensor<?x?xf32> {linalg.inplaceable = true})
+  ->  (tensor<4x4xf32>, tensor<4x4xf32>)
+{
+  // Step 4. %sB forward propagates to an inplace write in %D.
+  // %sB backward propagates to %B which is not inplaceable.
+  // As a consequence this is bufferized out of place.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %sB = subtensor %B[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+
+  // Step 1. %sB backprops to the subtensor producer which is not considered an
+  // interference. This bufferizes inplace.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %D = linalg.matmul  ins(%B, %C: tensor<?x?xf32>, tensor<?x?xf32>)
+                     outs(%sB: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  // Step 3. %sC forward propagates to an inplace write in %E.
+  // %sC backward propagates to %C which is inplaceable.
+  // As a consequence this is bufferized inplace.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %sC = subtensor %C[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+
+  // Step 1. %sC backprops to the subtensor producer which is not considered an
+  // interference. This bufferizes inplace.
+  //     CHECK: linalg.matmul
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %E = linalg.matmul  ins(%A, %A: tensor<4x4xf32>, tensor<4x4xf32>)
+                     outs(%sC: tensor<4x4xf32>)
+    -> tensor<4x4xf32>
+
+  return %D, %E: tensor<4x4xf32>, tensor<4x4xf32>
+}
+
+// -----
+
+// CHECK-LABEL: func @nested_subtensor_and_insert
+func @nested_subtensor_and_insert(
+    %A : tensor<?x?xf32>,
+    %B : tensor<?x?xf32> {linalg.inplaceable = true},
+    %C : tensor<?x?xf32> {linalg.inplaceable = true},
+    %idx : index)
+  ->  (tensor<?x?xf32>, tensor<?x?xf32>, tensor<?x?xf32>)
+{
+  %f0 = constant 0.0 : f32
+
+  // 2-level matching subtensor / subtensor_insert into non inplaceable %A.
+  //   - %rA is not inplaceable because %A is not inplaceable at function boundary.
+  //   - once %rA is deemed not inplaceable, nothing prevent %rsA to be inplaceable
+  //   - this propagates to %FA and %ssA being inplaceable.
+  //   - %sA would then bufferize to an inplace write (i.e. %FA) but %A is not
+  //     inplaceable and so %sA is not inplaceable.
+  //     CHECK: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  // CHECK-NEXT: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: fill
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  %sA = subtensor %A[0, 0][%idx, %idx][1, 1] : tensor<?x?xf32> to tensor<?x?xf32>
+  %ssA = subtensor %sA[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+  %FA = linalg.fill(%ssA, %f0) : tensor<4x4xf32>, f32 -> tensor<4x4xf32>
+  %rsA = subtensor_insert %FA into %sA[0, 0][4, 4][1, 1] : tensor<4x4xf32> into tensor<?x?xf32>
+  %rA = subtensor_insert %rsA into %A[0, 0][%idx, %idx][1, 1] : tensor<?x?xf32> into tensor<?x?xf32>
+
+  // 3-level matching subtensor / subtensor_insert into inplaceable %B.
+  // CHECK-NEXT: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor
+  // Atm, this 2nd subtensor fails to bufferize inplace because clobbering
+  // analysis conservatively test for equivalent buffers.
+  // TODO: This is currently too restrictive and misses clobberings.
+  // When available, use container-containee analysis.
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  // CHECK-NEXT: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: fill
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %sB = subtensor %B[0, 0][%idx, %idx][1, 1] : tensor<?x?xf32> to tensor<?x?xf32>
+  %ssB = subtensor %sB[0, 0][4, %idx][1, 1] : tensor<?x?xf32> to tensor<4x?xf32>
+  %sssB = subtensor %ssB[0, 0][4, 4][1, 1] : tensor<4x?xf32> to tensor<4x4xf32>
+  %FB = linalg.fill(%sssB, %f0) : tensor<4x4xf32>, f32 -> tensor<4x4xf32>
+  %rssB = subtensor_insert %FB into %ssB[0, 0][4, 4][1, 1] : tensor<4x4xf32> into tensor<4x?xf32>
+  %rsB = subtensor_insert %rssB into %sB[0, 0][4, %idx][1, 1] : tensor<4x?xf32> into tensor<?x?xf32>
+  %rB = subtensor_insert %rsB into %B[0, 0][%idx, %idx][1, 1] : tensor<?x?xf32> into tensor<?x?xf32>
+
+  // 2-level matching subtensor / subtensor_insert into inplaceable %C with a twist.
+  // Throw a wrench in the system: %rsC production sizes do not match %ssC.
+  // CHECK-NEXT: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // The subtensor_insert that would be candidate for matching does not actually
+  // match. That subtensor_insert can still be bufferized inplace nonetheless
+  // but this subtensor, which bufferizes to an inplace write, cannot.
+  // CHECK-NEXT: subtensor
+  // CHECK-SAME: {__inplace_results_attr__ = ["false"]}
+  // CHECK-NEXT: fill
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  // CHECK-NEXT: subtensor_insert
+  // CHECK-SAME: {__inplace_results_attr__ = ["true"]}
+  %sC = subtensor %C[0, 0][%idx, %idx][1, 1] : tensor<?x?xf32> to tensor<?x?xf32>
+  %ssC = subtensor %sC[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
+  %FC = linalg.fill(%ssC, %f0) : tensor<4x4xf32>, f32 -> tensor<4x4xf32>
+  %rsC = subtensor_insert %FC into %sC[0, 0][12345, 67890][1, 1] : tensor<4x4xf32> into tensor<?x?xf32>
+  %rC = subtensor_insert %rsC into %C[0, 0][%idx, %idx][1, 1] : tensor<?x?xf32> into tensor<?x?xf32>
+
+  return %rA, %rB, %rC: tensor<?x?xf32>, tensor<?x?xf32>, tensor<?x?xf32>
+}
+

mlir/test/Dialect/Linalg/comprehensive-func-bufferize.mlir

 // RUN: mlir-opt %s -linalg-comprehensive-func-bufferize -split-input-file | FileCheck %s
-// RUN: mlir-opt %s -linalg-comprehensive-func-bufferize=test-analysis-only -split-input-file | FileCheck %s --check-prefix=ANALYSIS
 
 // CHECK-DAG: #[[$map_2d_dyn:.*]] = affine_map<(d0)[s0, s1] -> (d0 * s1 + s0)>
 
 // CHECK-LABEL: func @fill_inplace(
 //  CHECK-SAME:   %[[A:[a-zA-Z0-9]*]]: tensor<?xf32> {linalg.inplaceable = true})
 func @fill_inplace(%A : tensor<?xf32> {linalg.inplaceable = true}) -> tensor<?xf32> {
   //     CHECK: %[[I:.*]] = memref.buffer_cast %[[A]] : memref<?xf32, #[[$map_2d_dyn]]>
 
func @vec_not_inplace(%A : tensor<?xf32> {linalg.inplaceable = true}, %vec : vector<4xf32>)
   // CHECK-NEXT: vector.transfer_write {{.*}}, %[[BUFFER_CAST]]
   %r1 = vector.transfer_write %vec, %A[%c1] : vector<4xf32>, tensor<?xf32>
   return %r0, %r1: tensor<?xf32>, tensor<?xf32>
 }
 
 // -----
 
 // CHECK-LABEL: func @subtensor_insert_fun
-func @subtensor_insert_fun(%A : tensor<?xf32> {linalg.inplaceable = true}, %t : tensor<4xf32>)
-  ->  tensor<?xf32>
-{
-  //      CHECK: %[[BUFFER_CAST_A:.*]] = memref.buffer_cast {{.*}} : memref<?xf32
-  //      CHECK: %[[BUFFER_CAST_B:.*]] = memref.buffer_cast {{.*}} : memref<4xf32
+func @subtensor_insert_fun(%A0 : tensor<?xf32>, %A1 : tensor<?xf32> {linalg.inplaceable = true},
+                           %t0 : tensor<4xf32>, %t1 : tensor<4xf32> {linalg.inplaceable = true})
+  ->  (tensor<?xf32>, tensor<?xf32>, tensor<?xf32>, tensor<?xf32>)
+{
+  //      CHECK: %[[BUFFER_CAST_A0:.*]] = memref.buffer_cast {{.*}} : memref<?xf32
+  //      CHECK: %[[BUFFER_CAST_A1:.*]] = memref.buffer_cast {{.*}} : memref<?xf32
+  //      CHECK: %[[BUFFER_CAST_t0:.*]] = memref.buffer_cast {{.*}} : memref<4xf32
+  //      CHECK: %[[BUFFER_CAST_t1:.*]] = memref.buffer_cast {{.*}} : memref<4xf32
+
+  // Alloc and copy the whole result tensor. Copy the subtensor.
+  //      CHECK: %[[REALLOC_A0:.*]] = memref.alloc
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_A0]]
+  //      CHECK: %[[SV_A0:.*]] = memref.subview %[[REALLOC_A0]]
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_t0]], %[[SV_A0]])
+  %r0 = subtensor_insert %t0 into %A0[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  // Alloc and copy the whole result tensor. Copy the subtensor.
+  //      CHECK: %[[REALLOC_A0_2:.*]] = memref.alloc
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_A0]]
+  //      CHECK: %[[SV_A0_2:.*]] = memref.subview %[[REALLOC_A0_2]]
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_t1]], %[[SV_A0_2]])
+  %r1 = subtensor_insert %t1 into %A0[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  //  Still alloc the large tensor because %A1 is read after. Copy the subtensor.
+  //      CHECK: %[[REALLOC_A1:.*]] = memref.alloc
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_A1]]
+  //      CHECK: %[[SV_A1:.*]] = memref.subview %[[REALLOC_A1]]
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_t0]], %[[SV_A1]])
+  %r2 = subtensor_insert %t0 into %A1[0][4][1] : tensor<4xf32> into tensor<?xf32>
 
+  //  Do not realloc the large tensor. Copy the subtensor.
   //  CHECK-NOT: alloc
-  //      CHECK: %[[SV:.*]] = memref.subview %[[BUFFER_CAST_A]]
-  //      CHECK: linalg.copy(%[[BUFFER_CAST_B]], %[[SV]])
-  %r0 = subtensor_insert %t into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
-  return %r0: tensor<?xf32>
+  //      CHECK: %[[SV_A1_2:.*]] = memref.subview %[[BUFFER_CAST_A1]]
+  //      CHECK: linalg.copy(%[[BUFFER_CAST_t1]], %[[SV_A1_2]])
+  %r3 = subtensor_insert %t1 into %A1[0][4][1] : tensor<4xf32> into tensor<?xf32>
+
+  return %r0, %r1, %r2, %r3: tensor<?xf32>, tensor<?xf32>, tensor<?xf32>, tensor<?xf32>
 }
 
 // -----
 
 // CHECK-LABEL: func @subtensor_insert_fun
 func @subtensor_insert_fun(%A : tensor<?xf32> {linalg.inplaceable = true}, %t : tensor<4xf32>)
   -> tensor<?xf32>
 {

 // -----
 
 // CHECK-LABEL: func @subtensor_insert_fun_not_inplace
 func @subtensor_insert_fun_not_inplace(%A : tensor<?xf32> {linalg.inplaceable = true}, %t : tensor<4xf32>)
   -> (tensor<?xf32>, tensor<?xf32>)
 {
   %f0 = constant 0.0 : f32
 
-  //      CHECK: %[[BUFFER_CAST_A:.*]] = memref.buffer_cast {{.*}} : memref<?xf32
-  //      CHECK: %[[BUFFER_CAST_B:.*]] = memref.buffer_cast {{.*}} : memref<4xf32
+  //  CHECK-DAG: %[[BUFFER_CAST_A:.*]] = memref.buffer_cast {{.*}} : memref<?xf32{{.*}}
+  //  CHECK-DAG: %[[BUFFER_CAST_B:.*]] = memref.buffer_cast {{.*}} : memref<4xf32{{.*}}
 
-  //      CHECK: %[[ALLOC:.*]] = memref.alloc(%{{.*}}) : memref<?xf32>
-  //      CHECK: linalg.copy(%[[BUFFER_CAST_A]], %[[ALLOC]]) : memref<?xf32{{.*}}, memref<?xf32>
-  //      CHECK: %[[SV:.*]] = memref.subview %[[ALLOC]][0] [4] [1] : memref<?xf32> to memref<4xf32>
-  //      CHECK: linalg.copy(%[[BUFFER_CAST_B]], %[[SV]]) : memref<4xf32, #map>, memref<4xf32>
+  // subtensor_insert is bufferized first, %A is inplaceable so we can make this inplace
+  //  CHECK-DAG: %[[SV:.*]] = memref.subview %[[BUFFER_CAST_A]][0] [4] [1] : memref<?xf32, {{.*}}> to memref<4xf32, {{.*}}>
+  //  CHECK-DAG: linalg.copy(%[[BUFFER_CAST_B]], %[[SV]]) : memref<4xf32, {{.*}}>, memref<4xf32, {{.*}}>
   %r0 = subtensor_insert %t into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
 
-  // TODO: WAW optimization where result is overwritten without being read.
-  //      CHECK: linalg.fill(%[[BUFFER_CAST_A]]
+  // fill would interfere with %r0 that is also being returned.
+  // So we need to bufferize it out of place and make a new alloc.
+  //  CHECK-DAG: %[[ALLOC:.*]] = memref.alloc({{.*}}) : memref<?xf32>
+  //  CHECK-DAG: %[[ALLOC_CAST_DYNAMIC:.*]] = memref.cast %[[ALLOC]] : memref<?xf32> to memref<?xf32, {{.*}}
+  //      CHECK: linalg.fill(%[[ALLOC_CAST_DYNAMIC]]
   //      CHECK: memref.dealloc %[[ALLOC]] : memref<?xf32>
   %r1 = linalg.fill(%A, %f0) : tensor<?xf32>, f32 -> tensor<?xf32>
-  return %r0, %r1: tensor<?xf32>, tensor<?xf32>
+
+  //  CHECK-DAG: %[[RET_A:.*]] = memref.tensor_load %[[BUFFER_CAST_A]] : memref<?xf32, {{.*}}
+  //  CHECK-DAG: %[[RET_B:.*]] = memref.tensor_load %[[ALLOC_CAST_DYNAMIC]] : memref<?xf32, {{.*}}
+  //      CHECK: return %[[RET_B]], %[[RET_A]]
+  return %r1, %r0: tensor<?xf32>, tensor<?xf32>
 }
 
 // -----
 
 // CHECK-LABEL: func @subtensor_fun
 func @subtensor_fun(%A : tensor<?xf32> {linalg.inplaceable = true})
   ->  tensor<4xf32>
 {
-  //      CHECK: %[[BUFFER_CAST_A:.*]] = memref.buffer_cast {{.*}} : memref<?xf32
-
-  // CHECK: %[[ALLOC:.*]] = memref.alloc() : memref<4xf32>
-  // CHECK: %[[SV:.*]] = memref.subview %[[BUFFER_CAST_A]][0] [4] [1]
-  // CHECK: linalg.copy(%[[SV]], %[[ALLOC]])
+  // This bufferizes to a pattern that the cross-function boundary pass needs to
+  // convert into a new memref argument at all call site; this may be either:
+  //   - an externally created aliasing subview (if we want to allow aliasing
+  //     function arguments).
+  //   - a new alloc + copy (more expensive but does not create new function
+  //     argument aliasing).
+  // CHECK-NOT: alloc
+  // CHECK-NOT: copy
+  //     CHECK: %[[BUFFER_CAST_A:.*]] = memref.buffer_cast {{.*}} : memref<?xf32
+  //     CHECK: %[[SV:.*]] = memref.subview %[[BUFFER_CAST_A]][0] [4] [1]
+  //     CHECK: %[[RES:.*]] = memref.tensor_load %[[SV]]
   %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
-  return %r0: tensor<4xf32>
-}
 
-// -----
-
-// ANALYSIS-LABEL: func @subtensor_readonly_use
-func @subtensor_readonly_use(
-    %A : tensor<?x?xf32> {linalg.inplaceable = true},
-    %B : tensor<4x4xf32>, %C : tensor<4x4xf32>) ->  tensor<4x4xf32>
-{
-  // subtensor is only used as a read.
-  //     ANALYSIS: subtensor {{.*}} {__inplace_results_attr__ = ["true"]}
-  %sA = subtensor %A[0, 0][4, 4][1, 1] : tensor<?x?xf32> to tensor<4x4xf32>
-  // matmul output operand is not inplaceable at the function boundary.
-  //     ANALYSIS: linalg.matmul {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %D = linalg.matmul  ins(%sA, %B: tensor<4x4xf32>, tensor<4x4xf32>)
-                     outs(%B: tensor<4x4xf32>)
-    -> tensor<4x4xf32>
-  return %D: tensor<4x4xf32>
-}
-
-// -----
-
-// ANALYSIS-LABEL: func @subtensor_nonmatching_subtensor_insert_inplace
-func @subtensor_nonmatching_subtensor_insert_inplace(
-    %A : tensor<?xf32> {linalg.inplaceable = true}, %idx: index)
-  ->  tensor<?xf32>
-{
-  // subtensor has no matching subtensor_insert and is not just used by known
-  // readonly ops.
-  //     ANALYSIS: subtensor {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
-  // subtensor_insert can bufferize inplace fine.
-  //     ANALYSIS: subtensor_insert {{.*}} {__inplace_results_attr__ = ["true"]}
-  %r1 = subtensor_insert %r0 into %A[%idx][4][1] : tensor<4xf32> into tensor<?xf32>
-  return %r1: tensor<?xf32>
-}
-
-// -----
-
-// ANALYSIS-LABEL: func @subtensor_nonmatching_subtensor_insert_non_inplace
-func @subtensor_nonmatching_subtensor_insert_non_inplace(
-    %A : tensor<?xf32> {linalg.inplaceable = false}, %idx: index)
-  ->  tensor<?xf32>
-{
-  // subtensor has no matching subtensor_insert and is not just used by known
-  // readonly ops.
-  //     ANALYSIS: subtensor {{.*}} {__inplace_results_attr__ = ["true"]}
-  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
-  // subtensor_insert cannot bufferize inplace.
-  //     ANALYSIS: subtensor_insert {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r1 = subtensor_insert %r0 into %A[%idx][4][1] : tensor<4xf32> into tensor<?xf32>
-  return %r1: tensor<?xf32>
-}
-
-// -----
-
-// ANALYSIS-LABEL: func @subtensor_matching_subtensor_insert
-func @subtensor_matching_subtensor_insert(%A : tensor<?xf32> {linalg.inplaceable = true})
-  ->  tensor<?xf32>
-{
-  // subtensor has a matching subtensor_insert that bufferizes inplace.
-  // TODO: Atm subtensor is not inplaceable but can be.
-  // In the grander scheme, this will canonicalize away beforehand.
-  //     ANALYSIS: subtensor {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
-  // subtensor_insert can bufferize inplace fine.
-  //     ANALYSIS: subtensor_insert {{.*}} {__inplace_results_attr__ = ["true"]}
-  %r1 = subtensor_insert %r0 into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
-  return %r1: tensor<?xf32>
-}
-
-// -----
-
-// ANALYSIS-LABEL: func @subtensor_matching_and_nonmatching_1
-func @subtensor_matching_and_nonmatching_1(%A : tensor<?xf32> {linalg.inplaceable = true}, %idx: index)
-  ->  (tensor<?xf32>, tensor<?xf32>)
-{
-  // %r1 is not inplaceable and %r2 is a matching subtensor_insert so %r0 could
-  // be inplaceable.
-  // In the grander scheme, %r2 will canonicalize away beforehand but %r0 will still
-  // not be inplaceable as the production of %r1 may involve a self-copy.
-  //     ANALYSIS: subtensor {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
-  //     ANALYSIS: subtensor_insert {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r1 = subtensor_insert %r0 into %A[%idx][4][1] : tensor<4xf32> into tensor<?xf32>
-  //     ANALYSIS: subtensor_insert {{.*}} {__inplace_results_attr__ = ["true"]}
-  %r2 = subtensor_insert %r0 into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
-  return %r1, %r2: tensor<?xf32>, tensor<?xf32>
-}
-
-// -----
-
-// ANALYSIS-LABEL: func @subtensor_matching_and_nonmatching_2
-func @subtensor_matching_and_nonmatching_2(%A : tensor<?xf32> {linalg.inplaceable = true}, %idx: index)
-  ->  (tensor<?xf32>, tensor<?xf32>)
-{
-  // %r1 is not inplaceable and %r2 is a matching subtensor_insert so %r0 should
-  // be inplaceable.
-  // In the grander scheme, %r2 will canonicalize away beforehand and %r0 will become
-  // inplaceable by reducing to the `subtensor_nonmatching_subtensor_insert_non_inplace`
-  // case,
-  //     ANALYSIS: subtensor {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r0 = subtensor %A[0][4][1] : tensor<?xf32> to tensor<4xf32>
-  //     ANALYSIS: subtensor_insert {{.*}}
-  // ANALYSIS-NOT: {__inplace_results_attr__ = ["true"]}
-  %r2 = subtensor_insert %r0 into %A[0][4][1] : tensor<4xf32> into tensor<?xf32>
-  //     ANALYSIS: subtensor_insert {{.*}} {__inplace_results_attr__ = ["true"]}
-  %r1 = subtensor_insert %r0 into %A[%idx][4][1] : tensor<4xf32> into tensor<?xf32>
-
-  return %r1, %r2: tensor<?xf32>, tensor<?xf32>
+  //     CHECK: return %[[RES]]
+  return %r0: tensor<4xf32>
 }
 
-// -----
-
-// TODO: unknown ops, linalg chain success, linalg chain failure.
-