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

#Td = #sparse_tensor.encoding<{ dimLevelType = [ "dense" ] }>

#Tddd = #sparse_tensor.encoding<{ dimLevelType = [ "dense",      "dense",      "dense"      ] }>
#Tdds = #sparse_tensor.encoding<{ dimLevelType = [ "dense",      "dense",      "compressed" ] }>
#Tdsd = #sparse_tensor.encoding<{ dimLevelType = [ "dense",      "compressed", "dense"      ] }>
#Tdss = #sparse_tensor.encoding<{ dimLevelType = [ "dense",      "compressed", "compressed" ] }>
#Tsdd = #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense",      "dense"      ] }>
#Tsds = #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense",      "compressed" ] }>
#Tssd = #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense"      ] }>
#Tsss = #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ] }>

#trait3 = {
  indexing_maps = [
    affine_map<(i,j,k) -> (i,j,k)>,  // A
    affine_map<(i,j,k) -> (i,j,k)>,  // B
    affine_map<(i,j,k) -> (i,j,k)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel", "parallel"],
  doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
}

// CHECK-LABEL:   func @add_ddd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_11:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_10]], %[[VAL_11]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_13:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_14:.*]] = arith.muli %[[VAL_12]], %[[VAL_4]] : index
// CHECK:               %[[VAL_15:.*]] = arith.addi %[[VAL_14]], %[[VAL_13]] : index
// CHECK:               scf.for %[[VAL_16:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_17:.*]] = arith.muli %[[VAL_15]], %[[VAL_5]] : 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_12]], %[[VAL_13]], %[[VAL_16]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_21:.*]] = arith.addf %[[VAL_19]], %[[VAL_20]] : f32
// CHECK:                 memref.store %[[VAL_21]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_16]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_22:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_22]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_ddd(%arga: tensor<32x16x8xf32, #Tddd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tddd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_ddd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_11:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_10]], %[[VAL_11]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_13:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:               %[[VAL_14:.*]] = arith.muli %[[VAL_12]], %[[VAL_4]] : index
// CHECK:               %[[VAL_15:.*]] = arith.addi %[[VAL_14]], %[[VAL_13]] : index
// CHECK:               scf.for %[[VAL_16:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_17:.*]] = arith.muli %[[VAL_15]], %[[VAL_5]] : 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_12]], %[[VAL_13]], %[[VAL_16]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_21:.*]] = arith.mulf %[[VAL_19]], %[[VAL_20]] : f32
// CHECK:                 memref.store %[[VAL_21]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_16]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_22:.*]] = bufferization.to_tensor %[[VAL_11]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_22]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_ddd(%arga: tensor<32x16x8xf32, #Tddd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tddd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_dds(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_9:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_15:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_14]], %[[VAL_15]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_16:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_9]] {
// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:               %[[VAL_18:.*]] = arith.muli %[[VAL_16]], %[[VAL_5]] : index
// CHECK:               %[[VAL_19:.*]] = arith.addi %[[VAL_18]], %[[VAL_17]] : index
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:               %[[VAL_21:.*]] = arith.addi %[[VAL_19]], %[[VAL_9]] : index
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:               %[[VAL_23:.*]]:2 = scf.while (%[[VAL_24:.*]] = %[[VAL_20]], %[[VAL_25:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_26:.*]] = arith.cmpi ult, %[[VAL_24]], %[[VAL_22]] : index
// CHECK:                 scf.condition(%[[VAL_26]]) %[[VAL_24]], %[[VAL_25]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
// CHECK:                 %[[VAL_29:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
// CHECK:                 %[[VAL_30:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_28]] : index
// CHECK:                 scf.if %[[VAL_30]] {
// CHECK:                   %[[VAL_31:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xf32>
// CHECK:                   %[[VAL_32:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
// CHECK:                   %[[VAL_33:.*]] = arith.addf %[[VAL_31]], %[[VAL_32]] : f32
// CHECK:                   memref.store %[[VAL_33]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_8]] {
// CHECK:                     %[[VAL_34:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_34]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_35:.*]] = arith.cmpi eq, %[[VAL_29]], %[[VAL_28]] : index
// CHECK:                 %[[VAL_36:.*]] = arith.addi %[[VAL_27]], %[[VAL_9]] : index
// CHECK:                 %[[VAL_37:.*]] = select %[[VAL_35]], %[[VAL_36]], %[[VAL_27]] : index
// CHECK:                 %[[VAL_38:.*]] = arith.addi %[[VAL_28]], %[[VAL_9]] : index
// CHECK:                 scf.yield %[[VAL_37]], %[[VAL_38]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_39:.*]] = %[[VAL_40:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                 %[[VAL_41:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_39]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_41]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_39]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_42:.*]] = bufferization.to_tensor %[[VAL_15]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_42]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_dds(%arga: tensor<32x16x8xf32, #Tdds>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tdds>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_dds(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK:           %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK:           %[[VAL_5:.*]] = arith.constant 16 : index
// CHECK:           %[[VAL_6:.*]] = arith.constant 0 : index
// CHECK:           %[[VAL_7:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_12]], %[[VAL_13]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
// CHECK:             scf.for %[[VAL_15:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
// CHECK:               %[[VAL_16:.*]] = arith.muli %[[VAL_14]], %[[VAL_5]] : index
// CHECK:               %[[VAL_17:.*]] = arith.addi %[[VAL_16]], %[[VAL_15]] : index
// CHECK:               %[[VAL_18:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:               %[[VAL_19:.*]] = arith.addi %[[VAL_17]], %[[VAL_7]] : index
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_7]] {
// CHECK:                 %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:                 %[[VAL_23:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xf32>
// CHECK:                 %[[VAL_24:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_22]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_25:.*]] = arith.mulf %[[VAL_23]], %[[VAL_24]] : f32
// CHECK:                 memref.store %[[VAL_25]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_22]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_26:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_26]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_dds(%arga: tensor<32x16x8xf32, #Tdds>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tdds>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_dsd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_14:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_13]], %[[VAL_14]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_7]] to %[[VAL_3]] step %[[VAL_8]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.addi %[[VAL_15]], %[[VAL_8]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_7]]) : (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_10]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_26:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:               scf.if %[[VAL_26]] {
// CHECK:                 scf.for %[[VAL_27:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                   %[[VAL_28:.*]] = arith.muli %[[VAL_23]], %[[VAL_5]] : index
// CHECK:                   %[[VAL_29:.*]] = arith.addi %[[VAL_28]], %[[VAL_27]] : index
// CHECK:                   %[[VAL_30:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_29]]] : memref<?xf32>
// CHECK:                   %[[VAL_31:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
// CHECK:                   %[[VAL_32:.*]] = arith.addf %[[VAL_30]], %[[VAL_31]] : f32
// CHECK:                   memref.store %[[VAL_32]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:                 scf.if %[[VAL_6]] {
// CHECK:                   scf.for %[[VAL_33:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                     %[[VAL_34:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_33]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_34]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_33]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:               %[[VAL_35:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:               %[[VAL_36:.*]] = arith.addi %[[VAL_23]], %[[VAL_8]] : index
// CHECK:               %[[VAL_37:.*]] = select %[[VAL_35]], %[[VAL_36]], %[[VAL_23]] : index
// CHECK:               %[[VAL_38:.*]] = arith.addi %[[VAL_24]], %[[VAL_8]] : index
// CHECK:               scf.yield %[[VAL_37]], %[[VAL_38]] : index, index
// CHECK:             }
// CHECK:             scf.for %[[VAL_39:.*]] = %[[VAL_40:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:               scf.for %[[VAL_41:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                 %[[VAL_42:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_39]], %[[VAL_41]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_42]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_39]], %[[VAL_41]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_43:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_43]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_dsd(%arga: tensor<32x16x8xf32, #Tdsd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tdsd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_dsd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_12:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_11]], %[[VAL_12]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
// CHECK:             %[[VAL_14:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_13]]] : memref<?xindex>
// CHECK:             %[[VAL_15:.*]] = arith.addi %[[VAL_13]], %[[VAL_6]] : index
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_14]] to %[[VAL_16]] step %[[VAL_6]] {
// CHECK:               %[[VAL_18:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:                 %[[VAL_20:.*]] = arith.muli %[[VAL_17]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_21:.*]] = arith.addi %[[VAL_20]], %[[VAL_19]] : index
// CHECK:                 %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xf32>
// CHECK:                 %[[VAL_23:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_19]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_24:.*]] = arith.mulf %[[VAL_22]], %[[VAL_23]] : f32
// CHECK:                 memref.store %[[VAL_24]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_19]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_25:.*]] = bufferization.to_tensor %[[VAL_12]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_25]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_dsd(%arga: tensor<32x16x8xf32, #Tdsd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tdsd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_dss(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_9:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_12:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_17:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_16]], %[[VAL_17]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_18:.*]] = %[[VAL_8]] to %[[VAL_4]] step %[[VAL_9]] {
// CHECK:             %[[VAL_19:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:             %[[VAL_20:.*]] = arith.addi %[[VAL_18]], %[[VAL_9]] : index
// CHECK:             %[[VAL_21:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<?xindex>
// CHECK:             %[[VAL_22:.*]]:2 = scf.while (%[[VAL_23:.*]] = %[[VAL_19]], %[[VAL_24:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:               %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_21]] : index
// CHECK:               scf.condition(%[[VAL_25]]) %[[VAL_23]], %[[VAL_24]] : index, index
// CHECK:             } do {
// CHECK:             ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
// CHECK:               %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
// CHECK:               %[[VAL_29:.*]] = arith.cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
// CHECK:               scf.if %[[VAL_29]] {
// CHECK:                 %[[VAL_30:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xindex>
// CHECK:                 %[[VAL_31:.*]] = arith.addi %[[VAL_26]], %[[VAL_9]] : index
// CHECK:                 %[[VAL_32:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_31]]] : memref<?xindex>
// CHECK:                 %[[VAL_33:.*]]:2 = scf.while (%[[VAL_34:.*]] = %[[VAL_30]], %[[VAL_35:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:                   %[[VAL_36:.*]] = arith.cmpi ult, %[[VAL_34]], %[[VAL_32]] : index
// CHECK:                   scf.condition(%[[VAL_36]]) %[[VAL_34]], %[[VAL_35]] : index, index
// CHECK:                 } do {
// CHECK:                 ^bb0(%[[VAL_37:.*]]: index, %[[VAL_38:.*]]: index):
// CHECK:                   %[[VAL_39:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:                   %[[VAL_40:.*]] = arith.cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
// CHECK:                   scf.if %[[VAL_40]] {
// CHECK:                     %[[VAL_41:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_37]]] : memref<?xf32>
// CHECK:                     %[[VAL_42:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
// CHECK:                     %[[VAL_43:.*]] = arith.addf %[[VAL_41]], %[[VAL_42]] : f32
// CHECK:                     memref.store %[[VAL_43]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
// CHECK:                   } else {
// CHECK:                     scf.if %[[VAL_7]] {
// CHECK:                       %[[VAL_44:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
// CHECK:                       memref.store %[[VAL_44]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
// CHECK:                     } else {
// CHECK:                     }
// CHECK:                   }
// CHECK:                   %[[VAL_45:.*]] = arith.cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
// CHECK:                   %[[VAL_46:.*]] = arith.addi %[[VAL_37]], %[[VAL_9]] : index
// CHECK:                   %[[VAL_47:.*]] = select %[[VAL_45]], %[[VAL_46]], %[[VAL_37]] : index
// CHECK:                   %[[VAL_48:.*]] = arith.addi %[[VAL_38]], %[[VAL_9]] : index
// CHECK:                   scf.yield %[[VAL_47]], %[[VAL_48]] : index, index
// CHECK:                 }
// CHECK:                 scf.for %[[VAL_49:.*]] = %[[VAL_50:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                   %[[VAL_51:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_49]]] : memref<32x16x8xf32>
// CHECK:                   memref.store %[[VAL_51]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_49]]] : memref<32x16x8xf32>
// CHECK:                 }
// CHECK:               } else {
// CHECK:                 scf.if %[[VAL_7]] {
// CHECK:                   scf.for %[[VAL_52:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                     %[[VAL_53:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_52]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_53]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_52]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                 }
// CHECK:               }
// CHECK:               %[[VAL_54:.*]] = arith.cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
// CHECK:               %[[VAL_55:.*]] = arith.addi %[[VAL_26]], %[[VAL_9]] : index
// CHECK:               %[[VAL_56:.*]] = select %[[VAL_54]], %[[VAL_55]], %[[VAL_26]] : index
// CHECK:               %[[VAL_57:.*]] = arith.addi %[[VAL_27]], %[[VAL_9]] : index
// CHECK:               scf.yield %[[VAL_56]], %[[VAL_57]] : index, index
// CHECK:             }
// CHECK:             scf.for %[[VAL_58:.*]] = %[[VAL_59:.*]]#1 to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:               scf.for %[[VAL_60:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                 %[[VAL_61:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_58]], %[[VAL_60]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_61]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_58]], %[[VAL_60]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_62:.*]] = bufferization.to_tensor %[[VAL_17]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_62]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_dss(%arga: tensor<32x16x8xf32, #Tdss>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tdss>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_dss(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_14:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_13]], %[[VAL_14]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_17:.*]] = arith.addi %[[VAL_15]], %[[VAL_6]] : index
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_19:.*]] = %[[VAL_16]] to %[[VAL_18]] step %[[VAL_6]] {
// CHECK:               %[[VAL_20:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:               %[[VAL_22:.*]] = arith.addi %[[VAL_19]], %[[VAL_6]] : index
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_6]] {
// CHECK:                 %[[VAL_25:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xf32>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_20]], %[[VAL_25]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_28:.*]] = arith.mulf %[[VAL_26]], %[[VAL_27]] : f32
// CHECK:                 memref.store %[[VAL_28]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_20]], %[[VAL_25]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_29:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_29]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_dss(%arga: tensor<32x16x8xf32, #Tdss>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tdss>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_sdd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_14:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_13]], %[[VAL_14]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_8]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_15]], %[[VAL_19:.*]] = %[[VAL_7]]) : (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_10]]{{\[}}%[[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_7]] to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:                 %[[VAL_26:.*]] = arith.muli %[[VAL_21]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_27:.*]] = arith.addi %[[VAL_26]], %[[VAL_25]] : index
// CHECK:                 scf.for %[[VAL_28:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                   %[[VAL_29:.*]] = arith.muli %[[VAL_27]], %[[VAL_5]] : index
// CHECK:                   %[[VAL_30:.*]] = arith.addi %[[VAL_29]], %[[VAL_28]] : index
// CHECK:                   %[[VAL_31:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_30]]] : memref<?xf32>
// CHECK:                   %[[VAL_32:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_22]], %[[VAL_25]], %[[VAL_28]]] : memref<32x16x8xf32>
// CHECK:                   %[[VAL_33:.*]] = arith.addf %[[VAL_31]], %[[VAL_32]] : f32
// CHECK:                   memref.store %[[VAL_33]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_25]], %[[VAL_28]]] : memref<32x16x8xf32>
// CHECK:                 }
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_6]] {
// CHECK:                 scf.for %[[VAL_34:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:                   scf.for %[[VAL_35:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                     %[[VAL_36:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_22]], %[[VAL_34]], %[[VAL_35]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_36]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_34]], %[[VAL_35]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_37:.*]] = arith.cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
// CHECK:             %[[VAL_38:.*]] = arith.addi %[[VAL_21]], %[[VAL_8]] : index
// CHECK:             %[[VAL_39:.*]] = select %[[VAL_37]], %[[VAL_38]], %[[VAL_21]] : index
// CHECK:             %[[VAL_40:.*]] = arith.addi %[[VAL_22]], %[[VAL_8]] : index
// CHECK:             scf.yield %[[VAL_39]], %[[VAL_40]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_41:.*]] = %[[VAL_42:.*]]#1 to %[[VAL_3]] step %[[VAL_8]] {
// CHECK:             scf.for %[[VAL_43:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:               scf.for %[[VAL_44:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                 %[[VAL_45:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_41]], %[[VAL_43]], %[[VAL_44]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_45]], %[[VAL_14]]{{\[}}%[[VAL_41]], %[[VAL_43]], %[[VAL_44]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_46:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_46]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_sdd(%arga: tensor<32x16x8xf32, #Tsdd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tsdd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_sdd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_12:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_11]], %[[VAL_12]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_6]] {
// CHECK:             %[[VAL_16:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
// CHECK:               %[[VAL_18:.*]] = arith.muli %[[VAL_15]], %[[VAL_3]] : index
// CHECK:               %[[VAL_19:.*]] = arith.addi %[[VAL_18]], %[[VAL_17]] : index
// CHECK:               scf.for %[[VAL_20:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:                 %[[VAL_21:.*]] = arith.muli %[[VAL_19]], %[[VAL_4]] : index
// CHECK:                 %[[VAL_22:.*]] = arith.addi %[[VAL_21]], %[[VAL_20]] : index
// CHECK:                 %[[VAL_23:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xf32>
// CHECK:                 %[[VAL_24:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_20]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_25:.*]] = arith.mulf %[[VAL_23]], %[[VAL_24]] : f32
// CHECK:                 memref.store %[[VAL_25]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_20]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_26:.*]] = bufferization.to_tensor %[[VAL_12]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_26]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_sdd(%arga: tensor<32x16x8xf32, #Tsdd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tsdd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_sds(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_9:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_12:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_16:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_17:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_16]], %[[VAL_17]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
// CHECK:           %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_18]], %[[VAL_22:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_23:.*]] = arith.cmpi ult, %[[VAL_21]], %[[VAL_19]] : index
// CHECK:             scf.condition(%[[VAL_23]]) %[[VAL_21]], %[[VAL_22]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_24:.*]]: index, %[[VAL_25:.*]]: index):
// CHECK:             %[[VAL_26:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xindex>
// CHECK:             %[[VAL_27:.*]] = arith.cmpi eq, %[[VAL_26]], %[[VAL_25]] : index
// CHECK:             scf.if %[[VAL_27]] {
// CHECK:               scf.for %[[VAL_28:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:                 %[[VAL_29:.*]] = arith.muli %[[VAL_24]], %[[VAL_5]] : index
// CHECK:                 %[[VAL_30:.*]] = arith.addi %[[VAL_29]], %[[VAL_28]] : index
// CHECK:                 %[[VAL_31:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_30]]] : memref<?xindex>
// CHECK:                 %[[VAL_32:.*]] = arith.addi %[[VAL_30]], %[[VAL_9]] : index
// CHECK:                 %[[VAL_33:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_32]]] : memref<?xindex>
// CHECK:                 %[[VAL_34:.*]]:2 = scf.while (%[[VAL_35:.*]] = %[[VAL_31]], %[[VAL_36:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:                   %[[VAL_37:.*]] = arith.cmpi ult, %[[VAL_35]], %[[VAL_33]] : index
// CHECK:                   scf.condition(%[[VAL_37]]) %[[VAL_35]], %[[VAL_36]] : index, index
// CHECK:                 } do {
// CHECK:                 ^bb0(%[[VAL_38:.*]]: index, %[[VAL_39:.*]]: index):
// CHECK:                   %[[VAL_40:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_38]]] : memref<?xindex>
// CHECK:                   %[[VAL_41:.*]] = arith.cmpi eq, %[[VAL_40]], %[[VAL_39]] : index
// CHECK:                   scf.if %[[VAL_41]] {
// CHECK:                     %[[VAL_42:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_38]]] : memref<?xf32>
// CHECK:                     %[[VAL_43:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
// CHECK:                     %[[VAL_44:.*]] = arith.addf %[[VAL_42]], %[[VAL_43]] : f32
// CHECK:                     memref.store %[[VAL_44]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
// CHECK:                   } else {
// CHECK:                     scf.if %[[VAL_7]] {
// CHECK:                       %[[VAL_45:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
// CHECK:                       memref.store %[[VAL_45]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
// CHECK:                     } else {
// CHECK:                     }
// CHECK:                   }
// CHECK:                   %[[VAL_46:.*]] = arith.cmpi eq, %[[VAL_40]], %[[VAL_39]] : index
// CHECK:                   %[[VAL_47:.*]] = arith.addi %[[VAL_38]], %[[VAL_9]] : index
// CHECK:                   %[[VAL_48:.*]] = select %[[VAL_46]], %[[VAL_47]], %[[VAL_38]] : index
// CHECK:                   %[[VAL_49:.*]] = arith.addi %[[VAL_39]], %[[VAL_9]] : index
// CHECK:                   scf.yield %[[VAL_48]], %[[VAL_49]] : index, index
// CHECK:                 }
// CHECK:                 scf.for %[[VAL_50:.*]] = %[[VAL_51:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                   %[[VAL_52:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_50]]] : memref<32x16x8xf32>
// CHECK:                   memref.store %[[VAL_52]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_50]]] : memref<32x16x8xf32>
// CHECK:                 }
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_7]] {
// CHECK:                 scf.for %[[VAL_53:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:                   scf.for %[[VAL_54:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                     %[[VAL_55:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_53]], %[[VAL_54]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_55]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_53]], %[[VAL_54]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_56:.*]] = arith.cmpi eq, %[[VAL_26]], %[[VAL_25]] : index
// CHECK:             %[[VAL_57:.*]] = arith.addi %[[VAL_24]], %[[VAL_9]] : index
// CHECK:             %[[VAL_58:.*]] = select %[[VAL_56]], %[[VAL_57]], %[[VAL_24]] : index
// CHECK:             %[[VAL_59:.*]] = arith.addi %[[VAL_25]], %[[VAL_9]] : index
// CHECK:             scf.yield %[[VAL_58]], %[[VAL_59]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_60:.*]] = %[[VAL_61:.*]]#1 to %[[VAL_4]] step %[[VAL_9]] {
// CHECK:             scf.for %[[VAL_62:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:               scf.for %[[VAL_63:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                 %[[VAL_64:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_60]], %[[VAL_62]], %[[VAL_63]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_64]], %[[VAL_17]]{{\[}}%[[VAL_60]], %[[VAL_62]], %[[VAL_63]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_65:.*]] = bufferization.to_tensor %[[VAL_17]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_65]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_sds(%arga: tensor<32x16x8xf32, #Tsds>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tsds>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_sds(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : 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:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_14:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_13]], %[[VAL_14]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_15:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_15]] to %[[VAL_16]] step %[[VAL_6]] {
// CHECK:             %[[VAL_18:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
// CHECK:               %[[VAL_20:.*]] = arith.muli %[[VAL_17]], %[[VAL_4]] : index
// CHECK:               %[[VAL_21:.*]] = arith.addi %[[VAL_20]], %[[VAL_19]] : index
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:               %[[VAL_23:.*]] = arith.addi %[[VAL_21]], %[[VAL_6]] : index
// CHECK:               %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_22]] to %[[VAL_24]] step %[[VAL_6]] {
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xindex>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xf32>
// CHECK:                 %[[VAL_28:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_18]], %[[VAL_19]], %[[VAL_26]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_29:.*]] = arith.mulf %[[VAL_27]], %[[VAL_28]] : f32
// CHECK:                 memref.store %[[VAL_29]], %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_19]], %[[VAL_26]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_30:.*]] = bufferization.to_tensor %[[VAL_14]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_30]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_sds(%arga: tensor<32x16x8xf32, #Tsds>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tsds>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_ssd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_12:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_16:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_15]], %[[VAL_16]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
// CHECK:           %[[VAL_18:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_8]]] : memref<?xindex>
// CHECK:           %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_17]], %[[VAL_21:.*]] = %[[VAL_7]]) : (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_10]]{{\[}}%[[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_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_28:.*]] = arith.addi %[[VAL_23]], %[[VAL_8]] : index
// CHECK:               %[[VAL_29:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:               %[[VAL_30:.*]]:2 = scf.while (%[[VAL_31:.*]] = %[[VAL_27]], %[[VAL_32:.*]] = %[[VAL_7]]) : (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_12]]{{\[}}%[[VAL_34]]] : memref<?xindex>
// CHECK:                 %[[VAL_37:.*]] = arith.cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
// CHECK:                 scf.if %[[VAL_37]] {
// CHECK:                   scf.for %[[VAL_38:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                     %[[VAL_39:.*]] = arith.muli %[[VAL_34]], %[[VAL_5]] : index
// CHECK:                     %[[VAL_40:.*]] = arith.addi %[[VAL_39]], %[[VAL_38]] : index
// CHECK:                     %[[VAL_41:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xf32>
// CHECK:                     %[[VAL_42:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_38]]] : memref<32x16x8xf32>
// CHECK:                     %[[VAL_43:.*]] = arith.addf %[[VAL_41]], %[[VAL_42]] : f32
// CHECK:                     memref.store %[[VAL_43]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_38]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_6]] {
// CHECK:                     scf.for %[[VAL_44:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                       %[[VAL_45:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_44]]] : memref<32x16x8xf32>
// CHECK:                       memref.store %[[VAL_45]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_44]]] : memref<32x16x8xf32>
// CHECK:                     }
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_46:.*]] = arith.cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
// CHECK:                 %[[VAL_47:.*]] = arith.addi %[[VAL_34]], %[[VAL_8]] : index
// CHECK:                 %[[VAL_48:.*]] = select %[[VAL_46]], %[[VAL_47]], %[[VAL_34]] : index
// CHECK:                 %[[VAL_49:.*]] = arith.addi %[[VAL_35]], %[[VAL_8]] : index
// CHECK:                 scf.yield %[[VAL_48]], %[[VAL_49]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_50:.*]] = %[[VAL_51:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:                 scf.for %[[VAL_52:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                   %[[VAL_53:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_50]], %[[VAL_52]]] : memref<32x16x8xf32>
// CHECK:                   memref.store %[[VAL_53]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_50]], %[[VAL_52]]] : memref<32x16x8xf32>
// CHECK:                 }
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_6]] {
// CHECK:                 scf.for %[[VAL_54:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:                   scf.for %[[VAL_55:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                     %[[VAL_56:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_54]], %[[VAL_55]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_56]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_54]], %[[VAL_55]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_57:.*]] = arith.cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
// CHECK:             %[[VAL_58:.*]] = arith.addi %[[VAL_23]], %[[VAL_8]] : index
// CHECK:             %[[VAL_59:.*]] = select %[[VAL_57]], %[[VAL_58]], %[[VAL_23]] : index
// CHECK:             %[[VAL_60:.*]] = arith.addi %[[VAL_24]], %[[VAL_8]] : index
// CHECK:             scf.yield %[[VAL_59]], %[[VAL_60]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_61:.*]] = %[[VAL_62:.*]]#1 to %[[VAL_3]] step %[[VAL_8]] {
// CHECK:             scf.for %[[VAL_63:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:               scf.for %[[VAL_64:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:                 %[[VAL_65:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_61]], %[[VAL_63]], %[[VAL_64]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_65]], %[[VAL_16]]{{\[}}%[[VAL_61]], %[[VAL_63]], %[[VAL_64]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_66:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_66]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_ssd(%arga: tensor<32x16x8xf32, #Tssd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tssd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_ssd(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_6:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_13:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_12]], %[[VAL_13]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// 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_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
// CHECK:             %[[VAL_19:.*]] = arith.addi %[[VAL_16]], %[[VAL_5]] : index
// CHECK:             %[[VAL_20:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_5]] {
// CHECK:               %[[VAL_22:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_23:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
// CHECK:                 %[[VAL_24:.*]] = arith.muli %[[VAL_21]], %[[VAL_3]] : index
// CHECK:                 %[[VAL_25:.*]] = arith.addi %[[VAL_24]], %[[VAL_23]] : index
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xf32>
// CHECK:                 %[[VAL_27:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_23]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_28:.*]] = arith.mulf %[[VAL_26]], %[[VAL_27]] : f32
// CHECK:                 memref.store %[[VAL_28]], %[[VAL_13]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_23]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_29:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_29]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_ssd(%arga: tensor<32x16x8xf32, #Tssd>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tssd>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @add_sss(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 32 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 16 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 8 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant true
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_9:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_12:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_15:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_16:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_17:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_18:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_19:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_18]], %[[VAL_19]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_20:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
// CHECK:           %[[VAL_21:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
// CHECK:           %[[VAL_22:.*]]:2 = scf.while (%[[VAL_23:.*]] = %[[VAL_20]], %[[VAL_24:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:             %[[VAL_25:.*]] = arith.cmpi ult, %[[VAL_23]], %[[VAL_21]] : index
// CHECK:             scf.condition(%[[VAL_25]]) %[[VAL_23]], %[[VAL_24]] : index, index
// CHECK:           } do {
// CHECK:           ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
// CHECK:             %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
// CHECK:             %[[VAL_29:.*]] = arith.cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
// CHECK:             scf.if %[[VAL_29]] {
// CHECK:               %[[VAL_30:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xindex>
// CHECK:               %[[VAL_31:.*]] = arith.addi %[[VAL_26]], %[[VAL_9]] : index
// CHECK:               %[[VAL_32:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_31]]] : memref<?xindex>
// CHECK:               %[[VAL_33:.*]]:2 = scf.while (%[[VAL_34:.*]] = %[[VAL_30]], %[[VAL_35:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:                 %[[VAL_36:.*]] = arith.cmpi ult, %[[VAL_34]], %[[VAL_32]] : index
// CHECK:                 scf.condition(%[[VAL_36]]) %[[VAL_34]], %[[VAL_35]] : index, index
// CHECK:               } do {
// CHECK:               ^bb0(%[[VAL_37:.*]]: index, %[[VAL_38:.*]]: index):
// CHECK:                 %[[VAL_39:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:                 %[[VAL_40:.*]] = arith.cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
// CHECK:                 scf.if %[[VAL_40]] {
// CHECK:                   %[[VAL_41:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_37]]] : memref<?xindex>
// CHECK:                   %[[VAL_42:.*]] = arith.addi %[[VAL_37]], %[[VAL_9]] : index
// CHECK:                   %[[VAL_43:.*]] = memref.load %[[VAL_14]]{{\[}}%[[VAL_42]]] : memref<?xindex>
// CHECK:                   %[[VAL_44:.*]]:2 = scf.while (%[[VAL_45:.*]] = %[[VAL_41]], %[[VAL_46:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
// CHECK:                     %[[VAL_47:.*]] = arith.cmpi ult, %[[VAL_45]], %[[VAL_43]] : index
// CHECK:                     scf.condition(%[[VAL_47]]) %[[VAL_45]], %[[VAL_46]] : index, index
// CHECK:                   } do {
// CHECK:                   ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
// CHECK:                     %[[VAL_50:.*]] = memref.load %[[VAL_15]]{{\[}}%[[VAL_48]]] : memref<?xindex>
// CHECK:                     %[[VAL_51:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_49]] : index
// CHECK:                     scf.if %[[VAL_51]] {
// CHECK:                       %[[VAL_52:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_48]]] : memref<?xf32>
// CHECK:                       %[[VAL_53:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
// CHECK:                       %[[VAL_54:.*]] = arith.addf %[[VAL_52]], %[[VAL_53]] : f32
// CHECK:                       memref.store %[[VAL_54]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
// CHECK:                     } else {
// CHECK:                       scf.if %[[VAL_7]] {
// CHECK:                         %[[VAL_55:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
// CHECK:                         memref.store %[[VAL_55]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
// CHECK:                       } else {
// CHECK:                       }
// CHECK:                     }
// CHECK:                     %[[VAL_56:.*]] = arith.cmpi eq, %[[VAL_50]], %[[VAL_49]] : index
// CHECK:                     %[[VAL_57:.*]] = arith.addi %[[VAL_48]], %[[VAL_9]] : index
// CHECK:                     %[[VAL_58:.*]] = select %[[VAL_56]], %[[VAL_57]], %[[VAL_48]] : index
// CHECK:                     %[[VAL_59:.*]] = arith.addi %[[VAL_49]], %[[VAL_9]] : index
// CHECK:                     scf.yield %[[VAL_58]], %[[VAL_59]] : index, index
// CHECK:                   }
// CHECK:                   scf.for %[[VAL_60:.*]] = %[[VAL_61:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                     %[[VAL_62:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_60]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_62]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_60]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 } else {
// CHECK:                   scf.if %[[VAL_7]] {
// CHECK:                     scf.for %[[VAL_63:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                       %[[VAL_64:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_63]]] : memref<32x16x8xf32>
// CHECK:                       memref.store %[[VAL_64]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_63]]] : memref<32x16x8xf32>
// CHECK:                     }
// CHECK:                   } else {
// CHECK:                   }
// CHECK:                 }
// CHECK:                 %[[VAL_65:.*]] = arith.cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
// CHECK:                 %[[VAL_66:.*]] = arith.addi %[[VAL_37]], %[[VAL_9]] : index
// CHECK:                 %[[VAL_67:.*]] = select %[[VAL_65]], %[[VAL_66]], %[[VAL_37]] : index
// CHECK:                 %[[VAL_68:.*]] = arith.addi %[[VAL_38]], %[[VAL_9]] : index
// CHECK:                 scf.yield %[[VAL_67]], %[[VAL_68]] : index, index
// CHECK:               }
// CHECK:               scf.for %[[VAL_69:.*]] = %[[VAL_70:.*]]#1 to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:                 scf.for %[[VAL_71:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                   %[[VAL_72:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_69]], %[[VAL_71]]] : memref<32x16x8xf32>
// CHECK:                   memref.store %[[VAL_72]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_69]], %[[VAL_71]]] : memref<32x16x8xf32>
// CHECK:                 }
// CHECK:               }
// CHECK:             } else {
// CHECK:               scf.if %[[VAL_7]] {
// CHECK:                 scf.for %[[VAL_73:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:                   scf.for %[[VAL_74:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                     %[[VAL_75:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_73]], %[[VAL_74]]] : memref<32x16x8xf32>
// CHECK:                     memref.store %[[VAL_75]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_73]], %[[VAL_74]]] : memref<32x16x8xf32>
// CHECK:                   }
// CHECK:                 }
// CHECK:               } else {
// CHECK:               }
// CHECK:             }
// CHECK:             %[[VAL_76:.*]] = arith.cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
// CHECK:             %[[VAL_77:.*]] = arith.addi %[[VAL_26]], %[[VAL_9]] : index
// CHECK:             %[[VAL_78:.*]] = select %[[VAL_76]], %[[VAL_77]], %[[VAL_26]] : index
// CHECK:             %[[VAL_79:.*]] = arith.addi %[[VAL_27]], %[[VAL_9]] : index
// CHECK:             scf.yield %[[VAL_78]], %[[VAL_79]] : index, index
// CHECK:           }
// CHECK:           scf.for %[[VAL_80:.*]] = %[[VAL_81:.*]]#1 to %[[VAL_4]] step %[[VAL_9]] {
// CHECK:             scf.for %[[VAL_82:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
// CHECK:               scf.for %[[VAL_83:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
// CHECK:                 %[[VAL_84:.*]] = memref.load %[[VAL_17]]{{\[}}%[[VAL_80]], %[[VAL_82]], %[[VAL_83]]] : memref<32x16x8xf32>
// CHECK:                 memref.store %[[VAL_84]], %[[VAL_19]]{{\[}}%[[VAL_80]], %[[VAL_82]], %[[VAL_83]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_85:.*]] = bufferization.to_tensor %[[VAL_19]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_85]] : tensor<32x16x8xf32>
// CHECK:         }
func @add_sss(%arga: tensor<32x16x8xf32, #Tsss>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tsss>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.addf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

// CHECK-LABEL:   func @mul_sss(
// CHECK-SAME:                  %[[VAL_0:.*]]: tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                  %[[VAL_1:.*]]: tensor<32x16x8xf32>,
// CHECK-SAME:                  %[[VAL_2:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
// CHECK-DAG:           %[[VAL_3:.*]] = arith.constant 2 : index
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_6:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_11:.*]] = sparse_tensor.indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_12:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<32x16x8xf32, #sparse_tensor.encoding<{ dimLevelType = [ "compressed", "compressed", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_13:.*]] = bufferization.to_memref %[[VAL_1]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_14:.*]] = bufferization.to_memref %[[VAL_2]] : memref<32x16x8xf32>
// CHECK:           %[[VAL_15:.*]] = memref.alloc() : memref<32x16x8xf32>
// CHECK:           memref.copy %[[VAL_14]], %[[VAL_15]] : memref<32x16x8xf32> to memref<32x16x8xf32>
// CHECK:           %[[VAL_16:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
// CHECK:           %[[VAL_17:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
// CHECK:           scf.for %[[VAL_18:.*]] = %[[VAL_16]] to %[[VAL_17]] step %[[VAL_5]] {
// CHECK:             %[[VAL_19:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:             %[[VAL_20:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:             %[[VAL_21:.*]] = arith.addi %[[VAL_18]], %[[VAL_5]] : index
// CHECK:             %[[VAL_22:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:             scf.for %[[VAL_23:.*]] = %[[VAL_20]] to %[[VAL_22]] step %[[VAL_5]] {
// CHECK:               %[[VAL_24:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_25:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xindex>
// CHECK:               %[[VAL_26:.*]] = arith.addi %[[VAL_23]], %[[VAL_5]] : index
// CHECK:               %[[VAL_27:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_28:.*]] = %[[VAL_25]] to %[[VAL_27]] step %[[VAL_5]] {
// CHECK:                 %[[VAL_29:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
// CHECK:                 %[[VAL_30:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xf32>
// CHECK:                 %[[VAL_31:.*]] = memref.load %[[VAL_13]]{{\[}}%[[VAL_19]], %[[VAL_24]], %[[VAL_29]]] : memref<32x16x8xf32>
// CHECK:                 %[[VAL_32:.*]] = arith.mulf %[[VAL_30]], %[[VAL_31]] : f32
// CHECK:                 memref.store %[[VAL_32]], %[[VAL_15]]{{\[}}%[[VAL_19]], %[[VAL_24]], %[[VAL_29]]] : memref<32x16x8xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_33:.*]] = bufferization.to_tensor %[[VAL_15]] : memref<32x16x8xf32>
// CHECK:           return %[[VAL_33]] : tensor<32x16x8xf32>
// CHECK:         }
func @mul_sss(%arga: tensor<32x16x8xf32, #Tsss>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
  %0 = linalg.generic #trait3
     ins(%arga, %argb: tensor<32x16x8xf32, #Tsss>, tensor<32x16x8xf32>)
    outs(%argx: tensor<32x16x8xf32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        linalg.yield %0 : f32
  } -> tensor<32x16x8xf32>
  return %0 : tensor<32x16x8xf32>
}

#trait_kernel_3d = {
  indexing_maps = [
    affine_map<(i,j,k,l) -> (i,k,l)>,  // B
    affine_map<(i,j,k,l) -> (k,j)>,    // C
    affine_map<(i,j,k,l) -> (l,j)>,    // D
    affine_map<(i,j,k,l) -> (i,j)>     // A (out)
  ],
  iterator_types = ["parallel", "parallel", "reduction", "reduction"],
  doc = "A(i,j) += SUM_k,l B(i,k,l) * C(k,j) * D(l,j)"
}

// CHECK-LABEL:   func @kernel_3d(
// CHECK-SAME:                    %[[VAL_0:.*0]]: tensor<?x?xf32>,
// CHECK-SAME:                    %[[VAL_1:.*1]]: tensor<?x?x?xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// 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 2 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_1]], %[[VAL_4]] : tensor<?x?x?xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.indices %[[VAL_1]], %[[VAL_4]] : tensor<?x?x?xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xindex>
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?x?x?xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense", "dense", "compressed" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_10:.*]] = tensor.dim %[[VAL_2]], %[[VAL_5]] : tensor<?x?xf32>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<?x?xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_3]] : memref<?x?xf32>
// CHECK:           %[[VAL_13:.*]] = tensor.dim %[[VAL_0]], %[[VAL_5]] : tensor<?x?xf32>
// CHECK:           %[[VAL_14:.*]] = tensor.dim %[[VAL_0]], %[[VAL_6]] : tensor<?x?xf32>
// CHECK:           %[[VAL_15:.*]] = bufferization.to_memref %[[VAL_0]] : memref<?x?xf32>
// CHECK:           %[[VAL_16:.*]] = memref.alloc(%[[VAL_13]], %[[VAL_14]]) : memref<?x?xf32>
// CHECK:           memref.copy %[[VAL_15]], %[[VAL_16]] : memref<?x?xf32> to memref<?x?xf32>
// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_5]] to %[[VAL_13]] step %[[VAL_6]] {
// CHECK:             scf.for %[[VAL_18:.*]] = %[[VAL_5]] to %[[VAL_10]] step %[[VAL_6]] {
// CHECK:               %[[VAL_19:.*]] = arith.muli %[[VAL_10]], %[[VAL_17]] : index
// CHECK:               %[[VAL_20:.*]] = arith.addi %[[VAL_19]], %[[VAL_18]] : index
// CHECK:               %[[VAL_21:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_20]]] : memref<?xindex>
// CHECK:               %[[VAL_22:.*]] = arith.addi %[[VAL_20]], %[[VAL_6]] : index
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_22]]] : memref<?xindex>
// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_6]] {
// CHECK:                 %[[VAL_25:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_24]]] : memref<?xindex>
// CHECK:                 %[[VAL_26:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xf32>
// CHECK:                 scf.for %[[VAL_27:.*]] = %[[VAL_5]] to %[[VAL_14]] step %[[VAL_6]] {
// CHECK:                   %[[VAL_28:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_18]], %[[VAL_27]]] : memref<?x?xf32>
// CHECK:                   %[[VAL_29:.*]] = arith.mulf %[[VAL_26]], %[[VAL_28]] : f32
// CHECK:                   %[[VAL_30:.*]] = memref.load %[[VAL_12]]{{\[}}%[[VAL_25]], %[[VAL_27]]] : memref<?x?xf32>
// CHECK:                   %[[VAL_31:.*]] = arith.mulf %[[VAL_29]], %[[VAL_30]] : f32
// CHECK:                   %[[VAL_32:.*]] = memref.load %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_27]]] : memref<?x?xf32>
// CHECK:                   %[[VAL_33:.*]] = arith.addf %[[VAL_31]], %[[VAL_32]] : f32
// CHECK:                   memref.store %[[VAL_33]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_27]]] : memref<?x?xf32>
// CHECK:                 }
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_34:.*]] = bufferization.to_tensor %[[VAL_16]] : memref<?x?xf32>
// CHECK:           return %[[VAL_34]] : tensor<?x?xf32>
// CHECK:         }
func @kernel_3d(%arga: tensor<?x?xf32>,
                %argb: tensor<?x?x?xf32, #Tdds>,
                %argc: tensor<?x?xf32>,
	        %argd: tensor<?x?xf32>) -> tensor<?x?xf32> {
  %0 = linalg.generic #trait_kernel_3d
       ins(%argb, %argc, %argd: tensor<?x?x?xf32, #Tdds>, tensor<?x?xf32>, tensor<?x?xf32>)
      outs(%arga: tensor<?x?xf32>) {
    ^bb(%b: f32, %c: f32, %d: f32, %a: f32):
      %0 = arith.mulf %b, %c : f32
      %1 = arith.mulf %0, %d : f32
      %2 = arith.addf %1, %a : f32
      linalg.yield %2 : f32
  } -> tensor<?x?xf32>
  return %0 : tensor<?x?xf32>
}

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

// CHECK-LABEL:   func @sum_reduction(
// CHECK-SAME:       %[[VAL_0:.*]]: tensor<10x20x30xf32, #sparse_tensor.encoding<{{{.*}}}>>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<f32>) -> tensor<f32> {
// CHECK:           %[[VAL_2:.*]] = arith.constant 0 : index
// CHECK:           %[[VAL_3:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_4:.*]] = arith.constant 2 : index
// CHECK:           %[[VAL_5:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_2]] : tensor<10x20x30xf32, #sparse_tensor.encoding<{{{.*}}>>
// CHECK:           %[[VAL_6:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_3]] : tensor<10x20x30xf32, #sparse_tensor.encoding<{{{.*}}>>
// CHECK:           %[[VAL_7:.*]] = sparse_tensor.pointers %[[VAL_0]], %[[VAL_4]] : tensor<10x20x30xf32, #sparse_tensor.encoding<{{{.*}}}>>
// CHECK:           %[[VAL_8:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<10x20x30xf32, #sparse_tensor.encoding<{{{.*}}}>>
// CHECK:           %[[VAL_9:.*]] = bufferization.to_memref %[[VAL_1]] : memref<f32>
// CHECK:           %[[VAL_10:.*]] = memref.alloc() : memref<f32>
// CHECK:           memref.copy %[[VAL_9]], %[[VAL_10]] : memref<f32> to memref<f32>
// CHECK:           %[[VAL_11:.*]] = memref.load %[[VAL_10]][] : memref<f32>
// CHECK:           %[[VAL_12:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_2]]] : memref<?xindex>
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
// CHECK:           %[[VAL_14:.*]] = scf.for %[[VAL_15:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_3]] iter_args(%[[VAL_16:.*]] = %[[VAL_11]]) -> (f32) {
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
// CHECK:             %[[VAL_18:.*]] = arith.addi %[[VAL_15]], %[[VAL_3]] : index
// CHECK:             %[[VAL_19:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_18]]] : memref<?xindex>
// CHECK:             %[[VAL_20:.*]] = scf.for %[[VAL_21:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_3]] iter_args(%[[VAL_22:.*]] = %[[VAL_16]]) -> (f32) {
// CHECK:               %[[VAL_23:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_21]]] : memref<?xindex>
// CHECK:               %[[VAL_24:.*]] = arith.addi %[[VAL_21]], %[[VAL_3]] : index
// CHECK:               %[[VAL_25:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_24]]] : memref<?xindex>
// CHECK:               %[[VAL_26:.*]] = scf.for %[[VAL_27:.*]] = %[[VAL_23]] to %[[VAL_25]] step %[[VAL_3]] iter_args(%[[VAL_28:.*]] = %[[VAL_22]]) -> (f32) {
// CHECK:                 %[[VAL_29:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xf32>
// CHECK:                 %[[VAL_30:.*]] = arith.addf %[[VAL_28]], %[[VAL_29]] : f32
// CHECK:                 scf.yield %[[VAL_30]] : f32
// CHECK:               }
// CHECK:               scf.yield %[[VAL_26]] : f32
// CHECK:             }
// CHECK:             scf.yield %[[VAL_20]] : f32
// CHECK:           }
// CHECK:           memref.store %[[VAL_14]], %[[VAL_10]][] : memref<f32>
// CHECK:           %[[VAL_34:.*]] = bufferization.to_tensor %[[VAL_10]] : memref<f32>
// CHECK:           return %[[VAL_34]] : tensor<f32>
// CHECK:         }
func @sum_reduction(%arga: tensor<10x20x30xf32, #Tsss>, %argx: tensor<f32>) -> tensor<f32> {
  %0 = linalg.generic #trait_sum_reduction
     ins(%arga: tensor<10x20x30xf32, #Tsss>)
    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_sum_reduction_inv = {
  indexing_maps = [
    affine_map<(i,j,k) -> (i,j,k)>,  // A
    affine_map<(i,j,k) -> (i)>,      // b
    affine_map<(i,j,k) -> ()>        // x (scalar out)
  ],
  iterator_types = ["reduction", "reduction", "reduction"],
  doc = "x += SUM_i A(i,j,k) * b(i)"
}

// CHECK-LABEL:   func @sum_reduction_inv(
// CHECK-SAME:      %[[VAL_0:.*]]: tensor<?x?x?xf32>,
// CHECK-SAME:      %[[VAL_1:.*]]: tensor<?xf32, #sparse_tensor.encoding<{{{.*}}}>>
// CHECK-SAME:      %[[VAL_2:.*]]: tensor<f32>) -> tensor<f32> {
// CHECK:           %[[VAL_3:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_4:.*]] = arith.constant 2 : index
// CHECK:           %[[VAL_5:.*]] = arith.constant 0 : index
// CHECK:           %[[VAL_6:.*]] = tensor.dim %[[VAL_0]], %[[VAL_3]] : tensor<?x?x?xf32>
// CHECK:           %[[VAL_7:.*]] = tensor.dim %[[VAL_0]], %[[VAL_4]] : tensor<?x?x?xf32>
// CHECK:           %[[VAL_8:.*]] = bufferization.to_memref %[[VAL_0]] : memref<?x?x?xf32>
// CHECK:           %[[VAL_9:.*]] = tensor.dim %[[VAL_1]], %[[VAL_5]] : tensor<?xf32, #sparse_tensor.encoding<{{{.*}}}>>
// CHECK:           %[[VAL_10:.*]] = sparse_tensor.values %[[VAL_1]] : tensor<?xf32, #sparse_tensor.encoding<{{{.*}}}>>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<f32>
// CHECK:           %[[VAL_12:.*]] = memref.alloc() : memref<f32>
// CHECK:           memref.copy %[[VAL_11]], %[[VAL_12]] : memref<f32> to memref<f32>
// CHECK:           %[[VAL_13:.*]] = memref.load %[[VAL_12]][] : memref<f32>
// CHECK:           %[[VAL_14:.*]] = scf.for %[[VAL_15:.*]] = %[[VAL_5]] to %[[VAL_9]] step %[[VAL_3]] iter_args(%[[VAL_16:.*]] = %[[VAL_13]]) -> (f32) {
// CHECK:             %[[VAL_17:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_15]]] : memref<?xf32>
// CHECK:             %[[VAL_18:.*]] = scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_6]] step %[[VAL_3]] iter_args(%[[VAL_20:.*]] = %[[VAL_16]]) -> (f32) {
// CHECK:               %[[VAL_21:.*]] = scf.for %[[VAL_22:.*]] = %[[VAL_5]] to %[[VAL_7]] step %[[VAL_3]] iter_args(%[[VAL_23:.*]] = %[[VAL_20]]) -> (f32) {
// CHECK:                 %[[VAL_24:.*]] = memref.load %[[VAL_8]]{{\[}}%[[VAL_15]], %[[VAL_19]], %[[VAL_22]]] : memref<?x?x?xf32>
// CHECK:                 %[[VAL_25:.*]] = arith.mulf %[[VAL_24]], %[[VAL_17]] : f32
// CHECK:                 %[[VAL_26:.*]] = arith.addf %[[VAL_23]], %[[VAL_25]] : f32
// CHECK:                 scf.yield %[[VAL_26]] : f32
// CHECK:               }
// CHECK:               scf.yield %[[VAL_21]] : f32
// CHECK:             }
// CHECK:             scf.yield %[[VAL_18]] : f32
// CHECK:           }
// CHECK:           memref.store %[[VAL_14]], %[[VAL_12]][] : memref<f32>
// CHECK:           %[[VAL_30:.*]] = bufferization.to_tensor %[[VAL_12]] : memref<f32>
// CHECK:           return %[[VAL_30]] : tensor<f32>
// CHECK:         }
func @sum_reduction_inv(%arga: tensor<?x?x?xf32>,
                        %argb: tensor<?xf32, #Td>,
		        %argx: tensor<f32>) -> tensor<f32> {
  %0 = linalg.generic #trait_sum_reduction_inv
    ins(%arga, %argb: tensor<?x?x?xf32>, tensor<?xf32, #Td>)
    outs(%argx: tensor<f32>) {
      ^bb(%a: f32, %b: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        %1 = arith.addf %x, %0 : f32
        linalg.yield %1 : f32
  } -> tensor<f32>
  return %0 : tensor<f32>
}

#trait_invariants = {
  indexing_maps = [
    affine_map<(i,j,k) -> (i)>,      // a
    affine_map<(i,j,k) -> (j)>,      // b
    affine_map<(i,j,k) -> (k)>,      // c
    affine_map<(i,j,k) -> (i,j,k)>   // X (out)
  ],
  iterator_types = ["parallel", "parallel", "parallel"],
  doc = "X(i,j,k) = a(i) * b(j) * c(k)"
}

// CHECK-LABEL:   func @invariants(
// CHECK-SAME:                     %[[VAL_0:.*]]: tensor<10xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>>,
// CHECK-SAME:                     %[[VAL_1:.*]]: tensor<20xf32>,
// CHECK-SAME:                     %[[VAL_2:.*]]: tensor<30xf32>,
// CHECK-SAME:                     %[[VAL_3:.*]]: tensor<10x20x30xf32>) -> tensor<10x20x30xf32> {
// CHECK-DAG:           %[[VAL_4:.*]] = arith.constant 10 : index
// CHECK-DAG:           %[[VAL_5:.*]] = arith.constant 20 : index
// CHECK-DAG:           %[[VAL_6:.*]] = arith.constant 30 : index
// CHECK-DAG:           %[[VAL_7:.*]] = arith.constant 0 : index
// CHECK-DAG:           %[[VAL_8:.*]] = arith.constant 1 : index
// CHECK:           %[[VAL_9:.*]] = sparse_tensor.values %[[VAL_0]] : tensor<10xf32, #sparse_tensor.encoding<{ dimLevelType = [ "dense" ], pointerBitWidth = 0, indexBitWidth = 0 }>> to memref<?xf32>
// CHECK:           %[[VAL_10:.*]] = bufferization.to_memref %[[VAL_1]] : memref<20xf32>
// CHECK:           %[[VAL_11:.*]] = bufferization.to_memref %[[VAL_2]] : memref<30xf32>
// CHECK:           %[[VAL_12:.*]] = bufferization.to_memref %[[VAL_3]] : memref<10x20x30xf32>
// CHECK:           %[[VAL_13:.*]] = memref.alloc() : memref<10x20x30xf32>
// CHECK:           memref.copy %[[VAL_12]], %[[VAL_13]] : memref<10x20x30xf32> to memref<10x20x30xf32>
// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
// CHECK:             %[[VAL_15:.*]] = memref.load %[[VAL_9]]{{\[}}%[[VAL_14]]] : memref<?xf32>
// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
// CHECK:               %[[VAL_17:.*]] = memref.load %[[VAL_10]]{{\[}}%[[VAL_16]]] : memref<20xf32>
// CHECK:               scf.for %[[VAL_18:.*]] = %[[VAL_7]] to %[[VAL_6]] step %[[VAL_8]] {
// CHECK:                 %[[VAL_19:.*]] = arith.mulf %[[VAL_15]], %[[VAL_17]] : f32
// CHECK:                 %[[VAL_20:.*]] = memref.load %[[VAL_11]]{{\[}}%[[VAL_18]]] : memref<30xf32>
// CHECK:                 %[[VAL_21:.*]] = arith.mulf %[[VAL_19]], %[[VAL_20]] : f32
// CHECK:                 memref.store %[[VAL_21]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_16]], %[[VAL_18]]] : memref<10x20x30xf32>
// CHECK:               }
// CHECK:             }
// CHECK:           }
// CHECK:           %[[VAL_22:.*]] = bufferization.to_tensor %[[VAL_13]] : memref<10x20x30xf32>
// CHECK:           return %[[VAL_22]] : tensor<10x20x30xf32>
// CHECK:         }
func @invariants(%arga: tensor<10xf32, #Td>,
                 %argb: tensor<20xf32>,
                 %argc: tensor<30xf32>,
                 %argx: tensor<10x20x30xf32>) -> tensor<10x20x30xf32> {
  %0 = linalg.generic #trait_invariants
     ins(%arga, %argb, %argc : tensor<10xf32, #Td>, tensor<20xf32>, tensor<30xf32>)
    outs(%argx: tensor<10x20x30xf32>) {
      ^bb(%a: f32, %b: f32, %c: f32, %x: f32):
        %0 = arith.mulf %a, %b : f32
        %1 = arith.mulf %0, %c : f32
        linalg.yield %1 : f32
  } -> tensor<10x20x30xf32>
  return %0 : tensor<10x20x30xf32>
}