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Differential D148470

[mlir][vector] Fix integer promotion type mismatch
ClosedPublic

Authored by antiagainst on Apr 16 2023, 8:51 AM.

Details

Reviewers
kuhar
aartbik
nicolasvasilache
dcaballe
ThomasRaoux
Commits
rG5041fe8439c1: [mlir][vector] Fix integer promotion type mismatch
Summary

We need to create a new type with transposed shape after
transposing the operand in CanonicalizeContractMatmulToMMT.

Diff Detail

Event Timeline

antiagainst created this revision.Apr 16 2023, 8:51 AM
Herald added a reviewer: aartbik. · View Herald TranscriptApr 16 2023, 8:51 AM
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Herald added subscribers: bviyer, Moerafaat, zero9178 and 24 others. · View Herald Transcript
antiagainst requested review of this revision.Apr 16 2023, 8:51 AM
Herald added a reviewer: nicolasvasilache. · View Herald TranscriptApr 16 2023, 8:51 AM
Herald added a reviewer: dcaballe. · View Herald Transcript
Herald added a project: Restricted Project. · View Herald Transcript
Herald added subscribers: stephenneuendorffer, nicolasvasilache. · View Herald Transcript
antiagainst added a reviewer: ThomasRaoux.Apr 16 2023, 8:56 AM
Harbormaster completed remote builds in B225943: Diff 514021.Apr 16 2023, 9:05 AM
kuhar accepted this revision.Apr 16 2023, 10:27 AM

Thanks for fixing!

mlir/lib/Dialect/Vector/Transforms/VectorTransforms.cpp
1082

nit: prefer the free cast functions

This revision is now accepted and ready to land.Apr 16 2023, 10:27 AM
dcaballe accepted this revision.Apr 17 2023, 10:59 AM
dcaballe added inline comments.
mlir/lib/Dialect/Vector/Transforms/VectorTransforms.cpp
1090

Probably easier to just use the VectorType::get factory.

Closed by commit rG5041fe8439c1: [mlir][vector] Fix integer promotion type mismatch (authored by antiagainst). · Explain WhyApr 17 2023, 11:29 AM
This revision was automatically updated to reflect the committed changes.
antiagainst marked 2 inline comments as done.
antiagainst added a commit: rG5041fe8439c1: [mlir][vector] Fix integer promotion type mismatch.

Revision Contents

PathSize
mlir/
lib/
Dialect/
Vector/
Transforms/
8 lines
test/
Dialect/
Vector/
62 lines

Diff 514021

mlir/lib/Dialect/Vector/Transforms/VectorTransforms.cpp

Show First 20 Lines • Show All 1,073 Lines • ▼ Show 20 Lines if (maps == canonicalForm)
return rewriter.notifyMatchFailure(op, "already in the canonical form"); return rewriter.notifyMatchFailure(op, "already in the canonical form");
// Create a vector transpose making sure to emit zero/sign-extend at the // Create a vector transpose making sure to emit zero/sign-extend at the
// end. // end.
auto createTranspose = [&rewriter, loc](Value mat) -> Value { auto createTranspose = [&rewriter, loc](Value mat) -> Value {
if (auto sext = mat.getDefiningOp<arith::ExtSIOp>()) { if (auto sext = mat.getDefiningOp<arith::ExtSIOp>()) {
Value trans = Value trans =
rewriter.create<vector::TransposeOp>(loc, sext.getIn(), perm); rewriter.create<vector::TransposeOp>(loc, sext.getIn(), perm);
return rewriter.create<arith::ExtSIOp>(loc, mat.getType(), trans); VectorType newType = trans.getType().cast<VectorType>().cloneWith(
kuharUnsubmitted
Done
ReplyInline Actions

nit: prefer the free cast functions

kuhar: nit: prefer the free cast functions
std::nullopt, mat.getType().cast<VectorType>().getElementType());
return rewriter.create<arith::ExtSIOp>(loc, newType, trans);
} }
if (auto zext = mat.getDefiningOp<arith::ExtUIOp>()) { if (auto zext = mat.getDefiningOp<arith::ExtUIOp>()) {
Value trans = Value trans =
rewriter.create<vector::TransposeOp>(loc, zext.getIn(), perm); rewriter.create<vector::TransposeOp>(loc, zext.getIn(), perm);
return rewriter.create<arith::ExtUIOp>(loc, mat.getType(), trans); VectorType newType = trans.getType().cast<VectorType>().cloneWith(
std::nullopt, mat.getType().cast<VectorType>().getElementType());
dcaballeUnsubmitted
Done
ReplyInline Actions

Probably easier to just use the VectorType::get factory.

dcaballe: Probably easier to just use the `VectorType::get` factory.
return rewriter.create<arith::ExtUIOp>(loc, newType, trans);
} }
return rewriter.create<vector::TransposeOp>(loc, mat, perm); return rewriter.create<vector::TransposeOp>(loc, mat, perm);
}; };
if (maps == infer({{m, k}, {k, n}, {m, n}})) { if (maps == infer({{m, k}, {k, n}, {m, n}})) {
rhs = createTranspose(rhs); rhs = createTranspose(rhs);
} else if (maps == infer({{k, m}, {n, k}, {m, n}})) { } else if (maps == infer({{k, m}, {n, k}, {m, n}})) {
lhs = createTranspose(lhs); lhs = createTranspose(lhs);
▲ Show 20 Lines • Show All 79 Lines • Show Last 20 Lines

mlir/test/Dialect/Vector/vector-contract-matmul-transforms.mlir

Show All 36 Linesfunc.func @matmul_mk_kn_mn_4x4xi32(%arg0: vector<4x4xi32>, %arg1: vector<4x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> {
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>,
affine_map<(d0, d1, d2) -> (d2, d1)>, affine_map<(d0, d1, d2) -> (d2, d1)>,
affine_map<(d0, d1, d2) -> (d0, d1)>], affine_map<(d0, d1, d2) -> (d0, d1)>],
iterator_types = ["parallel", "parallel", "reduction"], iterator_types = ["parallel", "parallel", "reduction"],
kind = #vector.kind<add>} %arg0, %arg1, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32> kind = #vector.kind<add>} %arg0, %arg1, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32>
return %res : vector<4x4xi32> return %res : vector<4x4xi32>
} }
// CHECK-LABEL: func.func @matmul_mk_kn_mn_4x4xi8_extsi_i32 // CHECK-LABEL: func.func @matmul_mk_kn_mn_8x16xi8_extsi_i32
// CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi8>, [[ARG1:%.+]]: vector<4x4xi8>, [[ARG2:%.+]]: vector<4x4xi32>) // CHECK-SAME: ([[ARG0:%.+]]: vector<8x4xi8>, [[ARG1:%.+]]: vector<4x16xi8>, [[ARG2:%.+]]: vector<8x16xi32>)
// CHECK-NEXT: [[LHS:%.+]] = arith.extsi [[ARG0]] : vector<4x4xi8> to vector<4x4xi32> // CHECK-NEXT: [[LHS:%.+]] = arith.extsi [[ARG0]] : vector<8x4xi8> to vector<8x4xi32>
// CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<4x4xi8> to vector<4x4xi8> // CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<4x16xi8> to vector<16x4xi8>
// CHECK-NEXT: [[RHS:%.+]] = arith.extsi [[TRANS]] : vector<4x4xi8> to vector<4x4xi32> // CHECK-NEXT: [[RHS:%.+]] = arith.extsi [[TRANS]] : vector<16x4xi8> to vector<16x4xi32>
// CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[LHS]], [[RHS]], [[ARG2]] // CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[LHS]], [[RHS]], [[ARG2]]
// CHECK-NEXT: return [[RES]] // CHECK-NEXT: return [[RES]]
func.func @matmul_mk_kn_mn_4x4xi8_extsi_i32(%arg0: vector<4x4xi8>, %arg1: vector<4x4xi8>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> { func.func @matmul_mk_kn_mn_8x16xi8_extsi_i32(%arg0: vector<8x4xi8>, %arg1: vector<4x16xi8>, %arg2: vector<8x16xi32>) -> vector<8x16xi32> {
%lhs = arith.extsi %arg0: vector<4x4xi8> to vector<4x4xi32> %lhs = arith.extsi %arg0: vector<8x4xi8> to vector<8x4xi32>
%rhs = arith.extsi %arg1: vector<4x4xi8> to vector<4x4xi32> %rhs = arith.extsi %arg1: vector<4x16xi8> to vector<4x16xi32>
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>,
affine_map<(d0, d1, d2) -> (d2, d1)>, affine_map<(d0, d1, d2) -> (d2, d1)>,
affine_map<(d0, d1, d2) -> (d0, d1)>], affine_map<(d0, d1, d2) -> (d0, d1)>],
iterator_types = ["parallel", "parallel", "reduction"], iterator_types = ["parallel", "parallel", "reduction"],
kind = #vector.kind<add>} %lhs, %rhs, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32> kind = #vector.kind<add>} %lhs, %rhs, %arg2 : vector<8x4xi32>, vector<4x16xi32> into vector<8x16xi32>
return %res : vector<4x4xi32> return %res : vector<8x16xi32>
} }
// Check that non-square shapes are also handled. // Check that non-square shapes are also handled.
// CHECK-LABEL: func.func @matmul_mk_kn_mn_4x16xi32 // CHECK-LABEL: func.func @matmul_mk_kn_mn_4x16xi32
// CHECK-SAME: ([[ARG0:%.+]]: vector<4x16xi32>, [[ARG1:%.+]]: vector<16x4xi32>, [[ARG2:%.+]]: vector<4x4xi32>) // CHECK-SAME: ([[ARG0:%.+]]: vector<4x16xi32>, [[ARG1:%.+]]: vector<16x4xi32>, [[ARG2:%.+]]: vector<4x4xi32>)
// CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<16x4xi32> to vector<4x16xi32> // CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<16x4xi32> to vector<4x16xi32>
// CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[ARG0]], [[TRANS]], [[ARG2]] // CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[ARG0]], [[TRANS]], [[ARG2]]
// CHECK-NEXT: return [[RES]] // CHECK-NEXT: return [[RES]]
func.func @matmul_mk_kn_mn_4x16xi32(%arg0: vector<4x16xi32>, %arg1: vector<16x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> { func.func @matmul_mk_kn_mn_4x16xi32(%arg0: vector<4x16xi32>, %arg1: vector<16x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> {
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>,
affine_map<(d0, d1, d2) -> (d2, d1)>, affine_map<(d0, d1, d2) -> (d2, d1)>,
affine_map<(d0, d1, d2) -> (d0, d1)>], affine_map<(d0, d1, d2) -> (d0, d1)>],
iterator_types = ["parallel", "parallel", "reduction"], iterator_types = ["parallel", "parallel", "reduction"],
kind = #vector.kind<add>} %arg0, %arg1, %arg2 : vector<4x16xi32>, vector<16x4xi32> into vector<4x4xi32> kind = #vector.kind<add>} %arg0, %arg1, %arg2 : vector<4x16xi32>, vector<16x4xi32> into vector<4x4xi32>
return %res : vector<4x4xi32> return %res : vector<4x4xi32>
} }
// CHECK-LABEL: func.func @matmul_mk_kn_mn_4x4xi8_extui_i32 // CHECK-LABEL: func.func @matmul_mk_kn_mn_8x16xi8_extui_i32
// CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi8>, [[ARG1:%.+]]: vector<4x4xi8>, [[ARG2:%.+]]: vector<4x4xi32>) // CHECK-SAME: ([[ARG0:%.+]]: vector<8x4xi8>, [[ARG1:%.+]]: vector<4x16xi8>, [[ARG2:%.+]]: vector<8x16xi32>)
// CHECK-NEXT: [[LHS:%.+]] = arith.extui [[ARG0]] : vector<4x4xi8> to vector<4x4xi32> // CHECK-NEXT: [[LHS:%.+]] = arith.extui [[ARG0]] : vector<8x4xi8> to vector<8x4xi32>
// CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<4x4xi8> to vector<4x4xi8> // CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<4x16xi8> to vector<16x4xi8>
// CHECK-NEXT: [[RHS:%.+]] = arith.extui [[TRANS]] : vector<4x4xi8> to vector<4x4xi32> // CHECK-NEXT: [[RHS:%.+]] = arith.extui [[TRANS]] : vector<16x4xi8> to vector<16x4xi32>
// CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[LHS]], [[RHS]], [[ARG2]] // CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[LHS]], [[RHS]], [[ARG2]]
// CHECK-NEXT: return [[RES]] // CHECK-NEXT: return [[RES]]
func.func @matmul_mk_kn_mn_4x4xi8_extui_i32(%arg0: vector<4x4xi8>, %arg1: vector<4x4xi8>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> { func.func @matmul_mk_kn_mn_8x16xi8_extui_i32(%arg0: vector<8x4xi8>, %arg1: vector<4x16xi8>, %arg2: vector<8x16xi32>) -> vector<8x16xi32> {
%lhs = arith.extui %arg0: vector<4x4xi8> to vector<4x4xi32> %lhs = arith.extui %arg0: vector<8x4xi8> to vector<8x4xi32>
%rhs = arith.extui %arg1: vector<4x4xi8> to vector<4x4xi32> %rhs = arith.extui %arg1: vector<4x16xi8> to vector<4x16xi32>
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>,
affine_map<(d0, d1, d2) -> (d2, d1)>, affine_map<(d0, d1, d2) -> (d2, d1)>,
affine_map<(d0, d1, d2) -> (d0, d1)>], affine_map<(d0, d1, d2) -> (d0, d1)>],
iterator_types = ["parallel", "parallel", "reduction"], iterator_types = ["parallel", "parallel", "reduction"],
kind = #vector.kind<add>} %lhs, %rhs, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32> kind = #vector.kind<add>} %lhs, %rhs, %arg2 : vector<8x4xi32>, vector<4x16xi32> into vector<8x16xi32>
return %res : vector<4x4xi32> return %res : vector<8x16xi32>
} }
// CHECK-LABEL: func.func @matmul_km_nk_mn_4x4xi32 // CHECK-LABEL: func.func @matmul_km_nk_mn_4x4xi32
// CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi32>, [[ARG1:%.+]]: vector<4x4xi32>, [[ARG2:%.+]]: vector<4x4xi32>) // CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi32>, [[ARG1:%.+]]: vector<4x4xi32>, [[ARG2:%.+]]: vector<4x4xi32>)
// CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG0]], [1, 0] : vector<4x4xi32> to vector<4x4xi32> // CHECK-NEXT: [[TRANS:%.+]] = vector.transpose [[ARG0]], [1, 0] : vector<4x4xi32> to vector<4x4xi32>
// CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[TRANS]], [[ARG1]], [[ARG2]] // CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[TRANS]], [[ARG1]], [[ARG2]]
// CHECK-NEXT: return [[RES]] // CHECK-NEXT: return [[RES]]
func.func @matmul_km_nk_mn_4x4xi32(%arg0: vector<4x4xi32>, %arg1: vector<4x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> { func.func @matmul_km_nk_mn_4x4xi32(%arg0: vector<4x4xi32>, %arg1: vector<4x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> {
Show All 15 Linesfunc.func @matmul_km_kn_mn_4x4xi32(%arg0: vector<4x4xi32>, %arg1: vector<4x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> {
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d2, d0)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d2, d0)>,
affine_map<(d0, d1, d2) -> (d2, d1)>, affine_map<(d0, d1, d2) -> (d2, d1)>,
affine_map<(d0, d1, d2) -> (d0, d1)>], affine_map<(d0, d1, d2) -> (d0, d1)>],
iterator_types = ["parallel", "parallel", "reduction"], iterator_types = ["parallel", "parallel", "reduction"],
kind = #vector.kind<add>} %arg0, %arg1, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32> kind = #vector.kind<add>} %arg0, %arg1, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32>
return %res : vector<4x4xi32> return %res : vector<4x4xi32>
} }
// CHECK-LABEL: func.func @matmul_km_kn_mn_4x4xi8_mixed_ext_i32 // CHECK-LABEL: func.func @matmul_km_kn_mn_8x16xi8_mixed_ext_i32
// CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi8>, [[ARG1:%.+]]: vector<4x4xi8>, [[ARG2:%.+]]: vector<4x4xi32>) // CHECK-SAME: ([[ARG0:%.+]]: vector<4x8xi8>, [[ARG1:%.+]]: vector<4x16xi8>, [[ARG2:%.+]]: vector<8x16xi32>)
// CHECK-DAG: [[LHST:%.+]] = vector.transpose [[ARG0]], [1, 0] : vector<4x4xi8> to vector<4x4xi8> // CHECK-DAG: [[LHST:%.+]] = vector.transpose [[ARG0]], [1, 0] : vector<4x8xi8> to vector<8x4xi8>
// CHECK-DAG: [[LHS:%.+]] = arith.extsi [[LHST]] : vector<4x4xi8> to vector<4x4xi32> // CHECK-DAG: [[LHS:%.+]] = arith.extsi [[LHST]] : vector<8x4xi8> to vector<8x4xi32>
// CHECK-DAG: [[RHST:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<4x4xi8> to vector<4x4xi8> // CHECK-DAG: [[RHST:%.+]] = vector.transpose [[ARG1]], [1, 0] : vector<4x16xi8> to vector<16x4xi8>
// CHECK-DAG: [[RHS:%.+]] = arith.extui [[RHST]] : vector<4x4xi8> to vector<4x4xi32> // CHECK-DAG: [[RHS:%.+]] = arith.extui [[RHST]] : vector<16x4xi8> to vector<16x4xi32>
// CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[LHS]], [[RHS]], [[ARG2]] // CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[LHS]], [[RHS]], [[ARG2]]
// CHECK-NEXT: return [[RES]] // CHECK-NEXT: return [[RES]]
func.func @matmul_km_kn_mn_4x4xi8_mixed_ext_i32(%arg0: vector<4x4xi8>, %arg1: vector<4x4xi8>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> { func.func @matmul_km_kn_mn_8x16xi8_mixed_ext_i32(%arg0: vector<4x8xi8>, %arg1: vector<4x16xi8>, %arg2: vector<8x16xi32>) -> vector<8x16xi32> {
%lhs = arith.extsi %arg0 : vector<4x4xi8> to vector<4x4xi32> %lhs = arith.extsi %arg0 : vector<4x8xi8> to vector<4x8xi32>
%rhs = arith.extui %arg1 : vector<4x4xi8> to vector<4x4xi32> %rhs = arith.extui %arg1 : vector<4x16xi8> to vector<4x16xi32>
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d2, d0)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d2, d0)>,
affine_map<(d0, d1, d2) -> (d2, d1)>, affine_map<(d0, d1, d2) -> (d2, d1)>,
affine_map<(d0, d1, d2) -> (d0, d1)>], affine_map<(d0, d1, d2) -> (d0, d1)>],
iterator_types = ["parallel", "parallel", "reduction"], iterator_types = ["parallel", "parallel", "reduction"],
kind = #vector.kind<add>} %lhs, %rhs, %arg2 : vector<4x4xi32>, vector<4x4xi32> into vector<4x4xi32> kind = #vector.kind<add>} %lhs, %rhs, %arg2 : vector<4x8xi32>, vector<4x16xi32> into vector<8x16xi32>
return %res : vector<4x4xi32> return %res : vector<8x16xi32>
} }
// CHECK-LABEL: func.func @matmul_mk_nk_nm_4x4xi32 // CHECK-LABEL: func.func @matmul_mk_nk_nm_4x4xi32
// CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi32>, [[ARG1:%.+]]: vector<4x4xi32>, [[ARG2:%.+]]: vector<4x4xi32>) // CHECK-SAME: ([[ARG0:%.+]]: vector<4x4xi32>, [[ARG1:%.+]]: vector<4x4xi32>, [[ARG2:%.+]]: vector<4x4xi32>)
// CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[ARG1]], [[ARG0]], [[ARG2]] // CHECK-NEXT: [[RES:%.+]] = vector.contract {{.+}} [[ARG1]], [[ARG0]], [[ARG2]]
// CHECK-NEXT: return [[RES]] // CHECK-NEXT: return [[RES]]
func.func @matmul_mk_nk_nm_4x4xi32(%arg0: vector<4x4xi32>, %arg1: vector<4x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> { func.func @matmul_mk_nk_nm_4x4xi32(%arg0: vector<4x4xi32>, %arg1: vector<4x4xi32>, %arg2: vector<4x4xi32>) -> vector<4x4xi32> {
%res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>, %res = vector.contract {indexing_maps = [affine_map<(d0, d1, d2) -> (d0, d2)>,
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