Reapply "[mlir][linalg] Restrict linalg.pack to not have artificial padding." (#150675) (#150680)

This reverts commit
0844812
with a shape fix in
1db4c6b

The revision restrict the `linalg.pack` op to not have artificial
padding semantics. E.g., the below is valid without the change, and it
becomes invalid with the change.

```mlir
func.func @foo(%src: tensor<9xf32>) -> tensor<100x8xf32> {
  %cst = arith.constant 0.000000e+00 : f32
  %dest = tensor.empty() : tensor<100x8xf32>
  %pack = linalg.pack %src
    padding_value(%cst : f32)
    inner_dims_pos = [0]
    inner_tiles = [8] into %dest
    : tensor<9xf32> -> tensor<100x8xf32>
  return %pack : tensor<100x8xf32>
}
```

IMO, it is a misuse if we use pack ops with artificial padding sizes
because the intention of the pack op is to relayout the source based on
target intrinsics, etc. The output shape is expected to be
`tensor<2x8xf32>`. If people need extra padding sizes, they can create a
new pad op followed by the pack op.

This also makes consumer tiling much easier because the consumer fusion
does not support artificial padding sizes. It is very hard to make it
work without using ad-hoc patterns because the tiling sizes are about
source, which implies that you don't have a core_id/thread_id to write
padding values to the whole tile.

People may have a question how why pad tiling implementation works. The
answer is that it creates an `if-else` branch to handle the case. In my
experience, it is very struggle in transformation because most of the
time people only need one side of the branch given that the tile sizes
are usually greater than padding sizes. However, the implementation is
conservatively correct in terms of semantics. Given that the
introduction of `pack` op is to serve the relayout needs better, having
the restriction makes sense to me.

Removed tests:
-
`no_bubble_up_pack_extending_dimension_through_expand_cannot_reassociate`
from `data-layout-propagation.mlir`: it is a dup test to
`bubble_up_pack_non_expanded_dims_through_expand` after we fix the
shape.
- `fuse_pack_consumer_with_untiled_extra_padding` from
`tile-and-fuse-consumer.mlir`: it was created for artificial padding in
the consumer fusion implementation.

The other changes in lit tests are just fixing the shape.

---------

Signed-off-by: hanhanW <[email protected]>

Author: hanhanW

mlir/include/mlir/Dialect/Linalg/IR/LinalgRelayoutOps.td

@@ -106,7 +106,9 @@ def Linalg_PackOp : Linalg_RelayoutOp<"pack", [
      result tensor in the order in which they appear, i.e.
      `shape(result)[rank(result) + i] = inner_tiles[i]` for `0 <= i < k`.
      - The following relationship for the tiled dimensions holds:
-     `shape(result)[inner_dims_pos[i]] = shape(source)[inner_dims_pos[i]] / inner_tiles[i]`.
+     `shape(result)[inner_dims_pos[i]] = shape(source)[inner_dims_pos[i]] / inner_tiles[i]`,
+     where (⌈/⌉ indicates CeilDiv).
+
 
     Example: If `inner_tiles = [16, 32]`, the result tensor has a shape of
     `...x16x32`. If `inner_dims_pos = [0, 1]`, the 0th source dimension is tiled
@@ -150,9 +152,17 @@ def Linalg_PackOp : Linalg_RelayoutOp<"pack", [
 
     `padding_value` specifies a padding value at the boundary on non-perfectly
     divisible dimensions. Padding is optional:
-    - If absent, it is UB if the tile does not perfectly divide the dimension.
+    - If absent, it is assumed that for all inner tiles,
+      `shape(source)[inner_dims_pos[i]] % inner_tiles[i] == 0`, i.e. all inner
+      tiles divide perfectly the corresponding outer dimension in the result
+      tensor. It is UB if the tile does not perfectly divide the dimension.
     - If present, it will pad along high dimensions (high-padding) to make the
-      tile complete.
+      tile complete. Note that it is not allowed to have artificial padding that
+      is not strictly required by linalg.pack (i.e., padding past what is needed
+      to complete the last tile along each packed dimension). It is UB if extra
+      padding is requested.
+    It is not possible to verify the requirements statically with dynamic
+    shapes, so they are treated as UB.
 
     Example:
     ```mlir
@@ -167,6 +177,15 @@ def Linalg_PackOp : Linalg_RelayoutOp<"pack", [
     //
     // Note: Only tiled dimensions can be padded.
     ```
+
+    Invalid example that has artificial padding:
+    ```mlir
+    %0 = linalg.pack %src padding_value(%cst : f32) inner_dims_pos = [0]
+        inner_tiles = [8] into %dest
+        : tensor<9xf32> -> tensor<3x8xf32>
+    //                             \
+    //            expect tensor<2x8xf32> because CeilDiv(9, 8) = 2
+    ```
   }];
   let arguments = (ins AnyRankedTensor:$source,
                        AnyRankedTensor:$dest,

mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp

@@ -32,6 +32,7 @@
 #include "mlir/IR/OpImplementation.h"
 #include "mlir/IR/OperationSupport.h"
 #include "mlir/IR/PatternMatch.h"
+#include "mlir/IR/TypeUtilities.h"
 #include "mlir/Interfaces/InferTypeOpInterface.h"
 #include "mlir/Interfaces/SideEffectInterfaces.h"
 
@@ -4622,22 +4623,6 @@ static bool isInvalidPackingPosSpecification(ArrayRef<int64_t> dimsPos,
   });
 }
 
-/// Returns true if the dimension of `sourceShape` is smaller than the dimension
-/// of the `limitShape`.
-static bool areAllInBound(ArrayRef<int64_t> sourceShape,
-                          ArrayRef<int64_t> limitShape) {
-  assert(
-      sourceShape.size() == limitShape.size() &&
-      "expected source shape rank, and limit of the shape to have same rank");
-  return llvm::all_of(
-      llvm::zip(sourceShape, limitShape), [](std::tuple<int64_t, int64_t> it) {
-        int64_t sourceExtent = std::get<0>(it);
-        int64_t limit = std::get<1>(it);
-        return ShapedType::isDynamic(sourceExtent) ||
-               ShapedType::isDynamic(limit) || sourceExtent <= limit;
-      });
-}
-
 template <typename OpTy>
 static LogicalResult commonVerifierPackAndUnPackOp(OpTy packOrUnPack) {
   static_assert(llvm::is_one_of<OpTy, PackOp, UnPackOp>::value,
@@ -4696,11 +4681,6 @@ static LogicalResult commonVerifierPackAndUnPackOp(OpTy packOrUnPack) {
   // represents full tiles.
   RankedTensorType expectedPackedType = PackOp::inferPackedType(
       unpackedType, packOrUnPack.getStaticTiles(), innerDimsPos, outerDimPerm);
-  if (!areAllInBound(expectedPackedType.getShape(), packedType.getShape())) {
-    return op->emitError("the shape of output is not large enough to hold the "
-                         "packed data. Expected at least ")
-           << expectedPackedType << ", got " << packedType;
-  }
   if (!llvm::all_of(
           llvm::zip(packedType.getShape().take_back(mixedTiles.size()),
                     mixedTiles),
@@ -4717,6 +4697,12 @@ static LogicalResult commonVerifierPackAndUnPackOp(OpTy packOrUnPack) {
     return op->emitError("mismatch in inner tile sizes specified and shaped of "
                          "tiled dimension in the packed type");
   }
+  if (failed(verifyCompatibleShape(expectedPackedType.getShape(),
+                                   packedType.getShape()))) {
+    return op->emitError("expected ")
+           << expectedPackedType << " for the packed domain value, got "
+           << packedType;
+  }
   return success();
 }
 

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

@@ -10,6 +10,7 @@
 #include "mlir/Dialect/Linalg/Transforms/Transforms.h"
 #include "mlir/Dialect/Tensor/IR/Tensor.h"
 #include "mlir/Dialect/Utils/IndexingUtils.h"
+#include "mlir/Dialect/Utils/StaticValueUtils.h"
 #include "mlir/IR/PatternMatch.h"
 
 namespace mlir {

mlir/test/Dialect/Linalg/canonicalize.mlir

@@ -1387,51 +1387,52 @@ func.func @recursive_effect(%arg : tensor<1xf32>) {
 // CHECK-LABEL: @recursive_effect
 //       CHECK: linalg.map
 
+// -----
+
 //===----------------------------------------------------------------------===//
 // linalg.pack
 //===----------------------------------------------------------------------===//
 
 // CHECK-LABEL: func @fold_pack_constant_splat
 //   CHECK-NOT: linalg.pack
-//       CHECK: arith.constant dense<1.000000e-01> : tensor<8x16x8x32xf32>
-func.func @fold_pack_constant_splat(%dest : tensor<8x16x8x32xf32>) -> tensor<8x16x8x32xf32> {
+//       CHECK: arith.constant dense<1.000000e-01> : tensor<4x8x8x32xf32>
+func.func @fold_pack_constant_splat(%dest : tensor<4x8x8x32xf32>) -> tensor<4x8x8x32xf32> {
   %cst = arith.constant dense<1.000000e-01> : tensor<64x128xf32>
   %0 = linalg.pack %cst outer_dims_perm = [1, 0] inner_dims_pos = [0, 1]
-    inner_tiles = [8, 32] into %dest : tensor<64x128xf32> -> tensor<8x16x8x32xf32>
-  return %0 : tensor<8x16x8x32xf32>
+    inner_tiles = [8, 32] into %dest : tensor<64x128xf32> -> tensor<4x8x8x32xf32>
+  return %0 : tensor<4x8x8x32xf32>
 }
 
 // -----
 
 // CHECK-LABEL: func @fold_padding_value_pack_constant_splat
 //   CHECK-NOT: linalg.pack
-//       CHECK: arith.constant dense<1.000000e-01> : tensor<8x16x8x32xf32>
-func.func @fold_padding_value_pack_constant_splat(%dest : tensor<8x16x8x32xf32>) -> tensor<8x16x8x32xf32> {
+//       CHECK: arith.constant dense<1.000000e-01> : tensor<4x8x8x32xf32>
+func.func @fold_padding_value_pack_constant_splat(%dest : tensor<4x8x8x32xf32>) -> tensor<4x8x8x32xf32> {
   %pad = arith.constant 1.000000e-01 : f32
   %cst = arith.constant dense<1.000000e-01> : tensor<63x127xf32>
   %0 = linalg.pack %cst
     padding_value(%pad : f32)
     outer_dims_perm = [1, 0] inner_dims_pos = [0, 1]
-    inner_tiles = [8, 32] into %dest : tensor<63x127xf32> -> tensor<8x16x8x32xf32>
-  return %0 : tensor<8x16x8x32xf32>
+    inner_tiles = [8, 32] into %dest : tensor<63x127xf32> -> tensor<4x8x8x32xf32>
+  return %0 : tensor<4x8x8x32xf32>
 }
 
-
 // -----
 
 // CHECK-LABEL: func @nofold_padding_value_pack_constant_splat
 //       CHECK: arith.constant dense<1.000000e-01> : tensor<63x127xf32>
 //       CHECK: linalg.pack
-func.func @nofold_padding_value_pack_constant_splat(%dest : tensor<8x16x8x32xf32>) -> tensor<8x16x8x32xf32> {
+func.func @nofold_padding_value_pack_constant_splat(%dest : tensor<4x8x8x32xf32>) -> tensor<4x8x8x32xf32> {
   %pad = arith.constant 0.0 : f32
   %cst = arith.constant dense<1.000000e-01> : tensor<63x127xf32>
   %0 = linalg.pack %cst
     padding_value(%pad : f32)
     outer_dims_perm = [1, 0]
     inner_dims_pos = [0, 1]
     inner_tiles = [8, 32]
-    into %dest : tensor<63x127xf32> -> tensor<8x16x8x32xf32>
-  return %0 : tensor<8x16x8x32xf32>
+    into %dest : tensor<63x127xf32> -> tensor<4x8x8x32xf32>
+  return %0 : tensor<4x8x8x32xf32>
 }
 
 // -----

mlir/test/Dialect/Linalg/data-layout-propagation.mlir

@@ -1295,24 +1295,6 @@ func.func @no_bubble_up_pack_expanded_padding_through_expand_cannot_reassociate(
 
 // -----
 
-func.func @no_bubble_up_pack_extending_dimension_through_expand_cannot_reassociate(%arg0: tensor<32x64xf32>) -> tensor<8x4x16x8xf32> {
-  %empty = tensor.empty() : tensor<8x4x16x8xf32>
-  %expanded = tensor.expand_shape %arg0 [[0], [1, 2]] output_shape [32, 4, 16] : tensor<32x64xf32> into tensor<32x4x16xf32>
-  %pack = linalg.pack %expanded inner_dims_pos = [0] inner_tiles = [8] into %empty : tensor<32x4x16xf32> -> tensor<8x4x16x8xf32>
-  return %pack : tensor<8x4x16x8xf32>
-}
-// CHECK-LABEL: func.func @no_bubble_up_pack_extending_dimension_through_expand_cannot_reassociate(
-// CHECK-SAME:      %[[ARG0:[a-zA-Z0-9]+]]
-// CHECK:         %[[EMPTY:.+]] = tensor.empty() : tensor<8x4x16x8xf32>
-// CHECK:         %[[EXPANDED:.+]] = tensor.expand_shape %[[ARG0]] {{\[}}[0], [1, 2]]
-// CHECK-SAME:      output_shape [32, 4, 16] : tensor<32x64xf32> into tensor<32x4x16xf32>
-// CHECK:         %[[PACK:.+]] = linalg.pack %[[EXPANDED]]
-// CHECK-SAME:      inner_dims_pos = [0] inner_tiles = [8] into %[[EMPTY]]
-// CHECK-SAME:      : tensor<32x4x16xf32> -> tensor<8x4x16x8xf32>
-// CHECK:         return %[[PACK]] : tensor<8x4x16x8xf32>
-
-// -----
-
 func.func @push_down_unpack_through_expand(%5: tensor<?x32x8x8xf32>, %dim: index, %sz0: index) -> tensor<?x256x256xf32> {
   %6 = tensor.empty(%dim) : tensor<?x256xf32>
   %unpack = linalg.unpack %5 outer_dims_perm = [0, 1] inner_dims_pos = [0, 1] inner_tiles = [8, 8] into %6 : tensor<?x32x8x8xf32> -> tensor<?x256xf32>

mlir/test/Dialect/Linalg/invalid.mlir

@@ -1760,6 +1760,7 @@ func.func @pack_invalid(%input: tensor<256x128xf32>, %output: tensor<8x8x32x16xf
 }
 
 // -----
+
 func.func @pack_mismatch_inner_tile_size_and_output_shape(
   %input : tensor<?x?xf32>, %output : tensor<?x?x8x8xf32>) -> tensor<?x?x8x8xf32> {
   // expected-error@+1 {{mismatch in inner tile sizes specified and shaped of tiled dimension in the packed type}}
@@ -1824,27 +1825,47 @@ func.func @unpack_invalid_outer_dims_perm(%source: tensor<128x256xf32>, %dest: t
 
 // -----
 
+func.func @pack_with_artificial_padding(%input: tensor<9xf32>, %output: tensor<3x8xf32>) -> tensor<3x8xf32> {
+  %cst = arith.constant 0.0 : f32
+  // expected-error@+1 {{expected 'tensor<2x8xf32>' for the packed domain value, got 'tensor<3x8xf32>'}}
+  %0 = linalg.pack %input padding_value(%cst : f32) inner_dims_pos = [0]
+      inner_tiles = [8] into %output
+      : tensor<9xf32> -> tensor<3x8xf32>
+  return %0 : tensor<3x8xf32>
+}
+
+// -----
+
 // The outer dims in the output tensor are incorrectly/unexpectedly transposed.
 // This could be fixed by adding `outer_dims_perm = [1, 0]` (the default value assumes no transpose).
 func.func @pack_invalid_result_shape(%input: tensor<256x128xf32>, %output: tensor<4x16x32x16xf32>) -> tensor<4x16x32x16xf32> {
-  // expected-error@+1 {{the shape of output is not large enough to hold the packed data. Expected at least 'tensor<16x4x32x16xf32>', got 'tensor<4x16x32x16xf32>'}}
+  // expected-error@+1 {{expected 'tensor<16x4x32x16xf32>' for the packed domain value, got 'tensor<4x16x32x16xf32>'}}
   %0 = linalg.pack %input inner_dims_pos = [1, 0] inner_tiles = [32, 16] into %output : tensor<256x128xf32> -> tensor<4x16x32x16xf32>
   return %0 : tensor<4x16x32x16xf32>
 }
 
 // -----
 
-func.func @pack_invalid(%input: tensor<256x128xf32>, %output: tensor<8x8x32x16xf32>) -> tensor<8x8x32x16xf32> {
-  // expected-error@+1 {{the shape of output is not large enough to hold the packed data. Expected at least 'tensor<8x8x16x32xf32>', got 'tensor<8x8x32x16xf32>'}}
-  %0 = linalg.pack %input inner_dims_pos = [1, 0] inner_tiles = [16, 32] into %output : tensor<256x128xf32> -> tensor<8x8x32x16xf32>
-  return %0 : tensor<8x8x32x16xf32>
+func.func @pack_invalid_result_shape(%input: tensor<256x128xf32>, %output: tensor<8x7x16x32xf32>) -> tensor<8x7x16x32xf32> {
+  // expected-error@+1 {{expected 'tensor<8x8x16x32xf32>' for the packed domain value, got 'tensor<8x7x16x32xf32>'}}
+  %0 = linalg.pack %input inner_dims_pos = [1, 0] inner_tiles = [16, 32] into %output : tensor<256x128xf32> -> tensor<8x7x16x32xf32>
+  return %0 : tensor<8x7x16x32xf32>
+}
+
+// -----
+
+func.func @unpack_with_artifical_tiles_that_are_dropped(%input: tensor<3x8xf32>, %output: tensor<9xf32>) -> tensor<9xf32> {
+  // expected-error@+1 {{expected 'tensor<2x8xf32>' for the packed domain value, got 'tensor<3x8xf32>'}}
+  %0 = linalg.unpack %input inner_dims_pos = [0] inner_tiles = [8] into %output
+      : tensor<3x8xf32> -> tensor<9xf32>
+  return %0 : tensor<9xf32>
 }
 
 // -----
 
-func.func @unpack_invalid(%output: tensor<256x128xf32>, %input: tensor<8x8x32x16xf32>) -> tensor<256x128xf32> {
-  // expected-error@+1 {{the shape of output is not large enough to hold the packed data. Expected at least 'tensor<8x32x4x32xf32>', got 'tensor<8x8x32x16xf32>'}}
-  %0 = linalg.unpack %input inner_dims_pos = [1, 0] inner_tiles = [4, 32] into %output : tensor<8x8x32x16xf32> -> tensor<256x128xf32>
+func.func @unpack_invalid_source_shape(%output: tensor<256x128xf32>, %input: tensor<8x8x4x32xf32>) -> tensor<256x128xf32> {
+  // expected-error@+1 {{expected 'tensor<8x32x4x32xf32>' for the packed domain value, got 'tensor<8x8x4x32xf32>'}}
+  %0 = linalg.unpack %input inner_dims_pos = [1, 0] inner_tiles = [4, 32] into %output : tensor<8x8x4x32xf32> -> tensor<256x128xf32>
   return %0 : tensor<256x128xf32>
 }
 

mlir/test/Dialect/Linalg/transform-lower-pack.mlir

@@ -326,23 +326,23 @@ module attributes {transform.with_named_sequence} {
 // -----
 
 // CHECK-LABEL: func.func @pack_with_pad(
-func.func @pack_with_pad(%src: tensor<4225x12xf32>, %dest: tensor<265x16x16x1xf32>)
-    -> tensor<265x16x16x1xf32> {
+func.func @pack_with_pad(%src: tensor<4225x12xf32>, %dest: tensor<265x12x16x1xf32>)
+    -> tensor<265x12x16x1xf32> {
   //      CHECK: tensor.pad {{.*}} low[0, 0]
-  //      CHECK:   : tensor<4225x12xf32> to tensor<4240x16xf32>
+  //      CHECK:   : tensor<4225x12xf32> to tensor<4240x12xf32>
   //      CHECK: tensor.expand_shape %{{.*}} {{\[}}[0, 1], [2, 3]]
-  // CHECK-SAME:   : tensor<4240x16xf32> into tensor<265x16x16x1xf32>
+  // CHECK-SAME:   : tensor<4240x12xf32> into tensor<265x16x12x1xf32>
   //      CHECK: linalg.transpose
-  // CHECK-SAME:   ins(%{{[a-zA-Z0-9]*}} : tensor<265x16x16x1xf32>)
-  // CHECK-SAME:   outs(%{{[a-zA-Z0-9]*}} : tensor<265x16x16x1xf32>)
+  // CHECK-SAME:   ins(%{{[a-zA-Z0-9]*}} : tensor<265x16x12x1xf32>)
+  // CHECK-SAME:   outs(%{{[a-zA-Z0-9]*}} : tensor<265x12x16x1xf32>)
   // CHECK-SAME:   permutation = [0, 2, 1, 3]
   %cst = arith.constant 0.000000e+00 : f32
   %0 = linalg.pack %src
     padding_value(%cst : f32)
     inner_dims_pos = [0, 1]
     inner_tiles = [16, 1] into %dest
-    : tensor<4225x12xf32> -> tensor<265x16x16x1xf32>
-  return %0 : tensor<265x16x16x1xf32>
+    : tensor<4225x12xf32> -> tensor<265x12x16x1xf32>
+  return %0 : tensor<265x12x16x1xf32>
 }
 
 module attributes {transform.with_named_sequence} {

mlir/test/Integration/Dialect/Linalg/CPU/pack-unpack-mmt4d.mlir

@@ -81,21 +81,21 @@ func.func private @matmul(%A: tensor<7x16xi32>, %B: tensor<16x13xi32>, %C: tenso
 func.func private @mmt4d(%A: tensor<7x16xi32>, %B: tensor<16x13xi32>, %C: tensor<7x13xi32>) -> tensor<7x13xi32> {
   %zero = arith.constant 0 : i32
 
-  %A_pack_empty = tensor.empty() : tensor<2x16x8x1xi32>
+  %A_pack_empty = tensor.empty() : tensor<1x16x8x1xi32>
   %B_pack_empty = tensor.empty() : tensor<2x16x8x1xi32>
-  %C_pack_empty = tensor.empty() : tensor<2x2x8x8xi32>
+  %C_pack_empty = tensor.empty() : tensor<1x2x8x8xi32>
 
   // Pack matrices
-  %A_pack = linalg.pack %A padding_value(%zero : i32) inner_dims_pos = [0, 1] inner_tiles = [8, 1] into %A_pack_empty : tensor<7x16xi32> -> tensor<2x16x8x1xi32>
+  %A_pack = linalg.pack %A padding_value(%zero : i32) inner_dims_pos = [0, 1] inner_tiles = [8, 1] into %A_pack_empty : tensor<7x16xi32> -> tensor<1x16x8x1xi32>
   %B_pack = linalg.pack %B padding_value(%zero : i32) outer_dims_perm = [1, 0] inner_dims_pos = [1, 0] inner_tiles = [8, 1] into %B_pack_empty : tensor<16x13xi32> -> tensor<2x16x8x1xi32>
-  %C_pack = linalg.pack %C padding_value(%zero : i32) outer_dims_perm = [0, 1] inner_dims_pos = [0, 1] inner_tiles = [8, 8] into %C_pack_empty : tensor<7x13xi32> -> tensor<2x2x8x8xi32>
+  %C_pack = linalg.pack %C padding_value(%zero : i32) outer_dims_perm = [0, 1] inner_dims_pos = [0, 1] inner_tiles = [8, 8] into %C_pack_empty : tensor<7x13xi32> -> tensor<1x2x8x8xi32>
 
   // MMT4D
-  %mmt4d = linalg.mmt4d ins(%A_pack, %B_pack : tensor<2x16x8x1xi32>, tensor<2x16x8x1xi32>) outs(%C_pack : tensor<2x2x8x8xi32>) -> tensor<2x2x8x8xi32>
+  %mmt4d = linalg.mmt4d ins(%A_pack, %B_pack : tensor<1x16x8x1xi32>, tensor<2x16x8x1xi32>) outs(%C_pack : tensor<1x2x8x8xi32>) -> tensor<1x2x8x8xi32>
 
   // Unpack output
   %C_out_empty = tensor.empty() : tensor<7x13xi32>
-  %C_out_unpack = linalg.unpack %mmt4d outer_dims_perm = [0, 1] inner_dims_pos = [0, 1] inner_tiles = [8, 8] into %C_out_empty : tensor<2x2x8x8xi32> -> tensor<7x13xi32>
+  %C_out_unpack = linalg.unpack %mmt4d outer_dims_perm = [0, 1] inner_dims_pos = [0, 1] inner_tiles = [8, 8] into %C_out_empty : tensor<1x2x8x8xi32> -> tensor<7x13xi32>
 
   return %C_out_unpack : tensor<7x13xi32>
 }