diff --git a/mlir/test/Dialect/SparseTensor/vectorize_reduction.mlir b/mlir/test/Dialect/SparseTensor/vectorize_reduction.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/SparseTensor/vectorize_reduction.mlir
@@ -0,0 +1,468 @@
+// RUN: mlir-opt %s -sparsification -cse -sparse-vectorization="vl=8" -cse -split-input-file | \
+// RUN:   FileCheck %s --check-prefix=CHECK-ON
+// RUN: mlir-opt %s -sparsification -cse -split-input-file | \
+// RUN:   FileCheck %s --check-prefix=CHECK-OFF
+
+// -----
+
+// Check that we recognize a reduction with a mul operator.
+// We use two dimensions here to check that the vectorization
+// is not affected by how the outer loop is layed out.
+// In other words, we should be able to vectorize the sparse inner loop
+// regardless of whether the outer loop is dense or sparse.
+//
+// For this particular test, we expect:
+// With vectorization on:
+// dense scf.for
+//   init vector_accumulator = {scalar_accumulator, 1.0, 1.0, ...}
+//   sparse scf.for
+//     vectorized mul in vector_accumulator, vector_input
+//   horizontal reduction of the vector_accumulator to scalar_accumulator
+// final store of scalar_accumulaor
+//
+// With vectorization off:
+// dense scf.for
+//   sparse scf.for
+//     mul in accumulator
+// final store
+//
+// CHECK-ON-LABEL:   func.func @sparse_product_reduction_dense_sparse(
+// CHECK-ON-SAME:                                                     %[[VAL_0:.*]]: tensor<f64>,
+// CHECK-ON-SAME:                                                     %[[VAL_1:.*]]: tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>>) -> tensor<f64> {
+// CHECK-ON-DAG:       %[[VAL_2:.*]] = arith.constant 8 : index
+// CHECK-ON-DAG:       %[[VAL_3:.*]] = arith.constant dense<1.000000e+00> : vector<8xf64>
+// CHECK-ON-DAG:       %[[VAL_4:.*]] = arith.constant dense<0.000000e+00> : vector<8xf64>
+// CHECK-ON-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
+// CHECK-ON-DAG:       %[[VAL_6:.*]] = arith.constant 1 : index
+// CHECK-ON-DAG:       %[[VAL_7:.*]] = tensor.dim %[[VAL_1]], %[[VAL_5]] : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>>
+// CHECK-ON:           %[[VAL_8:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 1 : index} : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>> to memref<?xindex>
+// CHECK-ON:           %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>> to memref<?xf64>
+// CHECK-ON:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_0]] : memref<f64>
+// CHECK-ON:           %[[VAL_11:.*]] = memref.load %[[VAL_10]][] : memref<f64>
+// CHECK-ON:           %[[VAL_12:.*]] = scf.for %[[VAL_13:.*]] = %[[VAL_5]] to %[[VAL_7]] step %[[VAL_6]] iter_args(%[[VAL_14:.*]] = %[[VAL_11]]) -> (f64) {
+// CHECK-ON:             %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK-ON:             %[[VAL_16:.*]] = arith.addi %[[VAL_13]], %[[VAL_6]] : index
+// CHECK-ON:             %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK-ON:             %[[VAL_18:.*]] = vector.insertelement %[[VAL_14]], %[[VAL_3]]{{\[}}%[[VAL_5]] : index] : vector<8xf64>
+// CHECK-ON:             %[[VAL_19:.*]] = scf.for %[[VAL_20:.*]] = %[[VAL_15]] to %[[VAL_17]] step %[[VAL_2]] iter_args(%[[VAL_21:.*]] = %[[VAL_18]]) -> (vector<8xf64>) {
+// CHECK-ON:               %[[VAL_22:.*]] = affine.min #map(%[[VAL_17]], %[[VAL_20]]){{\[}}%[[VAL_2]]]
+// CHECK-ON:               %[[VAL_23:.*]] = vector.create_mask %[[VAL_22]] : vector<8xi1>
+// CHECK-ON:               %[[VAL_24:.*]] = vector.maskedload %[[VAL_9]]{{\[}}%[[VAL_20]]], %[[VAL_23]], %[[VAL_4]] : memref<?xf64>, vector<8xi1>, vector<8xf64> into vector<8xf64>
+// CHECK-ON:               %[[VAL_25:.*]] = arith.mulf %[[VAL_21]], %[[VAL_24]] : vector<8xf64>
+// CHECK-ON:               %[[VAL_26:.*]] = arith.select %[[VAL_23]], %[[VAL_25]], %[[VAL_21]] : vector<8xi1>, vector<8xf64>
+// CHECK-ON:               scf.yield %[[VAL_26]] : vector<8xf64>
+// CHECK-ON:             } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:             %[[VAL_27:.*]] = vector.reduction <mul>, %[[VAL_28:.*]] : vector<8xf64> into f64
+// CHECK-ON:             scf.yield %[[VAL_27]] : f64
+// CHECK-ON:           } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:           memref.store %[[VAL_29:.*]], %[[VAL_10]][] : memref<f64>
+// CHECK-ON:           %[[VAL_30:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<f64>
+// CHECK-ON:           return %[[VAL_30]] : tensor<f64>
+// CHECK-ON:         }
+//
+// CHECK-OFF-LABEL:   func.func @sparse_product_reduction_dense_sparse(
+// CHECK-OFF-SAME:                                                     %[[VAL_0:.*]]: tensor<f64>,
+// CHECK-OFF-SAME:                                                     %[[VAL_1:.*]]: tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>>) -> tensor<f64> {
+// CHECK-OFF-DAG:       %[[VAL_2:.*]] = arith.constant 0 : index
+// CHECK-OFF-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
+// CHECK-OFF:           %[[VAL_4:.*]] = tensor.dim %[[VAL_1]], %[[VAL_2]] : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>>
+// CHECK-OFF:           %[[VAL_5:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 1 : index} : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>> to memref<?xindex>
+// CHECK-OFF:           %[[VAL_6:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ] }>> to memref<?xf64>
+// CHECK-OFF:           %[[VAL_7:.*]] = bufferization.to_memref %[[VAL_0]] : memref<f64>
+// CHECK-OFF:           %[[VAL_8:.*]] = memref.load %[[VAL_7]][] : memref<f64>
+// CHECK-OFF:           %[[VAL_9:.*]] = scf.for %[[VAL_10:.*]] = %[[VAL_2]] to %[[VAL_4]] step %[[VAL_3]] iter_args(%[[VAL_11:.*]] = %[[VAL_8]]) -> (f64) {
+// CHECK-OFF:             %[[VAL_12:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_10]]] : memref<?xindex>
+// CHECK-OFF:             %[[VAL_13:.*]] = arith.addi %[[VAL_10]], %[[VAL_3]] : index
+// CHECK-OFF:             %[[VAL_14:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK-OFF:             %[[VAL_15:.*]] = scf.for %[[VAL_16:.*]] = %[[VAL_12]] to %[[VAL_14]] step %[[VAL_3]] iter_args(%[[VAL_17:.*]] = %[[VAL_11]]) -> (f64) {
+// CHECK-OFF:               %[[VAL_18:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_16]]] : memref<?xf64>
+// CHECK-OFF:               %[[VAL_19:.*]] = arith.mulf %[[VAL_17]], %[[VAL_18]] : f64
+// CHECK-OFF:               scf.yield %[[VAL_19]] : f64
+// CHECK-OFF:             } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:             scf.yield %[[VAL_20:.*]] : f64
+// CHECK-OFF:           } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:           memref.store %[[VAL_21:.*]], %[[VAL_7]][] : memref<f64>
+// CHECK-OFF:           %[[VAL_22:.*]] = bufferization.to_tensor %[[VAL_7]] : memref<f64>
+// CHECK-OFF:           return %[[VAL_22]] : tensor<f64>
+// CHECK-OFF:         }
+
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["dense","compressed"]}>
+
+#trait = {
+  indexing_maps = [
+    affine_map<(i,j) -> (i,j)>,  // a (in)
+    affine_map<(i,j) -> ()>      // x (out)
+  ],
+  iterator_types = ["reduction", "reduction"]
+}
+
+func.func @sparse_product_reduction_dense_sparse(%argx: tensor<f64>,
+                             %arga: tensor<?x128xf64, #SparseVector>)
+ -> tensor<f64> {
+  %0 = linalg.generic #trait
+     ins(%arga: tensor<?x128xf64, #SparseVector>)
+      outs(%argx: tensor<f64>) {
+      ^bb(%a: f64, %x: f64):
+        %t = arith.mulf %x, %a: f64
+        linalg.yield %t : f64
+  } -> tensor<f64>
+  return %0 : tensor<f64>
+}
+
+// -----
+
+// Same as sparse_product_reduction_dense_sparse but with the outer loop being sparse.
+//
+// CHECK-ON-LABEL:   func.func @sparse_product_reduction_sparse_sparse(
+// CHECK-ON-SAME:                                                      %[[VAL_0:.*]]: tensor<f64>,
+// CHECK-ON-SAME:                                                      %[[VAL_1:.*]]: tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) -> tensor<f64> {
+// CHECK-ON-DAG:       %[[VAL_2:.*]] = arith.constant 8 : index
+// CHECK-ON-DAG:       %[[VAL_3:.*]] = arith.constant dense<1.000000e+00> : vector<8xf64>
+// CHECK-ON-DAG:       %[[VAL_4:.*]] = arith.constant dense<0.000000e+00> : vector<8xf64>
+// CHECK-ON-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
+// CHECK-ON-DAG:       %[[VAL_6:.*]] = arith.constant 1 : index
+// CHECK-ON:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> to memref<?xindex>
+// CHECK-ON:           %[[VAL_8:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 1 : index} : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> to memref<?xindex>
+// CHECK-ON:           %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> to memref<?xf64>
+// CHECK-ON:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_0]] : memref<f64>
+// CHECK-ON:           %[[VAL_11:.*]] = memref.load %[[VAL_10]][] : memref<f64>
+// CHECK-ON:           %[[VAL_12:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_13:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_14:.*]] = scf.for %[[VAL_15:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_6]] iter_args(%[[VAL_16:.*]] = %[[VAL_11]]) -> (f64) {
+// CHECK-ON:             %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK-ON:             %[[VAL_18:.*]] = arith.addi %[[VAL_15]], %[[VAL_6]] : index
+// CHECK-ON:             %[[VAL_19:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK-ON:             %[[VAL_20:.*]] = vector.insertelement %[[VAL_16]], %[[VAL_3]]{{\[}}%[[VAL_5]] : index] : vector<8xf64>
+// CHECK-ON:             %[[VAL_21:.*]] = scf.for %[[VAL_22:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_2]] iter_args(%[[VAL_23:.*]] = %[[VAL_20]]) -> (vector<8xf64>) {
+// CHECK-ON:               %[[VAL_24:.*]] = affine.min #map(%[[VAL_19]], %[[VAL_22]]){{\[}}%[[VAL_2]]]
+// CHECK-ON:               %[[VAL_25:.*]] = vector.create_mask %[[VAL_24]] : vector<8xi1>
+// CHECK-ON:               %[[VAL_26:.*]] = vector.maskedload %[[VAL_9]]{{\[}}%[[VAL_22]]], %[[VAL_25]], %[[VAL_4]] : memref<?xf64>, vector<8xi1>, vector<8xf64> into vector<8xf64>
+// CHECK-ON:               %[[VAL_27:.*]] = arith.mulf %[[VAL_23]], %[[VAL_26]] : vector<8xf64>
+// CHECK-ON:               %[[VAL_28:.*]] = arith.select %[[VAL_25]], %[[VAL_27]], %[[VAL_23]] : vector<8xi1>, vector<8xf64>
+// CHECK-ON:               scf.yield %[[VAL_28]] : vector<8xf64>
+// CHECK-ON:             } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:             %[[VAL_29:.*]] = vector.reduction <mul>, %[[VAL_30:.*]] : vector<8xf64> into f64
+// CHECK-ON:             scf.yield %[[VAL_29]] : f64
+// CHECK-ON:           } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:           memref.store %[[VAL_31:.*]], %[[VAL_10]][] : memref<f64>
+// CHECK-ON:           %[[VAL_32:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<f64>
+// CHECK-ON:           return %[[VAL_32]] : tensor<f64>
+// CHECK-ON:         }
+//
+// CHECK-OFF-LABEL:   func.func @sparse_product_reduction_sparse_sparse(
+// CHECK-OFF-SAME:                                                     %[[VAL_0:.*]]: tensor<f64>,
+// CHECK-OFF-SAME:                                                     %[[VAL_1:.*]]: tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>>) -> tensor<f64> {
+// CHECK-OFF-DAG:       %[[VAL_2:.*]] = arith.constant 0 : index
+// CHECK-OFF-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
+// CHECK-OFF:           %[[VAL_4:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> to memref<?xindex>
+// CHECK-OFF:           %[[VAL_5:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 1 : index} : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> to memref<?xindex>
+// CHECK-OFF:           %[[VAL_6:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x128xf64, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed" ] }>> to memref<?xf64>
+// CHECK-OFF:           %[[VAL_7:.*]] = bufferization.to_memref %[[VAL_0]] : memref<f64>
+// CHECK-OFF:           %[[VAL_8:.*]] = memref.load %[[VAL_7]][] : memref<f64>
+// CHECK-OFF:           %[[VAL_9:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_10:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_11:.*]] = scf.for %[[VAL_12:.*]] = %[[VAL_9]] to %[[VAL_10]] step %[[VAL_3]] iter_args(%[[VAL_13:.*]] = %[[VAL_8]]) -> (f64) {
+// CHECK-OFF:             %[[VAL_14:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK-OFF:             %[[VAL_15:.*]] = arith.addi %[[VAL_12]], %[[VAL_3]] : index
+// CHECK-OFF:             %[[VAL_16:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK-OFF:             %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_14]] to %[[VAL_16]] step %[[VAL_3]] iter_args(%[[VAL_19:.*]] = %[[VAL_13]]) -> (f64) {
+// CHECK-OFF:               %[[VAL_20:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_18]]] : memref<?xf64>
+// CHECK-OFF:               %[[VAL_21:.*]] = arith.mulf %[[VAL_19]], %[[VAL_20]] : f64
+// CHECK-OFF:               scf.yield %[[VAL_21]] : f64
+// CHECK-OFF:             } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:             scf.yield %[[VAL_22:.*]] : f64
+// CHECK-OFF:           } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:           memref.store %[[VAL_23:.*]], %[[VAL_7]][] : memref<f64>
+// CHECK-OFF:           %[[VAL_24:.*]] = bufferization.to_tensor %[[VAL_7]] : memref<f64>
+// CHECK-OFF:           return %[[VAL_24]] : tensor<f64>
+// CHECK-OFF:         }
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed","compressed"]}>
+
+#trait = {
+  indexing_maps = [
+    affine_map<(i,j) -> (i,j)>,  // a (in)
+    affine_map<(i,j) -> ()>      // x (out)
+  ],
+  iterator_types = ["reduction", "reduction"]
+}
+
+func.func @sparse_product_reduction_sparse_sparse(%argx: tensor<f64>,
+                             %arga: tensor<?x128xf64, #SparseVector>)
+ -> tensor<f64> {
+  %0 = linalg.generic #trait
+     ins(%arga: tensor<?x128xf64, #SparseVector>)
+      outs(%argx: tensor<f64>) {
+      ^bb(%a: f64, %x: f64):
+        %t = arith.mulf %x, %a: f64
+        linalg.yield %t : f64
+  } -> tensor<f64>
+  return %0 : tensor<f64>
+}
+
+// -----
+
+// sparse_product_reduction_dense_sparse and
+// sparse_product_reduction_sparse_sparse established that the outer loop
+// doesn't matter for vectorization.
+// As a result from this point forward, use tensors with fewer dimensions.
+
+// Check that we vectorize reductions with ori.
+// Note: The weird element type here is to check that we create the right
+// constant type for the pass-through value.
+// CHECK-ON-LABEL:   func.func @sparse_reduction_ori(
+// CHECK-ON-SAME:                                    %[[VAL_0:.*]]: tensor<i13>,
+// CHECK-ON-SAME:                                    %[[VAL_1:.*]]: tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>>) -> tensor<i13> {
+// CHECK-ON-DAG:       %[[VAL_2:.*]] = arith.constant 8 : index
+// CHECK-ON-DAG:       %[[VAL_3:.*]] = arith.constant dense<0> : vector<8xi13>
+// CHECK-ON-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
+// CHECK-ON-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
+// CHECK-ON:           %[[VAL_6:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xindex>
+// CHECK-ON:           %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xi13>
+// CHECK-ON:           %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_0]] : memref<i13>
+// CHECK-ON:           %[[VAL_9:.*]] = memref.load %[[VAL_8]][] : memref<i13>
+// CHECK-ON:           %[[VAL_10:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_11:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_12:.*]] = vector.broadcast %[[VAL_9]] : i13 to vector<8xi13>
+// CHECK-ON:           %[[VAL_13:.*]] = scf.for %[[VAL_14:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_2]] iter_args(%[[VAL_15:.*]] = %[[VAL_12]]) -> (vector<8xi13>) {
+// CHECK-ON:             %[[VAL_16:.*]] = affine.min #map(%[[VAL_11]], %[[VAL_14]]){{\[}}%[[VAL_2]]]
+// CHECK-ON:             %[[VAL_17:.*]] = vector.create_mask %[[VAL_16]] : vector<8xi1>
+// CHECK-ON:             %[[VAL_18:.*]] = vector.maskedload %[[VAL_7]]{{\[}}%[[VAL_14]]], %[[VAL_17]], %[[VAL_3]] : memref<?xi13>, vector<8xi1>, vector<8xi13> into vector<8xi13>
+// CHECK-ON:             %[[VAL_19:.*]] = arith.ori %[[VAL_15]], %[[VAL_18]] : vector<8xi13>
+// CHECK-ON:             %[[VAL_20:.*]] = arith.select %[[VAL_17]], %[[VAL_19]], %[[VAL_15]] : vector<8xi1>, vector<8xi13>
+// CHECK-ON:             scf.yield %[[VAL_20]] : vector<8xi13>
+// CHECK-ON:           } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:           %[[VAL_21:.*]] = vector.reduction <or>, %[[VAL_22:.*]] : vector<8xi13> into i13
+// CHECK-ON:           memref.store %[[VAL_21]], %[[VAL_8]][] : memref<i13>
+// CHECK-ON:           %[[VAL_23:.*]] = bufferization.to_tensor %[[VAL_8]] : memref<i13>
+// CHECK-ON:           return %[[VAL_23]] : tensor<i13>
+// CHECK-ON:         }
+//
+// CHECK-OFF-LABEL:   func.func @sparse_reduction_ori(
+// CHECK-OFF-SAME:                                    %[[VAL_0:.*]]: tensor<i13>,
+// CHECK-OFF-SAME:                                    %[[VAL_1:.*]]: tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>>) -> tensor<i13> {
+// CHECK-OFF-DAG:       %[[VAL_2:.*]] = arith.constant 0 : index
+// CHECK-OFF-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
+// CHECK-OFF:           %[[VAL_4:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xindex>
+// CHECK-OFF:           %[[VAL_5:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xi13>
+// CHECK-OFF:           %[[VAL_6:.*]] = bufferization.to_memref %[[VAL_0]] : memref<i13>
+// CHECK-OFF:           %[[VAL_7:.*]] = memref.load %[[VAL_6]][] : memref<i13>
+// CHECK-OFF:           %[[VAL_8:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_9:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_10:.*]] = scf.for %[[VAL_11:.*]] = %[[VAL_8]] to %[[VAL_9]] step %[[VAL_3]] iter_args(%[[VAL_12:.*]] = %[[VAL_7]]) -> (i13) {
+// CHECK-OFF:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xi13>
+// CHECK-OFF:             %[[VAL_14:.*]] = arith.ori %[[VAL_12]], %[[VAL_13]] : i13
+// CHECK-OFF:             scf.yield %[[VAL_14]] : i13
+// CHECK-OFF:           } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:           memref.store %[[VAL_15:.*]], %[[VAL_6]][] : memref<i13>
+// CHECK-OFF:           %[[VAL_16:.*]] = bufferization.to_tensor %[[VAL_6]] : memref<i13>
+// CHECK-OFF:           return %[[VAL_16]] : tensor<i13>
+// CHECK-OFF:         }
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+
+#trait = {
+  indexing_maps = [
+    affine_map<(i) -> (i)>,  // a (in)
+    affine_map<(i) -> ()>    // x (out)
+  ],
+  iterator_types = ["reduction"]
+}
+
+func.func @sparse_reduction_ori(%argx: tensor<i13>,
+                             %arga: tensor<?xi13, #SparseVector>)
+ -> tensor<i13> {
+  %0 = linalg.generic #trait
+     ins(%arga: tensor<?xi13, #SparseVector>)
+      outs(%argx: tensor<i13>) {
+      ^bb(%a: i13, %x: i13):
+        %t = arith.ori %x, %a: i13
+        linalg.yield %t : i13
+  } -> tensor<i13>
+  return %0 : tensor<i13>
+}
+
+// -----
+
+// Same test as sparse_reduction_ori except that the accumulator is on the
+// rhs of the operation.
+// This checks that we can recognize a reduction irrespective to where the
+// accumalator appears on commutative operations.
+
+// CHECK-ON-LABEL:   func.func @sparse_reduction_ori_accumulator_on_rhs(
+// CHECK-ON-SAME:                                    %[[VAL_0:.*]]: tensor<i13>,
+// CHECK-ON-SAME:                                    %[[VAL_1:.*]]: tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>>) -> tensor<i13> {
+// CHECK-ON-DAG:       %[[VAL_2:.*]] = arith.constant 8 : index
+// CHECK-ON-DAG:       %[[VAL_3:.*]] = arith.constant dense<0> : vector<8xi13>
+// CHECK-ON-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
+// CHECK-ON-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
+// CHECK-ON:           %[[VAL_6:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xindex>
+// CHECK-ON:           %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xi13>
+// CHECK-ON:           %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_0]] : memref<i13>
+// CHECK-ON:           %[[VAL_9:.*]] = memref.load %[[VAL_8]][] : memref<i13>
+// CHECK-ON:           %[[VAL_10:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_11:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_12:.*]] = vector.broadcast %[[VAL_9]] : i13 to vector<8xi13>
+// CHECK-ON:           %[[VAL_13:.*]] = scf.for %[[VAL_14:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_2]] iter_args(%[[VAL_15:.*]] = %[[VAL_12]]) -> (vector<8xi13>) {
+// CHECK-ON:             %[[VAL_16:.*]] = affine.min #map(%[[VAL_11]], %[[VAL_14]]){{\[}}%[[VAL_2]]]
+// CHECK-ON:             %[[VAL_17:.*]] = vector.create_mask %[[VAL_16]] : vector<8xi1>
+// CHECK-ON:             %[[VAL_18:.*]] = vector.maskedload %[[VAL_7]]{{\[}}%[[VAL_14]]], %[[VAL_17]], %[[VAL_3]] : memref<?xi13>, vector<8xi1>, vector<8xi13> into vector<8xi13>
+// CHECK-ON:             %[[VAL_19:.*]] = arith.ori %[[VAL_18]], %[[VAL_15]] : vector<8xi13>
+// CHECK-ON:             %[[VAL_20:.*]] = arith.select %[[VAL_17]], %[[VAL_19]], %[[VAL_15]] : vector<8xi1>, vector<8xi13>
+// CHECK-ON:             scf.yield %[[VAL_20]] : vector<8xi13>
+// CHECK-ON:           } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:           %[[VAL_21:.*]] = vector.reduction <or>, %[[VAL_22:.*]] : vector<8xi13> into i13
+// CHECK-ON:           memref.store %[[VAL_21]], %[[VAL_8]][] : memref<i13>
+// CHECK-ON:           %[[VAL_23:.*]] = bufferization.to_tensor %[[VAL_8]] : memref<i13>
+// CHECK-ON:           return %[[VAL_23]] : tensor<i13>
+// CHECK-ON:         }
+//
+// CHECK-OFF-LABEL:   func.func @sparse_reduction_ori_accumulator_on_rhs(
+// CHECK-OFF-SAME:                                    %[[VAL_0:.*]]: tensor<i13>,
+// CHECK-OFF-SAME:                                    %[[VAL_1:.*]]: tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>>) -> tensor<i13> {
+// CHECK-OFF-DAG:       %[[VAL_2:.*]] = arith.constant 0 : index
+// CHECK-OFF-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
+// CHECK-OFF:           %[[VAL_4:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xindex>
+// CHECK-OFF:           %[[VAL_5:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xi13, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xi13>
+// CHECK-OFF:           %[[VAL_6:.*]] = bufferization.to_memref %[[VAL_0]] : memref<i13>
+// CHECK-OFF:           %[[VAL_7:.*]] = memref.load %[[VAL_6]][] : memref<i13>
+// CHECK-OFF:           %[[VAL_8:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_9:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_10:.*]] = scf.for %[[VAL_11:.*]] = %[[VAL_8]] to %[[VAL_9]] step %[[VAL_3]] iter_args(%[[VAL_12:.*]] = %[[VAL_7]]) -> (i13) {
+// CHECK-OFF:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xi13>
+// CHECK-OFF:             %[[VAL_14:.*]] = arith.ori %[[VAL_13]], %[[VAL_12]] : i13
+// CHECK-OFF:             scf.yield %[[VAL_14]] : i13
+// CHECK-OFF:           } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:           memref.store %[[VAL_15:.*]], %[[VAL_6]][] : memref<i13>
+// CHECK-OFF:           %[[VAL_16:.*]] = bufferization.to_tensor %[[VAL_6]] : memref<i13>
+// CHECK-OFF:           return %[[VAL_16]] : tensor<i13>
+// CHECK-OFF:         }
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+
+#trait = {
+  indexing_maps = [
+    affine_map<(i) -> (i)>,  // a (in)
+    affine_map<(i) -> ()>    // x (out)
+  ],
+  iterator_types = ["reduction"]
+}
+
+func.func @sparse_reduction_ori_accumulator_on_rhs(%argx: tensor<i13>,
+                             %arga: tensor<?xi13, #SparseVector>)
+ -> tensor<i13> {
+  %0 = linalg.generic #trait
+     ins(%arga: tensor<?xi13, #SparseVector>)
+      outs(%argx: tensor<i13>) {
+      ^bb(%a: i13, %x: i13):
+        %t = arith.ori %a, %x: i13
+        linalg.yield %t : i13
+  } -> tensor<i13>
+  return %0 : tensor<i13>
+}
+
+// -----
+
+// Check that we vectorize reduction with subi.
+//
+// CHECK-ON-LABEL:   func.func @sparse_reduction_subi(
+// CHECK-ON-SAME:                                     %[[VAL_0:.*]]: tensor<i32>,
+// CHECK-ON-SAME:                                     %[[VAL_1:.*]]: tensor<?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>>) -> tensor<i32> {
+// CHECK-ON-DAG:       %[[VAL_2:.*]] = arith.constant 8 : index
+// CHECK-ON-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
+// CHECK-ON-DAG:       %[[VAL_4:.*]] = arith.constant dense<0> : vector<8xi32>
+// CHECK-ON-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
+// CHECK-ON:           %[[VAL_6:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xindex>
+// CHECK-ON:           %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xi32>
+// CHECK-ON:           %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_0]] : memref<i32>
+// CHECK-ON:           %[[VAL_9:.*]] = memref.load %[[VAL_8]][] : memref<i32>
+// CHECK-ON:           %[[VAL_10:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_11:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK-ON:           %[[VAL_12:.*]] = vector.insertelement %[[VAL_9]], %[[VAL_4]]{{\[}}%[[VAL_3]] : index] : vector<8xi32>
+// CHECK-ON:           %[[VAL_13:.*]] = scf.for %[[VAL_14:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_2]] iter_args(%[[VAL_15:.*]] = %[[VAL_12]]) -> (vector<8xi32>) {
+// CHECK-ON:             %[[VAL_16:.*]] = affine.min #map(%[[VAL_11]], %[[VAL_14]]){{\[}}%[[VAL_2]]]
+// CHECK-ON:             %[[VAL_17:.*]] = vector.create_mask %[[VAL_16]] : vector<8xi1>
+// CHECK-ON:             %[[VAL_18:.*]] = vector.maskedload %[[VAL_7]]{{\[}}%[[VAL_14]]], %[[VAL_17]], %[[VAL_4]] : memref<?xi32>, vector<8xi1>, vector<8xi32> into vector<8xi32>
+// CHECK-ON:             %[[VAL_19:.*]] = arith.subi %[[VAL_15]], %[[VAL_18]] : vector<8xi32>
+// CHECK-ON:             %[[VAL_20:.*]] = arith.select %[[VAL_17]], %[[VAL_19]], %[[VAL_15]] : vector<8xi1>, vector<8xi32>
+// CHECK-ON:             scf.yield %[[VAL_20]] : vector<8xi32>
+// CHECK-ON:           } {"Emitted from" = "linalg.generic"}
+// CHECK-ON:           %[[VAL_21:.*]] = vector.reduction <add>, %[[VAL_22:.*]] : vector<8xi32> into i32
+// CHECK-ON:           memref.store %[[VAL_21]], %[[VAL_8]][] : memref<i32>
+// CHECK-ON:           %[[VAL_23:.*]] = bufferization.to_tensor %[[VAL_8]] : memref<i32>
+// CHECK-ON:           return %[[VAL_23]] : tensor<i32>
+// CHECK-ON:         }
+//
+// CHECK-OFF-LABEL:   func.func @sparse_reduction_subi(
+// CHECK-OFF-SAME:                                     %[[VAL_0:.*]]: tensor<i32>,
+// CHECK-OFF-SAME:                                     %[[VAL_1:.*]]: tensor<?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>>) -> tensor<i32> {
+// CHECK-OFF-DAG:       %[[VAL_2:.*]] = arith.constant 0 : index
+// CHECK-OFF-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
+// CHECK-OFF:           %[[VAL_4:.*]] = sparse_tensor.pointers %[[VAL_1]] {dimension = 0 : index} : tensor<?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xindex>
+// CHECK-OFF:           %[[VAL_5:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xi32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>> to memref<?xi32>
+// CHECK-OFF:           %[[VAL_6:.*]] = bufferization.to_memref %[[VAL_0]] : memref<i32>
+// CHECK-OFF:           %[[VAL_7:.*]] = memref.load %[[VAL_6]][] : memref<i32>
+// CHECK-OFF:           %[[VAL_8:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_9:.*]] = memref.load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK-OFF:           %[[VAL_10:.*]] = scf.for %[[VAL_11:.*]] = %[[VAL_8]] to %[[VAL_9]] step %[[VAL_3]] iter_args(%[[VAL_12:.*]] = %[[VAL_7]]) -> (i32) {
+// CHECK-OFF:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xi32>
+// CHECK-OFF:             %[[VAL_14:.*]] = arith.subi %[[VAL_12]], %[[VAL_13]] : i32
+// CHECK-OFF:             scf.yield %[[VAL_14]] : i32
+// CHECK-OFF:           } {"Emitted from" = "linalg.generic"}
+// CHECK-OFF:           memref.store %[[VAL_15:.*]], %[[VAL_6]][] : memref<i32>
+// CHECK-OFF:           %[[VAL_16:.*]] = bufferization.to_tensor %[[VAL_6]] : memref<i32>
+// CHECK-OFF:           return %[[VAL_16]] : tensor<i32>
+// CHECK-OFF:         }
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+
+#trait = {
+  indexing_maps = [
+    affine_map<(i) -> (i)>,  // a (in)
+    affine_map<(i) -> ()>    // x (out)
+  ],
+  iterator_types = ["reduction"]
+}
+
+func.func @sparse_reduction_subi(%argx: tensor<i32>,
+                             %arga: tensor<?xi32, #SparseVector>)
+ -> tensor<i32> {
+  %0 = linalg.generic #trait
+     ins(%arga: tensor<?xi32, #SparseVector>)
+      outs(%argx: tensor<i32>) {
+      ^bb(%a: i32, %x: i32):
+        %t = arith.subi %x, %a: i32
+        linalg.yield %t : i32
+  } -> tensor<i32>
+  return %0 : tensor<i32>
+}
+
+// -----
+
+// Check that we don't vectorize subi when the input value is on the lhs.
+// I.e., res = res - input // Ok, tested in sparse_reduction_subi
+//       => vec_res = {res, 0, 0, ...} - vec_input
+//          vec = hadd vec_res
+//       res = input - res // Not ok
+//
+// This test is disabled for now, because it crashes the sparsification pass.
+// See llvm.org/PR59394
+
+// #SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+//
+// #trait = {
+//   indexing_maps = [
+//     affine_map<(i) -> (i)>,  // a (in)
+//     affine_map<(i) -> ()>    // x (out)
+//   ],
+//   iterator_types = ["reduction"]
+// }
+//
+// func.func @sparse_reduction_subi(%argx: tensor<i32>,
+//                              %arga: tensor<?xi32, #SparseVector>)
+//  -> tensor<i32> {
+//   %0 = linalg.generic #trait
+//      ins(%arga: tensor<?xi32, #SparseVector>)
+//       outs(%argx: tensor<i32>) {
+//       ^bb(%a: i32, %x: i32):
+//         %t = arith.subi %a, %x: i32
+//         linalg.yield %t : i32
+//   } -> tensor<i32>
+//   return %0 : tensor<i32>
+// }