File: sparse_2d.mlir

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// NOTE: Assertions have been autogenerated by utils/generate-test-checks.py
// RUN: mlir-opt %s -sparsification | FileCheck %s

#Tdd = #sparse_tensor.encoding<{ lvlTypes = [ "dense",      "dense"      ] }>
#Tds = #sparse_tensor.encoding<{ lvlTypes = [ "dense",      "compressed" ] }>
#Tsd = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense"      ] }>
#Tss = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>

#trait2 = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (i,j)>,  // B
    affine_map<(i,j) -> (i,j)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel"],
  doc = "X(i,j) = A(i,j) OP B(i,j)"
}

// CHECK-LABEL:   func @add_dd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_10]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:               %[[VAL_13:.*]] = arith.muli %[[VAL_11]], %[[VAL_4]] : index
// CHECK:               %[[VAL_14:.*]] = arith.addi %[[VAL_13]], %[[VAL_12]] : index
// CHECK:               %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:               %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:               %[[VAL_17:.*]] = arith.addf %[[VAL_15]], %[[VAL_16]] : f32
// CHECK:               memref.store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_18:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<32x16xf32>
// CHECK:           return %[[VAL_18]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_dd(%arga: tensor<32x16xf32, #Tdd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tdd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_dd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_10]] : memref<32x16xi1>)
// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_13:.*]] = arith.muli %[[VAL_11]], %[[VAL_4]] : index
// CHECK:               %[[VAL_14:.*]] = arith.addi %[[VAL_13]], %[[VAL_12]] : index
// CHECK:               %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:               %[[VAL_16:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:               %[[VAL_17:.*]] = arith.cmpf ult, %[[VAL_15]], %[[VAL_16]] : f32
// CHECK:               memref.store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_18:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<32x16xi1>
// CHECK:           return %[[VAL_18]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_dd(%arga: tensor<32x16xf32, #Tdd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tdd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_dd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_10]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:               %[[VAL_13:.*]] = arith.muli %[[VAL_11]], %[[VAL_4]] : index
// CHECK:               %[[VAL_14:.*]] = arith.addi %[[VAL_13]], %[[VAL_12]] : index
// CHECK:               %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:               %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:               %[[VAL_17:.*]] = arith.mulf %[[VAL_15]], %[[VAL_16]] : f32
// CHECK:               memref.store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_18:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<32x16xf32>
// CHECK:           return %[[VAL_18]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_dd(%arga: tensor<32x16xf32, #Tdd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tdd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_13]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             %[[VAL_16:.*]] = arith.addi %[[VAL_14]], %[[VAL_7]] : index
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:             %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_15]], %[[VAL_20:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
// CHECK:               %[[VAL_21:.*]] = arith.cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
// CHECK:               scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
// CHECK:               %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               %[[VAL_25:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:               scf.if %[[VAL_25]] {
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xf32>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_28:.*]] = arith.addf %[[VAL_26]], %[[VAL_27]] : f32
// CHECK:                 memref.store %[[VAL_28]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:               } else {
// CHECK:                 scf.if %[[VAL_6]] {
// CHECK:                   %[[VAL_29:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:                   memref.store %[[VAL_29]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:               %[[VAL_30:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:               %[[VAL_31:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:               %[[VAL_32:.*]] = arith.select %[[VAL_30]], %[[VAL_31]], %[[VAL_22]] : index
// CHECK:               %[[VAL_33:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               scf.yield %[[VAL_32]], %[[VAL_33]] : index, index
// CHECK:             }
// CHECK:             scf.for %[[VAL_34:.*]] = %[[VAL_35:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:               memref.store %[[VAL_36]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_37:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16xf32>
// CHECK:           return %[[VAL_37]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_ds(%arga: tensor<32x16xf32, #Tds>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tds>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_14]] : memref<32x16xi1>)
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.addi %[[VAL_15]], %[[VAL_7]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:               %[[VAL_22:.*]] = arith.cmpi ult, %[[VAL_20]], %[[VAL_18]] : index
// CHECK:               scf.condition(%[[VAL_22]]) %[[VAL_20]], %[[VAL_21]] : index, index
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
// CHECK:               %[[VAL_25:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_26:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:               scf.if %[[VAL_26]] {
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_23]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.cmpf ult, %[[VAL_27]], %[[VAL_28]] : f32
// CHECK:                 memref.store %[[VAL_29]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xi1>
// CHECK:               } else {
// CHECK:                 scf.if %[[VAL_8]] {
// CHECK:                   %[[VAL_30:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_31:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_30]] : f32
// CHECK:                   memref.store %[[VAL_31]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]]] : memref<32x16xi1>
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:               %[[VAL_32:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:               %[[VAL_33:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               %[[VAL_34:.*]] = arith.select %[[VAL_32]], %[[VAL_33]], %[[VAL_23]] : index
// CHECK:               %[[VAL_35:.*]] = arith.addi %[[VAL_24]], %[[VAL_7]] : index
// CHECK:               scf.yield %[[VAL_34]], %[[VAL_35]] : index, index
// CHECK:             } attributes
// CHECK:             scf.for %[[VAL_36:.*]] = %[[VAL_37:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_36]]] : memref<32x16xf32>
// CHECK:               %[[VAL_39:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_38]] : f32
// CHECK:               memref.store %[[VAL_39]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_36]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_40:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16xi1>
// CHECK:           return %[[VAL_40]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_ds(%arga: tensor<32x16xf32, #Tds>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tds>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_11]] : memref<32x16xf32>)
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK:             %[[VAL_13:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
// CHECK:             %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_5]] : index
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] {
// CHECK:               %[[VAL_17:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:               %[[VAL_18:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xf32>
// CHECK:               %[[VAL_19:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
// CHECK:               %[[VAL_20:.*]] = arith.mulf %[[VAL_18]], %[[VAL_19]] : f32
// CHECK:               memref.store %[[VAL_20]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_21:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<32x16xf32>
// CHECK:           return %[[VAL_21]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_ds(%arga: tensor<32x16xf32, #Tds>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tds>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_sd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_13]] : memref<32x16xf32>)
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]]:2 = scf.while (%[[VAL_17:.*]] = %[[VAL_14]], %[[VAL_18:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_19:.*]] = arith.cmpi ult, %[[VAL_17]], %[[VAL_15]] : index
// CHECK:             scf.condition(%[[VAL_19]]) %[[VAL_17]], %[[VAL_18]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_20:.*]]: index, %[[VAL_21:.*]]: index):
// CHECK:             %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xindex>
// CHECK:             %[[VAL_23:.*]] = arith.cmpi eq, %[[VAL_22]], %[[VAL_21]] : index
// CHECK:             scf.if %[[VAL_23]] {
// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_25:.*]] = arith.muli %[[VAL_20]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_26:.*]] = arith.addi %[[VAL_25]], %[[VAL_24]] : index
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.addf %[[VAL_27]], %[[VAL_28]] : f32
// CHECK:                 memref.store %[[VAL_29]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_5]] {
// CHECK:                 scf.for %[[VAL_30:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_31:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
// CHECK:                   memref.store %[[VAL_31]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_32:.*]] = arith.cmpi eq, %[[VAL_22]], %[[VAL_21]] : index
// CHECK:             %[[VAL_33:.*]] = arith.addi %[[VAL_20]], %[[VAL_7]] : index
// CHECK:             %[[VAL_34:.*]] = arith.select %[[VAL_32]], %[[VAL_33]], %[[VAL_20]] : index
// CHECK:             %[[VAL_35:.*]] = arith.addi %[[VAL_21]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_34]], %[[VAL_35]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_36:.*]] = %[[VAL_37:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_38:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
// CHECK:               memref.store %[[VAL_39]], %[[VAL_13]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_40:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16xf32>
// CHECK:           return %[[VAL_40]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_sd(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_sd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK:           %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_14]] : memref<32x16xi1>)
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_15]], %[[VAL_19:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_20:.*]] = arith.cmpi ult, %[[VAL_18]], %[[VAL_16]] : index
// CHECK:             scf.condition(%[[VAL_20]]) %[[VAL_18]], %[[VAL_19]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_21:.*]]: index, %[[VAL_22:.*]]: index):
// CHECK:             %[[VAL_23:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:             %[[VAL_24:.*]] = arith.cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
// CHECK:             scf.if %[[VAL_24]] {
// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_26:.*]] = arith.muli %[[VAL_21]], %[[VAL_3]] : index
// CHECK:                 %[[VAL_27:.*]] = arith.addi %[[VAL_26]], %[[VAL_25]] : index
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xf32>
// CHECK:                 %[[VAL_29:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_25]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_30:.*]] = arith.cmpf ult, %[[VAL_28]], %[[VAL_29]] : f32
// CHECK:                 memref.store %[[VAL_30]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_25]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_8]] {
// CHECK:                 scf.for %[[VAL_31:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_32:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_31]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_33:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_32]] : f32
// CHECK:                   memref.store %[[VAL_33]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_31]]] : memref<32x16xi1>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
// CHECK:             %[[VAL_35:.*]] = arith.addi %[[VAL_21]], %[[VAL_7]] : index
// CHECK:             %[[VAL_36:.*]] = arith.select %[[VAL_34]], %[[VAL_35]], %[[VAL_21]] : index
// CHECK:             %[[VAL_37:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_36]], %[[VAL_37]] : index, index
// CHECK:           } attributes
// CHECK:           scf.for %[[VAL_38:.*]] = %[[VAL_39:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_40:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_38]], %[[VAL_40]]] : memref<32x16xf32>
// CHECK:               %[[VAL_42:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_41]] : f32
// CHECK:               memref.store %[[VAL_42]], %[[VAL_14]]{{\[}}%[[VAL_38]], %[[VAL_40]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_43:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16xi1>
// CHECK:           return %[[VAL_43]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_sd(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_sd(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_11]] : memref<32x16xf32>)
// CHECK:           %[[VAL_12:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_5]] {
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK:               %[[VAL_17:.*]] = arith.muli %[[VAL_14]], %[[VAL_3]] : index
// CHECK:               %[[VAL_18:.*]] = arith.addi %[[VAL_17]], %[[VAL_16]] : index
// CHECK:               %[[VAL_19:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf32>
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
// CHECK:               %[[VAL_21:.*]] = arith.mulf %[[VAL_19]], %[[VAL_20]] : f32
// CHECK:               memref.store %[[VAL_21]], %[[VAL_11]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_22:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<32x16xf32>
// CHECK:           return %[[VAL_22]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_sd(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_ss(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_15]] : memref<32x16xf32>)
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_16]], %[[VAL_20:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_21:.*]] = arith.cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
// CHECK:             scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
// CHECK:             %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:             %[[VAL_25:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             scf.if %[[VAL_25]] {
// CHECK:               %[[VAL_26:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               %[[VAL_27:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:               %[[VAL_28:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_26]], %[[VAL_31:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_32:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_28]] : index
// CHECK:                 scf.condition(%[[VAL_32]]) %[[VAL_30]], %[[VAL_31]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_33:.*]]: index, %[[VAL_34:.*]]: index):
// CHECK:                 %[[VAL_35:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:                 %[[VAL_36:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 scf.if %[[VAL_36]] {
// CHECK:                   %[[VAL_37:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:                   %[[VAL_38:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_39:.*]] = arith.addf %[[VAL_37]], %[[VAL_38]] : f32
// CHECK:                   memref.store %[[VAL_39]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_5]] {
// CHECK:                     %[[VAL_40:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                     memref.store %[[VAL_40]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_41:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_42:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_43:.*]] = arith.select %[[VAL_41]], %[[VAL_42]], %[[VAL_33]] : index
// CHECK:                 %[[VAL_44:.*]] = arith.addi %[[VAL_34]], %[[VAL_7]] : index
// CHECK:                 scf.yield %[[VAL_43]], %[[VAL_44]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_45:.*]] = %[[VAL_46:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_47:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
// CHECK:                 memref.store %[[VAL_47]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_5]] {
// CHECK:                 scf.for %[[VAL_48:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_49:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
// CHECK:                   memref.store %[[VAL_49]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_50:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             %[[VAL_51:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:             %[[VAL_52:.*]] = arith.select %[[VAL_50]], %[[VAL_51]], %[[VAL_22]] : index
// CHECK:             %[[VAL_53:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_52]], %[[VAL_53]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_56:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_57:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
// CHECK:               memref.store %[[VAL_57]], %[[VAL_15]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_58:.*]] = bufferization.to_tensor %[[VAL_15]] : memref<32x16xf32>
// CHECK:           return %[[VAL_58]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_ss(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK:           %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK:           %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_5]] : i1) outs(%[[VAL_16]] : memref<32x16xi1>)
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_17]], %[[VAL_21:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_22:.*]] = arith.cmpi ult, %[[VAL_20]], %[[VAL_18]] : index
// CHECK:             scf.condition(%[[VAL_22]]) %[[VAL_20]], %[[VAL_21]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
// CHECK:             %[[VAL_25:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:             %[[VAL_26:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:             scf.if %[[VAL_26]] {
// CHECK:               %[[VAL_27:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_28:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               %[[VAL_29:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_30:.*]]:2 = scf.while (%[[VAL_31:.*]] = %[[VAL_27]], %[[VAL_32:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_33:.*]] = arith.cmpi ult, %[[VAL_31]], %[[VAL_29]] : index
// CHECK:                 scf.condition(%[[VAL_33]]) %[[VAL_31]], %[[VAL_32]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_34:.*]]: index, %[[VAL_35:.*]]: index):
// CHECK:                 %[[VAL_36:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_34]]] : memref<?xindex>
// CHECK:                 %[[VAL_37:.*]] = arith.cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
// CHECK:                 scf.if %[[VAL_37]] {
// CHECK:                   %[[VAL_38:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_34]]] : memref<?xf32>
// CHECK:                   %[[VAL_39:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_40:.*]] = arith.cmpf ult, %[[VAL_38]], %[[VAL_39]] : f32
// CHECK:                   memref.store %[[VAL_40]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xi1>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_8]] {
// CHECK:                     %[[VAL_41:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xf32>
// CHECK:                     %[[VAL_42:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_41]] : f32
// CHECK:                     memref.store %[[VAL_42]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]]] : memref<32x16xi1>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_43:.*]] = arith.cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
// CHECK:                 %[[VAL_44:.*]] = arith.addi %[[VAL_34]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_45:.*]] = arith.select %[[VAL_43]], %[[VAL_44]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.addi %[[VAL_35]], %[[VAL_7]] : index
// CHECK:                 scf.yield %[[VAL_45]], %[[VAL_46]] : index, index
// CHECK:               } attributes
// CHECK:               scf.for %[[VAL_47:.*]] = %[[VAL_48:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_49:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_47]]] : memref<32x16xf32>
// CHECK:                 %[[VAL_50:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_49]] : f32
// CHECK:                 memref.store %[[VAL_50]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_47]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_8]] {
// CHECK:                 scf.for %[[VAL_51:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_52:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_51]]] : memref<32x16xf32>
// CHECK:                   %[[VAL_53:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_52]] : f32
// CHECK:                   memref.store %[[VAL_53]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_51]]] : memref<32x16xi1>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:             %[[VAL_55:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:             %[[VAL_56:.*]] = arith.select %[[VAL_54]], %[[VAL_55]], %[[VAL_23]] : index
// CHECK:             %[[VAL_57:.*]] = arith.addi %[[VAL_24]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_56]], %[[VAL_57]] : index, index
// CHECK:           } attributes
// CHECK:           scf.for %[[VAL_58:.*]] = %[[VAL_59:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_60:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_61:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_58]], %[[VAL_60]]] : memref<32x16xf32>
// CHECK:               %[[VAL_62:.*]] = arith.cmpf ult, %[[VAL_9]], %[[VAL_61]] : f32
// CHECK:               memref.store %[[VAL_62]], %[[VAL_16]]{{\[}}%[[VAL_58]], %[[VAL_60]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_63:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16xi1>
// CHECK:           return %[[VAL_63]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

// CHECK-LABEL:   func @mul_ss(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16xf32>
// CHECK-DAG:       %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_12]] : memref<32x16xf32>)
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_4]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_18:.*]] = arith.addi %[[VAL_15]], %[[VAL_4]] : index
// CHECK:             %[[VAL_19:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_20:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_4]] {
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<?xindex>
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xf32>
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
// CHECK:               %[[VAL_24:.*]] = arith.mulf %[[VAL_22]], %[[VAL_23]] : f32
// CHECK:               memref.store %[[VAL_24]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_25:.*]] = bufferization.to_tensor %[[VAL_12]] : memref<32x16xf32>
// CHECK:           return %[[VAL_25]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_ss_ss(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_16]] : memref<32x16xf32>)
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_24:.*]] = arith.cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
// CHECK:             %[[VAL_26:.*]] = arith.andi %[[VAL_24]], %[[VAL_25]] : i1
// CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
// CHECK:             %[[VAL_29:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:             %[[VAL_30:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:             %[[VAL_31:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_32:.*]] = arith.select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_33:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_35:.*]] = arith.andi %[[VAL_33]], %[[VAL_34]] : i1
// CHECK:             scf.if %[[VAL_35]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_37:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_40:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
// CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_45:.*]] = arith.cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.andi %[[VAL_45]], %[[VAL_46]] : i1
// CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
// CHECK:                 %[[VAL_50:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
// CHECK:                 %[[VAL_52:.*]] = arith.cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_53:.*]] = arith.select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.andi %[[VAL_54]], %[[VAL_55]] : i1
// CHECK:                 scf.if %[[VAL_56]] {
// CHECK:                   %[[VAL_57:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                   %[[VAL_58:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                   %[[VAL_59:.*]] = arith.addf %[[VAL_57]], %[[VAL_58]] : f32
// CHECK:                   memref.store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                   %[[VAL_60:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                   scf.if %[[VAL_60]] {
// CHECK:                     %[[VAL_61:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                     memref.store %[[VAL_61]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                   } else {
// CHECK:                     %[[VAL_62:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                     scf.if %[[VAL_62]] {
// CHECK:                       %[[VAL_63:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                       memref.store %[[VAL_63]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                     } else {
// CHECK:                     }
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_64:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_65:.*]] = arith.addi %[[VAL_48]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_66:.*]] = arith.select %[[VAL_64]], %[[VAL_65]], %[[VAL_48]] : index
// CHECK:                 %[[VAL_67:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.addi %[[VAL_49]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_69:.*]] = arith.select %[[VAL_67]], %[[VAL_68]], %[[VAL_49]] : index
// CHECK:                 scf.yield %[[VAL_66]], %[[VAL_69]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_70:.*]] = %[[VAL_71:.*]]#0 to %[[VAL_38]] step %[[VAL_4]] {
// CHECK:                 %[[VAL_72:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_70]]] : memref<?xindex>
// CHECK:                 %[[VAL_73:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_70]]] : memref<?xf32>
// CHECK:                 memref.store %[[VAL_73]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_72]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:               scf.for %[[VAL_74:.*]] = %[[VAL_75:.*]]#1 to %[[VAL_41]] step %[[VAL_4]] {
// CHECK:                 %[[VAL_76:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_74]]] : memref<?xindex>
// CHECK:                 %[[VAL_77:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_74]]] : memref<?xf32>
// CHECK:                 memref.store %[[VAL_77]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_76]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               %[[VAL_78:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:               scf.if %[[VAL_78]] {
// CHECK:                 %[[VAL_79:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:                 %[[VAL_80:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_81:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_80]]] : memref<?xindex>
// CHECK:                 scf.for %[[VAL_82:.*]] = %[[VAL_79]] to %[[VAL_81]] step %[[VAL_4]] {
// CHECK:                   %[[VAL_83:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_82]]] : memref<?xindex>
// CHECK:                   %[[VAL_84:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_82]]] : memref<?xf32>
// CHECK:                   memref.store %[[VAL_84]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_83]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:                 %[[VAL_85:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:                 scf.if %[[VAL_85]] {
// CHECK:                   %[[VAL_86:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:                   %[[VAL_87:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:                   %[[VAL_88:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_87]]] : memref<?xindex>
// CHECK:                   scf.for %[[VAL_89:.*]] = %[[VAL_86]] to %[[VAL_88]] step %[[VAL_4]] {
// CHECK:                     %[[VAL_90:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_89]]] : memref<?xindex>
// CHECK:                     %[[VAL_91:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_89]]] : memref<?xf32>
// CHECK:                     memref.store %[[VAL_91]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_90]]] : memref<32x16xf32>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_92:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_93:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:             %[[VAL_94:.*]] = arith.select %[[VAL_92]], %[[VAL_93]], %[[VAL_27]] : index
// CHECK:             %[[VAL_95:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_96:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:             %[[VAL_97:.*]] = arith.select %[[VAL_95]], %[[VAL_96]], %[[VAL_28]] : index
// CHECK:             scf.yield %[[VAL_94]], %[[VAL_97]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_98:.*]] = %[[VAL_99:.*]]#0 to %[[VAL_18]] step %[[VAL_4]] {
// CHECK:             %[[VAL_100:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_98]]] : memref<?xindex>
// CHECK:             %[[VAL_101:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_98]]] : memref<?xindex>
// CHECK:             %[[VAL_102:.*]] = arith.addi %[[VAL_98]], %[[VAL_4]] : index
// CHECK:             %[[VAL_103:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_102]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_104:.*]] = %[[VAL_101]] to %[[VAL_103]] step %[[VAL_4]] {
// CHECK:               %[[VAL_105:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_104]]] : memref<?xindex>
// CHECK:               %[[VAL_106:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_104]]] : memref<?xf32>
// CHECK:               memref.store %[[VAL_106]], %[[VAL_16]]{{\[}}%[[VAL_100]], %[[VAL_105]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           scf.for %[[VAL_107:.*]] = %[[VAL_108:.*]]#1 to %[[VAL_20]] step %[[VAL_4]] {
// CHECK:             %[[VAL_109:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_107]]] : memref<?xindex>
// CHECK:             %[[VAL_110:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_107]]] : memref<?xindex>
// CHECK:             %[[VAL_111:.*]] = arith.addi %[[VAL_107]], %[[VAL_4]] : index
// CHECK:             %[[VAL_112:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_111]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_113:.*]] = %[[VAL_110]] to %[[VAL_112]] step %[[VAL_4]] {
// CHECK:               %[[VAL_114:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_113]]] : memref<?xindex>
// CHECK:               %[[VAL_115:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_113]]] : memref<?xf32>
// CHECK:               memref.store %[[VAL_115]], %[[VAL_16]]{{\[}}%[[VAL_109]], %[[VAL_114]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_116:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16xf32>
// CHECK:           return %[[VAL_116]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #Tss>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32, #Tss>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func.func @cmp_ss_ss(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xi1>) -> tensor<32x16xi1> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant false
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0.000000e+00 : f32
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_15:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_16:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:           %[[VAL_17:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xi1>
// CHECK:           linalg.fill ins(%[[VAL_3]] : i1) outs(%[[VAL_17]] : memref<32x16xi1>)
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_22:.*]]:2 = scf.while (%[[VAL_23:.*]] = %[[VAL_18]], %[[VAL_24:.*]] = %[[VAL_20]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_19]] : index
// CHECK:             %[[VAL_26:.*]] = arith.cmpi ult, %[[VAL_24]], %[[VAL_21]] : index
// CHECK:             %[[VAL_27:.*]] = arith.andi %[[VAL_25]], %[[VAL_26]] : i1
// CHECK:             scf.condition(%[[VAL_27]]) %[[VAL_23]], %[[VAL_24]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_28:.*]]: index, %[[VAL_29:.*]]: index):
// CHECK:             %[[VAL_30:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:             %[[VAL_31:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_29]]] : memref<?xindex>
// CHECK:             %[[VAL_32:.*]] = arith.cmpi ult, %[[VAL_31]], %[[VAL_30]] : index
// CHECK:             %[[VAL_33:.*]] = arith.select %[[VAL_32]], %[[VAL_31]], %[[VAL_30]] : index
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_33]] : index
// CHECK:             %[[VAL_35:.*]] = arith.cmpi eq, %[[VAL_31]], %[[VAL_33]] : index
// CHECK:             %[[VAL_36:.*]] = arith.andi %[[VAL_34]], %[[VAL_35]] : i1
// CHECK:             scf.if %[[VAL_36]] {
// CHECK:               %[[VAL_37:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_38:.*]] = arith.addi %[[VAL_28]], %[[VAL_5]] : index
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_38]]] : memref<?xindex>
// CHECK:               %[[VAL_40:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_29]]] : memref<?xindex>
// CHECK:               %[[VAL_41:.*]] = arith.addi %[[VAL_29]], %[[VAL_5]] : index
// CHECK:               %[[VAL_42:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_41]]] : memref<?xindex>
// CHECK:               %[[VAL_43:.*]]:2 = scf.while (%[[VAL_44:.*]] = %[[VAL_37]], %[[VAL_45:.*]] = %[[VAL_40]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi ult, %[[VAL_44]], %[[VAL_39]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.cmpi ult, %[[VAL_45]], %[[VAL_42]] : index
// CHECK:                 %[[VAL_48:.*]] = arith.andi %[[VAL_46]], %[[VAL_47]] : i1
// CHECK:                 scf.condition(%[[VAL_48]]) %[[VAL_44]], %[[VAL_45]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_49:.*]]: index, %[[VAL_50:.*]]: index):
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_49]]] : memref<?xindex>
// CHECK:                 %[[VAL_52:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_50]]] : memref<?xindex>
// CHECK:                 %[[VAL_53:.*]] = arith.cmpi ult, %[[VAL_52]], %[[VAL_51]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.select %[[VAL_53]], %[[VAL_52]], %[[VAL_51]] : index
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.cmpi eq, %[[VAL_52]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_57:.*]] = arith.andi %[[VAL_55]], %[[VAL_56]] : i1
// CHECK:                 scf.if %[[VAL_57]] {
// CHECK:                   %[[VAL_58:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                   %[[VAL_59:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_50]]] : memref<?xf32>
// CHECK:                   %[[VAL_60:.*]] = arith.cmpf ult, %[[VAL_58]], %[[VAL_59]] : f32
// CHECK:                   memref.store %[[VAL_60]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_54]]] : memref<32x16xi1>
// CHECK:                 } else {
// CHECK:                   %[[VAL_61:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_54]] : index
// CHECK:                   scf.if %[[VAL_61]] {
// CHECK:                     %[[VAL_62:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                     %[[VAL_63:.*]] = arith.cmpf ult, %[[VAL_62]], %[[VAL_6]] : f32
// CHECK:                     memref.store %[[VAL_63]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_54]]] : memref<32x16xi1>
// CHECK:                   } else {
// CHECK:                     %[[VAL_64:.*]] = arith.cmpi eq, %[[VAL_52]], %[[VAL_54]] : index
// CHECK:                     scf.if %[[VAL_64]] {
// CHECK:                       %[[VAL_65:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_50]]] : memref<?xf32>
// CHECK:                       %[[VAL_66:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_65]] : f32
// CHECK:                       memref.store %[[VAL_66]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_54]]] : memref<32x16xi1>
// CHECK:                     } else {
// CHECK:                     }
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_67:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.addi %[[VAL_49]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_69:.*]] = arith.select %[[VAL_67]], %[[VAL_68]], %[[VAL_49]] : index
// CHECK:                 %[[VAL_70:.*]] = arith.cmpi eq, %[[VAL_52]], %[[VAL_54]] : index
// CHECK:                 %[[VAL_71:.*]] = arith.addi %[[VAL_50]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_72:.*]] = arith.select %[[VAL_70]], %[[VAL_71]], %[[VAL_50]] : index
// CHECK:                 scf.yield %[[VAL_69]], %[[VAL_72]] : index, index
// CHECK:               } attributes
// CHECK:               scf.for %[[VAL_73:.*]] = %[[VAL_74:.*]]#0 to %[[VAL_39]] step %[[VAL_5]] {
// CHECK:                 %[[VAL_75:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_73]]] : memref<?xindex>
// CHECK:                 %[[VAL_76:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_73]]] : memref<?xf32>
// CHECK:                 %[[VAL_77:.*]] = arith.cmpf ult, %[[VAL_76]], %[[VAL_6]] : f32
// CHECK:                 memref.store %[[VAL_77]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_75]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:               scf.for %[[VAL_78:.*]] = %[[VAL_79:.*]]#1 to %[[VAL_42]] step %[[VAL_5]] {
// CHECK:                 %[[VAL_80:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_78]]] : memref<?xindex>
// CHECK:                 %[[VAL_81:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_78]]] : memref<?xf32>
// CHECK:                 %[[VAL_82:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_81]] : f32
// CHECK:                 memref.store %[[VAL_82]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_80]]] : memref<32x16xi1>
// CHECK:               }
// CHECK:             } else {
// CHECK:               %[[VAL_83:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_33]] : index
// CHECK:               scf.if %[[VAL_83]] {
// CHECK:                 %[[VAL_84:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:                 %[[VAL_85:.*]] = arith.addi %[[VAL_28]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_86:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_85]]] : memref<?xindex>
// CHECK:                 scf.for %[[VAL_87:.*]] = %[[VAL_84]] to %[[VAL_86]] step %[[VAL_5]] {
// CHECK:                   %[[VAL_88:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_87]]] : memref<?xindex>
// CHECK:                   %[[VAL_89:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_87]]] : memref<?xf32>
// CHECK:                   %[[VAL_90:.*]] = arith.cmpf ult, %[[VAL_89]], %[[VAL_6]] : f32
// CHECK:                   memref.store %[[VAL_90]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_88]]] : memref<32x16xi1>
// CHECK:                 }
// CHECK:               } else {
// CHECK:                 %[[VAL_91:.*]] = arith.cmpi eq, %[[VAL_31]], %[[VAL_33]] : index
// CHECK:                 scf.if %[[VAL_91]] {
// CHECK:                   %[[VAL_92:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_29]]] : memref<?xindex>
// CHECK:                   %[[VAL_93:.*]] = arith.addi %[[VAL_29]], %[[VAL_5]] : index
// CHECK:                   %[[VAL_94:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_93]]] : memref<?xindex>
// CHECK:                   scf.for %[[VAL_95:.*]] = %[[VAL_92]] to %[[VAL_94]] step %[[VAL_5]] {
// CHECK:                     %[[VAL_96:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_95]]] : memref<?xindex>
// CHECK:                     %[[VAL_97:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_95]]] : memref<?xf32>
// CHECK:                     %[[VAL_98:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_97]] : f32
// CHECK:                     memref.store %[[VAL_98]], %[[VAL_17]]{{\[}}%[[VAL_33]], %[[VAL_96]]] : memref<32x16xi1>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_99:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_33]] : index
// CHECK:             %[[VAL_100:.*]] = arith.addi %[[VAL_28]], %[[VAL_5]] : index
// CHECK:             %[[VAL_101:.*]] = arith.select %[[VAL_99]], %[[VAL_100]], %[[VAL_28]] : index
// CHECK:             %[[VAL_102:.*]] = arith.cmpi eq, %[[VAL_31]], %[[VAL_33]] : index
// CHECK:             %[[VAL_103:.*]] = arith.addi %[[VAL_29]], %[[VAL_5]] : index
// CHECK:             %[[VAL_104:.*]] = arith.select %[[VAL_102]], %[[VAL_103]], %[[VAL_29]] : index
// CHECK:             scf.yield %[[VAL_101]], %[[VAL_104]] : index, index
// CHECK:           } attributes
// CHECK:           scf.for %[[VAL_105:.*]] = %[[VAL_106:.*]]#0 to %[[VAL_19]] step %[[VAL_5]] {
// CHECK:             %[[VAL_107:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_105]]] : memref<?xindex>
// CHECK:             %[[VAL_108:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_105]]] : memref<?xindex>
// CHECK:             %[[VAL_109:.*]] = arith.addi %[[VAL_105]], %[[VAL_5]] : index
// CHECK:             %[[VAL_110:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_109]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_111:.*]] = %[[VAL_108]] to %[[VAL_110]] step %[[VAL_5]] {
// CHECK:               %[[VAL_112:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_111]]] : memref<?xindex>
// CHECK:               %[[VAL_113:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_111]]] : memref<?xf32>
// CHECK:               %[[VAL_114:.*]] = arith.cmpf ult, %[[VAL_113]], %[[VAL_6]] : f32
// CHECK:               memref.store %[[VAL_114]], %[[VAL_17]]{{\[}}%[[VAL_107]], %[[VAL_112]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           scf.for %[[VAL_115:.*]] = %[[VAL_116:.*]]#1 to %[[VAL_21]] step %[[VAL_5]] {
// CHECK:             %[[VAL_117:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_115]]] : memref<?xindex>
// CHECK:             %[[VAL_118:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_115]]] : memref<?xindex>
// CHECK:             %[[VAL_119:.*]] = arith.addi %[[VAL_115]], %[[VAL_5]] : index
// CHECK:             %[[VAL_120:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_119]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_121:.*]] = %[[VAL_118]] to %[[VAL_120]] step %[[VAL_5]] {
// CHECK:               %[[VAL_122:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_121]]] : memref<?xindex>
// CHECK:               %[[VAL_123:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_121]]] : memref<?xf32>
// CHECK:               %[[VAL_124:.*]] = arith.cmpf ult, %[[VAL_6]], %[[VAL_123]] : f32
// CHECK:               memref.store %[[VAL_124]], %[[VAL_17]]{{\[}}%[[VAL_117]], %[[VAL_122]]] : memref<32x16xi1>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_125:.*]] = bufferization.to_tensor %[[VAL_17]] : memref<32x16xi1>
// CHECK:           return %[[VAL_125]] : tensor<32x16xi1>
// CHECK:         }
func.func @cmp_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #Tss>, %argx: tensor<32x16xi1>) -> tensor<32x16xi1> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32, #Tss>)
    outs(%argx: tensor<32x16xi1>) {
      ^bb(%a: f32, %b: f32, %x: i1):
        %0 = arith.cmpf ult, %a, %b : f32
        linalg.yield %0 : i1
  } -> tensor<32x16xi1>
  return %0 : tensor<32x16xi1>
}

#BatchedVector = #sparse_tensor.encoding<{
  lvlTypes = [ "dense", "compressed-hi" ],
}>
// CHECK-LABEL:   func.func @sub_ss_batched(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<2x3xf64, #{{.*}}>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<2x3xf64, #{{.*}}>>) -> tensor<2x3xf64, #{{.*}}>> {
// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 2 : index
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = bufferization.alloc_tensor() : tensor<2x3xf64, #{{.*}}>>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<2x3xf64, #{{.*}}>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<2x3xf64, #{{.*}}>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<2x3xf64, #{{.*}}>> to memref<?xf64>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<2x3xf64, #{{.*}}>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<2x3xf64, #{{.*}}>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<2x3xf64, #{{.*}}>> to memref<?xf64>
// CHECK:           %[[VAL_12:.*]] = scf.for %[[VAL_13:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] iter_args(%[[VAL_14:.*]] = %[[VAL_5]]) -> (tensor<2x3xf64, #{{.*}}>>) {
// CHECK:             %[[VAL_15:.*]] = arith.muli %[[VAL_13]], %[[VAL_2]] : index
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.addi %[[VAL_15]], %[[VAL_4]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]] = arith.muli %[[VAL_13]], %[[VAL_2]] : index
// CHECK:             %[[VAL_20:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:             %[[VAL_21:.*]] = arith.addi %[[VAL_19]], %[[VAL_4]] : index
// CHECK:             %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:             %[[VAL_23:.*]]:3 = scf.while (%[[VAL_24:.*]] = %[[VAL_16]], %[[VAL_25:.*]] = %[[VAL_20]], %[[VAL_26:.*]] = %[[VAL_14]])
// CHECK:               %[[VAL_27:.*]] = arith.cmpi ult, %[[VAL_24]], %[[VAL_18]] : index
// CHECK:               %[[VAL_28:.*]] = arith.cmpi ult, %[[VAL_25]], %[[VAL_22]] : index
// CHECK:               %[[VAL_29:.*]] = arith.andi %[[VAL_27]], %[[VAL_28]] : i1
// CHECK:               scf.condition(%[[VAL_29]]) %[[VAL_24]], %[[VAL_25]], %[[VAL_26]] : index, index, tensor<2x3xf64, #{{.*}}>>
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_30:.*]]: index, %[[VAL_31:.*]]: index, %[[VAL_32:.*]]: tensor<2x3xf64, #{{.*}}>>):
// CHECK:               %[[VAL_33:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_30]]] : memref<?xindex>
// CHECK:               %[[VAL_34:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_31]]] : memref<?xindex>
// CHECK:               %[[VAL_35:.*]] = arith.cmpi ult, %[[VAL_34]], %[[VAL_33]] : index
// CHECK:               %[[VAL_36:.*]] = arith.select %[[VAL_35]], %[[VAL_34]], %[[VAL_33]] : index
// CHECK:               %[[VAL_37:.*]] = arith.cmpi eq, %[[VAL_33]], %[[VAL_36]] : index
// CHECK:               %[[VAL_38:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_36]] : index
// CHECK:               %[[VAL_39:.*]] = arith.andi %[[VAL_37]], %[[VAL_38]] : i1
// CHECK:               %[[VAL_40:.*]] = scf.if %[[VAL_39]] -> (tensor<2x3xf64, #{{.*}}>>) {
// CHECK:                 %[[VAL_41:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_30]]] : memref<?xf64>
// CHECK:                 %[[VAL_42:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_31]]] : memref<?xf64>
// CHECK:                 %[[VAL_43:.*]] = arith.subf %[[VAL_41]], %[[VAL_42]] : f64
// CHECK:                 %[[VAL_44:.*]] = sparse_tensor.insert %[[VAL_43]] into %[[VAL_32]]{{\[}}%[[VAL_13]], %[[VAL_36]]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                 scf.yield %[[VAL_44]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:               } else {
// CHECK:                 %[[VAL_45:.*]] = arith.cmpi eq, %[[VAL_33]], %[[VAL_36]] : index
// CHECK:                 %[[VAL_46:.*]] = scf.if %[[VAL_45]] -> (tensor<2x3xf64, #{{.*}}>>) {
// CHECK:                   %[[VAL_47:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_30]]] : memref<?xf64>
// CHECK:                   %[[VAL_48:.*]] = sparse_tensor.insert %[[VAL_47]] into %[[VAL_32]]{{\[}}%[[VAL_13]], %[[VAL_36]]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                   scf.yield %[[VAL_48]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                 } else {
// CHECK:                   %[[VAL_49:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_36]] : index
// CHECK:                   %[[VAL_50:.*]] = scf.if %[[VAL_49]] -> (tensor<2x3xf64, #{{.*}}>>) {
// CHECK:                     %[[VAL_51:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_31]]] : memref<?xf64>
// CHECK:                     %[[VAL_52:.*]] = arith.negf %[[VAL_51]] : f64
// CHECK:                     %[[VAL_53:.*]] = sparse_tensor.insert %[[VAL_52]] into %[[VAL_32]]{{\[}}%[[VAL_13]], %[[VAL_36]]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                     scf.yield %[[VAL_53]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                   } else {
// CHECK:                     scf.yield %[[VAL_32]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                   }
// CHECK:                   scf.yield %[[VAL_54:.*]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:                 }
// CHECK:                 scf.yield %[[VAL_55:.*]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:               }
// CHECK:               %[[VAL_56:.*]] = arith.cmpi eq, %[[VAL_33]], %[[VAL_36]] : index
// CHECK:               %[[VAL_57:.*]] = arith.addi %[[VAL_30]], %[[VAL_4]] : index
// CHECK:               %[[VAL_58:.*]] = arith.select %[[VAL_56]], %[[VAL_57]], %[[VAL_30]] : index
// CHECK:               %[[VAL_59:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_36]] : index
// CHECK:               %[[VAL_60:.*]] = arith.addi %[[VAL_31]], %[[VAL_4]] : index
// CHECK:               %[[VAL_61:.*]] = arith.select %[[VAL_59]], %[[VAL_60]], %[[VAL_31]] : index
// CHECK:               scf.yield %[[VAL_58]], %[[VAL_61]], %[[VAL_62:.*]] : index, index, tensor<2x3xf64, #{{.*}}>>
// CHECK:             } attributes
// CHECK:             %[[VAL_63:.*]] = scf.for %[[VAL_64:.*]] = %[[VAL_65:.*]]#0 to %[[VAL_18]] step %[[VAL_4]] iter_args(%[[VAL_66:.*]] = %[[VAL_65]]#2)
// CHECK:               %[[VAL_67:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_64]]] : memref<?xindex>
// CHECK:               %[[VAL_68:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_64]]] : memref<?xf64>
// CHECK:               %[[VAL_69:.*]] = sparse_tensor.insert %[[VAL_68]] into %[[VAL_66]]{{\[}}%[[VAL_13]], %[[VAL_67]]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:               scf.yield %[[VAL_69]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:             }
// CHECK:             %[[VAL_70:.*]] = scf.for %[[VAL_71:.*]] = %[[VAL_72:.*]]#1 to %[[VAL_22]] step %[[VAL_4]] iter_args(%[[VAL_73:.*]] = %[[VAL_74:.*]])
// CHECK:               %[[VAL_75:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_71]]] : memref<?xindex>
// CHECK:               %[[VAL_76:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_71]]] : memref<?xf64>
// CHECK:               %[[VAL_77:.*]] = arith.negf %[[VAL_76]] : f64
// CHECK:               %[[VAL_78:.*]] = sparse_tensor.insert %[[VAL_77]] into %[[VAL_73]]{{\[}}%[[VAL_13]], %[[VAL_75]]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:               scf.yield %[[VAL_78]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:             }
// CHECK:             scf.yield %[[VAL_79:.*]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:           }
// CHECK:           %[[VAL_80:.*]] = sparse_tensor.load %[[VAL_81:.*]] hasInserts : tensor<2x3xf64, #{{.*}}>>
// CHECK:           return %[[VAL_80]] : tensor<2x3xf64, #{{.*}}>>
// CHECK:         }
func.func @sub_ss_batched(%0: tensor<2x3xf64, #BatchedVector>, %1: tensor<2x3xf64, #BatchedVector>)
                           -> tensor<2x3xf64, #BatchedVector> {
  %2 = bufferization.alloc_tensor() : tensor<2x3xf64, #BatchedVector>
  %3 = linalg.generic #trait2
       ins(%0, %1 : tensor<2x3xf64, #BatchedVector>, tensor<2x3xf64, #BatchedVector>)
       outs(%2 : tensor<2x3xf64, #BatchedVector>) {
    ^bb0(%in: f64, %in_0: f64, %out: f64):
      %7 = arith.subf %in, %in_0 : f64
      linalg.yield %7 : f64
    } -> tensor<2x3xf64, #BatchedVector>
  return %3 : tensor<2x3xf64, #BatchedVector>
}

// CHECK-LABEL:   func @mul_ss_ss(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_16]] : memref<32x16xf32>)
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_24:.*]] = arith.cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
// CHECK:             %[[VAL_26:.*]] = arith.andi %[[VAL_24]], %[[VAL_25]] : i1
// CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
// CHECK:             %[[VAL_29:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:             %[[VAL_30:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:             %[[VAL_31:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_32:.*]] = arith.select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
// CHECK:             %[[VAL_33:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_34:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_35:.*]] = arith.andi %[[VAL_33]], %[[VAL_34]] : i1
// CHECK:             scf.if %[[VAL_35]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_37:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:               %[[VAL_39:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_40:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
// CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_45:.*]] = arith.cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.andi %[[VAL_45]], %[[VAL_46]] : i1
// CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
// CHECK:                 %[[VAL_50:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
// CHECK:                 %[[VAL_52:.*]] = arith.cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_53:.*]] = arith.select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.andi %[[VAL_54]], %[[VAL_55]] : i1
// CHECK:                 scf.if %[[VAL_56]] {
// CHECK:                   %[[VAL_57:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                   %[[VAL_58:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
// CHECK:                   %[[VAL_59:.*]] = arith.mulf %[[VAL_57]], %[[VAL_58]] : f32
// CHECK:                   memref.store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                 }
// CHECK:                 %[[VAL_60:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_61:.*]] = arith.addi %[[VAL_48]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_62:.*]] = arith.select %[[VAL_60]], %[[VAL_61]], %[[VAL_48]] : index
// CHECK:                 %[[VAL_63:.*]] = arith.cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
// CHECK:                 %[[VAL_64:.*]] = arith.addi %[[VAL_49]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_65:.*]] = arith.select %[[VAL_63]], %[[VAL_64]], %[[VAL_49]] : index
// CHECK:                 scf.yield %[[VAL_62]], %[[VAL_65]] : index, index
// CHECK:               }
// CHECK:             } else {
// CHECK:             }
// CHECK:             %[[VAL_66:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
// CHECK:             %[[VAL_67:.*]] = arith.addi %[[VAL_27]], %[[VAL_4]] : index
// CHECK:             %[[VAL_68:.*]] = arith.select %[[VAL_66]], %[[VAL_67]], %[[VAL_27]] : index
// CHECK:             %[[VAL_69:.*]] = arith.cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
// CHECK:             %[[VAL_70:.*]] = arith.addi %[[VAL_28]], %[[VAL_4]] : index
// CHECK:             %[[VAL_71:.*]] = arith.select %[[VAL_69]], %[[VAL_70]], %[[VAL_28]] : index
// CHECK:             scf.yield %[[VAL_68]], %[[VAL_71]] : index, index
// CHECK:           }
// CHECK:           %[[VAL_72:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16xf32>
// CHECK:           return %[[VAL_72]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #Tss>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tss>, tensor<32x16xf32, #Tss>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @add_sd_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_15]] : memref<32x16xf32>)
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_16]], %[[VAL_20:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_21:.*]] = arith.cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
// CHECK:             scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
// CHECK:             %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:             %[[VAL_25:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             scf.if %[[VAL_25]] {
// CHECK:               %[[VAL_26:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_27:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:               %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:               %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_26]], %[[VAL_31:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_32:.*]] = arith.cmpi ult, %[[VAL_30]], %[[VAL_28]] : index
// CHECK:                 scf.condition(%[[VAL_32]]) %[[VAL_30]], %[[VAL_31]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_33:.*]]: index, %[[VAL_34:.*]]: index):
// CHECK:                 %[[VAL_35:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:                 %[[VAL_36:.*]] = arith.muli %[[VAL_22]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_37:.*]] = arith.addi %[[VAL_36]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_38:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 scf.if %[[VAL_38]] {
// CHECK:                   %[[VAL_39:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_37]]] : memref<?xf32>
// CHECK:                   %[[VAL_40:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:                   %[[VAL_41:.*]] = arith.addf %[[VAL_39]], %[[VAL_40]] : f32
// CHECK:                   memref.store %[[VAL_41]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_6]] {
// CHECK:                     %[[VAL_42:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_37]]] : memref<?xf32>
// CHECK:                     memref.store %[[VAL_42]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_43:.*]] = arith.cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_44:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_45:.*]] = arith.select %[[VAL_43]], %[[VAL_44]], %[[VAL_33]] : index
// CHECK:                 %[[VAL_46:.*]] = arith.addi %[[VAL_34]], %[[VAL_7]] : index
// CHECK:                 scf.yield %[[VAL_45]], %[[VAL_46]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_47:.*]] = %[[VAL_48:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_49:.*]] = arith.muli %[[VAL_22]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_50:.*]] = arith.addi %[[VAL_49]], %[[VAL_47]] : index
// CHECK:                 %[[VAL_51:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_50]]] : memref<?xf32>
// CHECK:                 memref.store %[[VAL_51]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_47]]] : memref<32x16xf32>
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_6]] {
// CHECK:                 %[[VAL_52:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:                 %[[VAL_53:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_54:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_53]]] : memref<?xindex>
// CHECK:                 scf.for %[[VAL_55:.*]] = %[[VAL_52]] to %[[VAL_54]] step %[[VAL_7]] {
// CHECK:                   %[[VAL_56:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_55]]] : memref<?xindex>
// CHECK:                   %[[VAL_57:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_55]]] : memref<?xf32>
// CHECK:                   memref.store %[[VAL_57]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_56]]] : memref<32x16xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_58:.*]] = arith.cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
// CHECK:             %[[VAL_59:.*]] = arith.addi %[[VAL_22]], %[[VAL_7]] : index
// CHECK:             %[[VAL_60:.*]] = arith.select %[[VAL_58]], %[[VAL_59]], %[[VAL_22]] : index
// CHECK:             %[[VAL_61:.*]] = arith.addi %[[VAL_23]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_60]], %[[VAL_61]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_62:.*]] = %[[VAL_63:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             %[[VAL_64:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_62]]] : memref<?xindex>
// CHECK:             %[[VAL_65:.*]] = arith.addi %[[VAL_62]], %[[VAL_7]] : index
// CHECK:             %[[VAL_66:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_65]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_67:.*]] = %[[VAL_64]] to %[[VAL_66]] step %[[VAL_7]] {
// CHECK:               %[[VAL_68:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_67]]] : memref<?xindex>
// CHECK:               %[[VAL_69:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_67]]] : memref<?xf32>
// CHECK:               memref.store %[[VAL_69]], %[[VAL_15]]{{\[}}%[[VAL_62]], %[[VAL_68]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_70:.*]] = bufferization.to_tensor %[[VAL_15]] : memref<32x16xf32>
// CHECK:           return %[[VAL_70]] : tensor<32x16xf32>
// CHECK:         }
func.func @add_sd_ds(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32, #Tds>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32, #Tds>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

// CHECK-LABEL:   func @mul_sd_ds(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<32x16xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16xf32>
// CHECK:           linalg.fill ins(%{{.*}} : f32) outs(%[[VAL_13]] : memref<32x16xf32>)
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_16:.*]] = %[[VAL_14]] to %[[VAL_15]] step %[[VAL_5]] {
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]] = arith.addi %[[VAL_17]], %[[VAL_5]] : index
// CHECK:             %[[VAL_20:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_5]] {
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:               %[[VAL_23:.*]] = arith.muli %[[VAL_16]], %[[VAL_3]] : index
// CHECK:               %[[VAL_24:.*]] = arith.addi %[[VAL_23]], %[[VAL_22]] : index
// CHECK:               %[[VAL_25:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_24]]] : memref<?xf32>
// CHECK:               %[[VAL_26:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_21]]] : memref<?xf32>
// CHECK:               %[[VAL_27:.*]] = arith.mulf %[[VAL_25]], %[[VAL_26]] : f32
// CHECK:               memref.store %[[VAL_27]], %[[VAL_13]]{{\[}}%[[VAL_17]], %[[VAL_22]]] : memref<32x16xf32>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_28:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16xf32>
// CHECK:           return %[[VAL_28]] : tensor<32x16xf32>
// CHECK:         }
func.func @mul_sd_ds(%arga: tensor<32x16xf32, #Tsd>, %argb: tensor<32x16xf32, #Tds>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
  %0 = linalg.generic #trait2
     ins(%arga, %argb: tensor<32x16xf32, #Tsd>, tensor<32x16xf32, #Tds>)
    outs(%argx: tensor<32x16xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16xf32>
  return %0 : tensor<32x16xf32>
}

#trait_matvec = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (j)>,    // b
    affine_map<(i,j) -> (i)>     // x (out)
  ],
  iterator_types = ["parallel", "reduction"],
  doc = "x(i) += SUM_j A(i,j) * b(j)"
}

// CHECK-LABEL:   func @matvec(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<16x32xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<32xf32>,
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<16xf32>) -> tensor<16xf32> {
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<16x32xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<16x32xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<16x32xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<16xf32>
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK-DAG:         %[[VAL_13:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
// CHECK-DAG:         %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_5]] : index
// CHECK-DAG:         %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK-DAG:         %[[VAL_16:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
// CHECK:             %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f32) {
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf32>
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<32xf32>
// CHECK:               %[[VAL_23:.*]] = arith.mulf %[[VAL_21]], %[[VAL_22]] : f32
// CHECK:               %[[VAL_24:.*]] = arith.addf %[[VAL_23]], %[[VAL_19]] : f32
// CHECK:               scf.yield %[[VAL_24]] : f32
// CHECK:             }
// CHECK:             memref.store %[[VAL_17]], %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
// CHECK:           }
// CHECK:           %[[VAL_26:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<16xf32>
// CHECK:           return %[[VAL_26]] : tensor<16xf32>
// CHECK:         }
func.func @matvec(%argA: tensor<16x32xf32, #Tds>, %argb: tensor<32xf32>, %argx: tensor<16xf32>) -> tensor<16xf32> {
  %0 = linalg.generic #trait_matvec
       ins(%argA, %argb: tensor<16x32xf32, #Tds>, tensor<32xf32>)
      outs(%argx: tensor<16xf32>) {
    ^bb(%A: f32, %b: f32, %x: f32):
      %0 = arith.mulf %A, %b : f32
      %1 = arith.addf %0, %x : f32
      linalg.yield %1 : f32
  } -> tensor<16xf32>
  return %0 : tensor<16xf32>
}

#trait_sum_reduction = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>, // A
    affine_map<(i,j) -> ()>     // x (scalar out)
  ],
  iterator_types = ["reduction", "reduction"],
  doc = "x += SUM_ij A(i,j)"
}

// CHECK-LABEL:   func @sum_reduction(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<10x20xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<f32>) -> tensor<f32> {
// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 10 : index
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<10x20xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<10x20xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_1]] : memref<f32>
// CHECK:           %[[VAL_9:.*]] = memref.load %[[VAL_8]][] : memref<f32>
// CHECK:           %[[VAL_10:.*]] = scf.for %[[VAL_11:.*]] = %[[VAL_4]] to %[[VAL_2]] step %[[VAL_3]] iter_args(%[[VAL_12:.*]] = %[[VAL_9]]) -> (f32) {
// CHECK:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xindex>
// CHECK:             %[[VAL_14:.*]] = arith.addi %[[VAL_11]], %[[VAL_3]] : index
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             %[[VAL_16:.*]] = scf.for %[[VAL_17:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_3]] iter_args(%[[VAL_18:.*]] = %[[VAL_12]]) -> (f32) {
// CHECK:               %[[VAL_19:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_17]]] : memref<?xf32>
// CHECK:               %[[VAL_20:.*]] = arith.addf %[[VAL_18]], %[[VAL_19]] : f32
// CHECK:               scf.yield %[[VAL_20]] : f32
// CHECK:             }
// CHECK:             scf.yield %[[VAL_16]] : f32
// CHECK:           }
// CHECK:           memref.store %[[VAL_10]], %[[VAL_8]][] : memref<f32>
// CHECK:           %[[VAL_23:.*]] = bufferization.to_tensor %[[VAL_8]] : memref<f32>
// CHECK:           return %[[VAL_23]] : tensor<f32>
// CHECK:         }
func.func @sum_reduction(%arga: tensor<10x20xf32, #Tds>, %argx: tensor<f32>) -> tensor<f32> {
  %0 = linalg.generic #trait_sum_reduction
     ins(%arga: tensor<10x20xf32, #Tds>)
    outs(%argx: tensor<f32>) {
      ^bb(%a: f32, %x: f32):
        %0 = arith.addf %x, %a : f32
        linalg.yield %0 : f32
  } -> tensor<f32>
  return %0 : tensor<f32>
}

#trait_scale = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (i,j)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel"],
  doc = "X(i,j) = A(i,j) * SCALE"
}

// CHECK-LABEL:   func @scale(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<?x?xf64, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<?x?xf64>) -> tensor<?x?xf64> {
// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 2.000000e+00 : f64
// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<?x?xf64, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<?x?xf64, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<?x?xf64, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf64>
// CHECK-DAG:       %[[VAL_8:.*]] = tensor.dim %[[VAL_0]], %[[VAL_3]] : tensor<?x?xf64, #sparse_tensor.encoding<{{{.*}}}>>
// CHECK-DAG:       %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<?x?xf64>
// CHECK:           linalg.fill ins(%{{.*}} : f64) outs(%[[VAL_11]] : memref<?x?xf64>)
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_3]] to %[[VAL_8]] step %[[VAL_4]] {
// CHECK:             %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_12]]] : memref<?xindex>
// CHECK:             %[[VAL_14:.*]] = arith.addi %[[VAL_12]], %[[VAL_4]] : index
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_14]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_4]] {
// CHECK:               %[[VAL_17:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:               %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xf64>
// CHECK:               %[[VAL_19:.*]] = arith.mulf %[[VAL_18]], %[[VAL_2]] : f64
// CHECK:               memref.store %[[VAL_19]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<?x?xf64>
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_20:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<?x?xf64>
// CHECK:           return %[[VAL_20]] : tensor<?x?xf64>
// CHECK:         }
func.func @scale(%arga: tensor<?x?xf64, #Tds>, %argx: tensor<?x?xf64>) -> tensor<?x?xf64> {
  %0 = arith.constant 2.0 : f64
  %1 = linalg.generic #trait_scale
     ins(%arga: tensor<?x?xf64, #Tds>)
    outs(%argx: tensor<?x?xf64>) {
      ^bb(%a: f64, %x: f64):
        %2 = arith.mulf %a, %0 : f64
        linalg.yield %2 : f64
  } -> tensor<?x?xf64>
  return %1 : tensor<?x?xf64>
}

#trait_sampled_dense_dense = {
  indexing_maps = [
    affine_map<(i,j,k) -> (i,j)>,  // S
    affine_map<(i,j,k) -> (i,k)>,  // A
    affine_map<(i,j,k) -> (k,j)>,  // B
    affine_map<(i,j,k) -> (i,j)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel", "reduction"],
  doc = "X(i,j) += S(i,j) SUM_k A(i,k) B(k,j)"
}

// CHECK-LABEL:   func.func @sampled_dense_dense(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<?x?xf32>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<?x?xf32>,
// CHECK-SAME:      %[[VAL_3:.*3]]: tensor<?x?xf32>) -> tensor<?x?xf32> {
// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_6:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_7:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_8:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_11:.*]] = tensor.dim %[[VAL_1]], %[[VAL_4]] : tensor<?x?xf32>
// CHECK-DAG:       %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_1]] : memref<?x?xf32>
// CHECK-DAG:       %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<?x?xf32>
// CHECK-DAG:       %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_3]] : memref<?x?xf32>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_15]] to %[[VAL_16]] step %[[VAL_4]] {
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_11]] step %[[VAL_4]] {
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_18]], %[[VAL_19]]] : memref<?x?xf32>
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:               %[[VAL_22:.*]] = arith.addi %[[VAL_17]], %[[VAL_4]] : index
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_4]] {
// CHECK:                 %[[VAL_25:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xindex>
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_25]]] : memref<?x?xf32>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_19]], %[[VAL_25]]] : memref<?x?xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.mulf %[[VAL_20]], %[[VAL_28]] : f32
// CHECK:                 %[[VAL_30:.*]] = arith.mulf %[[VAL_27]], %[[VAL_29]] : f32
// CHECK:                 %[[VAL_31:.*]] = arith.addf %[[VAL_26]], %[[VAL_30]] : f32
// CHECK:                 memref.store %[[VAL_31]], %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_25]]] : memref<?x?xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_32:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<?x?xf32>
// CHECK:           return %[[VAL_32]] : tensor<?x?xf32>
// CHECK:         }
func.func @sampled_dense_dense(%args: tensor<?x?xf32, #Tss>,
                          %arga: tensor<?x?xf32>,
                          %argb: tensor<?x?xf32>,
                          %argx: tensor<?x?xf32>) -> tensor<?x?xf32> {
  %0 = linalg.generic #trait_sampled_dense_dense
     ins(%args, %arga, %argb: tensor<?x?xf32, #Tss>, tensor<?x?xf32>, tensor<?x?xf32>)
    outs(%argx: tensor<?x?xf32>) {
      ^bb(%s: f32, %a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        %1 = arith.mulf %s, %0 : f32
        %2 = arith.addf %x, %1 : f32
        linalg.yield %2 : f32
  } -> tensor<?x?xf32>
  return %0 : tensor<?x?xf32>
}

#trait_sum_kernel_with_inv = {
  indexing_maps = [
    affine_map<(i,j) -> (i,j)>,  // A
    affine_map<(i,j) -> (i,j)>,  // B
    affine_map<(i,j) -> (i,j)>,  // C
    affine_map<(i,j) -> (i)>,    // d
    affine_map<(i,j) -> ()>,     // e
    affine_map<(i,j) -> (i)>     // x (out)
  ],
  iterator_types = ["parallel", "reduction"],
  doc = "x(i) = SUM_j A(i,j) * B(i,j) * d(i) * e + C(i,j)"
}

// CHECK-LABEL:   func @sum_kernel_with_inv(
// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_2:.*2]]: tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>>,
// CHECK-SAME:      %[[VAL_3:.*3]]: tensor<?xf32>,
// CHECK-SAME:      %[[VAL_4:.*4]]: tensor<f32>,
// CHECK-SAME:      %[[VAL_5:.*5]]: tensor<?xf32>) -> tensor<?xf32> {
// CHECK-DAG:       %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:       %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK-DAG:       %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:       %[[VAL_9:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_10:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 0 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_11:.*]] = sparse_tensor.positions %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_12:.*]] = sparse_tensor.coordinates %[[VAL_0]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_13:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_14:.*]] = sparse_tensor.positions %[[VAL_1]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_15:.*]] = sparse_tensor.coordinates %[[VAL_1]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_17:.*]] = sparse_tensor.positions %[[VAL_2]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_18:.*]] = sparse_tensor.coordinates %[[VAL_2]] {level = 1 : index} : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xindex>
// CHECK-DAG:       %[[VAL_19:.*]] = sparse_tensor.values %[[VAL_2]] : tensor<?x?xf32, #sparse_tensor.encoding<{ lvlTypes = [ "dense", "compressed" ] }>> to memref<?xf32>
// CHECK-DAG:       %[[VAL_20:.*]] = bufferization.to_memref %[[VAL_3]] : memref<?xf32>
// CHECK-DAG:       %[[VAL_21:.*]] = bufferization.to_memref %[[VAL_4]] : memref<f32>
// CHECK-DAG:       %[[VAL_22:.*]] = tensor.dim %[[VAL_2]], %[[VAL_6]] : tensor<?x?xf32,
// CHECK-DAG:       %[[VAL_24:.*]] = bufferization.to_memref %[[VAL_5]] : memref<?xf32>
// CHECK:           %[[VAL_25:.*]] = memref.load %[[VAL_21]][] : memref<f32>
// CHECK:           %[[VAL_26:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           %[[VAL_27:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_28:.*]]:2 = scf.while (%[[VAL_29:.*]] = %[[VAL_26]], %[[VAL_30:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_31:.*]] = arith.cmpi ult, %[[VAL_29]], %[[VAL_27]] : index
// CHECK:             scf.condition(%[[VAL_31]]) %[[VAL_29]], %[[VAL_30]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_32:.*]]: index, %[[VAL_33:.*]]: index):
// CHECK:             %[[VAL_34:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_32]]] : memref<?xindex>
// CHECK:             %[[VAL_35:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_33]] : index
// CHECK:             scf.if %[[VAL_35]] {
// CHECK:               %[[VAL_36:.*]] = memref.load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:               %[[VAL_37:.*]] = memref.load %[[VAL_20]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:               %[[VAL_38:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_32]]] : memref<?xindex>
// CHECK:               %[[VAL_39:.*]] = arith.addi %[[VAL_32]], %[[VAL_7]] : index
// CHECK:               %[[VAL_40:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_39]]] : memref<?xindex>
// CHECK:               %[[VAL_41:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:               %[[VAL_42:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:               %[[VAL_43:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_42]]] : memref<?xindex>
// CHECK:               %[[VAL_44:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:               %[[VAL_45:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:               %[[VAL_46:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_45]]] : memref<?xindex>
// CHECK:               %[[VAL_47:.*]]:4 = scf.while (%[[VAL_48:.*]] = %[[VAL_38]], %[[VAL_49:.*]] = %[[VAL_41]], %[[VAL_50:.*]] = %[[VAL_44]], %[[VAL_51:.*]] = %[[VAL_36]]) : (index, index, index, f32) -> (index, index, index, f32) {
// CHECK:                 %[[VAL_52:.*]] = arith.cmpi ult, %[[VAL_48]], %[[VAL_40]] : index
// CHECK:                 %[[VAL_53:.*]] = arith.cmpi ult, %[[VAL_49]], %[[VAL_43]] : index
// CHECK:                 %[[VAL_54:.*]] = arith.andi %[[VAL_52]], %[[VAL_53]] : i1
// CHECK:                 %[[VAL_55:.*]] = arith.cmpi ult, %[[VAL_50]], %[[VAL_46]] : index
// CHECK:                 %[[VAL_56:.*]] = arith.andi %[[VAL_54]], %[[VAL_55]] : i1
// CHECK:                 scf.condition(%[[VAL_56]]) %[[VAL_48]], %[[VAL_49]], %[[VAL_50]], %[[VAL_51]] : index, index, index, f32
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_57:.*]]: index, %[[VAL_58:.*]]: index, %[[VAL_59:.*]]: index, %[[VAL_60:.*]]: f32):
// CHECK-DAG:             %[[VAL_61:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_57]]] : memref<?xindex>
// CHECK-DAG:             %[[VAL_62:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_58]]] : memref<?xindex>
// CHECK-DAG:             %[[VAL_65:.*]] = memref.load %[[VAL_18]]{{\[}}%[[VAL_59]]] : memref<?xindex>
// CHECK:                 %[[VAL_63:.*]] = arith.cmpi ult, %[[VAL_62]], %[[VAL_61]] : index
// CHECK:                 %[[VAL_64:.*]] = arith.select %[[VAL_63]], %[[VAL_62]], %[[VAL_61]] : index
// CHECK:                 %[[VAL_66:.*]] = arith.cmpi ult, %[[VAL_65]], %[[VAL_64]] : index
// CHECK:                 %[[VAL_67:.*]] = arith.select %[[VAL_66]], %[[VAL_65]], %[[VAL_64]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.cmpi eq, %[[VAL_61]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_69:.*]] = arith.cmpi eq, %[[VAL_62]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_70:.*]] = arith.andi %[[VAL_68]], %[[VAL_69]] : i1
// CHECK:                 %[[VAL_71:.*]] = arith.cmpi eq, %[[VAL_65]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_72:.*]] = arith.andi %[[VAL_70]], %[[VAL_71]] : i1
// CHECK:                 %[[VAL_73:.*]] = scf.if %[[VAL_72]] -> (f32) {
// CHECK:                   %[[VAL_74:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_57]]] : memref<?xf32>
// CHECK:                   %[[VAL_75:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_58]]] : memref<?xf32>
// CHECK:                   %[[VAL_76:.*]] = arith.mulf %[[VAL_74]], %[[VAL_75]] : f32
// CHECK:                   %[[VAL_77:.*]] = arith.mulf %[[VAL_76]], %[[VAL_37]] : f32
// CHECK:                   %[[VAL_78:.*]] = arith.mulf %[[VAL_77]], %[[VAL_25]] : f32
// CHECK:                   %[[VAL_79:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_59]]] : memref<?xf32>
// CHECK:                   %[[VAL_80:.*]] = arith.addf %[[VAL_78]], %[[VAL_79]] : f32
// CHECK:                   %[[VAL_81:.*]] = arith.addf %[[VAL_60]], %[[VAL_80]] : f32
// CHECK:                   scf.yield %[[VAL_81]] : f32
// CHECK:                 } else {
// CHECK:                   %[[VAL_82:.*]] = arith.cmpi eq, %[[VAL_61]], %[[VAL_67]] : index
// CHECK:                   %[[VAL_83:.*]] = arith.cmpi eq, %[[VAL_62]], %[[VAL_67]] : index
// CHECK:                   %[[VAL_84:.*]] = arith.andi %[[VAL_82]], %[[VAL_83]] : i1
// CHECK:                   %[[VAL_85:.*]] = scf.if %[[VAL_84]] -> (f32) {
// CHECK:                     %[[VAL_86:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_57]]] : memref<?xf32>
// CHECK:                     %[[VAL_87:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_58]]] : memref<?xf32>
// CHECK:                     %[[VAL_88:.*]] = arith.mulf %[[VAL_86]], %[[VAL_87]] : f32
// CHECK:                     %[[VAL_89:.*]] = arith.mulf %[[VAL_88]], %[[VAL_37]] : f32
// CHECK:                     %[[VAL_90:.*]] = arith.mulf %[[VAL_89]], %[[VAL_25]] : f32
// CHECK:                     %[[VAL_91:.*]] = arith.addf %[[VAL_60]], %[[VAL_90]] : f32
// CHECK:                     scf.yield %[[VAL_91]] : f32
// CHECK:                   } else {
// CHECK:                     %[[VAL_92:.*]] = arith.cmpi eq, %[[VAL_65]], %[[VAL_67]] : index
// CHECK:                     %[[VAL_93:.*]] = scf.if %[[VAL_92]] -> (f32) {
// CHECK:                       %[[VAL_94:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_59]]] : memref<?xf32>
// CHECK:                       %[[VAL_95:.*]] = arith.addf %[[VAL_60]], %[[VAL_94]] : f32
// CHECK:                       scf.yield %[[VAL_95]] : f32
// CHECK:                     } else {
// CHECK:                       scf.yield %[[VAL_60]] : f32
// CHECK:                     }
// CHECK:                     scf.yield %[[VAL_96:.*]] : f32
// CHECK:                   }
// CHECK:                   scf.yield %[[VAL_97:.*]] : f32
// CHECK:                 }
// CHECK:                 %[[VAL_98:.*]] = arith.cmpi eq, %[[VAL_61]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_99:.*]] = arith.addi %[[VAL_57]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_100:.*]] = arith.select %[[VAL_98]], %[[VAL_99]], %[[VAL_57]] : index
// CHECK:                 %[[VAL_101:.*]] = arith.cmpi eq, %[[VAL_62]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_102:.*]] = arith.addi %[[VAL_58]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_103:.*]] = arith.select %[[VAL_101]], %[[VAL_102]], %[[VAL_58]] : index
// CHECK:                 %[[VAL_104:.*]] = arith.cmpi eq, %[[VAL_65]], %[[VAL_67]] : index
// CHECK:                 %[[VAL_105:.*]] = arith.addi %[[VAL_59]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_106:.*]] = arith.select %[[VAL_104]], %[[VAL_105]], %[[VAL_59]] : index
// CHECK:                 scf.yield %[[VAL_100]], %[[VAL_103]], %[[VAL_106]], %[[VAL_107:.*]] : index, index, index, f32
// CHECK:               }
// CHECK:               %[[VAL_108:.*]]:3 = scf.while (%[[VAL_109:.*]] = %[[VAL_110:.*]]#0, %[[VAL_111:.*]] = %[[VAL_110]]#1, %[[VAL_112:.*]] = %[[VAL_110]]#3) : (index, index, f32) -> (index, index, f32) {
// CHECK:                 %[[VAL_113:.*]] = arith.cmpi ult, %[[VAL_109]], %[[VAL_40]] : index
// CHECK:                 %[[VAL_114:.*]] = arith.cmpi ult, %[[VAL_111]], %[[VAL_43]] : index
// CHECK:                 %[[VAL_115:.*]] = arith.andi %[[VAL_113]], %[[VAL_114]] : i1
// CHECK:                 scf.condition(%[[VAL_115]]) %[[VAL_109]], %[[VAL_111]], %[[VAL_112]] : index, index, f32
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_116:.*]]: index, %[[VAL_117:.*]]: index, %[[VAL_118:.*]]: f32):
// CHECK:                 %[[VAL_119:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_116]]] : memref<?xindex>
// CHECK:                 %[[VAL_120:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_117]]] : memref<?xindex>
// CHECK:                 %[[VAL_121:.*]] = arith.cmpi ult, %[[VAL_120]], %[[VAL_119]] : index
// CHECK:                 %[[VAL_122:.*]] = arith.select %[[VAL_121]], %[[VAL_120]], %[[VAL_119]] : index
// CHECK:                 %[[VAL_123:.*]] = arith.cmpi eq, %[[VAL_119]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_124:.*]] = arith.cmpi eq, %[[VAL_120]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_125:.*]] = arith.andi %[[VAL_123]], %[[VAL_124]] : i1
// CHECK:                 %[[VAL_126:.*]] = scf.if %[[VAL_125]] -> (f32) {
// CHECK:                   %[[VAL_127:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_116]]] : memref<?xf32>
// CHECK:                   %[[VAL_128:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_117]]] : memref<?xf32>
// CHECK:                   %[[VAL_129:.*]] = arith.mulf %[[VAL_127]], %[[VAL_128]] : f32
// CHECK:                   %[[VAL_130:.*]] = arith.mulf %[[VAL_129]], %[[VAL_37]] : f32
// CHECK:                   %[[VAL_131:.*]] = arith.mulf %[[VAL_130]], %[[VAL_25]] : f32
// CHECK:                   %[[VAL_132:.*]] = arith.addf %[[VAL_118]], %[[VAL_131]] : f32
// CHECK:                   scf.yield %[[VAL_132]] : f32
// CHECK:                 } else {
// CHECK:                   scf.yield %[[VAL_118]] : f32
// CHECK:                 }
// CHECK:                 %[[VAL_133:.*]] = arith.cmpi eq, %[[VAL_119]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_134:.*]] = arith.addi %[[VAL_116]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_135:.*]] = arith.select %[[VAL_133]], %[[VAL_134]], %[[VAL_116]] : index
// CHECK:                 %[[VAL_136:.*]] = arith.cmpi eq, %[[VAL_120]], %[[VAL_122]] : index
// CHECK:                 %[[VAL_137:.*]] = arith.addi %[[VAL_117]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_138:.*]] = arith.select %[[VAL_136]], %[[VAL_137]], %[[VAL_117]] : index
// CHECK:                 scf.yield %[[VAL_135]], %[[VAL_138]], %[[VAL_139:.*]] : index, index, f32
// CHECK:               }
// CHECK:               %[[VAL_140:.*]] = scf.for %[[VAL_141:.*]] = %[[VAL_142:.*]]#2 to %[[VAL_46]] step %[[VAL_7]] iter_args(%[[VAL_143:.*]] = %[[VAL_144:.*]]#2) -> (f32) {
// CHECK:                 %[[VAL_145:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_141]]] : memref<?xf32>
// CHECK:                 %[[VAL_146:.*]] = arith.addf %[[VAL_143]], %[[VAL_145]] : f32
// CHECK:                 scf.yield %[[VAL_146]] : f32
// CHECK:               }
// CHECK:               memref.store %[[VAL_147:.*]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_8]] {
// CHECK:                 %[[VAL_148:.*]] = memref.load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:                 %[[VAL_149:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_33]]] : memref<?xindex>
// CHECK:                 %[[VAL_150:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:                 %[[VAL_151:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_150]]] : memref<?xindex>
// CHECK:                 %[[VAL_152:.*]] = scf.for %[[VAL_153:.*]] = %[[VAL_149]] to %[[VAL_151]] step %[[VAL_7]] iter_args(%[[VAL_154:.*]] = %[[VAL_148]]) -> (f32) {
// CHECK:                   %[[VAL_155:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_153]]] : memref<?xf32>
// CHECK:                   %[[VAL_156:.*]] = arith.addf %[[VAL_154]], %[[VAL_155]] : f32
// CHECK:                   scf.yield %[[VAL_156]] : f32
// CHECK:                 }
// CHECK:                 memref.store %[[VAL_157:.*]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_158:.*]] = arith.cmpi eq, %[[VAL_34]], %[[VAL_33]] : index
// CHECK:             %[[VAL_159:.*]] = arith.addi %[[VAL_32]], %[[VAL_7]] : index
// CHECK:             %[[VAL_160:.*]] = arith.select %[[VAL_158]], %[[VAL_159]], %[[VAL_32]] : index
// CHECK:             %[[VAL_161:.*]] = arith.addi %[[VAL_33]], %[[VAL_7]] : index
// CHECK:             scf.yield %[[VAL_160]], %[[VAL_161]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_162:.*]] = %[[VAL_163:.*]]#1 to %[[VAL_22]] step %[[VAL_7]] {
// CHECK:             %[[VAL_164:.*]] = memref.load %[[VAL_24]]{{\[}}%[[VAL_162]]] : memref<?xf32>
// CHECK:             %[[VAL_165:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_162]]] : memref<?xindex>
// CHECK:             %[[VAL_166:.*]] = arith.addi %[[VAL_162]], %[[VAL_7]] : index
// CHECK:             %[[VAL_167:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_166]]] : memref<?xindex>
// CHECK:             %[[VAL_168:.*]] = scf.for %[[VAL_169:.*]] = %[[VAL_165]] to %[[VAL_167]] step %[[VAL_7]] iter_args(%[[VAL_170:.*]] = %[[VAL_164]]) -> (f32) {
// CHECK:               %[[VAL_171:.*]] = memref.load %[[VAL_19]]{{\[}}%[[VAL_169]]] : memref<?xf32>
// CHECK:               %[[VAL_172:.*]] = arith.addf %[[VAL_170]], %[[VAL_171]] : f32
// CHECK:               scf.yield %[[VAL_172]] : f32
// CHECK:             }
// CHECK:             memref.store %[[VAL_173:.*]], %[[VAL_24]]{{\[}}%[[VAL_162]]] : memref<?xf32>
// CHECK:           }
// CHECK:           %[[VAL_174:.*]] = bufferization.to_tensor %[[VAL_24]] : memref<?xf32>
// CHECK:           return %[[VAL_174]] : tensor<?xf32>
// CHECK:         }
func.func @sum_kernel_with_inv(%arga: tensor<?x?xf32, #Tss>,
                          %argb: tensor<?x?xf32, #Tds>,
                          %argc: tensor<?x?xf32, #Tds>,
                          %argd: tensor<?xf32>,
                          %arge: tensor<f32>,
                          %argx: tensor<?xf32>) -> tensor<?xf32> {
  %0 = linalg.generic #trait_sum_kernel_with_inv
    ins(%arga, %argb, %argc, %argd, %arge : tensor<?x?xf32, #Tss>,
                                            tensor<?x?xf32, #Tds>,
                                            tensor<?x?xf32, #Tds>,
                                            tensor<?xf32>,
                                            tensor<f32>)
    outs(%argx: tensor<?xf32>) {
      ^bb(%a: f32, %b: f32, %c: f32, %d: f32, %e: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        %1 = arith.mulf %0, %d : f32
        %2 = arith.mulf %1, %e : f32
        %3 = arith.addf %2, %c : f32
        %4 = arith.addf %x, %3 : f32
        linalg.yield %4 : f32
  } -> tensor<?xf32>
  return %0 : tensor<?xf32>
}