[mlir][sparse] sparse tensor storage implementation

[aartbik]

Summary

This revision connects the generated sparse code with an actual
sparse storage scheme, which can be initialized from a test file.
Lacking a first-class citizen SparseTensor type (with buffer),
the storage is hidden behind an opaque pointer with some "glue"
to bring the pointer back to tensor land. Rather than generating
sparse setup code for each different annotated tensor (viz. the
"pack" methods in TACO), a single "one-size-fits-all" implementation
has been added to the runtime support library. Many details and
abstractions need to be refined in the future, but this revision
allows full end-to-end integration testing and performance
benchmarking (with on one end, an annotated Lingalg
op and, on the other end, a JIT/AOT executable).

[aartbik]

removed some testing code

[aartbik]

typo

[aartbik]

rebase + refine

[bixia]

It is a very nice PR, thanks for the great work! I finish one round of reading the code and haven't read the MLIR tests yet. Would like to send out my comments I have so far.

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

524

I think the second line of the comment is not necessary, as this routine is checking whether the operand is in the form of a sparse tensor storage representation and dense content tensor certainly can be represented via sparse tensor storage.

534–535

Sorry I don't understand the last part of the comment starting from "or ...".
Is that true that what we want to say here is "the routine returns a buffer for the output and the buffer is initialized"?

578

I think we need to remove this line. Because in line 618, the way allDense is used, it should just correspond to whether the tensor is in SparseTensorStorage representation. Am I right here? If I am right here, I would recommend the consolidate the two variables, atSparse and allDense, to one variable isSparseTensor.

mlir/lib/ExecutionEngine/SparseUtils.cpp

106

implement

128

Initializes

168

pass

288–289

struct

[aartbik]

addressed comments

[aartbik]

Thanks for the speedy review, Bixia!

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

524

Okay, removed. It was to contrast "true" dense tensors (i.e. the ones that are marked as such in the annotations and are passed true tensor types) for "test" dense tensors (i.e. marked as dense but passed an opaque pointer that is set up with an artificial all-dense sparse storage scheme just for stress testing). But I removed the comment.

534–535

Set to your suggestion. I was trying to give too much background information here, but got lost in the woods of details.

578

Good observation, but this is a bit tricky. There are two sources for sparsity: the annotations, and the fact that we feed in a "glue" node from opaque pointer to tensor. The latter is relatively new, and is only temporary (this will go away once we have a proper sparse type). So most tests will still need the allDense to be set based on annotations, but the opague pointer needs the different DimOp. Once we have one type, this will indeed converge to one again.

[ftynse]

Looks okay in general. I would like some higher-level description of the storage scheme somewhere.

Please do not commit until @nicolasvasilache had an opportunity to look at Linalg ops.

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

525 ↗

(On Diff #321014)

All these could use some examples in let description and a better specification of what the underlying assumptons are.

539 ↗

(On Diff #321014)

Nit: we use arg-type to result-type for cast-like operations, better to be consistent.

552 ↗

(On Diff #321014)

Are we sure this are going to be side effect-free in all cases? It seems to assume a specific underlying storage scheme for tensors, at which point it may be possible to just extract a pointer and wrap it into a memref. If the actual scheme is different, it may be allocating a memref and copying data into it...

575 ↗

(On Diff #321014)

Array sounds like it is 1D.

576 ↗

(On Diff #321014)

I feel like the there should be more invariants about some of these ops. Can it really convert _any_ tensor into _any_ strided memref? 4D tensor into a 2D column-major memref?

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

7

Something went wrong here.

26–28

If you take ValueRange instead of ArrayRef<Value> (which you anyway should unless there is a strong reason not to), you can drop this and call operands.getTypes().

78–82

Nit: LLVM-style early return would be something like

if (!eltType.isIndex() && !eltType.isInteger(64))
  return rewriter.notifyMatchFailure("unsupported element type");
StringRef name = "sparsePtrsI64";

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

526

Nit: we have isa_and_nonnull to avoid the actual cast when you don't need the result

mlir/lib/ExecutionEngine/SparseUtils.cpp

111

Nit: we prefer taking non-nullable mutable arguments by reference

132

Do we want to make this function private?

175

Maybe make the element type a template parameter of the enclosing class?

297

MemRef1DU64 plz, we may need other ranks.

[bixia]

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

575 ↗

(On Diff #321014)

I think it is 1D. See also my response to the comment below.

576 ↗

(On Diff #321014)

I think the answer is YES, and the stride is trivial 1. The three Linalg_SparseTensorToXYZMemRefOp here are converting the SparseTensorStorage.positions[x]/indices[y]/values to MemRefOp as can be seen from the C APIs from the same source file.

[ftynse]

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

575 ↗

(On Diff #321014)

If it is indeed 1D, than we should say so in the result type constraint or the verifier.

576 ↗

(On Diff #321014)

2D memref have offset, 2 sizes and 2 strides. What are those numbers in case of 4D tensor input? 8D tensor input? Where do they come from? I see how this can be converted to a 1D memref<?xType> with an external indexing scheme (which still requires to verify that the operand and the result types have the same element type rather than accepting _anything_).

[aartbik]

Thanks all for the very detailed and useful feedback!

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

525 ↗

(On Diff #321014)

You are right. These ops are probably short lived until we get a SparseType with ops but even then we can carry documentation over. Added.

552 ↗

(On Diff #321014)

You are right it is safer to remove this given the opaque implementation for now. It does not matter much for performance anyway, since the sparse compiler hoists these to the top loop always.

576 ↗

(On Diff #321014)

Any tensor in (since we still live in dense tensor land), but only 1D arrays out. I added that constraint so legality is verified better.

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

7

Ah, good catch! Thanks.

26–28

Elegant. Thanks.

78–82

Agreed in general, but this is a bit forward looking on adding more types here (which would make the early return a bit harder)

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

526

Also more elegant. Thanks.

578

On second though I don't think we needed the specialized DimOp and thus this logic. Simplified again.

mlir/lib/ExecutionEngine/SparseUtils.cpp

175

You are way ahead of me. This class will indeed be templated by value type, index type and pointer type in the future (for now I just showed how the default f64/index/index case would be lowered. But added this just to indicate the future direction.

[aartbik]

Alex @ftynse, it would also be nice to use the memref in the input parameters, for example

void *newSparseTensor(char *filename, MemRef1DI1 ref) {
  assert(ref.stride == 1);
  return newSparseTensorC(filename, ref.base + ref.off);
}

instead of

void *newSparseTensor(char *filename, bool *abase, bool *adata, uint64_t aoff,
                      uint64_t asize, uint64_t astride) {
  assert(astride == 1);
  return newSparseTensorC(filename, abase + aoff);
}

but this seems ABI incompatible with the ways arguments are passed C style for structs.
Do you know of any clever trick to make this work? It would read easiser....

[aartbik]

addressed more comments

[ftynse]

In D95847#2539736, @aartbik wrote:

Alex @ftynse, it would also be nice to use the memref in the input parameters, for example

void *newSparseTensor(char *filename, MemRef1DI1 ref) {
  assert(ref.stride == 1);
  return newSparseTensorC(filename, ref.base + ref.off);
}

instead of

void *newSparseTensor(char *filename, bool *abase, bool *adata, uint64_t aoff,
                      uint64_t asize, uint64_t astride) {
  assert(astride == 1);
  return newSparseTensorC(filename, abase + aoff);
}

but this seems ABI incompatible with the ways arguments are passed C style for structs.
Do you know of any clever trick to make this work? It would read easiser....

Add the llvm.emit_c_interface attribute to the relevant functions, this will generate _mlir_ciface_<original_name> wrappers that take a pointer to the struct, unpack it, and forward the descriptor components to the actual call. More info here https://mlir.llvm.org/docs/LLVMDialectMemRefConvention/#c-compatible-wrapper-emission

[aartbik]

In D95847#2548322, @ftynse wrote:

Add the llvm.emit_c_interface attribute to the relevant functions, this will generate _mlir_ciface_<original_name> wrappers that take a pointer to the struct, unpack it, and forward the descriptor components to the actual call. More info here https://mlir.llvm.org/docs/LLVMDialectMemRefConvention/#c-compatible-wrapper-emission

Ah, thanks for the pointer to a detailed description (I had seen examples of this). This wrapper nicely hides these details, but I was really hoping for some direct C magic to either let MLIR pass by struct or C to scalarize the struct :-)

[mehdi_amini]

In D95847#2549473, @aartbik wrote:

In D95847#2548322, @ftynse wrote:

Add the llvm.emit_c_interface attribute to the relevant functions, this will generate _mlir_ciface_<original_name> wrappers that take a pointer to the struct, unpack it, and forward the descriptor components to the actual call. More info here https://mlir.llvm.org/docs/LLVMDialectMemRefConvention/#c-compatible-wrapper-emission

Ah, thanks for the pointer to a detailed description (I had seen examples of this). This wrapper nicely hides these details, but I was really hoping for some direct C magic to either let MLIR pass by struct or C to scalarize the struct :-)

This is quite tricky as the way C-level types map to the LLVM level is dependent on the ABI, and all this logic is builtin clang itself. It would be a nice project to extract this from clang and make it reusable though :)

[aartbik]

In D95847#2549558, @mehdi_amini wrote:

It would be a nice project to extract this from clang and make it reusable though :)

Ah, perhaps a cool summer intern starter project ;-)

[aartbik]

In D95847#2538684, @ftynse wrote:

Looks okay in general. I would like some higher-level description of the storage scheme somewhere.

Please do not commit until @nicolasvasilache had an opportunity to look at Linalg ops.

@nicolasvasilache since you were explicitly called out, would you mind having a look at the Linalg ops.
I suspect you are okay, since these form a short-lived glue until we have a sparse tensor type, but perhaps you have some other insights?

[aartbik]

rebasing to avoid bit-rot

[nicolasvasilache]

Please introduce the new ops independently with roundtrip, verifier and independent testing so their behavior is well-understood + tested and not just assumed by a single-file compiler.
The amount of tests involved here is quite scary to me: I assume it is well-understood that they will be unsupported in the future as the proper refactoring work starts?

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

453 ↗

(On Diff #322234)

Let's please isolate these ops in a new LinalgSparseOps.td for now.
Once things are integrated and compose at the level of transformations, we can pull the abstractions that make the cut in LinalgOps.td.

491 ↗

(On Diff #322234)

tensor_to_memref folds away as bufferization occurs.
This does not fold away but rather gets converted to calls and ends up being executed.

At lowering time I see: `// Lower sparse primitives to calls into runtime support library.`

Please improve the doc so we understand what this does in practice.
This requires some diagrams with what data is input and what data is output.

The way we proceed in MLIR for adding such ops is to add them one by one with proper roundtrip and invalid tests + in your case execution tests.

Once the op semantics are well-understood and tested in isolation, composition becomes possible.

I am not pasting this for each op but please do treat it as a comment for all ops that actually materialize into executable IR: they need to be introduced independently with all the supporting testing / semantics.

[aartbik]

In D95847#2550660, @nicolasvasilache wrote:

Please introduce the new ops independently with roundtrip, verifier and independent testing so their behavior is well-understood + tested and not just assumed by a single-file compiler.
The amount of tests involved here is quite scary to me: I assume it is well-understood that they will be unsupported in the future as the proper refactoring work starts?

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

453 ↗

(On Diff #322234)

I have moved this into its own file now, and added more documentation to the ops themselves (but without going to the public Linalg doc for now). I also added roundtrip and isolated lowering tests.

491 ↗

(On Diff #322234)

I modified the doc and added some diagram at the top of the new file.

[aartbik]

isolated sparse linalg ops in separate file, added roundtrip and lowering tests

[bixia]

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

22

I see and extra "em" in this word.

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

1046

s/Set/Sets/

[aartbik]

Thanks Bixia!

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

22

Right you are! Thanks for catching.

[aartbik]

fixed typos

[bondhugula]

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

120–123

Nit: invert the condition and return failure() and drop the else.

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

532

Inputs / read-only args should be passed by const reference. const CodeGen &codegen?

mlir/lib/ExecutionEngine/SparseUtils.cpp

173–175

All of these are missing doc comments - triple doc comment instead of the trailing one.

401–404

Regular // comment block.

[aartbik]

Thanks Nicolas and Bixia. I saw some last minute feedback came in after submitting, will address that in follow up changes.

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

120–123

This was suggested earlier too, but there will be more types added later (else ifs), where this kind of flow makes more sense.

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

532

I will make a pass to see where we can safely add const

mlir/lib/ExecutionEngine/SparseUtils.cpp

401–404

Ok will change

mlir/include/mlir/Dialect/Linalg/IR/CMakeLists.txt

 
 set(LLVM_TARGET_DEFINITIONS LinalgStructuredOps.td)
 mlir_tablegen(LinalgStructuredOps.h.inc -gen-op-decls)
 mlir_tablegen(LinalgStructuredOps.cpp.inc -gen-op-defs)
 add_public_tablegen_target(MLIRLinalgStructuredOpsIncGen)
 add_dependencies(MLIRLinalgStructuredOpsIncGen LinalgOdsGen)
 add_dependencies(mlir-headers MLIRLinalgStructuredOpsIncGen)
 
+set(LLVM_TARGET_DEFINITIONS LinalgSparseOps.td)
+mlir_tablegen(LinalgSparseOps.h.inc -gen-op-decls)
+mlir_tablegen(LinalgSparseOps.cpp.inc -gen-op-defs)
+add_public_tablegen_target(MLIRLinalgSparseOpsIncGen)
+add_dependencies(mlir-headers MLIRLinalgSparseOpsIncGen)
+
 set(LLVM_TARGET_DEFINITIONS LinalgInterfaces.td)
 mlir_tablegen(LinalgInterfaces.h.inc -gen-op-interface-decls)
 mlir_tablegen(LinalgInterfaces.cpp.inc -gen-op-interface-defs)
 add_public_tablegen_target(MLIRLinalgInterfacesIncGen)
 add_dependencies(mlir-headers MLIRLinalgInterfacesIncGen)

mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.h

 #include "mlir/Dialect/Linalg/IR/LinalgInterfaces.h"
 
 #define GET_OP_CLASSES
 #include "mlir/Dialect/Linalg/IR/LinalgOps.h.inc"
 
 #define GET_OP_CLASSES
 #include "mlir/Dialect/Linalg/IR/LinalgStructuredOps.h.inc"
 
+#define GET_OP_CLASSES
+#include "mlir/Dialect/Linalg/IR/LinalgSparseOps.h.inc"
+
 #endif // MLIR_DIALECT_LINALG_LINALGOPS_H_

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

+//===- LinalgSparseOps.td - Linalg dialect sparse ops ------*- tablegen -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// The following operations bootstrap working with sparse tensors solely
+// within the Linalg dialect. They provide temporary bridges between a
+// future SparseTensorType (now an opaque pointer), the actual TensorType,
+// and MemRef arrays underlying an actual sparse storage scheme in memory.
+//
+// Lacking a proper sparse tensor type, the 'sparse_tensor' operation
+// provides a bridge between an opaque pointer and a regular tensor type
+// just to simplify feeding the value into a Linalg op. The operation
+// simply disappears during lowering.
+//
+// The other operations form the bridge between the opaque pointer and
+// the actual storage of pointers, indices, and values. These operations
+// resemble 'tensor_to_memref' in the sense that they map tensors to
+// their bufferized memrefs, but they lower into actual calls since
+// sparse storage does not bufferize into a single memrefs, as dense
+// tensors do, but into a hierarchical storage scheme where pointers
+// access memrefs with indices and eventually into values.
+//
+// TODO: introduce SparseTensorType as first class citizen in MLIR
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LINALG_SPARSE_OPS
+#define LINALG_SPARSE_OPS
+
+include "mlir/Dialect/Linalg/IR/LinalgBase.td"
+
+// Base class.
+class Linalg_SparseOp<string mnemonic> : Op<Linalg_Dialect, mnemonic, []> {
+  let printer = [{ return ::print(p, *this); }];
+  let verifier = ?;
+  let parser = [{ return ::parse$cppClass(parser, result); }];
+}
+
+def Linalg_SparseTensorFromPointerOp :
+    Linalg_SparseOp<"sparse_tensor">,
+    Arguments<(ins AnyType:$ptr)>,
+    Results<(outs AnyTensor:$result)> {
+  let summary = "Views an opaque sparse tensor pointer as a tensor";
+  let description = [{
+     Lacking a first class citizen type for sparse tensors, this operation
+     forms the glue between a sparse storage scheme (behind an opaque
+     pointer) and the (dense) tensors used in the kernel definitions.
+     This operation merely provides a way to assign a proper tensor
+     type and shape to the incoming opaque pointer. It disappears
+     completely during lowering.
+
+     Example:
+
+    ```mlir
+     !SparseTensor = type !llvm.ptr<i8>
+
+     %0 = linalg.sparse_tensor %arg0 : !SparseTensor to tensor<64x64xf64>
+    ```
+  }];
+  let assemblyFormat = "$ptr attr-dict `:` type($ptr) `to` type($result)";
+}
+
+def Linalg_SparseTensorToPointersMemRefOp :
+    Linalg_SparseOp<"sparse_pointers">,
+    Arguments<(ins AnyTensor:$tensor, Index:$dim)>,
+    Results<(outs AnyStridedMemRefOfRank<1>:$result)> {
+  let summary = "Extract pointers array at given dimension from a tensor";
+  let description = [{
+     Returns the pointers array of the sparse storage scheme at the
+     given dimension for the given tensor. This is similar to the
+     `tensor_to_memref` operation in the sense that it provides a bridge
+     between a tensor world view and a bufferized world view. Unlike the
+     `tensor_to_memref` operation, however, this sparse operation actually
+     lowers into a call into a support library to obtain access to the
+     pointers array.
+
+     Example:
+
+    ```mlir
+    %1 = linalg.sparse_pointers %0, %c1 : tensor<64x64xf64> to memref<?xindex>
+    ```
+  }];
+  let assemblyFormat = "$tensor `,` $dim attr-dict `:` type($tensor)"
+      " `to` type($result)";
+}
+
+def Linalg_SparseTensorToIndicesMemRefOp :
+    Linalg_SparseOp<"sparse_indices">,
+    Arguments<(ins AnyTensor:$tensor, Index:$dim)>,
+    Results<(outs AnyStridedMemRefOfRank<1>:$result)> {
+  let summary = "Extract indices array at given dimension from a tensor";
+  let description = [{
+     Returns the indices array of the sparse storage scheme at the
+     given dimension for the given tensor. This is similar to the
+     `tensor_to_memref` operation in the sense that it provides a bridge
+     between a tensor world view and a bufferized world view. Unlike the
+     `tensor_to_memref` operation, however, this sparse operation actually
+     lowers into a call into a support library to obtain access to the
+     indices array.
+
+     Example:
+
+    ```mlir
+    %1 = linalg.sparse_indices %0, %c1 : tensor<64x64xf64> to memref<?xindex>
+    ```
+  }];
+  let assemblyFormat = "$tensor `,` $dim attr-dict `:` type($tensor)"
+      " `to` type($result)";
+}
+
+def Linalg_SparseTensorToValuesMemRefOp :
+    Linalg_SparseOp<"sparse_values">,
+    Arguments<(ins AnyTensor:$tensor)>,
+    Results<(outs AnyStridedMemRefOfRank<1>:$result)> {
+  let summary = "Extract numerical values array from a tensor";
+  let description = [{
+     Returns the values array of the sparse storage scheme for the given
+     tensor, independent of the actual dimension. This is similar to the
+     `tensor_to_memref` operation in the sense that it provides a bridge
+     between a tensor world view and a bufferized world view. Unlike the
+     `tensor_to_memref` operation, however, this sparse operation actually
+     lowers into a call into a support library to obtain access to the
+     values array.
+
+     Example:
+
+    ```mlir
+    %1 = linalg.sparse_values %0 : tensor<64x64xf64> to memref<?xf64>
+    ```
+  }];
+  let assemblyFormat = "$tensor attr-dict `:` type($tensor) `to` type($result)";
+}
+
+#endif // LINALG_SPARSE_OPS

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

 /// stored entries per indirection level for the "pointers" and the maximum
 /// value of each tensor index over all dimensions for the "indices").
 enum class SparseIntType { kNative, kI64, kI32, kI16, kI8 };
 
 /// Sparsification options.
 struct SparsificationOptions {
   SparsificationOptions(SparseParallelizationStrategy p,
                         SparseVectorizationStrategy v, unsigned vl,
-                        SparseIntType pt, SparseIntType it)
+                        SparseIntType pt, SparseIntType it, bool fo)
       : parallelizationStrategy(p), vectorizationStrategy(v), vectorLength(vl),
-        ptrType(pt), indType(it) {
+        ptrType(pt), indType(it), fastOutput(fo) {
     // TODO: remove restriction when vectors with index elements are supported
     assert((v != SparseVectorizationStrategy::kAnyStorageInnerLoop ||
             (ptrType != SparseIntType::kNative &&
              indType != SparseIntType::kNative)) &&
            "This combination requires support for vectors with index elements");
   }
   SparsificationOptions()
       : SparsificationOptions(SparseParallelizationStrategy::kNone,
                               SparseVectorizationStrategy::kNone, 1u,
-                              SparseIntType::kNative, SparseIntType::kNative) {}
+                              SparseIntType::kNative, SparseIntType::kNative,
+                              false) {}
   SparseParallelizationStrategy parallelizationStrategy;
   SparseVectorizationStrategy vectorizationStrategy;
   unsigned vectorLength;
   SparseIntType ptrType;
   SparseIntType indType;
+  bool fastOutput; // experimental: fast output buffers
 };
 
-/// Set up sparsification rewriting rules with the given options.
+/// Sets up sparsification rewriting rules with the given options.
 void populateSparsificationPatterns(
     MLIRContext *context, OwningRewritePatternList &patterns,
     const SparsificationOptions &options = SparsificationOptions());
 
+/// Sets up sparsification conversion rules with the given options.
+void populateSparsificationConversionPatterns(
+    MLIRContext *context, OwningRewritePatternList &patterns);
+
 } // namespace linalg
 } // namespace mlir
 
 #endif // DIALECT_LINALG_TRANSFORMS_TRANSFORMS_H_

mlir/integration_test/Sparse/CPU/sparse_sum.mlir

+// RUN: mlir-opt %s \
+// RUN:   --test-sparsification="lower" \
+// RUN:   --convert-linalg-to-loops \
+// RUN:   --func-bufferize --tensor-constant-bufferize --tensor-bufferize --finalizing-bufferize  \
+// RUN:   --convert-scf-to-std --convert-vector-to-llvm --convert-std-to-llvm | \
+// RUN: TENSOR0="%mlir_integration_test_dir/data/test.mtx" \
+// RUN: mlir-cpu-runner \
+// RUN:  -e entry -entry-point-result=void  \
+// RUN:  -shared-libs=%mlir_integration_test_dir/libmlir_c_runner_utils%shlibext | \
+// RUN: FileCheck %s
+
+//
+// Use descriptive names for opaque pointers.
+//
+!Filename     = type !llvm.ptr<i8>
+!SparseTensor = type !llvm.ptr<i8>
+
+#trait_sum_reduce = {
+  indexing_maps = [
+    affine_map<(i,j) -> (i,j)>, // A
+    affine_map<(i,j) -> ()>     // x (out)
+  ],
+  sparse = [
+    [ "S", "S" ], // A
+    [          ]  // x
+  ],
+  iterator_types = ["reduction", "reduction"],
+  doc = "x += A(i,j)"
+}
+
+//
+// Integration test that lowers a kernel annotated as sparse to
+// actual sparse code, initializes a matching sparse storage scheme
+// from file, and runs the resulting code with the JIT compiler.
+//
+module {
+  //
+  // The kernel expressed as an annotated Linalg op. The kernel
+  // sum reduces a matrix to a single scalar.
+  //
+  func @kernel_sum_reduce(%argA: !SparseTensor,
+                          %argx: tensor<f64>) -> tensor<f64> {
+    %arga = linalg.sparse_tensor %argA : !SparseTensor to tensor<?x?xf64>
+    %0 = linalg.generic #trait_sum_reduce
+      ins(%arga: tensor<?x?xf64>)
+      outs(%argx: tensor<f64>) {
+      ^bb(%a: f64, %x: f64):
+        %0 = addf %x, %a : f64
+        linalg.yield %0 : f64
+    } -> tensor<f64>
+    return %0 : tensor<f64>
+  }
+
+  //
+  // Runtime support library that is called directly from here.
+  //
+  func private @getTensorFilename(index) -> (!Filename)
+  func private @newSparseTensor(!Filename, memref<?xi1>) -> (!SparseTensor)
+  func private @delSparseTensor(!SparseTensor) -> ()
+  func private @print_memref_f64(%ptr : tensor<*xf64>)
+
+  //
+  // Main driver that reads matrix from file and calls the sparse kernel.
+  //
+  func @entry() {
+    %d0 = constant 0.0 : f64
+    %c0 = constant 0 : index
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+
+    // Mark both dimensions of the matrix as sparse
+    // (this must match the annotation in the trait).
+    %annotations = alloc(%c2) : memref<?xi1>
+    %sparse = constant true
+    store %sparse, %annotations[%c0] : memref<?xi1>
+    store %sparse, %annotations[%c1] : memref<?xi1>
+
+    // Setup memory for a single reduction scalar,
+    // initialized to zero.
+    %xdata = alloc() : memref<f64>
+    store %d0, %xdata[] : memref<f64>
+    %x = tensor_load %xdata : memref<f64>
+
+    // Read the sparse matrix from file, construct sparse storage
+    // according to <sparse,sparse> in memory, and call the kernel.
+    %fileName = call @getTensorFilename(%c0) : (index) -> (!Filename)
+    %a = call @newSparseTensor(%fileName, %annotations)
+      : (!Filename, memref<?xi1>) -> (!SparseTensor)
+    %0 = call @kernel_sum_reduce(%a, %x)
+      : (!SparseTensor, tensor<f64>) -> tensor<f64>
+
+    // Print the result for verification.
+    //
+    // CHECK: 28.2
+    //
+    %m = tensor_to_memref %0 : memref<f64>
+    %v = load %m[] : memref<f64>
+    vector.print %v : f64
+
+    // Release the resources.
+    call @delSparseTensor(%a) : (!SparseTensor) -> ()
+    dealloc %xdata : memref<f64>
+
+    return
+  }
+}

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

 #include "mlir/Dialect/Linalg/IR/LinalgNamedStructuredOps.cpp.inc"
 
 #define GET_OP_CLASSES
 #include "mlir/Dialect/Linalg/IR/LinalgOps.cpp.inc"
 
 #define GET_OP_CLASSES
 #include "mlir/Dialect/Linalg/IR/LinalgStructuredOps.cpp.inc"
 
+#define GET_OP_CLASSES
+#include "mlir/Dialect/Linalg/IR/LinalgSparseOps.cpp.inc"
+
 /// Return the dims that are `iteratorTypeName` loops in the LinalgOp `op`.
 /// Assumes `op` is a LinalgOp.
 void mlir::linalg::getDimsOfType(Operation *op, StringRef iteratorTypeName,
                                  SmallVectorImpl<AffineExpr> &res) {
   if (!cast<LinalgOp>(op).iterator_types())
     return;
 
   unsigned dim = 0;

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

void mlir::linalg::LinalgDialect::initialize() {
   addOperations<
 #define GET_OP_LIST
 #include "mlir/Dialect/Linalg/IR/LinalgOps.cpp.inc"
       >();
   addOperations<
 #define GET_OP_LIST
 #include "mlir/Dialect/Linalg/IR/LinalgStructuredOps.cpp.inc"
       >();
+  addOperations<
+#define GET_OP_LIST
+#include "mlir/Dialect/Linalg/IR/LinalgSparseOps.cpp.inc"
+      >();
 
   addInterfaces<LinalgInlinerInterface>();
 }
 
 Type mlir::linalg::LinalgDialect::parseType(DialectAsmParser &parser) const {
   // Parse the main keyword for the type.
   StringRef keyword;
   if (parser.parseKeyword(&keyword))

mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt

 add_mlir_dialect_library(MLIRLinalgTransforms
   Bufferize.cpp
   CodegenStrategy.cpp
   DropUnitDims.cpp
   ElementwiseToLinalg.cpp
   Fusion.cpp
   FusionOnTensors.cpp
   Generalization.cpp
   Hoisting.cpp
   Interchange.cpp
   Loops.cpp
   Promotion.cpp
+  SparseLowering.cpp
   Sparsification.cpp
   Tiling.cpp
   Transforms.cpp
   Vectorization.cpp
 
   ADDITIONAL_HEADER_DIRS
   ${MLIR_MAIN_INCLUDE_DIR}/mlir/Dialect/Linalg
 

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

+//===- SparseLowering.cpp - Lowers sparse primitives to library calls.  ---===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Dialect/LLVMIR/LLVMTypes.h"
+#include "mlir/Dialect/Linalg/IR/LinalgOps.h"
+#include "mlir/Dialect/Linalg/Transforms/Transforms.h"
+
+using namespace mlir;
+
+namespace {
+
+/// Returns function reference (first hit also inserts into module).
+static FlatSymbolRefAttr getFunc(Operation *op, StringRef name, Type result,
+                                 ValueRange operands) {
+  MLIRContext *context = op->getContext();
+  auto module = op->getParentOfType<ModuleOp>();
+  auto func = module.lookupSymbol<FuncOp>(name);
+  if (!func) {
+    OpBuilder moduleBuilder(module.getBodyRegion());
+    moduleBuilder
+        .create<FuncOp>(op->getLoc(), name,
+                        FunctionType::get(context, operands.getTypes(), result))
+        .setPrivate();
+  }
+  return SymbolRefAttr::get(context, name);
+}
+
+/// Sparse conversion rule to remove opaque pointer cast.
+class TensorFromPointerConverter
+    : public OpConversionPattern<linalg::SparseTensorFromPointerOp> {
+  using OpConversionPattern::OpConversionPattern;
+  LogicalResult
+  matchAndRewrite(linalg::SparseTensorFromPointerOp op,
+                  ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    rewriter.replaceOp(op, operands[0]);
+    return success();
+  }
+};
+
+/// Sparse conversion rule for dimension accesses.
+class TensorToDimSizeConverter : public OpConversionPattern<DimOp> {
+public:
+  using OpConversionPattern::OpConversionPattern;
+  LogicalResult
+  matchAndRewrite(DimOp op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    if (!operands[0].getType().isa<LLVM::LLVMPointerType>())
+      return failure();
+    Type resType = op.getType();
+    StringRef name = "sparseDimSize";
+    rewriter.replaceOpWithNewOp<CallOp>(
+        op, resType, getFunc(op, name, resType, operands), operands);
+    return success();
+  }
+};
+
+/// Sparse conversion rule for pointer accesses.
+class TensorToPointersConverter
+    : public OpConversionPattern<linalg::SparseTensorToPointersMemRefOp> {
+public:
+  using OpConversionPattern::OpConversionPattern;
+  LogicalResult
+  matchAndRewrite(linalg::SparseTensorToPointersMemRefOp op,
+                  ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    Type resType = op.getType();
+    Type eltType = resType.cast<ShapedType>().getElementType();
+    StringRef name;
+    if (eltType.isIndex() || eltType.isInteger(64))
+      name = "sparsePtrsI64";
+    else
+      return failure();
+    rewriter.replaceOpWithNewOp<CallOp>(
+        op, resType, getFunc(op, name, resType, operands), operands);
+    return success();
+  }
+};
+
+/// Sparse conversion rule for index accesses.
+class TensorToIndicesConverter
+    : public OpConversionPattern<linalg::SparseTensorToIndicesMemRefOp> {
+public:
+  using OpConversionPattern::OpConversionPattern;
+  LogicalResult
+  matchAndRewrite(linalg::SparseTensorToIndicesMemRefOp op,
+                  ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    Type resType = op.getType();
+    Type eltType = resType.cast<ShapedType>().getElementType();
+    StringRef name;
+    if (eltType.isIndex() || eltType.isInteger(64))
+      name = "sparseIndxsI64";
+    else
+      return failure();
+    rewriter.replaceOpWithNewOp<CallOp>(
+        op, resType, getFunc(op, name, resType, operands), operands);
+    return success();
+  }
+};
+
+/// Sparse conversion rule for value accesses.
+class TensorToValuesConverter
+    : public OpConversionPattern<linalg::SparseTensorToValuesMemRefOp> {
+public:
+  using OpConversionPattern::OpConversionPattern;
+  LogicalResult
+  matchAndRewrite(linalg::SparseTensorToValuesMemRefOp op,
+                  ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    Type resType = op.getType();
+    Type eltType = resType.cast<ShapedType>().getElementType();
+    StringRef name;
+    if (eltType.isF64())
+      name = "sparseValsF64";
+    else
+      return failure();
+    rewriter.replaceOpWithNewOp<CallOp>(
+        op, resType, getFunc(op, name, resType, operands), operands);
+    return success();
+  }
+};
+
+} // namespace
+
+/// Populates the given patterns list with conversion rules required for
+/// the sparsification of linear algebra operations.
+void linalg::populateSparsificationConversionPatterns(
+    MLIRContext *context, OwningRewritePatternList &patterns) {
+  patterns.insert<TensorFromPointerConverter, TensorToDimSizeConverter,
+                  TensorToPointersConverter, TensorToIndicesConverter,
+                  TensorToValuesConverter>(context);
+}

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

static Type genIntType(PatternRewriter &rewriter, linalg::SparseIntType tp) {
   case linalg::SparseIntType::kI16:
     return rewriter.getIntegerType(16);
   case linalg::SparseIntType::kI8:
     return rewriter.getIntegerType(8);
   }
   llvm_unreachable("unexpected SparseIntType");
 }
 
+/// Returns true if tensor was set up with sparse storage scheme.
+static bool linkedSparse(linalg::GenericOp op, unsigned tensor) {
+  if (tensor < op.getNumInputs())
+    return isa_and_nonnull<linalg::SparseTensorFromPointerOp>(
+        op.getInput(tensor).getDefiningOp());
+  return false;
+}
+
+/// Generates buffer for the output tensor.
+static Value genOutputBuffer(CodeGen &codegen, PatternRewriter &rewriter,
+                             linalg::GenericOp op, MemRefType denseTp,
+                             ArrayRef<Value> args) {
+  Location loc = op.getLoc();
+  Value tensor = op.getOutput(0);
+  // The output tensor simply could materialize from the buffer that will
+  // be generated for the tensor present in the outs() clause. This has
+  // the major advantage that the sparse kernel only updates the nonzero
+  // positions for the output tensor. Currently this results in functional,
+  // but slightly imprecise IR, so it is put under an experimental option.
+  if (codegen.options.fastOutput)
+    return rewriter.create<TensorToMemrefOp>(loc, denseTp, tensor);
+  // By default, a new buffer is allocated which is initialized to the
+  // tensor defined in the outs() clause. This is always correct but
+  // introduces a dense initialization component that may negatively
+  // impact the running complexity of the sparse kernel.
+  Value init = rewriter.create<TensorToMemrefOp>(loc, denseTp, tensor);
+  Value alloc = rewriter.create<AllocOp>(loc, denseTp, args);
+  rewriter.create<linalg::CopyOp>(loc, init, alloc);
+  return alloc;
+}
+
 /// Local bufferization of all dense and sparse data structures.
 /// This code enables testing the first prototype sparse compiler.
 // TODO: replace this with a proliferated bufferization strategy
 static void genBuffers(Merger &merger, CodeGen &codegen,
                        PatternRewriter &rewriter, linalg::GenericOp op) {
   Location loc = op.getLoc();
   unsigned numTensors = op.getNumShapedOperands();
   unsigned numInputs = op.getNumInputs();
   assert(numTensors == numInputs + 1);
-
-  // For now, set all unknown dimensions to 999.
-  // TODO: compute these values (using sparsity or by reading tensor)
-  Value unknown = rewriter.create<ConstantIndexOp>(loc, 999);
-
   // For every tensor, find lower and upper bound on dimensions, set the
-  // same bounds on loop indices, and allocate dense or sparse buffer(s).
+  // same bounds on loop indices, and obtain dense or sparse buffer(s).
   SmallVector<Value, 4> args;
   for (unsigned t = 0; t < numTensors; t++) {
+    Value tensor = t < numInputs ? op.getInput(t) : op.getOutput(0);
     auto tensorType = op.getShapedType(t);
     auto shape = tensorType.getShape();
     auto map = op.getIndexingMap(t);
     // Scan all dimensions of current tensor.
-    bool allDense = true;
+    bool dense = !linkedSparse(op, t);
     args.clear();
     for (unsigned d = 0, rank = shape.size(); d < rank; d++) {
       unsigned i = map.getDimPosition(d);
       // Handle sparse storage schemes.
       if (merger.isDim(t, i, Dim::kSparse)) {
-        allDense = false;
+        dense = false;
         auto dynShape = {ShapedType::kDynamicSize};
         auto ptrTp = MemRefType::get(
             dynShape, genIntType(rewriter, codegen.options.ptrType));
         auto indTp = MemRefType::get(
             dynShape, genIntType(rewriter, codegen.options.indType));
-        codegen.pointers[t][i] = rewriter.create<AllocaOp>(loc, ptrTp, unknown);
-        codegen.indices[t][i] = rewriter.create<AllocaOp>(loc, indTp, unknown);
+        Value dim = rewriter.create<ConstantIndexOp>(loc, d);
+        // Generate sparse primitives to obtains pointer and indices.
+        codegen.pointers[t][i] =
+            rewriter.create<linalg::SparseTensorToPointersMemRefOp>(
+                loc, ptrTp, tensor, dim);
+        codegen.indices[t][i] =
+            rewriter.create<linalg::SparseTensorToIndicesMemRefOp>(loc, indTp,
+                                                                   tensor, dim);
       }
       // Find lower and upper bound in current dimension.
       Value up;
       if (shape[d] == TensorType::kDynamicSize) {
-        Value arg = t < numInputs ? op.getInput(t) : op.getOutput(0);
-        up = rewriter.create<DimOp>(loc, arg, d);
+        up = rewriter.create<DimOp>(loc, tensor, d);
         args.push_back(up);
       } else {
         up = rewriter.create<ConstantIndexOp>(loc, shape[d]);
       }
       codegen.sizes[i] = codegen.highs[t][i] = up;
     }
-    // Allocate dense or sparse buffer for numerical values.
-    if (allDense) {
+    // Perform the required bufferization. All dense inputs materialize
+    // from the input tensor. The dense output tensor needs special
+    // handling. Sparse inputs use a sparse primitive to obtain the values.
+    if (dense) {
       auto denseTp = MemRefType::get(shape, tensorType.getElementType());
-      codegen.buffers[t] = rewriter.create<AllocaOp>(loc, denseTp, args);
+      if (t < numInputs)
+        codegen.buffers[t] =
+            rewriter.create<TensorToMemrefOp>(loc, denseTp, tensor);
+      else
+        codegen.buffers[t] =
+            genOutputBuffer(codegen, rewriter, op, denseTp, args);
     } else {
-      auto sparseTp = MemRefType::get({ShapedType::kDynamicSize},
-                                      tensorType.getElementType());
-      codegen.buffers[t] = rewriter.create<AllocaOp>(loc, sparseTp, unknown);
+      auto dynShape = {ShapedType::kDynamicSize};
+      auto sparseTp = MemRefType::get(dynShape, tensorType.getElementType());
+      codegen.buffers[t] =
+          rewriter.create<linalg::SparseTensorToValuesMemRefOp>(loc, sparseTp,
+                                                                tensor);
     }
   }
 }
 
 /// Constructs vector type from pointer.
 static VectorType vectorType(CodeGen &codegen, Value ptr) {
   Type etp = ptr.getType().cast<MemRefType>().getElementType();
   return VectorType::get(codegen.curVecLength, etp);
static Value genTensorLoad(Merger &merger, CodeGen &codegen,
   // Test if the load was hoisted to a higher loop nest.
   Value val = merger.exp(exp).val;
   if (val)
     return val;
   // Actual load.
   SmallVector<Value, 4> args;
   unsigned tensor = merger.exp(exp).e0;
   auto map = op.getIndexingMap(tensor);
-  bool sparse = false;
+  bool sparse = linkedSparse(op, tensor);
   for (unsigned i = 0, m = map.getNumResults(); i < m; ++i) {
     unsigned idx = map.getDimPosition(i);
     args.push_back(codegen.loops[idx]); // universal dense index
     if (sparse || merger.isDim(tensor, idx, Dim::kSparse)) {
       sparse = true;
       args.clear();
       args.push_back(codegen.pidxs[tensor][idx]); // position index
     }

mlir/lib/ExecutionEngine/SparseUtils.cpp

static bool lexOrder(const Element &e1, const Element &e2) {
     for (int64_t r = 0, rank = e1.indices.size(); r < rank; r++) {
       if (e1.indices[r] == e2.indices[r])
         continue;
       return e1.indices[r] < e2.indices[r];
     }
     return false;
   }
 
+public:
   std::vector<uint64_t> sizes; // per-rank dimension sizes
   std::vector<Element> elements;
   uint64_t pos;
 };
 
+/// A memory-resident sparse tensor using a storage scheme based on per-rank
+/// annotations on dense/sparse. This data structure provides a bufferized
+/// form of an imaginary SparseTensorType, until such a type becomes a
+/// first-class citizen of MLIR. In contrast to generating setup methods for
+/// each differently annotated sparse tensor, this method provides a convenient
+/// "one-size-fits-all" solution that simply takes an input tensor and
+/// annotations to implement all required setup in a general manner.
+template <typename P, typename I, typename V>
+class SparseTensorStorage {
+public:
+  /// Constructs sparse tensor storage scheme following the given
+  /// per-rank dimension dense/sparse annotations.
+  SparseTensorStorage(SparseTensor *tensor, bool *sparsity)
+      : sizes(tensor->sizes), positions(sizes.size()), indices(sizes.size()) {
+    // Provide hints on capacity.
+    // TODO: needs fine-tuning based on sparsity
+    values.reserve(tensor->elements.size());
+    for (uint64_t d = 0, s = 1, rank = sizes.size(); d < rank; d++) {
+      s *= tensor->sizes[d];
+      if (sparsity[d]) {
+        positions[d].reserve(s + 1);
+        indices[d].reserve(s);
+        s = 1;
+      }
+    }
+    // Then setup the tensor.
+    traverse(tensor, sparsity, 0, tensor->elements.size(), 0);
+  }
+
+private:
+  /// Initializes sparse tensor storage scheme from a memory-resident
+  /// representation of an external sparse tensor. This method prepares
+  /// the pointers and indices arrays under the given per-rank dimension
+  /// dense/sparse annotations.
+  void traverse(SparseTensor *tensor, bool *sparsity, uint64_t lo, uint64_t hi,
+                uint64_t d) {
+    const std::vector<Element> &elements = tensor->elements;
+    // Once dimensions are exhausted, insert the numerical values.
+    if (d == sizes.size()) {
+      values.push_back(lo < hi ? elements[lo].value : 0.0);
+      return;
+    }
+    // Prepare a sparse pointer structure at this dimension.
+    if (sparsity[d] && positions[d].empty())
+      positions[d].push_back(0);
+    // Visit all elements in this interval.
+    uint64_t full = 0;
+    while (lo < hi) {
+      // Find segment in interval with same index elements in this dimension.
+      unsigned idx = elements[lo].indices[d];
+      unsigned seg = lo + 1;
+      while (seg < hi && elements[seg].indices[d] == idx)
+        seg++;
+      // Handle segment in interval for sparse or dense dimension.
+      if (sparsity[d]) {
+        indices[d].push_back(idx);
+      } else {
+        for (; full < idx; full++)
+          traverse(tensor, sparsity, 0, 0, d + 1); // pass empty
+        full++;
+      }
+      traverse(tensor, sparsity, lo, seg, d + 1);
+      // And move on to next segment in interval.
+      lo = seg;
+    }
+    // Finalize the sparse pointer structure at this dimension.
+    if (sparsity[d]) {
+      positions[d].push_back(indices[d].size());
+    } else {
+      for (uint64_t sz = tensor->sizes[d]; full < sz; full++)
+        traverse(tensor, sparsity, 0, 0, d + 1); // pass empty
+    }
+  }
+
+public:
+  std::vector<uint64_t> sizes; // per-rank dimension sizes
+  std::vector<std::vector<P>> positions;
+  std::vector<std::vector<I>> indices;
+  std::vector<V> values;
+};
+
+typedef SparseTensorStorage<uint64_t, uint64_t, double>
+    SparseTensorStorageU64U64F64;
+
 /// Helper to convert string to lower case.
 static char *toLower(char *token) {
   for (char *c = token; *c; c++)
     *c = tolower(*c);
   return token;
 }
 
 /// Read the MME header of a general sparse matrix of type real.

 //     %d = load %ddata[%c0] : memref<?xf64>
 //     .. process next nonzero element A[i][j] = d
 //        where the elements appear in lexicographic order ..
 //   }
 //   call @closeTensor(%tensor) : (!llvm.ptr<i8>) -> ()
 //
 //
 // Note that input parameters in the "MLIRized" version of a function mimic
-// the data layout of a MemRef<?xT>:
-//
-//   struct MemRef {
-//     T *base;
-//     T *data;
-//     int64_t off;
-//     int64_t sizes[1];
-//     int64_t strides[1];
-//   }
+// the data layout of a MemRef<?xT> (but cannot use a direct struct). The
+// output parameter uses a direct struct.
 //
 //===----------------------------------------------------------------------===//
 
+extern "C" {
+
+/// Cannot use templates with C linkage.
+
+struct MemRef1DU64 {
+  const uint64_t *base;
+  const uint64_t *data;
+  uint64_t off;
+  uint64_t sizes[1];
+  uint64_t strides[1];
+};
+
+struct MemRef1DF64 {
+  const double *base;
+  const double *data;
+  uint64_t off;
+  uint64_t sizes[1];
+  uint64_t strides[1];
+};
+
 /// Reads in a sparse tensor with the given filename. The call yields a
 /// pointer to an opaque memory-resident sparse tensor object that is only
 /// understood by other methods in the sparse runtime support library. An
 /// array parameter is used to pass the rank, the number of nonzero elements,
 /// and the dimension sizes (one per rank).
-extern "C" void *openTensorC(char *filename, uint64_t *idata) {
+void *openTensorC(char *filename, uint64_t *idata) {
   // Open the file.
   FILE *file = fopen(filename, "r");
   if (!file) {
     fprintf(stderr, "Cannot find %s\n", filename);
     exit(1);
   }
   // Perform some file format dependent set up.
   if (strstr(filename, ".mtx")) {
void *openTensorC(char *filename, uint64_t *idata) {
   }
   // Close the file and return sorted tensor.
   fclose(file);
   tensor->sort(); // sort lexicographically
   return tensor;
 }
 
 /// "MLIRized" version.
-extern "C" void *openTensor(char *filename, uint64_t *ibase, uint64_t *idata,
-                            uint64_t ioff, uint64_t isize, uint64_t istride) {
+void *openTensor(char *filename, uint64_t *ibase, uint64_t *idata,
   assert(istride == 1);
   return openTensorC(filename, idata + ioff);
 }
 
 /// Yields the next element from the given opaque sparse tensor object.
-extern "C" void readTensorItemC(void *tensor, uint64_t *idata, double *ddata) {
+void readTensorItemC(void *tensor, uint64_t *idata, double *ddata) {
   const Element &e = static_cast<SparseTensor *>(tensor)->next();
   for (uint64_t r = 0, rank = e.indices.size(); r < rank; r++)
     idata[r] = e.indices[r];
   ddata[0] = e.value;
 }
 
 /// "MLIRized" version.
-extern "C" void readTensorItem(void *tensor, uint64_t *ibase, uint64_t *idata,
-                               uint64_t ioff, uint64_t isize, uint64_t istride,
-                               double *dbase, double *ddata, uint64_t doff,
-                               uint64_t dsize, uint64_t dstride) {
+void readTensorItem(void *tensor, uint64_t *ibase, uint64_t *idata,
+                    double *dbase, double *ddata, uint64_t doff, uint64_t dsize,
+                    uint64_t dstride) {
   assert(istride == 1 && dstride == 1);
   readTensorItemC(tensor, idata + ioff, ddata + doff);
 }
 
 /// Closes the given opaque sparse tensor object, releasing its memory
-/// resources. After this call, the opague object cannot be used anymore.
-extern "C" void closeTensor(void *tensor) {
-  delete static_cast<SparseTensor *>(tensor);
-}
+/// resources. After this call, the opaque object cannot be used anymore.
+void closeTensor(void *tensor) { delete static_cast<SparseTensor *>(tensor); }
 
 /// Helper method to read a sparse tensor filename from the environment,
 /// defined with the naming convention ${TENSOR0}, ${TENSOR1}, etc.
-extern "C" char *getTensorFilename(uint64_t id) {
+char *getTensorFilename(uint64_t id) {
   char var[80];
   sprintf(var, "TENSOR%" PRIu64, id);
   char *env = getenv(var);
   return env;
 }
 
+///
+/// Sparse primitives that support an opaque implementation of a bufferized
+/// SparseTensor in MLIR. This could be replaced by actual codegen in MLIR.
+///
+
+void *newSparseTensorC(char *filename, bool *annotations) {
+  uint64_t idata[64];
+  SparseTensor *t = static_cast<SparseTensor *>(openTensorC(filename, idata));
+  SparseTensorStorageU64U64F64 *tensor =
+      new SparseTensorStorageU64U64F64(t, annotations);
+  delete t;
+  return tensor;
+}
+
+/// "MLIRized" version.
+void *newSparseTensor(char *filename, bool *abase, bool *adata, uint64_t aoff,
+                      uint64_t asize, uint64_t astride) {
+  assert(astride == 1);
+  return newSparseTensorC(filename, abase + aoff);
+}
+
+uint64_t sparseDimSize(void *tensor, uint64_t d) {
+  return static_cast<SparseTensorStorageU64U64F64 *>(tensor)->sizes[d];
+}
+
+MemRef1DU64 sparsePtrsI64(void *tensor, uint64_t d) {
+  const std::vector<uint64_t> &v =
+      static_cast<SparseTensorStorageU64U64F64 *>(tensor)->positions[d];
+  return {v.data(), v.data(), 0, {v.size()}, {1}};
+}
+
+MemRef1DU64 sparseIndxsI64(void *tensor, uint64_t d) {
+  const std::vector<uint64_t> &v =
+      static_cast<SparseTensorStorageU64U64F64 *>(tensor)->indices[d];
+  return {v.data(), v.data(), 0, {v.size()}, {1}};
+}
+
+MemRef1DF64 sparseValsF64(void *tensor) {
+  const std::vector<double> &v =
+      static_cast<SparseTensorStorageU64U64F64 *>(tensor)->values;
+  return {v.data(), v.data(), 0, {v.size()}, {1}};
+}
+
+void delSparseTensor(void *tensor) {
+  delete static_cast<SparseTensorStorageU64U64F64 *>(tensor);
+}
+
+} // extern "C"
+
 #endif // MLIR_CRUNNERUTILS_DEFINE_FUNCTIONS

mlir/test/Dialect/Linalg/sparse_1d.mlir

 
 // CHECK-LABEL:   func @add_d(
 // CHECK-SAME:                %[[VAL_0:.*]]: tensor<32xf32>,
 // CHECK-SAME:                %[[VAL_1:.*]]: f32,
 // CHECK-SAME:                %[[VAL_2:.*]]: tensor<32xf32>) -> tensor<32xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 0 : index
 // CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<32xf32>
-// CHECK:           scf.for %[[VAL_8:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_9:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_8]]] : memref<32xf32>
-// CHECK:             %[[VAL_10:.*]] = addf %[[VAL_9]], %[[VAL_1]] : f32
-// CHECK:             store %[[VAL_10]], %[[VAL_7]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK:           %[[VAL_6:.*]] = tensor_to_memref %[[VAL_0]] : memref<32xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_8:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_7]], %[[VAL_8]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]]] : memref<32xf32>
+// CHECK:             %[[VAL_11:.*]] = addf %[[VAL_10]], %[[VAL_1]] : f32
+// CHECK:             store %[[VAL_11]], %[[VAL_8]]{{\[}}%[[VAL_9]]] : memref<32xf32>
 // CHECK:           }
-// CHECK:           %[[VAL_11:.*]] = tensor_load %[[VAL_7]] : memref<32xf32>
-// CHECK:           return %[[VAL_11]] : tensor<32xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_load %[[VAL_8]] : memref<32xf32>
+// CHECK:           return %[[VAL_12]] : tensor<32xf32>
 // CHECK:         }
 func @add_d(%arga: tensor<32xf32>, %argb: f32, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_d
      ins(%arga: tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %x: f32):
         %0 = addf %a, %argb : f32
         linalg.yield %0 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @mul_d(
 // CHECK-SAME:                %[[VAL_0:.*]]: tensor<32xf32>,
 // CHECK-SAME:                %[[VAL_1:.*]]: f32,
 // CHECK-SAME:                %[[VAL_2:.*]]: tensor<32xf32>) -> tensor<32xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 0 : index
 // CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<32xf32>
-// CHECK:           scf.for %[[VAL_8:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_9:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_8]]] : memref<32xf32>
-// CHECK:             %[[VAL_10:.*]] = mulf %[[VAL_9]], %[[VAL_1]] : f32
-// CHECK:             store %[[VAL_10]], %[[VAL_7]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK:           %[[VAL_6:.*]] = tensor_to_memref %[[VAL_0]] : memref<32xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_8:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_7]], %[[VAL_8]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]]] : memref<32xf32>
+// CHECK:             %[[VAL_11:.*]] = mulf %[[VAL_10]], %[[VAL_1]] : f32
+// CHECK:             store %[[VAL_11]], %[[VAL_8]]{{\[}}%[[VAL_9]]] : memref<32xf32>
 // CHECK:           }
-// CHECK:           %[[VAL_11:.*]] = tensor_load %[[VAL_7]] : memref<32xf32>
-// CHECK:           return %[[VAL_11]] : tensor<32xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_load %[[VAL_8]] : memref<32xf32>
+// CHECK:           return %[[VAL_12]] : tensor<32xf32>
 // CHECK:         }
 func @mul_d(%arga: tensor<32xf32>, %argb: f32, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_d
      ins(%arga: tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %x: f32):
         %0 = mulf %a, %argb : f32
         linalg.yield %0 : f32
#trait_s = {
   iterator_types = ["parallel"],
   doc = "x(i) = a(i) OP b"
 }
 
 // CHECK-LABEL:   func @add_s(
 // CHECK-SAME:                %[[VAL_0:.*]]: tensor<32xf32>,
 // CHECK-SAME:                %[[VAL_1:.*]]: f32,
 // CHECK-SAME:                %[[VAL_2:.*]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant true
-// CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_12:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]]:2 = scf.while (%[[VAL_15:.*]] = %[[VAL_12]], %[[VAL_16:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant true
+// CHECK:           %[[VAL_6:.*]] = constant 1 : index
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_11:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]]:2 = scf.while (%[[VAL_15:.*]] = %[[VAL_12]], %[[VAL_16:.*]] = %[[VAL_4]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_17:.*]] = cmpi ult, %[[VAL_15]], %[[VAL_13]] : index
 // CHECK:             scf.condition(%[[VAL_17]]) %[[VAL_15]], %[[VAL_16]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_18:.*]]: index, %[[VAL_19:.*]]: index):
-// CHECK:             %[[VAL_20:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK:             %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
 // CHECK:             %[[VAL_21:.*]] = cmpi eq, %[[VAL_20]], %[[VAL_19]] : index
 // CHECK:             scf.if %[[VAL_21]] {
-// CHECK:               %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<?xf32>
+// CHECK:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_18]]] : memref<?xf32>
 // CHECK:               %[[VAL_23:.*]] = addf %[[VAL_22]], %[[VAL_1]] : f32
 // CHECK:               store %[[VAL_23]], %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<32xf32>
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_6]] {
+// CHECK:               scf.if %[[VAL_5]] {
 // CHECK:                 store %[[VAL_1]], %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<32xf32>
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_24:.*]] = cmpi eq, %[[VAL_20]], %[[VAL_19]] : index
-// CHECK:             %[[VAL_25:.*]] = addi %[[VAL_18]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_25:.*]] = addi %[[VAL_18]], %[[VAL_6]] : index
 // CHECK:             %[[VAL_26:.*]] = select %[[VAL_24]], %[[VAL_25]], %[[VAL_18]] : index
-// CHECK:             %[[VAL_27:.*]] = addi %[[VAL_19]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_27:.*]] = addi %[[VAL_19]], %[[VAL_6]] : index
 // CHECK:             scf.yield %[[VAL_26]], %[[VAL_27]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_28:.*]] = %[[VAL_29:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:           scf.for %[[VAL_28:.*]] = %[[VAL_29:.*]]#1 to %[[VAL_3]] step %[[VAL_6]] {
 // CHECK:             store %[[VAL_1]], %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_30:.*]] = tensor_load %[[VAL_11]] : memref<32xf32>
 // CHECK:           return %[[VAL_30]] : tensor<32xf32>
 // CHECK:         }
 func @add_s(%arga: tensor<32xf32>, %argb: f32, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_s
      ins(%arga: tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %x: f32):
         %0 = addf %a, %argb : f32
         linalg.yield %0 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @repeated_add_s(
 // CHECK-SAME:                         %[[VAL_0:.*]]: tensor<32xf32>,
 // CHECK-SAME:                         %[[VAL_1:.*]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_2:.*]] = constant 999 : index
-// CHECK:           %[[VAL_3:.*]] = constant 0 : index
-// CHECK:           %[[VAL_4:.*]] = constant 1 : index
-// CHECK:           %[[VAL_5:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_9:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_9]] to %[[VAL_10]] step %[[VAL_4]] {
-// CHECK:             %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xindex>
-// CHECK:             %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_11]]] : memref<?xf32>
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_11]]] : memref<?xf32>
+// CHECK:           %[[VAL_2:.*]] = constant 0 : index
+// CHECK:           %[[VAL_3:.*]] = constant 1 : index
+// CHECK:           %[[VAL_4:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_2]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_2]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_1]] : memref<32xf32>
+// CHECK:           %[[VAL_8:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_7]], %[[VAL_8]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_9:.*]] = load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_9]] to %[[VAL_10]] step %[[VAL_3]] {
+// CHECK:             %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xindex>
+// CHECK:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xf32>
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xf32>
 // CHECK:             %[[VAL_15:.*]] = addf %[[VAL_13]], %[[VAL_14]] : f32
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_11]]] : memref<?xf32>
-// CHECK:             %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_11]]] : memref<?xf32>
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xf32>
+// CHECK:             %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xf32>
 // CHECK:             %[[VAL_18:.*]] = addf %[[VAL_16]], %[[VAL_17]] : f32
 // CHECK:             %[[VAL_19:.*]] = addf %[[VAL_15]], %[[VAL_18]] : f32
 // CHECK:             store %[[VAL_19]], %[[VAL_8]]{{\[}}%[[VAL_12]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_20:.*]] = tensor_load %[[VAL_8]] : memref<32xf32>
 // CHECK:           return %[[VAL_20]] : tensor<32xf32>
 // CHECK:         }
 func @repeated_add_s(%arga: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_s
      ins(%arga: tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %x: f32):
         %0 = addf %a, %a : f32  // same tensor
         %1 = addf %a, %a : f32  // should yield
         %2 = addf %0, %1 : f32  // one guard
         linalg.yield %2 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @mul_s(
 // CHECK-SAME:                %[[VAL_0:.*]]: tensor<32xf32>,
 // CHECK-SAME:                %[[VAL_1:.*]]: f32,
 // CHECK-SAME:                %[[VAL_2:.*]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_12]]] : memref<?xindex>
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_12]]] : memref<?xf32>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_9:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_8]], %[[VAL_9]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_10:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_12]]] : memref<?xf32>
 // CHECK:             %[[VAL_15:.*]] = mulf %[[VAL_14]], %[[VAL_1]] : f32
 // CHECK:             store %[[VAL_15]], %[[VAL_9]]{{\[}}%[[VAL_13]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_16:.*]] = tensor_load %[[VAL_9]] : memref<32xf32>
 // CHECK:           return %[[VAL_16]] : tensor<32xf32>
 // CHECK:         }
 func @mul_s(%arga: tensor<32xf32>, %argb: f32, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_s

 
 // CHECK-LABEL:   func @add_dd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 0 : index
 // CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32xf32>
-// CHECK:           scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]]] : memref<32xf32>
-// CHECK:             %[[VAL_11:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_9]]] : memref<32xf32>
-// CHECK:             %[[VAL_12:.*]] = addf %[[VAL_10]], %[[VAL_11]] : f32
-// CHECK:             store %[[VAL_12]], %[[VAL_8]]{{\[}}%[[VAL_9]]] : memref<32xf32>
+// CHECK:           %[[VAL_6:.*]] = tensor_to_memref %[[VAL_0]] : memref<32xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_1]] : memref<32xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_9:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_8]], %[[VAL_9]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           scf.for %[[VAL_10:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_10]]] : memref<32xf32>
+// CHECK:             %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_10]]] : memref<32xf32>
+// CHECK:             %[[VAL_13:.*]] = addf %[[VAL_11]], %[[VAL_12]] : f32
+// CHECK:             store %[[VAL_13]], %[[VAL_9]]{{\[}}%[[VAL_10]]] : memref<32xf32>
 // CHECK:           }
-// CHECK:           %[[VAL_13:.*]] = tensor_load %[[VAL_8]] : memref<32xf32>
-// CHECK:           return %[[VAL_13]] : tensor<32xf32>
+// CHECK:           %[[VAL_14:.*]] = tensor_load %[[VAL_9]] : memref<32xf32>
+// CHECK:           return %[[VAL_14]] : tensor<32xf32>
 // CHECK:         }
 func @add_dd(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_dd
      ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @mul_dd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 0 : index
 // CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32xf32>
-// CHECK:           scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]]] : memref<32xf32>
-// CHECK:             %[[VAL_11:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_9]]] : memref<32xf32>
-// CHECK:             %[[VAL_12:.*]] = mulf %[[VAL_10]], %[[VAL_11]] : f32
-// CHECK:             store %[[VAL_12]], %[[VAL_8]]{{\[}}%[[VAL_9]]] : memref<32xf32>
+// CHECK:           %[[VAL_6:.*]] = tensor_to_memref %[[VAL_0]] : memref<32xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_1]] : memref<32xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_9:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_8]], %[[VAL_9]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           scf.for %[[VAL_10:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_10]]] : memref<32xf32>
+// CHECK:             %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_10]]] : memref<32xf32>
+// CHECK:             %[[VAL_13:.*]] = mulf %[[VAL_11]], %[[VAL_12]] : f32
+// CHECK:             store %[[VAL_13]], %[[VAL_9]]{{\[}}%[[VAL_10]]] : memref<32xf32>
 // CHECK:           }
-// CHECK:           %[[VAL_13:.*]] = tensor_load %[[VAL_8]] : memref<32xf32>
-// CHECK:           return %[[VAL_13]] : tensor<32xf32>
+// CHECK:           %[[VAL_14:.*]] = tensor_load %[[VAL_9]] : memref<32xf32>
+// CHECK:           return %[[VAL_14]] : tensor<32xf32>
 // CHECK:         }
 func @mul_dd(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_dd
      ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_ds = {
   iterator_types = ["parallel"],
   doc = "x(i) = a(i) OP b(i)"
 }
 
 // CHECK-LABEL:   func @add_ds(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant true
-// CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]]:2 = scf.while (%[[VAL_16:.*]] = %[[VAL_13]], %[[VAL_17:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant true
+// CHECK:           %[[VAL_6:.*]] = constant 1 : index
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_0]] : memref<32xf32>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]]:2 = scf.while (%[[VAL_16:.*]] = %[[VAL_13]], %[[VAL_17:.*]] = %[[VAL_4]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_18:.*]] = cmpi ult, %[[VAL_16]], %[[VAL_14]] : index
 // CHECK:             scf.condition(%[[VAL_18]]) %[[VAL_16]], %[[VAL_17]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_19:.*]]: index, %[[VAL_20:.*]]: index):
-// CHECK:             %[[VAL_21:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:             %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
 // CHECK:             %[[VAL_22:.*]] = cmpi eq, %[[VAL_21]], %[[VAL_20]] : index
 // CHECK:             scf.if %[[VAL_22]] {
-// CHECK:               %[[VAL_23:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<32xf32>
-// CHECK:               %[[VAL_24:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<?xf32>
+// CHECK:               %[[VAL_23:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_20]]] : memref<32xf32>
+// CHECK:               %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<?xf32>
 // CHECK:               %[[VAL_25:.*]] = addf %[[VAL_23]], %[[VAL_24]] : f32
 // CHECK:               store %[[VAL_25]], %[[VAL_12]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_6]] {
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<32xf32>
+// CHECK:               scf.if %[[VAL_5]] {
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:                 store %[[VAL_26]], %[[VAL_12]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_27:.*]] = cmpi eq, %[[VAL_21]], %[[VAL_20]] : index
-// CHECK:             %[[VAL_28:.*]] = addi %[[VAL_19]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_28:.*]] = addi %[[VAL_19]], %[[VAL_6]] : index
 // CHECK:             %[[VAL_29:.*]] = select %[[VAL_27]], %[[VAL_28]], %[[VAL_19]] : index
-// CHECK:             %[[VAL_30:.*]] = addi %[[VAL_20]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_30:.*]] = addi %[[VAL_20]], %[[VAL_6]] : index
 // CHECK:             scf.yield %[[VAL_29]], %[[VAL_30]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_31:.*]] = %[[VAL_32:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:             %[[VAL_33:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_31]]] : memref<32xf32>
+// CHECK:           scf.for %[[VAL_31:.*]] = %[[VAL_32:.*]]#1 to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK:             %[[VAL_33:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_31]]] : memref<32xf32>
 // CHECK:             store %[[VAL_33]], %[[VAL_12]]{{\[}}%[[VAL_31]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_34:.*]] = tensor_load %[[VAL_12]] : memref<32xf32>
 // CHECK:           return %[[VAL_34]] : tensor<32xf32>
 // CHECK:         }
 func @add_ds(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_ds
      ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @mul_ds(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_11:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_11]] to %[[VAL_12]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_13]]] : memref<?xindex>
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<32xf32>
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_13]]] : memref<?xf32>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = tensor_to_memref %[[VAL_0]] : memref<32xf32>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_10:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_9]], %[[VAL_10]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_11]] to %[[VAL_12]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_14]]] : memref<32xf32>
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_13]]] : memref<?xf32>
 // CHECK:             %[[VAL_17:.*]] = mulf %[[VAL_15]], %[[VAL_16]] : f32
 // CHECK:             store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_14]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_18:.*]] = tensor_load %[[VAL_10]] : memref<32xf32>
 // CHECK:           return %[[VAL_18]] : tensor<32xf32>
 // CHECK:         }
 func @mul_ds(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_ds
#trait_sd = {
   iterator_types = ["parallel"],
   doc = "x(i) = a(i) OP b(i)"
 }
 
 // CHECK-LABEL:   func @add_sd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant true
-// CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]]:2 = scf.while (%[[VAL_16:.*]] = %[[VAL_13]], %[[VAL_17:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant true
+// CHECK:           %[[VAL_6:.*]] = constant 1 : index
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<32xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]]:2 = scf.while (%[[VAL_16:.*]] = %[[VAL_13]], %[[VAL_17:.*]] = %[[VAL_4]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_18:.*]] = cmpi ult, %[[VAL_16]], %[[VAL_14]] : index
 // CHECK:             scf.condition(%[[VAL_18]]) %[[VAL_16]], %[[VAL_17]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_19:.*]]: index, %[[VAL_20:.*]]: index):
-// CHECK:             %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:             %[[VAL_21:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
 // CHECK:             %[[VAL_22:.*]] = cmpi eq, %[[VAL_21]], %[[VAL_20]] : index
 // CHECK:             scf.if %[[VAL_22]] {
-// CHECK:               %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<?xf32>
-// CHECK:               %[[VAL_24:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_20]]] : memref<32xf32>
+// CHECK:               %[[VAL_23:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xf32>
+// CHECK:               %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:               %[[VAL_25:.*]] = addf %[[VAL_23]], %[[VAL_24]] : f32
 // CHECK:               store %[[VAL_25]], %[[VAL_12]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_6]] {
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_20]]] : memref<32xf32>
+// CHECK:               scf.if %[[VAL_5]] {
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:                 store %[[VAL_26]], %[[VAL_12]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_27:.*]] = cmpi eq, %[[VAL_21]], %[[VAL_20]] : index
-// CHECK:             %[[VAL_28:.*]] = addi %[[VAL_19]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_28:.*]] = addi %[[VAL_19]], %[[VAL_6]] : index
 // CHECK:             %[[VAL_29:.*]] = select %[[VAL_27]], %[[VAL_28]], %[[VAL_19]] : index
-// CHECK:             %[[VAL_30:.*]] = addi %[[VAL_20]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_30:.*]] = addi %[[VAL_20]], %[[VAL_6]] : index
 // CHECK:             scf.yield %[[VAL_29]], %[[VAL_30]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_31:.*]] = %[[VAL_32:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:             %[[VAL_33:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_31]]] : memref<32xf32>
+// CHECK:           scf.for %[[VAL_31:.*]] = %[[VAL_32:.*]]#1 to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK:             %[[VAL_33:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_31]]] : memref<32xf32>
 // CHECK:             store %[[VAL_33]], %[[VAL_12]]{{\[}}%[[VAL_31]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_34:.*]] = tensor_load %[[VAL_12]] : memref<32xf32>
 // CHECK:           return %[[VAL_34]] : tensor<32xf32>
 // CHECK:         }
 func @add_sd(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_sd
      ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @mul_sd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_11]] to %[[VAL_12]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_13]]] : memref<?xindex>
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_13]]] : memref<?xf32>
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_14]]] : memref<32xf32>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_1]] : memref<32xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_10:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_9]], %[[VAL_10]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_11:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_11]] to %[[VAL_12]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_13]]] : memref<?xf32>
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<32xf32>
 // CHECK:             %[[VAL_17:.*]] = mulf %[[VAL_15]], %[[VAL_16]] : f32
 // CHECK:             store %[[VAL_17]], %[[VAL_10]]{{\[}}%[[VAL_14]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_18:.*]] = tensor_load %[[VAL_10]] : memref<32xf32>
 // CHECK:           return %[[VAL_18]] : tensor<32xf32>
 // CHECK:         }
 func @mul_sd(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_sd
#trait_ss = {
   iterator_types = ["parallel"],
   doc = "x(i) = a(i) OP b(i)"
 }
 
 // CHECK-LABEL:   func @add_ss(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
 // CHECK:           %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_13]], %[[VAL_19:.*]] = %[[VAL_15]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_20:.*]] = cmpi ult, %[[VAL_18]], %[[VAL_14]] : index
 // CHECK:             %[[VAL_21:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_16]] : index
 // CHECK:             %[[VAL_22:.*]] = and %[[VAL_20]], %[[VAL_21]] : i1
 // CHECK:             scf.condition(%[[VAL_22]]) %[[VAL_18]], %[[VAL_19]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
-// CHECK:             %[[VAL_25:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:             %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK:             %[[VAL_25:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:             %[[VAL_26:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xindex>
 // CHECK:             %[[VAL_27:.*]] = cmpi ult, %[[VAL_26]], %[[VAL_25]] : index
 // CHECK:             %[[VAL_28:.*]] = select %[[VAL_27]], %[[VAL_26]], %[[VAL_25]] : index
 // CHECK:             %[[VAL_29:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_28]] : index
 // CHECK:             %[[VAL_30:.*]] = cmpi eq, %[[VAL_26]], %[[VAL_28]] : index
 // CHECK:             %[[VAL_31:.*]] = and %[[VAL_29]], %[[VAL_30]] : i1
 // CHECK:             scf.if %[[VAL_31]] {
-// CHECK:               %[[VAL_32:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_23]]] : memref<?xf32>
-// CHECK:               %[[VAL_33:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:               %[[VAL_32:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK:               %[[VAL_33:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xf32>
 // CHECK:               %[[VAL_34:.*]] = addf %[[VAL_32]], %[[VAL_33]] : f32
 // CHECK:               store %[[VAL_34]], %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<32xf32>
 // CHECK:             } else {
 // CHECK:               %[[VAL_35:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_28]] : index
 // CHECK:               scf.if %[[VAL_35]] {
-// CHECK:                 %[[VAL_36:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK:                 %[[VAL_36:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_23]]] : memref<?xf32>
 // CHECK:                 store %[[VAL_36]], %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<32xf32>
 // CHECK:               } else {
 // CHECK:                 %[[VAL_37:.*]] = cmpi eq, %[[VAL_26]], %[[VAL_28]] : index
 // CHECK:                 scf.if %[[VAL_37]] {
-// CHECK:                   %[[VAL_38:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:                   %[[VAL_38:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xf32>
 // CHECK:                   store %[[VAL_38]], %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<32xf32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_39:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_28]] : index
-// CHECK:             %[[VAL_40:.*]] = addi %[[VAL_23]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_40:.*]] = addi %[[VAL_23]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_41:.*]] = select %[[VAL_39]], %[[VAL_40]], %[[VAL_23]] : index
 // CHECK:             %[[VAL_42:.*]] = cmpi eq, %[[VAL_26]], %[[VAL_28]] : index
-// CHECK:             %[[VAL_43:.*]] = addi %[[VAL_24]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_43:.*]] = addi %[[VAL_24]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_44:.*]] = select %[[VAL_42]], %[[VAL_43]], %[[VAL_24]] : index
 // CHECK:             scf.yield %[[VAL_41]], %[[VAL_44]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_45:.*]] = %[[VAL_46:.*]]#0 to %[[VAL_14]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_47:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_45]]] : memref<?xindex>
-// CHECK:             %[[VAL_48:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_45]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_45:.*]] = %[[VAL_46:.*]]#0 to %[[VAL_14]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_47:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_45]]] : memref<?xindex>
+// CHECK:             %[[VAL_48:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_45]]] : memref<?xf32>
 // CHECK:             store %[[VAL_48]], %[[VAL_12]]{{\[}}%[[VAL_47]]] : memref<32xf32>
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_49:.*]] = %[[VAL_50:.*]]#1 to %[[VAL_16]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_51:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_49]]] : memref<?xindex>
-// CHECK:             %[[VAL_52:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_49:.*]] = %[[VAL_50:.*]]#1 to %[[VAL_16]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_51:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_49]]] : memref<?xindex>
+// CHECK:             %[[VAL_52:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:             store %[[VAL_52]], %[[VAL_12]]{{\[}}%[[VAL_51]]] : memref<32xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_53:.*]] = tensor_load %[[VAL_12]] : memref<32xf32>
 // CHECK:           return %[[VAL_53]] : tensor<32xf32>
 // CHECK:         }
 func @add_ss(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_ss
      ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>)
     outs(%argx: tensor<32xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32xf32>
   return %0 : tensor<32xf32>
 }
 
 // CHECK-LABEL:   func @mul_ss(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32xf32>) -> tensor<32xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32xf32>, memref<32xf32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
 // CHECK:           %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_13]], %[[VAL_19:.*]] = %[[VAL_15]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_20:.*]] = cmpi ult, %[[VAL_18]], %[[VAL_14]] : index
 // CHECK:             %[[VAL_21:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_16]] : index
 // CHECK:             %[[VAL_22:.*]] = and %[[VAL_20]], %[[VAL_21]] : i1
 // CHECK:             scf.condition(%[[VAL_22]]) %[[VAL_18]], %[[VAL_19]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
-// CHECK:             %[[VAL_25:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:             %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK:             %[[VAL_25:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:             %[[VAL_26:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xindex>
 // CHECK:             %[[VAL_27:.*]] = cmpi ult, %[[VAL_26]], %[[VAL_25]] : index
 // CHECK:             %[[VAL_28:.*]] = select %[[VAL_27]], %[[VAL_26]], %[[VAL_25]] : index
 // CHECK:             %[[VAL_29:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_28]] : index
 // CHECK:             %[[VAL_30:.*]] = cmpi eq, %[[VAL_26]], %[[VAL_28]] : index
 // CHECK:             %[[VAL_31:.*]] = and %[[VAL_29]], %[[VAL_30]] : i1
 // CHECK:             scf.if %[[VAL_31]] {
-// CHECK:               %[[VAL_32:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_23]]] : memref<?xf32>
-// CHECK:               %[[VAL_33:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:               %[[VAL_32:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK:               %[[VAL_33:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xf32>
 // CHECK:               %[[VAL_34:.*]] = mulf %[[VAL_32]], %[[VAL_33]] : f32
 // CHECK:               store %[[VAL_34]], %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<32xf32>
 // CHECK:             } else {
 // CHECK:             }
 // CHECK:             %[[VAL_35:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_28]] : index
-// CHECK:             %[[VAL_36:.*]] = addi %[[VAL_23]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_36:.*]] = addi %[[VAL_23]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_37:.*]] = select %[[VAL_35]], %[[VAL_36]], %[[VAL_23]] : index
 // CHECK:             %[[VAL_38:.*]] = cmpi eq, %[[VAL_26]], %[[VAL_28]] : index
-// CHECK:             %[[VAL_39:.*]] = addi %[[VAL_24]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_39:.*]] = addi %[[VAL_24]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_40:.*]] = select %[[VAL_38]], %[[VAL_39]], %[[VAL_24]] : index
 // CHECK:             scf.yield %[[VAL_37]], %[[VAL_40]] : index, index
 // CHECK:           }
 // CHECK:           %[[VAL_41:.*]] = tensor_load %[[VAL_12]] : memref<32xf32>
 // CHECK:           return %[[VAL_41]] : tensor<32xf32>
 // CHECK:         }
 func @mul_ss(%arga: tensor<32xf32>, %argb: tensor<32xf32>, %argx: tensor<32xf32>) -> tensor<32xf32> {
   %0 = linalg.generic #trait_ss
#trait_two_way_inv = {
   doc = "x(i) = a(i) * c + b(i) * c"
 }
 
 // CHECK-LABEL:   func @two_way_inv(
 // CHECK-SAME:                      %[[VAL_0:.*0]]: tensor<16xf32>,
 // CHECK-SAME:                      %[[VAL_1:.*1]]: tensor<16xf32>,
 // CHECK-SAME:                      %[[VAL_2:.*2]]: f32,
 // CHECK-SAME:                      %[[VAL_3:.*3]]: tensor<16xf32>) -> tensor<16xf32> {
-// CHECK:           %[[VAL_4:.*]] = constant 999 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<16xf32>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]]:3 = scf.while (%[[VAL_19:.*]] = %[[VAL_14]], %[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_5]]) : (index, index, index) -> (index, index, index) {
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_3]] : memref<16xf32>
+// CHECK:           %[[VAL_13:.*]] = alloc() : memref<16xf32>
+// CHECK:           linalg.copy(%[[VAL_12]], %[[VAL_13]]) : memref<16xf32>, memref<16xf32>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]]:3 = scf.while (%[[VAL_19:.*]] = %[[VAL_14]], %[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_4]]) : (index, index, index) -> (index, index, index) {
 // CHECK:             %[[VAL_22:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_15]] : index
 // CHECK:             %[[VAL_23:.*]] = cmpi ult, %[[VAL_20]], %[[VAL_17]] : index
 // CHECK:             %[[VAL_24:.*]] = and %[[VAL_22]], %[[VAL_23]] : i1
 // CHECK:             scf.condition(%[[VAL_24]]) %[[VAL_19]], %[[VAL_20]], %[[VAL_21]] : index, index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_25:.*]]: index, %[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
-// CHECK:             %[[VAL_28:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:             %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:             %[[VAL_28:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_25]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xindex>
 // CHECK:             %[[VAL_30:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_31:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_32:.*]] = and %[[VAL_30]], %[[VAL_31]] : i1
 // CHECK:             scf.if %[[VAL_32]] {
-// CHECK:               %[[VAL_33:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:               %[[VAL_33:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xf32>
 // CHECK:               %[[VAL_34:.*]] = mulf %[[VAL_33]], %[[VAL_2]] : f32
-// CHECK:               %[[VAL_35:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK:               %[[VAL_35:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xf32>
 // CHECK:               %[[VAL_36:.*]] = mulf %[[VAL_35]], %[[VAL_2]] : f32
 // CHECK:               %[[VAL_37:.*]] = addf %[[VAL_34]], %[[VAL_36]] : f32
 // CHECK:               store %[[VAL_37]], %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<16xf32>
 // CHECK:             } else {
 // CHECK:               %[[VAL_38:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
 // CHECK:               scf.if %[[VAL_38]] {
-// CHECK:                 %[[VAL_39:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:                 %[[VAL_39:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xf32>
 // CHECK:                 %[[VAL_40:.*]] = mulf %[[VAL_39]], %[[VAL_2]] : f32
 // CHECK:                 store %[[VAL_40]], %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<16xf32>
 // CHECK:               } else {
 // CHECK:                 %[[VAL_41:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_27]] : index
 // CHECK:                 scf.if %[[VAL_41]] {
-// CHECK:                   %[[VAL_42:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK:                   %[[VAL_42:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xf32>
 // CHECK:                   %[[VAL_43:.*]] = mulf %[[VAL_42]], %[[VAL_2]] : f32
 // CHECK:                   store %[[VAL_43]], %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<16xf32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_44:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
-// CHECK:             %[[VAL_45:.*]] = addi %[[VAL_25]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_45:.*]] = addi %[[VAL_25]], %[[VAL_5]] : index
 // CHECK:             %[[VAL_46:.*]] = select %[[VAL_44]], %[[VAL_45]], %[[VAL_25]] : index
 // CHECK:             %[[VAL_47:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_27]] : index
-// CHECK:             %[[VAL_48:.*]] = addi %[[VAL_26]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_48:.*]] = addi %[[VAL_26]], %[[VAL_5]] : index
 // CHECK:             %[[VAL_49:.*]] = select %[[VAL_47]], %[[VAL_48]], %[[VAL_26]] : index
-// CHECK:             %[[VAL_50:.*]] = addi %[[VAL_27]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_50:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
 // CHECK:             scf.yield %[[VAL_46]], %[[VAL_49]], %[[VAL_50]] : index, index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_51:.*]] = %[[VAL_52:.*]]#0 to %[[VAL_15]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_53:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_51]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_51:.*]] = %[[VAL_52:.*]]#0 to %[[VAL_15]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_53:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_51]]] : memref<?xf32>
 // CHECK:             %[[VAL_54:.*]] = mulf %[[VAL_53]], %[[VAL_2]] : f32
 // CHECK:             store %[[VAL_54]], %[[VAL_13]]{{\[}}%[[VAL_52]]#2] : memref<16xf32>
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_55:.*]] = %[[VAL_56:.*]]#1 to %[[VAL_17]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_57:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_55]]] : memref<?xindex>
-// CHECK:             %[[VAL_58:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_55]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_55:.*]] = %[[VAL_56:.*]]#1 to %[[VAL_17]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_57:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_55]]] : memref<?xindex>
+// CHECK:             %[[VAL_58:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_55]]] : memref<?xf32>
 // CHECK:             %[[VAL_59:.*]] = mulf %[[VAL_58]], %[[VAL_2]] : f32
 // CHECK:             store %[[VAL_59]], %[[VAL_13]]{{\[}}%[[VAL_57]]] : memref<16xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_60:.*]] = tensor_load %[[VAL_13]] : memref<16xf32>
 // CHECK:           return %[[VAL_60]] : tensor<16xf32>
 // CHECK:         }
 func @two_way_inv(%arga: tensor<16xf32>, %argb: tensor<16xf32>, %argc: f32, %argx: tensor<16xf32>) -> tensor<16xf32> {
   %0 = linalg.generic #trait_two_way_inv
     ins(%arga, %argb: tensor<16xf32>, tensor<16xf32>)
     outs(%argx: tensor<16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %argc : f32
         %1 = mulf %b, %argc : f32
         %2 = addf %0, %1 : f32
         linalg.yield %2 : f32
   } -> tensor<16xf32>
   return %0 : tensor<16xf32>
 }
 
 // CHECK-LABEL:   func @two_way_inv_alt(
 // CHECK-SAME:                          %[[VAL_0:.*0]]: tensor<16xf32>,
 // CHECK-SAME:                          %[[VAL_1:.*1]]: tensor<16xf32>,
 // CHECK-SAME:                          %[[VAL_2:.*2]]: f32,
 // CHECK-SAME:                          %[[VAL_3:.*3]]: tensor<16xf32>) -> tensor<16xf32> {
-// CHECK:           %[[VAL_4:.*]] = constant 999 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<16xf32>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]]:3 = scf.while (%[[VAL_19:.*]] = %[[VAL_14]], %[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_5]]) : (index, index, index) -> (index, index, index) {
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_3]] : memref<16xf32>
+// CHECK:           %[[VAL_13:.*]] = alloc() : memref<16xf32>
+// CHECK:           linalg.copy(%[[VAL_12]], %[[VAL_13]]) : memref<16xf32>, memref<16xf32>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]]:3 = scf.while (%[[VAL_19:.*]] = %[[VAL_14]], %[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_4]]) : (index, index, index) -> (index, index, index) {
 // CHECK:             %[[VAL_22:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_15]] : index
 // CHECK:             %[[VAL_23:.*]] = cmpi ult, %[[VAL_20]], %[[VAL_17]] : index
 // CHECK:             %[[VAL_24:.*]] = and %[[VAL_22]], %[[VAL_23]] : i1
 // CHECK:             scf.condition(%[[VAL_24]]) %[[VAL_19]], %[[VAL_20]], %[[VAL_21]] : index, index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_25:.*]]: index, %[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
-// CHECK:             %[[VAL_28:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:             %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:             %[[VAL_28:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_25]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xindex>
 // CHECK:             %[[VAL_30:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_31:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_32:.*]] = and %[[VAL_30]], %[[VAL_31]] : i1
 // CHECK:             scf.if %[[VAL_32]] {
-// CHECK:               %[[VAL_33:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_25]]] : memref<?xf32>
-// CHECK:               %[[VAL_34:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK:               %[[VAL_33:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:               %[[VAL_34:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xf32>
 // CHECK:               %[[VAL_35:.*]] = addf %[[VAL_33]], %[[VAL_34]] : f32
 // CHECK:               %[[VAL_36:.*]] = mulf %[[VAL_35]], %[[VAL_2]] : f32
 // CHECK:               store %[[VAL_36]], %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<16xf32>
 // CHECK:             } else {
 // CHECK:               %[[VAL_37:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
 // CHECK:               scf.if %[[VAL_37]] {
-// CHECK:                 %[[VAL_38:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:                 %[[VAL_38:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xf32>
 // CHECK:                 %[[VAL_39:.*]] = mulf %[[VAL_38]], %[[VAL_2]] : f32
 // CHECK:                 store %[[VAL_39]], %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<16xf32>
 // CHECK:               } else {
 // CHECK:                 %[[VAL_40:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_27]] : index
 // CHECK:                 scf.if %[[VAL_40]] {
-// CHECK:                   %[[VAL_41:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK:                   %[[VAL_41:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xf32>
 // CHECK:                   %[[VAL_42:.*]] = mulf %[[VAL_41]], %[[VAL_2]] : f32
 // CHECK:                   store %[[VAL_42]], %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<16xf32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_43:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
-// CHECK:             %[[VAL_44:.*]] = addi %[[VAL_25]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_44:.*]] = addi %[[VAL_25]], %[[VAL_5]] : index
 // CHECK:             %[[VAL_45:.*]] = select %[[VAL_43]], %[[VAL_44]], %[[VAL_25]] : index
 // CHECK:             %[[VAL_46:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_27]] : index
-// CHECK:             %[[VAL_47:.*]] = addi %[[VAL_26]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_47:.*]] = addi %[[VAL_26]], %[[VAL_5]] : index
 // CHECK:             %[[VAL_48:.*]] = select %[[VAL_46]], %[[VAL_47]], %[[VAL_26]] : index
-// CHECK:             %[[VAL_49:.*]] = addi %[[VAL_27]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_49:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
 // CHECK:             scf.yield %[[VAL_45]], %[[VAL_48]], %[[VAL_49]] : index, index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_50:.*]] = %[[VAL_51:.*]]#0 to %[[VAL_15]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_52:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_50]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_50:.*]] = %[[VAL_51:.*]]#0 to %[[VAL_15]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_52:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_50]]] : memref<?xf32>
 // CHECK:             %[[VAL_53:.*]] = mulf %[[VAL_52]], %[[VAL_2]] : f32
 // CHECK:             store %[[VAL_53]], %[[VAL_13]]{{\[}}%[[VAL_51]]#2] : memref<16xf32>
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#1 to %[[VAL_17]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_56:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_54]]] : memref<?xindex>
-// CHECK:             %[[VAL_57:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_54]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#1 to %[[VAL_17]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_56:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_54]]] : memref<?xindex>
+// CHECK:             %[[VAL_57:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_54]]] : memref<?xf32>
 // CHECK:             %[[VAL_58:.*]] = mulf %[[VAL_57]], %[[VAL_2]] : f32
 // CHECK:             store %[[VAL_58]], %[[VAL_13]]{{\[}}%[[VAL_56]]] : memref<16xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_59:.*]] = tensor_load %[[VAL_13]] : memref<16xf32>
 // CHECK:           return %[[VAL_59]] : tensor<16xf32>
 // CHECK:         }
 func @two_way_inv_alt(%arga: tensor<16xf32>,
                       %argb: tensor<16xf32>, %argc: f32, %argx: tensor<16xf32>) -> tensor<16xf32> {
#trait_sum_reduction = {
   ],
   iterator_types = ["reduction"],
   doc = "x += SUM_i a(i)"
 }
 
 // CHECK-LABEL:   func @sum_reduction(
 // CHECK-SAME:                        %[[VAL_0:.*]]: tensor<?xf32>,
 // CHECK-SAME:                        %[[VAL_1:.*]]: tensor<f32>) -> tensor<f32> {
-// CHECK:           %[[VAL_2:.*]] = constant 999 : index
-// CHECK:           %[[VAL_3:.*]] = constant 0 : index
-// CHECK:           %[[VAL_4:.*]] = constant 1 : index
-// CHECK:           %[[VAL_5:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<f32>
-// CHECK:           %[[VAL_8:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_2:.*]] = constant 0 : index
+// CHECK:           %[[VAL_3:.*]] = constant 1 : index
+// CHECK:           %[[VAL_4:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_2]] : tensor<?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<?xf32> to memref<?xf32>
+// CHECK:           %[[VAL_6:.*]] = tensor_to_memref %[[VAL_1]] : memref<f32>
+// CHECK:           %[[VAL_7:.*]] = alloc() : memref<f32>
+// CHECK:           linalg.copy(%[[VAL_6]], %[[VAL_7]]) : memref<f32>, memref<f32>
+// CHECK:           %[[VAL_8:.*]] = load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
 // CHECK:           %[[VAL_10:.*]] = load %[[VAL_7]][] : memref<f32>
-// CHECK:           %[[VAL_11:.*]] = scf.for %[[VAL_12:.*]] = %[[VAL_8]] to %[[VAL_9]] step %[[VAL_4]] iter_args(%[[VAL_13:.*]] = %[[VAL_10]]) -> (f32) {
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = scf.for %[[VAL_12:.*]] = %[[VAL_8]] to %[[VAL_9]] step %[[VAL_3]] iter_args(%[[VAL_13:.*]] = %[[VAL_10]]) -> (f32) {
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_12]]] : memref<?xf32>
 // CHECK:             %[[VAL_15:.*]] = addf %[[VAL_13]], %[[VAL_14]] : f32
 // CHECK:             scf.yield %[[VAL_15]] : f32
 // CHECK:           }
 // CHECK:           store %[[VAL_16:.*]], %[[VAL_7]][] : memref<f32>
 // CHECK:           %[[VAL_17:.*]] = tensor_load %[[VAL_7]] : memref<f32>
 // CHECK:           return %[[VAL_17]] : tensor<f32>
 // CHECK:         }
 func @sum_reduction(%arga: tensor<?xf32>, %argx: tensor<f32>) -> tensor<f32> {
#trait_sum_reduction_ss = {
   iterator_types = ["reduction"],
   doc = "x += SUM_i a(i) + b(i)"
 }
 
 // CHECK-LABEL:   func @sum_reduction_ss(
 // CHECK-SAME:                           %[[VAL_0:.*0]]: tensor<16xf32>,
 // CHECK-SAME:                           %[[VAL_1:.*1]]: tensor<16xf32>,
 // CHECK-SAME:                           %[[VAL_2:.*2]]: tensor<f32>) -> tensor<f32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<f32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]]:3 = scf.while (%[[VAL_18:.*]] = %[[VAL_13]], %[[VAL_19:.*]] = %[[VAL_15]], %[[VAL_20:.*]] = %[[VAL_4]]) : (index, index, index) -> (index, index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<f32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<f32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<f32>, memref<f32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_17:.*]]:3 = scf.while (%[[VAL_18:.*]] = %[[VAL_13]], %[[VAL_19:.*]] = %[[VAL_15]], %[[VAL_20:.*]] = %[[VAL_3]]) : (index, index, index) -> (index, index, index) {
 // CHECK:             %[[VAL_21:.*]] = cmpi ult, %[[VAL_18]], %[[VAL_14]] : index
 // CHECK:             %[[VAL_22:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_16]] : index
 // CHECK:             %[[VAL_23:.*]] = and %[[VAL_21]], %[[VAL_22]] : i1
 // CHECK:             scf.condition(%[[VAL_23]]) %[[VAL_18]], %[[VAL_19]], %[[VAL_20]] : index, index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_24:.*]]: index, %[[VAL_25:.*]]: index, %[[VAL_26:.*]]: index):
-// CHECK:             %[[VAL_27:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_24]]] : memref<?xindex>
-// CHECK:             %[[VAL_28:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xindex>
+// CHECK:             %[[VAL_27:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK:             %[[VAL_28:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_25]]] : memref<?xindex>
 // CHECK:             %[[VAL_29:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
 // CHECK:             %[[VAL_30:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_26]] : index
 // CHECK:             %[[VAL_31:.*]] = and %[[VAL_29]], %[[VAL_30]] : i1
 // CHECK:             scf.if %[[VAL_31]] {
 // CHECK:               %[[VAL_32:.*]] = load %[[VAL_12]][] : memref<f32>
-// CHECK:               %[[VAL_33:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_24]]] : memref<?xf32>
-// CHECK:               %[[VAL_34:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:               %[[VAL_33:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:               %[[VAL_34:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xf32>
 // CHECK:               %[[VAL_35:.*]] = addf %[[VAL_33]], %[[VAL_34]] : f32
 // CHECK:               %[[VAL_36:.*]] = addf %[[VAL_32]], %[[VAL_35]] : f32
 // CHECK:               store %[[VAL_36]], %[[VAL_12]][] : memref<f32>
 // CHECK:             } else {
 // CHECK:               %[[VAL_37:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
 // CHECK:               scf.if %[[VAL_37]] {
 // CHECK:                 %[[VAL_38:.*]] = load %[[VAL_12]][] : memref<f32>
-// CHECK:                 %[[VAL_39:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:                 %[[VAL_39:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_24]]] : memref<?xf32>
 // CHECK:                 %[[VAL_40:.*]] = addf %[[VAL_38]], %[[VAL_39]] : f32
 // CHECK:                 store %[[VAL_40]], %[[VAL_12]][] : memref<f32>
 // CHECK:               } else {
 // CHECK:                 %[[VAL_41:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_26]] : index
 // CHECK:                 scf.if %[[VAL_41]] {
 // CHECK:                   %[[VAL_42:.*]] = load %[[VAL_12]][] : memref<f32>
-// CHECK:                   %[[VAL_43:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:                   %[[VAL_43:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xf32>
 // CHECK:                   %[[VAL_44:.*]] = addf %[[VAL_42]], %[[VAL_43]] : f32
 // CHECK:                   store %[[VAL_44]], %[[VAL_12]][] : memref<f32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_45:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
-// CHECK:             %[[VAL_46:.*]] = addi %[[VAL_24]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_46:.*]] = addi %[[VAL_24]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_47:.*]] = select %[[VAL_45]], %[[VAL_46]], %[[VAL_24]] : index
 // CHECK:             %[[VAL_48:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_26]] : index
-// CHECK:             %[[VAL_49:.*]] = addi %[[VAL_25]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_49:.*]] = addi %[[VAL_25]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_50:.*]] = select %[[VAL_48]], %[[VAL_49]], %[[VAL_25]] : index
-// CHECK:             %[[VAL_51:.*]] = addi %[[VAL_26]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_51:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
 // CHECK:             scf.yield %[[VAL_47]], %[[VAL_50]], %[[VAL_51]] : index, index, index
 // CHECK:           }
 // CHECK:           %[[VAL_52:.*]] = load %[[VAL_12]][] : memref<f32>
-// CHECK:           %[[VAL_53:.*]] = scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#0 to %[[VAL_14]] step %[[VAL_5]] iter_args(%[[VAL_56:.*]] = %[[VAL_52]]) -> (f32) {
-// CHECK:             %[[VAL_57:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_54]]] : memref<?xf32>
+// CHECK:           %[[VAL_53:.*]] = scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#0 to %[[VAL_14]] step %[[VAL_4]] iter_args(%[[VAL_56:.*]] = %[[VAL_52]]) -> (f32) {
+// CHECK:             %[[VAL_57:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_54]]] : memref<?xf32>
 // CHECK:             %[[VAL_58:.*]] = addf %[[VAL_56]], %[[VAL_57]] : f32
 // CHECK:             scf.yield %[[VAL_58]] : f32
 // CHECK:           }
-// CHECK:           %[[VAL_59:.*]] = scf.for %[[VAL_60:.*]] = %[[VAL_61:.*]]#1 to %[[VAL_16]] step %[[VAL_5]] iter_args(%[[VAL_62:.*]] = %[[VAL_63:.*]]) -> (f32) {
-// CHECK:             %[[VAL_64:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_60]]] : memref<?xf32>
+// CHECK:           %[[VAL_59:.*]] = scf.for %[[VAL_60:.*]] = %[[VAL_61:.*]]#1 to %[[VAL_16]] step %[[VAL_4]] iter_args(%[[VAL_62:.*]] = %[[VAL_63:.*]]) -> (f32) {
+// CHECK:             %[[VAL_64:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_60]]] : memref<?xf32>
 // CHECK:             %[[VAL_65:.*]] = addf %[[VAL_62]], %[[VAL_64]] : f32
 // CHECK:             scf.yield %[[VAL_65]] : f32
 // CHECK:           }
 // CHECK:           store %[[VAL_66:.*]], %[[VAL_12]][] : memref<f32>
 // CHECK:           %[[VAL_67:.*]] = tensor_load %[[VAL_12]] : memref<f32>
 // CHECK:           return %[[VAL_67]] : tensor<f32>
 // CHECK:         }
 func @sum_reduction_ss(%arga: tensor<16xf32>,
#trait_sum_reduction_inv_ss = {
   doc = "x += SUM_i a(i) * b + c(i)"
 }
 
 // CHECK-LABEL:   func @sum_reduction_inv(
 // CHECK-SAME:                            %[[VAL_0:.*0]]: tensor<16xf32>,
 // CHECK-SAME:                            %[[VAL_1:.*1]]: tensor<f32>,
 // CHECK-SAME:                            %[[VAL_2:.*2]]: tensor<16xf32>,
 // CHECK-SAME:                            %[[VAL_3:.*3]]: tensor<f32>) -> tensor<f32> {
-// CHECK:           %[[VAL_4:.*]] = constant 999 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<f32>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca() : memref<f32>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_10]][] : memref<f32>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]]:3 = scf.while (%[[VAL_21:.*]] = %[[VAL_16]], %[[VAL_22:.*]] = %[[VAL_18]], %[[VAL_23:.*]] = %[[VAL_5]]) : (index, index, index) -> (index, index, index) {
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<f32>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_2]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_2]], %[[VAL_4]] : tensor<16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_values %[[VAL_2]] : tensor<16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_3]] : memref<f32>
+// CHECK:           %[[VAL_14:.*]] = alloc() : memref<f32>
+// CHECK:           linalg.copy(%[[VAL_13]], %[[VAL_14]]) : memref<f32>, memref<f32>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_9]][] : memref<f32>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_20:.*]]:3 = scf.while (%[[VAL_21:.*]] = %[[VAL_16]], %[[VAL_22:.*]] = %[[VAL_18]], %[[VAL_23:.*]] = %[[VAL_4]]) : (index, index, index) -> (index, index, index) {
 // CHECK:             %[[VAL_24:.*]] = cmpi ult, %[[VAL_21]], %[[VAL_17]] : index
 // CHECK:             %[[VAL_25:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_19]] : index
 // CHECK:             %[[VAL_26:.*]] = and %[[VAL_24]], %[[VAL_25]] : i1
 // CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_21]], %[[VAL_22]], %[[VAL_23]] : index, index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index, %[[VAL_29:.*]]: index):
-// CHECK:             %[[VAL_30:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:             %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:             %[[VAL_30:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:             %[[VAL_31:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
 // CHECK:             %[[VAL_32:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_33:.*]] = cmpi eq, %[[VAL_31]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_34:.*]] = and %[[VAL_32]], %[[VAL_33]] : i1
 // CHECK:             scf.if %[[VAL_34]] {
 // CHECK:               %[[VAL_35:.*]] = load %[[VAL_14]][] : memref<f32>
-// CHECK:               %[[VAL_36:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_27]]] : memref<?xf32>
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xf32>
 // CHECK:               %[[VAL_37:.*]] = mulf %[[VAL_36]], %[[VAL_15]] : f32
-// CHECK:               %[[VAL_38:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xf32>
+// CHECK:               %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xf32>
 // CHECK:               %[[VAL_39:.*]] = addf %[[VAL_37]], %[[VAL_38]] : f32
 // CHECK:               %[[VAL_40:.*]] = addf %[[VAL_35]], %[[VAL_39]] : f32
 // CHECK:               store %[[VAL_40]], %[[VAL_14]][] : memref<f32>
 // CHECK:             } else {
 // CHECK:               %[[VAL_41:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:               scf.if %[[VAL_41]] {
 // CHECK:                 %[[VAL_42:.*]] = load %[[VAL_14]][] : memref<f32>
-// CHECK:                 %[[VAL_43:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_27]]] : memref<?xf32>
+// CHECK:                 %[[VAL_43:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xf32>
 // CHECK:                 %[[VAL_44:.*]] = mulf %[[VAL_43]], %[[VAL_15]] : f32
 // CHECK:                 %[[VAL_45:.*]] = addf %[[VAL_42]], %[[VAL_44]] : f32
 // CHECK:                 store %[[VAL_45]], %[[VAL_14]][] : memref<f32>
 // CHECK:               } else {
 // CHECK:                 %[[VAL_46:.*]] = cmpi eq, %[[VAL_31]], %[[VAL_29]] : index
 // CHECK:                 scf.if %[[VAL_46]] {
 // CHECK:                   %[[VAL_47:.*]] = load %[[VAL_14]][] : memref<f32>
-// CHECK:                   %[[VAL_48:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xf32>
+// CHECK:                   %[[VAL_48:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xf32>
 // CHECK:                   %[[VAL_49:.*]] = addf %[[VAL_47]], %[[VAL_48]] : f32
 // CHECK:                   store %[[VAL_49]], %[[VAL_14]][] : memref<f32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_50:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_29]] : index
-// CHECK:             %[[VAL_51:.*]] = addi %[[VAL_27]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_51:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
 // CHECK:             %[[VAL_52:.*]] = select %[[VAL_50]], %[[VAL_51]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_53:.*]] = cmpi eq, %[[VAL_31]], %[[VAL_29]] : index
-// CHECK:             %[[VAL_54:.*]] = addi %[[VAL_28]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_54:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
 // CHECK:             %[[VAL_55:.*]] = select %[[VAL_53]], %[[VAL_54]], %[[VAL_28]] : index
-// CHECK:             %[[VAL_56:.*]] = addi %[[VAL_29]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_56:.*]] = addi %[[VAL_29]], %[[VAL_5]] : index
 // CHECK:             scf.yield %[[VAL_52]], %[[VAL_55]], %[[VAL_56]] : index, index, index
 // CHECK:           }
 // CHECK:           %[[VAL_57:.*]] = load %[[VAL_14]][] : memref<f32>
-// CHECK:           %[[VAL_58:.*]] = scf.for %[[VAL_59:.*]] = %[[VAL_60:.*]]#0 to %[[VAL_17]] step %[[VAL_6]] iter_args(%[[VAL_61:.*]] = %[[VAL_57]]) -> (f32) {
-// CHECK:             %[[VAL_62:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_59]]] : memref<?xf32>
+// CHECK:           %[[VAL_58:.*]] = scf.for %[[VAL_59:.*]] = %[[VAL_60:.*]]#0 to %[[VAL_17]] step %[[VAL_5]] iter_args(%[[VAL_61:.*]] = %[[VAL_57]]) -> (f32) {
+// CHECK:             %[[VAL_62:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_59]]] : memref<?xf32>
 // CHECK:             %[[VAL_63:.*]] = mulf %[[VAL_62]], %[[VAL_15]] : f32
 // CHECK:             %[[VAL_64:.*]] = addf %[[VAL_61]], %[[VAL_63]] : f32
 // CHECK:             scf.yield %[[VAL_64]] : f32
 // CHECK:           }
-// CHECK:           %[[VAL_65:.*]] = scf.for %[[VAL_66:.*]] = %[[VAL_67:.*]]#1 to %[[VAL_19]] step %[[VAL_6]] iter_args(%[[VAL_68:.*]] = %[[VAL_69:.*]]) -> (f32) {
-// CHECK:             %[[VAL_70:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_66]]] : memref<?xf32>
+// CHECK:           %[[VAL_65:.*]] = scf.for %[[VAL_66:.*]] = %[[VAL_67:.*]]#1 to %[[VAL_19]] step %[[VAL_5]] iter_args(%[[VAL_68:.*]] = %[[VAL_69:.*]]) -> (f32) {
+// CHECK:             %[[VAL_70:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_66]]] : memref<?xf32>
 // CHECK:             %[[VAL_71:.*]] = addf %[[VAL_68]], %[[VAL_70]] : f32
 // CHECK:             scf.yield %[[VAL_71]] : f32
 // CHECK:           }
 // CHECK:           store %[[VAL_72:.*]], %[[VAL_14]][] : memref<f32>
 // CHECK:           %[[VAL_73:.*]] = tensor_load %[[VAL_14]] : memref<f32>
 // CHECK:           return %[[VAL_73]] : tensor<f32>
 // CHECK:         }
 func @sum_reduction_inv(%arga: tensor<16xf32>,

mlir/test/Dialect/Linalg/sparse_2d.mlir

 // CHECK-LABEL:   func @add_dd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 16 : index
 // CHECK:           %[[VAL_5:.*]] = constant 0 : index
 // CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           scf.for %[[VAL_10:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
-// CHECK:             scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_10]], %[[VAL_11]]] : memref<32x16xf32>
-// CHECK:               %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_10]], %[[VAL_11]]] : memref<32x16xf32>
-// CHECK:               %[[VAL_14:.*]] = addf %[[VAL_12]], %[[VAL_13]] : f32
-// CHECK:               store %[[VAL_14]], %[[VAL_9]]{{\[}}%[[VAL_10]], %[[VAL_11]]] : memref<32x16xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_0]] : memref<32x16xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_10:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_9]], %[[VAL_10]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK:               %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
+// CHECK:               %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
+// CHECK:               %[[VAL_15:.*]] = addf %[[VAL_13]], %[[VAL_14]] : f32
+// CHECK:               store %[[VAL_15]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_15:.*]] = tensor_load %[[VAL_9]] : memref<32x16xf32>
-// CHECK:           return %[[VAL_15]] : tensor<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = tensor_load %[[VAL_10]] : memref<32x16xf32>
+// CHECK:           return %[[VAL_16]] : tensor<32x16xf32>
 // CHECK:         }
 func @add_dd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_dd
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16xf32>
   return %0 : tensor<32x16xf32>
 }
 
 // CHECK-LABEL:   func @mul_dd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 16 : index
 // CHECK:           %[[VAL_5:.*]] = constant 0 : index
 // CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           scf.for %[[VAL_10:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
-// CHECK:             scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_10]], %[[VAL_11]]] : memref<32x16xf32>
-// CHECK:               %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_10]], %[[VAL_11]]] : memref<32x16xf32>
-// CHECK:               %[[VAL_14:.*]] = mulf %[[VAL_12]], %[[VAL_13]] : f32
-// CHECK:               store %[[VAL_14]], %[[VAL_9]]{{\[}}%[[VAL_10]], %[[VAL_11]]] : memref<32x16xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_0]] : memref<32x16xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_10:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_9]], %[[VAL_10]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK:               %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
+// CHECK:               %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
+// CHECK:               %[[VAL_15:.*]] = mulf %[[VAL_13]], %[[VAL_14]] : f32
+// CHECK:               store %[[VAL_15]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_15:.*]] = tensor_load %[[VAL_9]] : memref<32x16xf32>
-// CHECK:           return %[[VAL_15]] : tensor<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = tensor_load %[[VAL_10]] : memref<32x16xf32>
+// CHECK:           return %[[VAL_16]] : tensor<32x16xf32>
 // CHECK:         }
 func @mul_dd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_dd
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_ds = {
   iterator_types = ["parallel", "parallel"],
   doc = "X(i,j) = A(i,j) OP B(i,j)"
 }
 
 // CHECK-LABEL:   func @add_ds(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 16 : index
-// CHECK:           %[[VAL_6:.*]] = constant 0 : index
-// CHECK:           %[[VAL_7:.*]] = constant true
-// CHECK:           %[[VAL_8:.*]] = constant 1 : index
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_8]] {
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_14]]] : memref<?xindex>
-// CHECK:             %[[VAL_16:.*]] = addi %[[VAL_14]], %[[VAL_8]] : index
-// CHECK:             %[[VAL_17:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:             %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_15]], %[[VAL_20:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 16 : index
+// CHECK:           %[[VAL_5:.*]] = constant 0 : index
+// CHECK:           %[[VAL_6:.*]] = constant true
+// CHECK:           %[[VAL_7:.*]] = constant 1 : index
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_7]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_7]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_13:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_12]], %[[VAL_13]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_7]] {
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK:             %[[VAL_16:.*]] = addi %[[VAL_14]], %[[VAL_7]] : index
+// CHECK:             %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK:             %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_15]], %[[VAL_20:.*]] = %[[VAL_5]]) : (index, index) -> (index, index) {
 // CHECK:               %[[VAL_21:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
 // CHECK:               scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
 // CHECK:             } do {
 // CHECK:             ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
-// CHECK:               %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xindex>
+// CHECK:               %[[VAL_24:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
 // CHECK:               %[[VAL_25:.*]] = cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
 // CHECK:               scf.if %[[VAL_25]] {
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_22]]] : memref<?xf32>
-// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xf32>
+// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
 // CHECK:                 %[[VAL_28:.*]] = addf %[[VAL_26]], %[[VAL_27]] : f32
 // CHECK:                 store %[[VAL_28]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
 // CHECK:               } else {
-// CHECK:                 scf.if %[[VAL_7]] {
-// CHECK:                   %[[VAL_29:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
+// CHECK:                 scf.if %[[VAL_6]] {
+// CHECK:                   %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
 // CHECK:                   store %[[VAL_29]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]]] : memref<32x16xf32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:               %[[VAL_30:.*]] = cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
-// CHECK:               %[[VAL_31:.*]] = addi %[[VAL_22]], %[[VAL_8]] : index
+// CHECK:               %[[VAL_31:.*]] = addi %[[VAL_22]], %[[VAL_7]] : index
 // CHECK:               %[[VAL_32:.*]] = select %[[VAL_30]], %[[VAL_31]], %[[VAL_22]] : index
-// CHECK:               %[[VAL_33:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
+// CHECK:               %[[VAL_33:.*]] = addi %[[VAL_23]], %[[VAL_7]] : index
 // CHECK:               scf.yield %[[VAL_32]], %[[VAL_33]] : index, index
 // CHECK:             }
-// CHECK:             scf.for %[[VAL_34:.*]] = %[[VAL_35:.*]]#1 to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:               %[[VAL_36:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
+// CHECK:             scf.for %[[VAL_34:.*]] = %[[VAL_35:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
 // CHECK:               store %[[VAL_36]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_34]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_37:.*]] = tensor_load %[[VAL_13]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_37]] : tensor<32x16xf32>
 // CHECK:         }
 func @add_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_ds
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16xf32>
   return %0 : tensor<32x16xf32>
 }
 
 // CHECK-LABEL:   func @mul_ds(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_12]]] : memref<?xindex>
-// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_6]] : index
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:               %[[VAL_18:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_16]]] : memref<?xf32>
-// CHECK:               %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_11:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] {
+// CHECK:               %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK:               %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xf32>
+// CHECK:               %[[VAL_19:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
 // CHECK:               %[[VAL_20:.*]] = mulf %[[VAL_18]], %[[VAL_19]] : f32
 // CHECK:               store %[[VAL_20]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_21:.*]] = tensor_load %[[VAL_11]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_21]] : tensor<32x16xf32>
 // CHECK:         }
 func @mul_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
#trait_sd = {
   iterator_types = ["parallel", "parallel"],
   doc = "X(i,j) = A(i,j) OP B(i,j)"
 }
 
 // CHECK-LABEL:   func @add_sd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 16 : index
-// CHECK:           %[[VAL_6:.*]] = constant true
-// CHECK:           %[[VAL_7:.*]] = constant 0 : index
-// CHECK:           %[[VAL_8:.*]] = constant 1 : index
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_8]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]]:2 = scf.while (%[[VAL_17:.*]] = %[[VAL_14]], %[[VAL_18:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 16 : index
+// CHECK:           %[[VAL_5:.*]] = constant true
+// CHECK:           %[[VAL_6:.*]] = constant 0 : index
+// CHECK:           %[[VAL_7:.*]] = constant 1 : index
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_6]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_6]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_13:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_12]], %[[VAL_13]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]]:2 = scf.while (%[[VAL_17:.*]] = %[[VAL_14]], %[[VAL_18:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_19:.*]] = cmpi ult, %[[VAL_17]], %[[VAL_15]] : index
 // CHECK:             scf.condition(%[[VAL_19]]) %[[VAL_17]], %[[VAL_18]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_20:.*]]: index, %[[VAL_21:.*]]: index):
-// CHECK:             %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<?xindex>
+// CHECK:             %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xindex>
 // CHECK:             %[[VAL_23:.*]] = cmpi eq, %[[VAL_22]], %[[VAL_21]] : index
 // CHECK:             scf.if %[[VAL_23]] {
-// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:                 %[[VAL_25:.*]] = muli %[[VAL_20]], %[[VAL_5]] : index
+// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:                 %[[VAL_25:.*]] = muli %[[VAL_20]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_26:.*]] = addi %[[VAL_25]], %[[VAL_24]] : index
-// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xf32>
-// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
+// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
 // CHECK:                 %[[VAL_29:.*]] = addf %[[VAL_27]], %[[VAL_28]] : f32
 // CHECK:                 store %[[VAL_29]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_24]]] : memref<32x16xf32>
 // CHECK:               }
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_6]] {
-// CHECK:                 scf.for %[[VAL_30:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
+// CHECK:               scf.if %[[VAL_5]] {
+// CHECK:                 scf.for %[[VAL_30:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
 // CHECK:                   store %[[VAL_31]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_30]]] : memref<32x16xf32>
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_32:.*]] = cmpi eq, %[[VAL_22]], %[[VAL_21]] : index
-// CHECK:             %[[VAL_33:.*]] = addi %[[VAL_20]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_33:.*]] = addi %[[VAL_20]], %[[VAL_7]] : index
 // CHECK:             %[[VAL_34:.*]] = select %[[VAL_32]], %[[VAL_33]], %[[VAL_20]] : index
-// CHECK:             %[[VAL_35:.*]] = addi %[[VAL_21]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_35:.*]] = addi %[[VAL_21]], %[[VAL_7]] : index
 // CHECK:             scf.yield %[[VAL_34]], %[[VAL_35]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_36:.*]] = %[[VAL_37:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
-// CHECK:             scf.for %[[VAL_38:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:               %[[VAL_39:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
+// CHECK:           scf.for %[[VAL_36:.*]] = %[[VAL_37:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
+// CHECK:             scf.for %[[VAL_38:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:               %[[VAL_39:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
 // CHECK:               store %[[VAL_39]], %[[VAL_13]]{{\[}}%[[VAL_36]], %[[VAL_38]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_40:.*]] = tensor_load %[[VAL_13]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_40]] : tensor<32x16xf32>
 // CHECK:         }
 func @add_sd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_sd
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16xf32>
   return %0 : tensor<32x16xf32>
 }
 
 // CHECK-LABEL:   func @mul_sd(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 16 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_14]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_17:.*]] = muli %[[VAL_14]], %[[VAL_4]] : index
+// CHECK:           %[[VAL_3:.*]] = constant 16 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_11:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:               %[[VAL_17:.*]] = muli %[[VAL_14]], %[[VAL_3]] : index
 // CHECK:               %[[VAL_18:.*]] = addi %[[VAL_17]], %[[VAL_16]] : index
-// CHECK:               %[[VAL_19:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_18]]] : memref<?xf32>
-// CHECK:               %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
+// CHECK:               %[[VAL_19:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf32>
+// CHECK:               %[[VAL_20:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
 // CHECK:               %[[VAL_21:.*]] = mulf %[[VAL_19]], %[[VAL_20]] : f32
 // CHECK:               store %[[VAL_21]], %[[VAL_11]]{{\[}}%[[VAL_15]], %[[VAL_16]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_22:.*]] = tensor_load %[[VAL_11]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_22]] : tensor<32x16xf32>
 // CHECK:         }
 func @mul_sd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
#trait_ss = {
   iterator_types = ["parallel", "parallel"],
   doc = "X(i,j) = A(i,j) OP B(i,j)"
 }
 
 // CHECK-LABEL:   func @add_ss(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 16 : index
-// CHECK:           %[[VAL_6:.*]] = constant true
-// CHECK:           %[[VAL_7:.*]] = constant 0 : index
-// CHECK:           %[[VAL_8:.*]] = constant 1 : index
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_15:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_8]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_16]], %[[VAL_20:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 16 : index
+// CHECK:           %[[VAL_5:.*]] = constant true
+// CHECK:           %[[VAL_6:.*]] = constant 0 : index
+// CHECK:           %[[VAL_7:.*]] = constant 1 : index
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_6]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_6]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_7]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_7]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_14:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_15:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_14]], %[[VAL_15]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]]:2 = scf.while (%[[VAL_19:.*]] = %[[VAL_16]], %[[VAL_20:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_21:.*]] = cmpi ult, %[[VAL_19]], %[[VAL_17]] : index
 // CHECK:             scf.condition(%[[VAL_21]]) %[[VAL_19]], %[[VAL_20]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
-// CHECK:             %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xindex>
+// CHECK:             %[[VAL_24:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
 // CHECK:             %[[VAL_25:.*]] = cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
 // CHECK:             scf.if %[[VAL_25]] {
-// CHECK:               %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_22]]] : memref<?xindex>
-// CHECK:               %[[VAL_27:.*]] = addi %[[VAL_22]], %[[VAL_8]] : index
-// CHECK:               %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:               %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_26]], %[[VAL_31:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
+// CHECK:               %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xindex>
+// CHECK:               %[[VAL_27:.*]] = addi %[[VAL_22]], %[[VAL_7]] : index
+// CHECK:               %[[VAL_28:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:               %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_26]], %[[VAL_31:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
 // CHECK:                 %[[VAL_32:.*]] = cmpi ult, %[[VAL_30]], %[[VAL_28]] : index
 // CHECK:                 scf.condition(%[[VAL_32]]) %[[VAL_30]], %[[VAL_31]] : index, index
 // CHECK:               } do {
 // CHECK:               ^bb0(%[[VAL_33:.*]]: index, %[[VAL_34:.*]]: index):
-// CHECK:                 %[[VAL_35:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xindex>
+// CHECK:                 %[[VAL_35:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_33]]] : memref<?xindex>
 // CHECK:                 %[[VAL_36:.*]] = cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
 // CHECK:                 scf.if %[[VAL_36]] {
-// CHECK:                   %[[VAL_37:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_33]]] : memref<?xf32>
-// CHECK:                   %[[VAL_38:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
+// CHECK:                   %[[VAL_37:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                   %[[VAL_38:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
 // CHECK:                   %[[VAL_39:.*]] = addf %[[VAL_37]], %[[VAL_38]] : f32
 // CHECK:                   store %[[VAL_39]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
 // CHECK:                 } else {
-// CHECK:                   scf.if %[[VAL_6]] {
-// CHECK:                     %[[VAL_40:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
+// CHECK:                   scf.if %[[VAL_5]] {
+// CHECK:                     %[[VAL_40:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
 // CHECK:                     store %[[VAL_40]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]]] : memref<32x16xf32>
 // CHECK:                   } else {
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:                 %[[VAL_41:.*]] = cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
-// CHECK:                 %[[VAL_42:.*]] = addi %[[VAL_33]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_42:.*]] = addi %[[VAL_33]], %[[VAL_7]] : index
 // CHECK:                 %[[VAL_43:.*]] = select %[[VAL_41]], %[[VAL_42]], %[[VAL_33]] : index
-// CHECK:                 %[[VAL_44:.*]] = addi %[[VAL_34]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_44:.*]] = addi %[[VAL_34]], %[[VAL_7]] : index
 // CHECK:                 scf.yield %[[VAL_43]], %[[VAL_44]] : index, index
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_45:.*]] = %[[VAL_46:.*]]#1 to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:                 %[[VAL_47:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
+// CHECK:               scf.for %[[VAL_45:.*]] = %[[VAL_46:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:                 %[[VAL_47:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
 // CHECK:                 store %[[VAL_47]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_45]]] : memref<32x16xf32>
 // CHECK:               }
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_6]] {
-// CHECK:                 scf.for %[[VAL_48:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:                   %[[VAL_49:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
+// CHECK:               scf.if %[[VAL_5]] {
+// CHECK:                 scf.for %[[VAL_48:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:                   %[[VAL_49:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
 // CHECK:                   store %[[VAL_49]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_48]]] : memref<32x16xf32>
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_50:.*]] = cmpi eq, %[[VAL_24]], %[[VAL_23]] : index
-// CHECK:             %[[VAL_51:.*]] = addi %[[VAL_22]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_51:.*]] = addi %[[VAL_22]], %[[VAL_7]] : index
 // CHECK:             %[[VAL_52:.*]] = select %[[VAL_50]], %[[VAL_51]], %[[VAL_22]] : index
-// CHECK:             %[[VAL_53:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_53:.*]] = addi %[[VAL_23]], %[[VAL_7]] : index
 // CHECK:             scf.yield %[[VAL_52]], %[[VAL_53]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
-// CHECK:             scf.for %[[VAL_56:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
-// CHECK:               %[[VAL_57:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
+// CHECK:           scf.for %[[VAL_54:.*]] = %[[VAL_55:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
+// CHECK:             scf.for %[[VAL_56:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK:               %[[VAL_57:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
 // CHECK:               store %[[VAL_57]], %[[VAL_15]]{{\[}}%[[VAL_54]], %[[VAL_56]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_58:.*]] = tensor_load %[[VAL_15]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_58]] : tensor<32x16xf32>
 // CHECK:         }
 func @add_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_ss
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16xf32>
   return %0 : tensor<32x16xf32>
 }
 
 // CHECK-LABEL:   func @mul_ss(
 // CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
-// CHECK:             %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_15]]] : memref<?xindex>
-// CHECK:             %[[VAL_18:.*]] = addi %[[VAL_15]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_19:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_20:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xindex>
-// CHECK:               %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<?xf32>
-// CHECK:               %[[VAL_23:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             %[[VAL_18:.*]] = addi %[[VAL_15]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_19:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_20:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_21:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<?xindex>
+// CHECK:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xf32>
+// CHECK:               %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
 // CHECK:               %[[VAL_24:.*]] = mulf %[[VAL_22]], %[[VAL_23]] : f32
 // CHECK:               store %[[VAL_24]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_21]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_25:.*]] = tensor_load %[[VAL_12]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_25]] : tensor<32x16xf32>
 // CHECK:         }
 func @mul_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
#trait_ss_ss = {
   iterator_types = ["parallel", "parallel"],
   doc = "X(i,j) = A(i,j) OP B(i,j)"
 }
 
 // CHECK-LABEL:   func @add_ss_ss(
 // CHECK-SAME:                    %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_15]], %[[VAL_16]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
 // CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_24:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
 // CHECK:             %[[VAL_25:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
 // CHECK:             %[[VAL_26:.*]] = and %[[VAL_24]], %[[VAL_25]] : i1
 // CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
-// CHECK:             %[[VAL_29:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:             %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:             %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
 // CHECK:             %[[VAL_31:.*]] = cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_32:.*]] = select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_33:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_34:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_35:.*]] = and %[[VAL_33]], %[[VAL_34]] : i1
 // CHECK:             scf.if %[[VAL_35]] {
-// CHECK:               %[[VAL_36:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_38:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_37]]] : memref<?xindex>
-// CHECK:               %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xindex>
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_38:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:               %[[VAL_39:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_41:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
 // CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
 // CHECK:                 %[[VAL_45:.*]] = cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
 // CHECK:                 %[[VAL_46:.*]] = cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
 // CHECK:                 %[[VAL_47:.*]] = and %[[VAL_45]], %[[VAL_46]] : i1
 // CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
 // CHECK:               } do {
 // CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
-// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xindex>
-// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xindex>
+// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
 // CHECK:                 %[[VAL_52:.*]] = cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_53:.*]] = select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_54:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_55:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_56:.*]] = and %[[VAL_54]], %[[VAL_55]] : i1
 // CHECK:                 scf.if %[[VAL_56]] {
-// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
-// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:                   %[[VAL_59:.*]] = addf %[[VAL_57]], %[[VAL_58]] : f32
 // CHECK:                   store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                 } else {
 // CHECK:                   %[[VAL_60:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
 // CHECK:                   scf.if %[[VAL_60]] {
-// CHECK:                     %[[VAL_61:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                     %[[VAL_61:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
 // CHECK:                     store %[[VAL_61]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                   } else {
 // CHECK:                     %[[VAL_62:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
 // CHECK:                     scf.if %[[VAL_62]] {
-// CHECK:                       %[[VAL_63:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:                       %[[VAL_63:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:                       store %[[VAL_63]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                     } else {
 // CHECK:                     }
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:                 %[[VAL_64:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_65:.*]] = addi %[[VAL_48]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_65:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_66:.*]] = select %[[VAL_64]], %[[VAL_65]], %[[VAL_48]] : index
 // CHECK:                 %[[VAL_67:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_68:.*]] = addi %[[VAL_49]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_68:.*]] = addi %[[VAL_49]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_69:.*]] = select %[[VAL_67]], %[[VAL_68]], %[[VAL_49]] : index
 // CHECK:                 scf.yield %[[VAL_66]], %[[VAL_69]] : index, index
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_70:.*]] = %[[VAL_71:.*]]#0 to %[[VAL_38]] step %[[VAL_5]] {
-// CHECK:                 %[[VAL_72:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_70]]] : memref<?xindex>
-// CHECK:                 %[[VAL_73:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_70]]] : memref<?xf32>
+// CHECK:               scf.for %[[VAL_70:.*]] = %[[VAL_71:.*]]#0 to %[[VAL_38]] step %[[VAL_4]] {
+// CHECK:                 %[[VAL_72:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_70]]] : memref<?xindex>
+// CHECK:                 %[[VAL_73:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_70]]] : memref<?xf32>
 // CHECK:                 store %[[VAL_73]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_72]]] : memref<32x16xf32>
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_74:.*]] = %[[VAL_75:.*]]#1 to %[[VAL_41]] step %[[VAL_5]] {
-// CHECK:                 %[[VAL_76:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_74]]] : memref<?xindex>
-// CHECK:                 %[[VAL_77:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_74]]] : memref<?xf32>
+// CHECK:               scf.for %[[VAL_74:.*]] = %[[VAL_75:.*]]#1 to %[[VAL_41]] step %[[VAL_4]] {
+// CHECK:                 %[[VAL_76:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_74]]] : memref<?xindex>
+// CHECK:                 %[[VAL_77:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_74]]] : memref<?xf32>
 // CHECK:                 store %[[VAL_77]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_76]]] : memref<32x16xf32>
 // CHECK:               }
 // CHECK:             } else {
 // CHECK:               %[[VAL_78:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
 // CHECK:               scf.if %[[VAL_78]] {
-// CHECK:                 %[[VAL_79:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:                 %[[VAL_80:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
-// CHECK:                 %[[VAL_81:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_80]]] : memref<?xindex>
-// CHECK:                 scf.for %[[VAL_82:.*]] = %[[VAL_79]] to %[[VAL_81]] step %[[VAL_5]] {
-// CHECK:                   %[[VAL_83:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_82]]] : memref<?xindex>
-// CHECK:                   %[[VAL_84:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_82]]] : memref<?xf32>
+// CHECK:                 %[[VAL_79:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:                 %[[VAL_80:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK:                 %[[VAL_81:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_80]]] : memref<?xindex>
+// CHECK:                 scf.for %[[VAL_82:.*]] = %[[VAL_79]] to %[[VAL_81]] step %[[VAL_4]] {
+// CHECK:                   %[[VAL_83:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_82]]] : memref<?xindex>
+// CHECK:                   %[[VAL_84:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_82]]] : memref<?xf32>
 // CHECK:                   store %[[VAL_84]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_83]]] : memref<32x16xf32>
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:                 %[[VAL_85:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
 // CHECK:                 scf.if %[[VAL_85]] {
-// CHECK:                   %[[VAL_86:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:                   %[[VAL_87:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
-// CHECK:                   %[[VAL_88:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_87]]] : memref<?xindex>
-// CHECK:                   scf.for %[[VAL_89:.*]] = %[[VAL_86]] to %[[VAL_88]] step %[[VAL_5]] {
-// CHECK:                     %[[VAL_90:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_89]]] : memref<?xindex>
-// CHECK:                     %[[VAL_91:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_89]]] : memref<?xf32>
+// CHECK:                   %[[VAL_86:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:                   %[[VAL_87:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
+// CHECK:                   %[[VAL_88:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_87]]] : memref<?xindex>
+// CHECK:                   scf.for %[[VAL_89:.*]] = %[[VAL_86]] to %[[VAL_88]] step %[[VAL_4]] {
+// CHECK:                     %[[VAL_90:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_89]]] : memref<?xindex>
+// CHECK:                     %[[VAL_91:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_89]]] : memref<?xf32>
 // CHECK:                     store %[[VAL_91]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_90]]] : memref<32x16xf32>
 // CHECK:                   }
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_92:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_93:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_93:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_94:.*]] = select %[[VAL_92]], %[[VAL_93]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_95:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_96:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_96:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_97:.*]] = select %[[VAL_95]], %[[VAL_96]], %[[VAL_28]] : index
 // CHECK:             scf.yield %[[VAL_94]], %[[VAL_97]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_98:.*]] = %[[VAL_99:.*]]#0 to %[[VAL_18]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_100:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_98]]] : memref<?xindex>
-// CHECK:             %[[VAL_101:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_98]]] : memref<?xindex>
-// CHECK:             %[[VAL_102:.*]] = addi %[[VAL_98]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_103:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_102]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_104:.*]] = %[[VAL_101]] to %[[VAL_103]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_105:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_104]]] : memref<?xindex>
-// CHECK:               %[[VAL_106:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_104]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_98:.*]] = %[[VAL_99:.*]]#0 to %[[VAL_18]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_100:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_98]]] : memref<?xindex>
+// CHECK:             %[[VAL_101:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_98]]] : memref<?xindex>
+// CHECK:             %[[VAL_102:.*]] = addi %[[VAL_98]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_103:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_102]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_104:.*]] = %[[VAL_101]] to %[[VAL_103]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_105:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_104]]] : memref<?xindex>
+// CHECK:               %[[VAL_106:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_104]]] : memref<?xf32>
 // CHECK:               store %[[VAL_106]], %[[VAL_16]]{{\[}}%[[VAL_100]], %[[VAL_105]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_107:.*]] = %[[VAL_108:.*]]#1 to %[[VAL_20]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_109:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_107]]] : memref<?xindex>
-// CHECK:             %[[VAL_110:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_107]]] : memref<?xindex>
-// CHECK:             %[[VAL_111:.*]] = addi %[[VAL_107]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_112:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_111]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_113:.*]] = %[[VAL_110]] to %[[VAL_112]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_114:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_113]]] : memref<?xindex>
-// CHECK:               %[[VAL_115:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_113]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_107:.*]] = %[[VAL_108:.*]]#1 to %[[VAL_20]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_109:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_107]]] : memref<?xindex>
+// CHECK:             %[[VAL_110:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_107]]] : memref<?xindex>
+// CHECK:             %[[VAL_111:.*]] = addi %[[VAL_107]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_112:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_111]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_113:.*]] = %[[VAL_110]] to %[[VAL_112]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_114:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_113]]] : memref<?xindex>
+// CHECK:               %[[VAL_115:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_113]]] : memref<?xf32>
 // CHECK:               store %[[VAL_115]], %[[VAL_16]]{{\[}}%[[VAL_109]], %[[VAL_114]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_116:.*]] = tensor_load %[[VAL_16]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_116]] : tensor<32x16xf32>
 // CHECK:         }
 func @add_ss_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_ss_ss
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16xf32>
   return %0 : tensor<32x16xf32>
 }
 
 // CHECK-LABEL:   func @mul_ss_ss(
 // CHECK-SAME:                    %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_15]], %[[VAL_16]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
 // CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_24:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
 // CHECK:             %[[VAL_25:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
 // CHECK:             %[[VAL_26:.*]] = and %[[VAL_24]], %[[VAL_25]] : i1
 // CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
-// CHECK:             %[[VAL_29:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:             %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:             %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
 // CHECK:             %[[VAL_31:.*]] = cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_32:.*]] = select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_33:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_34:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_35:.*]] = and %[[VAL_33]], %[[VAL_34]] : i1
 // CHECK:             scf.if %[[VAL_35]] {
-// CHECK:               %[[VAL_36:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_38:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_37]]] : memref<?xindex>
-// CHECK:               %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xindex>
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_38:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:               %[[VAL_39:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_41:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
 // CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
 // CHECK:                 %[[VAL_45:.*]] = cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
 // CHECK:                 %[[VAL_46:.*]] = cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
 // CHECK:                 %[[VAL_47:.*]] = and %[[VAL_45]], %[[VAL_46]] : i1
 // CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
 // CHECK:               } do {
 // CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
-// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xindex>
-// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xindex>
+// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
 // CHECK:                 %[[VAL_52:.*]] = cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_53:.*]] = select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_54:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_55:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_56:.*]] = and %[[VAL_54]], %[[VAL_55]] : i1
 // CHECK:                 scf.if %[[VAL_56]] {
-// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
-// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:                   %[[VAL_59:.*]] = mulf %[[VAL_57]], %[[VAL_58]] : f32
 // CHECK:                   store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:                 %[[VAL_60:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_61:.*]] = addi %[[VAL_48]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_61:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_62:.*]] = select %[[VAL_60]], %[[VAL_61]], %[[VAL_48]] : index
 // CHECK:                 %[[VAL_63:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_64:.*]] = addi %[[VAL_49]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_64:.*]] = addi %[[VAL_49]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_65:.*]] = select %[[VAL_63]], %[[VAL_64]], %[[VAL_49]] : index
 // CHECK:                 scf.yield %[[VAL_62]], %[[VAL_65]] : index, index
 // CHECK:               }
 // CHECK:             } else {
 // CHECK:             }
 // CHECK:             %[[VAL_66:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_67:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_67:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_68:.*]] = select %[[VAL_66]], %[[VAL_67]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_69:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_70:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_70:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_71:.*]] = select %[[VAL_69]], %[[VAL_70]], %[[VAL_28]] : index
 // CHECK:             scf.yield %[[VAL_68]], %[[VAL_71]] : index, index
 // CHECK:           }
 // CHECK:           %[[VAL_72:.*]] = tensor_load %[[VAL_16]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_72]] : tensor<32x16xf32>
 // CHECK:         }
 func @mul_ss_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_ss_ss
#trait_sd_ds = {
   iterator_types = ["parallel", "parallel"],
   doc = "X(i,j) = A(i,j) OP B(i,j)"
 }
 
 // CHECK-LABEL:   func @add_sd_ds(
 // CHECK-SAME:                    %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_15]], %[[VAL_16]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
 // CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_24:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
 // CHECK:             %[[VAL_25:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
 // CHECK:             %[[VAL_26:.*]] = and %[[VAL_24]], %[[VAL_25]] : i1
 // CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
-// CHECK:             %[[VAL_29:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:             %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:             %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
 // CHECK:             %[[VAL_31:.*]] = cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_32:.*]] = select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_33:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_34:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_35:.*]] = and %[[VAL_33]], %[[VAL_34]] : i1
 // CHECK:             scf.if %[[VAL_35]] {
-// CHECK:               %[[VAL_36:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_38:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_37]]] : memref<?xindex>
-// CHECK:               %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xindex>
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_38:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:               %[[VAL_39:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_41:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
 // CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
 // CHECK:                 %[[VAL_45:.*]] = cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
 // CHECK:                 %[[VAL_46:.*]] = cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
 // CHECK:                 %[[VAL_47:.*]] = and %[[VAL_45]], %[[VAL_46]] : i1
 // CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
 // CHECK:               } do {
 // CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
-// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xindex>
-// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xindex>
+// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
 // CHECK:                 %[[VAL_52:.*]] = cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_53:.*]] = select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_54:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_55:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_56:.*]] = and %[[VAL_54]], %[[VAL_55]] : i1
 // CHECK:                 scf.if %[[VAL_56]] {
-// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
-// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:                   %[[VAL_59:.*]] = addf %[[VAL_57]], %[[VAL_58]] : f32
 // CHECK:                   store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                 } else {
 // CHECK:                   %[[VAL_60:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
 // CHECK:                   scf.if %[[VAL_60]] {
-// CHECK:                     %[[VAL_61:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                     %[[VAL_61:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
 // CHECK:                     store %[[VAL_61]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                   } else {
 // CHECK:                     %[[VAL_62:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
 // CHECK:                     scf.if %[[VAL_62]] {
-// CHECK:                       %[[VAL_63:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:                       %[[VAL_63:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:                       store %[[VAL_63]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                     } else {
 // CHECK:                     }
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:                 %[[VAL_64:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_65:.*]] = addi %[[VAL_48]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_65:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_66:.*]] = select %[[VAL_64]], %[[VAL_65]], %[[VAL_48]] : index
 // CHECK:                 %[[VAL_67:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_68:.*]] = addi %[[VAL_49]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_68:.*]] = addi %[[VAL_49]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_69:.*]] = select %[[VAL_67]], %[[VAL_68]], %[[VAL_49]] : index
 // CHECK:                 scf.yield %[[VAL_66]], %[[VAL_69]] : index, index
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_70:.*]] = %[[VAL_71:.*]]#0 to %[[VAL_38]] step %[[VAL_5]] {
-// CHECK:                 %[[VAL_72:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_70]]] : memref<?xindex>
-// CHECK:                 %[[VAL_73:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_70]]] : memref<?xf32>
+// CHECK:               scf.for %[[VAL_70:.*]] = %[[VAL_71:.*]]#0 to %[[VAL_38]] step %[[VAL_4]] {
+// CHECK:                 %[[VAL_72:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_70]]] : memref<?xindex>
+// CHECK:                 %[[VAL_73:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_70]]] : memref<?xf32>
 // CHECK:                 store %[[VAL_73]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_72]]] : memref<32x16xf32>
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_74:.*]] = %[[VAL_75:.*]]#1 to %[[VAL_41]] step %[[VAL_5]] {
-// CHECK:                 %[[VAL_76:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_74]]] : memref<?xindex>
-// CHECK:                 %[[VAL_77:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_74]]] : memref<?xf32>
+// CHECK:               scf.for %[[VAL_74:.*]] = %[[VAL_75:.*]]#1 to %[[VAL_41]] step %[[VAL_4]] {
+// CHECK:                 %[[VAL_76:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_74]]] : memref<?xindex>
+// CHECK:                 %[[VAL_77:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_74]]] : memref<?xf32>
 // CHECK:                 store %[[VAL_77]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_76]]] : memref<32x16xf32>
 // CHECK:               }
 // CHECK:             } else {
 // CHECK:               %[[VAL_78:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
 // CHECK:               scf.if %[[VAL_78]] {
-// CHECK:                 %[[VAL_79:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:                 %[[VAL_80:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
-// CHECK:                 %[[VAL_81:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_80]]] : memref<?xindex>
-// CHECK:                 scf.for %[[VAL_82:.*]] = %[[VAL_79]] to %[[VAL_81]] step %[[VAL_5]] {
-// CHECK:                   %[[VAL_83:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_82]]] : memref<?xindex>
-// CHECK:                   %[[VAL_84:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_82]]] : memref<?xf32>
+// CHECK:                 %[[VAL_79:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:                 %[[VAL_80:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK:                 %[[VAL_81:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_80]]] : memref<?xindex>
+// CHECK:                 scf.for %[[VAL_82:.*]] = %[[VAL_79]] to %[[VAL_81]] step %[[VAL_4]] {
+// CHECK:                   %[[VAL_83:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_82]]] : memref<?xindex>
+// CHECK:                   %[[VAL_84:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_82]]] : memref<?xf32>
 // CHECK:                   store %[[VAL_84]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_83]]] : memref<32x16xf32>
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:                 %[[VAL_85:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
 // CHECK:                 scf.if %[[VAL_85]] {
-// CHECK:                   %[[VAL_86:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:                   %[[VAL_87:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
-// CHECK:                   %[[VAL_88:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_87]]] : memref<?xindex>
-// CHECK:                   scf.for %[[VAL_89:.*]] = %[[VAL_86]] to %[[VAL_88]] step %[[VAL_5]] {
-// CHECK:                     %[[VAL_90:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_89]]] : memref<?xindex>
-// CHECK:                     %[[VAL_91:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_89]]] : memref<?xf32>
+// CHECK:                   %[[VAL_86:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:                   %[[VAL_87:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
+// CHECK:                   %[[VAL_88:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_87]]] : memref<?xindex>
+// CHECK:                   scf.for %[[VAL_89:.*]] = %[[VAL_86]] to %[[VAL_88]] step %[[VAL_4]] {
+// CHECK:                     %[[VAL_90:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_89]]] : memref<?xindex>
+// CHECK:                     %[[VAL_91:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_89]]] : memref<?xf32>
 // CHECK:                     store %[[VAL_91]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_90]]] : memref<32x16xf32>
 // CHECK:                   }
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_92:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_93:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_93:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_94:.*]] = select %[[VAL_92]], %[[VAL_93]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_95:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_96:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_96:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_97:.*]] = select %[[VAL_95]], %[[VAL_96]], %[[VAL_28]] : index
 // CHECK:             scf.yield %[[VAL_94]], %[[VAL_97]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_98:.*]] = %[[VAL_99:.*]]#0 to %[[VAL_18]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_100:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_98]]] : memref<?xindex>
-// CHECK:             %[[VAL_101:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_98]]] : memref<?xindex>
-// CHECK:             %[[VAL_102:.*]] = addi %[[VAL_98]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_103:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_102]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_104:.*]] = %[[VAL_101]] to %[[VAL_103]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_105:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_104]]] : memref<?xindex>
-// CHECK:               %[[VAL_106:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_104]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_98:.*]] = %[[VAL_99:.*]]#0 to %[[VAL_18]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_100:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_98]]] : memref<?xindex>
+// CHECK:             %[[VAL_101:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_98]]] : memref<?xindex>
+// CHECK:             %[[VAL_102:.*]] = addi %[[VAL_98]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_103:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_102]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_104:.*]] = %[[VAL_101]] to %[[VAL_103]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_105:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_104]]] : memref<?xindex>
+// CHECK:               %[[VAL_106:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_104]]] : memref<?xf32>
 // CHECK:               store %[[VAL_106]], %[[VAL_16]]{{\[}}%[[VAL_100]], %[[VAL_105]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_107:.*]] = %[[VAL_108:.*]]#1 to %[[VAL_20]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_109:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_107]]] : memref<?xindex>
-// CHECK:             %[[VAL_110:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_107]]] : memref<?xindex>
-// CHECK:             %[[VAL_111:.*]] = addi %[[VAL_107]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_112:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_111]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_113:.*]] = %[[VAL_110]] to %[[VAL_112]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_114:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_113]]] : memref<?xindex>
-// CHECK:               %[[VAL_115:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_113]]] : memref<?xf32>
+// CHECK:           scf.for %[[VAL_107:.*]] = %[[VAL_108:.*]]#1 to %[[VAL_20]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_109:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_107]]] : memref<?xindex>
+// CHECK:             %[[VAL_110:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_107]]] : memref<?xindex>
+// CHECK:             %[[VAL_111:.*]] = addi %[[VAL_107]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_112:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_111]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_113:.*]] = %[[VAL_110]] to %[[VAL_112]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_114:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_113]]] : memref<?xindex>
+// CHECK:               %[[VAL_115:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_113]]] : memref<?xf32>
 // CHECK:               store %[[VAL_115]], %[[VAL_16]]{{\[}}%[[VAL_109]], %[[VAL_114]]] : memref<32x16xf32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_116:.*]] = tensor_load %[[VAL_16]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_116]] : tensor<32x16xf32>
 // CHECK:         }
 func @add_sd_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_ss_ss
      ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>)
     outs(%argx: tensor<32x16xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16xf32>
   return %0 : tensor<32x16xf32>
 }
 
 // CHECK-LABEL:   func @mul_sd_ds(
 // CHECK-SAME:                    %[[VAL_0:.*0]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_1:.*1]]: tensor<32x16xf32>,
 // CHECK-SAME:                    %[[VAL_2:.*2]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16xf32>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<32x16xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<32x16xf32> to memref<?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16xf32>
+// CHECK:           %[[VAL_16:.*]] = alloc() : memref<32x16xf32>
+// CHECK:           linalg.copy(%[[VAL_15]], %[[VAL_16]]) : memref<32x16xf32>, memref<32x16xf32>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
 // CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_17]], %[[VAL_23:.*]] = %[[VAL_19]]) : (index, index) -> (index, index) {
 // CHECK:             %[[VAL_24:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_18]] : index
 // CHECK:             %[[VAL_25:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_20]] : index
 // CHECK:             %[[VAL_26:.*]] = and %[[VAL_24]], %[[VAL_25]] : i1
 // CHECK:             scf.condition(%[[VAL_26]]) %[[VAL_22]], %[[VAL_23]] : index, index
 // CHECK:           } do {
 // CHECK:           ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
-// CHECK:             %[[VAL_29:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:             %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:             %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
 // CHECK:             %[[VAL_31:.*]] = cmpi ult, %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_32:.*]] = select %[[VAL_31]], %[[VAL_30]], %[[VAL_29]] : index
 // CHECK:             %[[VAL_33:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_34:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
 // CHECK:             %[[VAL_35:.*]] = and %[[VAL_33]], %[[VAL_34]] : i1
 // CHECK:             scf.if %[[VAL_35]] {
-// CHECK:               %[[VAL_36:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_38:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_37]]] : memref<?xindex>
-// CHECK:               %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xindex>
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:               %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_38:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:               %[[VAL_39:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:               %[[VAL_40:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_41:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_40]]] : memref<?xindex>
 // CHECK:               %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_36]], %[[VAL_44:.*]] = %[[VAL_39]]) : (index, index) -> (index, index) {
 // CHECK:                 %[[VAL_45:.*]] = cmpi ult, %[[VAL_43]], %[[VAL_38]] : index
 // CHECK:                 %[[VAL_46:.*]] = cmpi ult, %[[VAL_44]], %[[VAL_41]] : index
 // CHECK:                 %[[VAL_47:.*]] = and %[[VAL_45]], %[[VAL_46]] : i1
 // CHECK:                 scf.condition(%[[VAL_47]]) %[[VAL_43]], %[[VAL_44]] : index, index
 // CHECK:               } do {
 // CHECK:               ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
-// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xindex>
-// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xindex>
+// CHECK:                 %[[VAL_50:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK:                 %[[VAL_51:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_49]]] : memref<?xindex>
 // CHECK:                 %[[VAL_52:.*]] = cmpi ult, %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_53:.*]] = select %[[VAL_52]], %[[VAL_51]], %[[VAL_50]] : index
 // CHECK:                 %[[VAL_54:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_55:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
 // CHECK:                 %[[VAL_56:.*]] = and %[[VAL_54]], %[[VAL_55]] : i1
 // CHECK:                 scf.if %[[VAL_56]] {
-// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
-// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_49]]] : memref<?xf32>
+// CHECK:                   %[[VAL_57:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                   %[[VAL_58:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_49]]] : memref<?xf32>
 // CHECK:                   %[[VAL_59:.*]] = mulf %[[VAL_57]], %[[VAL_58]] : f32
 // CHECK:                   store %[[VAL_59]], %[[VAL_16]]{{\[}}%[[VAL_32]], %[[VAL_53]]] : memref<32x16xf32>
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:                 %[[VAL_60:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_61:.*]] = addi %[[VAL_48]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_61:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_62:.*]] = select %[[VAL_60]], %[[VAL_61]], %[[VAL_48]] : index
 // CHECK:                 %[[VAL_63:.*]] = cmpi eq, %[[VAL_51]], %[[VAL_53]] : index
-// CHECK:                 %[[VAL_64:.*]] = addi %[[VAL_49]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_64:.*]] = addi %[[VAL_49]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_65:.*]] = select %[[VAL_63]], %[[VAL_64]], %[[VAL_49]] : index
 // CHECK:                 scf.yield %[[VAL_62]], %[[VAL_65]] : index, index
 // CHECK:               }
 // CHECK:             } else {
 // CHECK:             }
 // CHECK:             %[[VAL_66:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_67:.*]] = addi %[[VAL_27]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_67:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_68:.*]] = select %[[VAL_66]], %[[VAL_67]], %[[VAL_27]] : index
 // CHECK:             %[[VAL_69:.*]] = cmpi eq, %[[VAL_30]], %[[VAL_32]] : index
-// CHECK:             %[[VAL_70:.*]] = addi %[[VAL_28]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_70:.*]] = addi %[[VAL_28]], %[[VAL_4]] : index
 // CHECK:             %[[VAL_71:.*]] = select %[[VAL_69]], %[[VAL_70]], %[[VAL_28]] : index
 // CHECK:             scf.yield %[[VAL_68]], %[[VAL_71]] : index, index
 // CHECK:           }
 // CHECK:           %[[VAL_72:.*]] = tensor_load %[[VAL_16]] : memref<32x16xf32>
 // CHECK:           return %[[VAL_72]] : tensor<32x16xf32>
 // CHECK:         }
 func @mul_sd_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>, %argx: tensor<32x16xf32>) -> tensor<32x16xf32> {
   %0 = linalg.generic #trait_ss_ss
sparse = [
     [ "D" ],       // b
     [ "D" ]        // x
   ],
   iterator_types = ["parallel", "reduction"],
   doc = "x(i) += SUM_j A(i,j) * b(j)"
 }
 
 // CHECK-LABEL:   func @matvec(
-// CHECK-SAME:                 %[[VAL_0:.*0]]: tensor<16x32xf32>,
-// CHECK-SAME:                 %[[VAL_1:.*1]]: tensor<32xf32>,
-// CHECK-SAME:                 %[[VAL_2:.*2]]: tensor<16xf32>) -> tensor<16xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 16 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<16xf32>
-// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_12]]] : memref<?xindex>
-// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_6]] : index
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK-SAME:                 %[[VAL_0:.*]]: tensor<16x32xf32>,
+// CHECK-SAME:                 %[[VAL_1:.*]]: tensor<32xf32>,
+// CHECK-SAME:                 %[[VAL_2:.*]]: tensor<16xf32>) -> tensor<16xf32> {
+// CHECK:           %[[VAL_3:.*]] = constant 16 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<16x32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<16x32xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<16x32xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<32xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<16xf32>
+// CHECK:           %[[VAL_11:.*]] = alloc() : memref<16xf32>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<16xf32>, memref<16xf32>
+// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
 // CHECK:             %[[VAL_16:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
-// CHECK:             %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_6]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f32) {
-// CHECK:               %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:               %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_18]]] : memref<?xf32>
-// CHECK:               %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<32xf32>
+// CHECK:             %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f32) {
+// CHECK:               %[[VAL_20:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK:               %[[VAL_21:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf32>
+// CHECK:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<32xf32>
 // CHECK:               %[[VAL_23:.*]] = mulf %[[VAL_21]], %[[VAL_22]] : f32
 // CHECK:               %[[VAL_24:.*]] = addf %[[VAL_23]], %[[VAL_19]] : f32
 // CHECK:               scf.yield %[[VAL_24]] : f32
 // CHECK:             }
 // CHECK:             store %[[VAL_25:.*]], %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
 // CHECK:           }
 // CHECK:           %[[VAL_26:.*]] = tensor_load %[[VAL_11]] : memref<16xf32>
 // CHECK:           return %[[VAL_26]] : tensor<16xf32>
#trait_sum_reduction = {
   ],
   iterator_types = ["reduction", "reduction"],
   doc = "x += SUM_ij A(i,j)"
 }
 
 // CHECK-LABEL:   func @sum_reduction(
 // CHECK-SAME:                        %[[VAL_0:.*]]: tensor<10x20xf32>,
 // CHECK-SAME:                        %[[VAL_1:.*]]: tensor<f32>) -> tensor<f32> {
-// CHECK:           %[[VAL_2:.*]] = constant 999 : index
-// CHECK:           %[[VAL_3:.*]] = constant 10 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<f32>
-// CHECK:           scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]]] : memref<?xindex>
-// CHECK:             %[[VAL_11:.*]] = addi %[[VAL_9]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xindex>
+// CHECK:           %[[VAL_2:.*]] = constant 10 : index
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<10x20xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<10x20xf32> to memref<?xf32>
+// CHECK:           %[[VAL_7:.*]] = tensor_to_memref %[[VAL_1]] : memref<f32>
+// CHECK:           %[[VAL_8:.*]] = alloc() : memref<f32>
+// CHECK:           linalg.copy(%[[VAL_7]], %[[VAL_8]]) : memref<f32>, memref<f32>
+// CHECK:           scf.for %[[VAL_9:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_10:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_9]]] : memref<?xindex>
+// CHECK:             %[[VAL_11:.*]] = addi %[[VAL_9]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_11]]] : memref<?xindex>
 // CHECK:             %[[VAL_13:.*]] = load %[[VAL_8]][] : memref<f32>
-// CHECK:             %[[VAL_14:.*]] = scf.for %[[VAL_15:.*]] = %[[VAL_10]] to %[[VAL_12]] step %[[VAL_5]] iter_args(%[[VAL_16:.*]] = %[[VAL_13]]) -> (f32) {
-// CHECK:               %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xf32>
+// CHECK:             %[[VAL_14:.*]] = scf.for %[[VAL_15:.*]] = %[[VAL_10]] to %[[VAL_12]] step %[[VAL_4]] iter_args(%[[VAL_16:.*]] = %[[VAL_13]]) -> (f32) {
+// CHECK:               %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xf32>
 // CHECK:               %[[VAL_18:.*]] = addf %[[VAL_16]], %[[VAL_17]] : f32
 // CHECK:               scf.yield %[[VAL_18]] : f32
 // CHECK:             }
 // CHECK:             store %[[VAL_19:.*]], %[[VAL_8]][] : memref<f32>
 // CHECK:           }
 // CHECK:           %[[VAL_20:.*]] = tensor_load %[[VAL_8]] : memref<f32>
 // CHECK:           return %[[VAL_20]] : tensor<f32>
 // CHECK:         }
#trait_scale = {
   iterator_types = ["parallel", "parallel"],
   doc = "X(i,j) = A(i,j) * SCALE"
 }
 
 // CHECK-LABEL:   func @scale(
 // CHECK-SAME:                %[[VAL_0:.*]]: tensor<?x?xf64>,
 // CHECK-SAME:                %[[VAL_1:.*]]: tensor<?x?xf64>) -> tensor<?x?xf64> {
 // CHECK:           %[[VAL_2:.*]] = constant 2.000000e+00 : f64
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 0 : index
-// CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xf64>
+// CHECK:           %[[VAL_3:.*]] = constant 0 : index
+// CHECK:           %[[VAL_4:.*]] = constant 1 : index
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<?x?xf64> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<?x?xf64> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<?x?xf64> to memref<?xf64>
+// CHECK:           %[[VAL_8:.*]] = dim %[[VAL_1]], %[[VAL_3]] : tensor<?x?xf64>
 // CHECK:           %[[VAL_9:.*]] = dim %[[VAL_1]], %[[VAL_4]] : tensor<?x?xf64>
-// CHECK:           %[[VAL_10:.*]] = dim %[[VAL_1]], %[[VAL_5]] : tensor<?x?xf64>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_9]], %[[VAL_10]]) : memref<?x?xf64>
-// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_9]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
-// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:               %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xf64>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<?x?xf64>
+// CHECK:           %[[VAL_11:.*]] = alloc(%[[VAL_8]], %[[VAL_9]]) : memref<?x?xf64>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<?x?xf64>, memref<?x?xf64>
+// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_3]] to %[[VAL_8]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_15:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK:               %[[VAL_18:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xf64>
 // CHECK:               %[[VAL_19:.*]] = mulf %[[VAL_18]], %[[VAL_2]] : f64
 // CHECK:               store %[[VAL_19]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]]] : memref<?x?xf64>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_20:.*]] = tensor_load %[[VAL_11]] : memref<?x?xf64>
 // CHECK:           return %[[VAL_20]] : tensor<?x?xf64>
 // CHECK:         }
 func @scale(%arga: tensor<?x?xf64>, %argx: tensor<?x?xf64>) -> tensor<?x?xf64> {
#trait_sampled_dense_dense = {
   doc = "X(i,j) += S(i,j) SUM_k A(i,k) B(k,j)"
 }
 
 // CHECK-LABEL:   func @sampled_dense_dense(
 // CHECK-SAME:                              %[[VAL_0:.*0]]: tensor<?x?xf32>,
 // CHECK-SAME:                              %[[VAL_1:.*1]]: tensor<?x?xf32>,
 // CHECK-SAME:                              %[[VAL_2:.*2]]: tensor<?x?xf32>,
 // CHECK-SAME:                              %[[VAL_3:.*3]]: tensor<?x?xf32>) -> tensor<?x?xf32> {
-// CHECK:           %[[VAL_4:.*]] = constant 999 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = dim %[[VAL_1]], %[[VAL_5]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_13:.*]] = dim %[[VAL_1]], %[[VAL_6]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_12]], %[[VAL_13]]) : memref<?x?xf32>
-// CHECK:           %[[VAL_15:.*]] = dim %[[VAL_2]], %[[VAL_5]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_16:.*]] = dim %[[VAL_2]], %[[VAL_6]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_17:.*]] = alloca(%[[VAL_15]], %[[VAL_16]]) : memref<?x?xf32>
-// CHECK:           %[[VAL_18:.*]] = dim %[[VAL_3]], %[[VAL_5]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_19:.*]] = dim %[[VAL_3]], %[[VAL_6]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_20:.*]] = alloca(%[[VAL_18]], %[[VAL_19]]) : memref<?x?xf32>
-// CHECK:           %[[VAL_21:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_22:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_23:.*]] = %[[VAL_21]] to %[[VAL_22]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_24:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_25:.*]] = %[[VAL_5]] to %[[VAL_15]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_26:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_25]]] : memref<?x?xf32>
-// CHECK:               %[[VAL_27:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:               %[[VAL_28:.*]] = addi %[[VAL_23]], %[[VAL_6]] : index
-// CHECK:               %[[VAL_29:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_30:.*]] = %[[VAL_27]] to %[[VAL_29]] step %[[VAL_6]] {
-// CHECK:                 %[[VAL_31:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_30]]] : memref<?xindex>
-// CHECK:                 %[[VAL_32:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_24]], %[[VAL_31]]] : memref<?x?xf32>
-// CHECK:                 %[[VAL_33:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_30]]] : memref<?xf32>
-// CHECK:                 %[[VAL_34:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_31]]] : memref<?x?xf32>
-// CHECK:                 %[[VAL_35:.*]] = mulf %[[VAL_26]], %[[VAL_34]] : f32
-// CHECK:                 %[[VAL_36:.*]] = mulf %[[VAL_33]], %[[VAL_35]] : f32
-// CHECK:                 %[[VAL_37:.*]] = addf %[[VAL_32]], %[[VAL_36]] : f32
-// CHECK:                 store %[[VAL_37]], %[[VAL_20]]{{\[}}%[[VAL_24]], %[[VAL_31]]] : memref<?x?xf32>
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<?x?xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_1]] : memref<?x?xf32>
+// CHECK:           %[[VAL_12:.*]] = dim %[[VAL_2]], %[[VAL_4]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_2]] : memref<?x?xf32>
+// CHECK:           %[[VAL_14:.*]] = dim %[[VAL_3]], %[[VAL_4]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_15:.*]] = dim %[[VAL_3]], %[[VAL_5]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_16:.*]] = tensor_to_memref %[[VAL_3]] : memref<?x?xf32>
+// CHECK:           %[[VAL_17:.*]] = alloc(%[[VAL_14]], %[[VAL_15]]) : memref<?x?xf32>
+// CHECK:           linalg.copy(%[[VAL_16]], %[[VAL_17]]) : memref<?x?xf32>, memref<?x?xf32>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_20:.*]] = %[[VAL_18]] to %[[VAL_19]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_21:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_20]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_22:.*]] = %[[VAL_4]] to %[[VAL_12]] step %[[VAL_5]] {
+// CHECK:               %[[VAL_23:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_21]], %[[VAL_22]]] : memref<?x?xf32>
+// CHECK:               %[[VAL_24:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<?xindex>
+// CHECK:               %[[VAL_25:.*]] = addi %[[VAL_20]], %[[VAL_5]] : index
+// CHECK:               %[[VAL_26:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_25]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_27:.*]] = %[[VAL_24]] to %[[VAL_26]] step %[[VAL_5]] {
+// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:                 %[[VAL_29:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_21]], %[[VAL_28]]] : memref<?x?xf32>
+// CHECK:                 %[[VAL_30:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_27]]] : memref<?xf32>
+// CHECK:                 %[[VAL_31:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_28]]] : memref<?x?xf32>
+// CHECK:                 %[[VAL_32:.*]] = mulf %[[VAL_23]], %[[VAL_31]] : f32
+// CHECK:                 %[[VAL_33:.*]] = mulf %[[VAL_30]], %[[VAL_32]] : f32
+// CHECK:                 %[[VAL_34:.*]] = addf %[[VAL_29]], %[[VAL_33]] : f32
+// CHECK:                 store %[[VAL_34]], %[[VAL_17]]{{\[}}%[[VAL_21]], %[[VAL_28]]] : memref<?x?xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_38:.*]] = tensor_load %[[VAL_20]] : memref<?x?xf32>
-// CHECK:           return %[[VAL_38]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_35:.*]] = tensor_load %[[VAL_17]] : memref<?x?xf32>
+// CHECK:           return %[[VAL_35]] : tensor<?x?xf32>
 // CHECK:         }
 func @sampled_dense_dense(%args: tensor<?x?xf32>,
                           %arga: tensor<?x?xf32>,
                           %argb: tensor<?x?xf32>,
                           %argx: tensor<?x?xf32>) -> tensor<?x?xf32> {
   %0 = linalg.generic #trait_sampled_dense_dense
      ins(%args, %arga, %argb: tensor<?x?xf32>, tensor<?x?xf32>, tensor<?x?xf32>)
     outs(%argx: tensor<?x?xf32>) {

 
 // CHECK-LABEL:   func @sum_kernel_with_inv(
 // CHECK-SAME:                              %[[VAL_0:.*0]]: tensor<?x?xf32>,
 // CHECK-SAME:                              %[[VAL_1:.*1]]: tensor<?x?xf32>,
 // CHECK-SAME:                              %[[VAL_2:.*2]]: tensor<?x?xf32>,
 // CHECK-SAME:                              %[[VAL_3:.*3]]: tensor<?xf32>,
 // CHECK-SAME:                              %[[VAL_4:.*4]]: tensor<f32>,
 // CHECK-SAME:                              %[[VAL_5:.*5]]: tensor<?xf32>) -> tensor<?xf32> {
-// CHECK:           %[[VAL_6:.*]] = constant 999 : index
-// CHECK:           %[[VAL_7:.*]] = constant 0 : index
-// CHECK:           %[[VAL_8:.*]] = constant true
-// CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_6]]) : memref<?xf32>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]] = alloca(%[[VAL_6]]) : memref<?xf32>
-// CHECK:           %[[VAL_18:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]] = alloca(%[[VAL_6]]) : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]] = alloca(%[[VAL_6]]) : memref<?xf32>
-// CHECK:           %[[VAL_21:.*]] = dim %[[VAL_3]], %[[VAL_7]] : tensor<?xf32>
-// CHECK:           %[[VAL_22:.*]] = alloca(%[[VAL_21]]) : memref<?xf32>
-// CHECK:           %[[VAL_23:.*]] = alloca() : memref<f32>
-// CHECK:           %[[VAL_24:.*]] = dim %[[VAL_5]], %[[VAL_7]] : tensor<?xf32>
-// CHECK:           %[[VAL_25:.*]] = alloca(%[[VAL_24]]) : memref<?xf32>
-// CHECK:           %[[VAL_26:.*]] = load %[[VAL_23]][] : memref<f32>
-// CHECK:           %[[VAL_27:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           %[[VAL_28:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
-// CHECK:           %[[VAL_29:.*]]:2 = scf.while (%[[VAL_30:.*]] = %[[VAL_27]], %[[VAL_31:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
-// CHECK:             %[[VAL_32:.*]] = cmpi ult, %[[VAL_30]], %[[VAL_28]] : index
-// CHECK:             scf.condition(%[[VAL_32]]) %[[VAL_30]], %[[VAL_31]] : index, index
+// CHECK:           %[[VAL_6:.*]] = constant 0 : index
+// CHECK:           %[[VAL_7:.*]] = constant true
+// CHECK:           %[[VAL_8:.*]] = constant 1 : index
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_6]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_6]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_8]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_8]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<?x?xf32> to memref<?xf32>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_8]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_8]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<?x?xf32> to memref<?xf32>
+// CHECK:           %[[VAL_17:.*]] = linalg.sparse_pointers %[[VAL_2]], %[[VAL_8]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = linalg.sparse_indices %[[VAL_2]], %[[VAL_8]] : tensor<?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = linalg.sparse_values %[[VAL_2]] : tensor<?x?xf32> to memref<?xf32>
+// CHECK:           %[[VAL_20:.*]] = tensor_to_memref %[[VAL_3]] : memref<?xf32>
+// CHECK:           %[[VAL_21:.*]] = tensor_to_memref %[[VAL_4]] : memref<f32>
+// CHECK:           %[[VAL_22:.*]] = dim %[[VAL_5]], %[[VAL_6]] : tensor<?xf32>
+// CHECK:           %[[VAL_23:.*]] = tensor_to_memref %[[VAL_5]] : memref<?xf32>
+// CHECK:           %[[VAL_24:.*]] = alloc(%[[VAL_22]]) : memref<?xf32>
+// CHECK:           linalg.copy(%[[VAL_23]], %[[VAL_24]]) : memref<?xf32>, memref<?xf32>
+// CHECK:           %[[VAL_25:.*]] = load %[[VAL_21]][] : memref<f32>
+// CHECK:           %[[VAL_26:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           %[[VAL_27:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_8]]] : memref<?xindex>
+// CHECK:           %[[VAL_28:.*]]:2 = scf.while (%[[VAL_29:.*]] = %[[VAL_26]], %[[VAL_30:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
+// CHECK:             %[[VAL_31:.*]] = cmpi ult, %[[VAL_29]], %[[VAL_27]] : index
+// CHECK:             scf.condition(%[[VAL_31]]) %[[VAL_29]], %[[VAL_30]] : index, index
 // CHECK:           } do {
-// CHECK:           ^bb0(%[[VAL_33:.*]]: index, %[[VAL_34:.*]]: index):
-// CHECK:             %[[VAL_35:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_33]]] : memref<?xindex>
-// CHECK:             %[[VAL_36:.*]] = cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
-// CHECK:             scf.if %[[VAL_36]] {
-// CHECK:               %[[VAL_37:.*]] = load %[[VAL_22]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:               %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_33]]] : memref<?xindex>
-// CHECK:               %[[VAL_39:.*]] = addi %[[VAL_33]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_40:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_39]]] : memref<?xindex>
-// CHECK:               %[[VAL_41:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_34]]] : memref<?xindex>
-// CHECK:               %[[VAL_42:.*]] = addi %[[VAL_34]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_43:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_42]]] : memref<?xindex>
-// CHECK:               %[[VAL_44:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_34]]] : memref<?xindex>
-// CHECK:               %[[VAL_45:.*]] = addi %[[VAL_34]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_46:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_45]]] : memref<?xindex>
-// CHECK:               %[[VAL_47:.*]]:4 = scf.while (%[[VAL_48:.*]] = %[[VAL_38]], %[[VAL_49:.*]] = %[[VAL_41]], %[[VAL_50:.*]] = %[[VAL_44]], %[[VAL_51:.*]] = %[[VAL_7]]) : (index, index, index, index) -> (index, index, index, index) {
-// CHECK:                 %[[VAL_52:.*]] = cmpi ult, %[[VAL_48]], %[[VAL_40]] : index
-// CHECK:                 %[[VAL_53:.*]] = cmpi ult, %[[VAL_49]], %[[VAL_43]] : index
-// CHECK:                 %[[VAL_54:.*]] = and %[[VAL_52]], %[[VAL_53]] : i1
-// CHECK:                 %[[VAL_55:.*]] = cmpi ult, %[[VAL_50]], %[[VAL_46]] : index
-// CHECK:                 %[[VAL_56:.*]] = and %[[VAL_54]], %[[VAL_55]] : i1
-// CHECK:                 scf.condition(%[[VAL_56]]) %[[VAL_48]], %[[VAL_49]], %[[VAL_50]], %[[VAL_51]] : index, index, index, index
+// CHECK:           ^bb0(%[[VAL_32:.*]]: index, %[[VAL_33:.*]]: index):
+// CHECK:             %[[VAL_34:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_32]]] : memref<?xindex>
+// CHECK:             %[[VAL_35:.*]] = cmpi eq, %[[VAL_34]], %[[VAL_33]] : index
+// CHECK:             scf.if %[[VAL_35]] {
+// CHECK:               %[[VAL_36:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:               %[[VAL_37:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_32]]] : memref<?xindex>
+// CHECK:               %[[VAL_38:.*]] = addi %[[VAL_32]], %[[VAL_8]] : index
+// CHECK:               %[[VAL_39:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_38]]] : memref<?xindex>
+// CHECK:               %[[VAL_40:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_33]]] : memref<?xindex>
+// CHECK:               %[[VAL_41:.*]] = addi %[[VAL_33]], %[[VAL_8]] : index
+// CHECK:               %[[VAL_42:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_41]]] : memref<?xindex>
+// CHECK:               %[[VAL_43:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_33]]] : memref<?xindex>
+// CHECK:               %[[VAL_44:.*]] = addi %[[VAL_33]], %[[VAL_8]] : index
+// CHECK:               %[[VAL_45:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_44]]] : memref<?xindex>
+// CHECK:               %[[VAL_46:.*]]:4 = scf.while (%[[VAL_47:.*]] = %[[VAL_37]], %[[VAL_48:.*]] = %[[VAL_40]], %[[VAL_49:.*]] = %[[VAL_43]], %[[VAL_50:.*]] = %[[VAL_6]]) : (index, index, index, index) -> (index, index, index, index) {
+// CHECK:                 %[[VAL_51:.*]] = cmpi ult, %[[VAL_47]], %[[VAL_39]] : index
+// CHECK:                 %[[VAL_52:.*]] = cmpi ult, %[[VAL_48]], %[[VAL_42]] : index
+// CHECK:                 %[[VAL_53:.*]] = and %[[VAL_51]], %[[VAL_52]] : i1
+// CHECK:                 %[[VAL_54:.*]] = cmpi ult, %[[VAL_49]], %[[VAL_45]] : index
+// CHECK:                 %[[VAL_55:.*]] = and %[[VAL_53]], %[[VAL_54]] : i1
+// CHECK:                 scf.condition(%[[VAL_55]]) %[[VAL_47]], %[[VAL_48]], %[[VAL_49]], %[[VAL_50]] : index, index, index, index
 // CHECK:               } do {
-// CHECK:               ^bb0(%[[VAL_57:.*]]: index, %[[VAL_58:.*]]: index, %[[VAL_59:.*]]: index, %[[VAL_60:.*]]: index):
-// CHECK:                 %[[VAL_61:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_57]]] : memref<?xindex>
-// CHECK:                 %[[VAL_62:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_58]]] : memref<?xindex>
-// CHECK:                 %[[VAL_63:.*]] = load %[[VAL_19]]{{\[}}%[[VAL_59]]] : memref<?xindex>
-// CHECK:                 %[[VAL_64:.*]] = cmpi eq, %[[VAL_61]], %[[VAL_60]] : index
-// CHECK:                 %[[VAL_65:.*]] = cmpi eq, %[[VAL_62]], %[[VAL_60]] : index
-// CHECK:                 %[[VAL_66:.*]] = and %[[VAL_64]], %[[VAL_65]] : i1
-// CHECK:                 %[[VAL_67:.*]] = cmpi eq, %[[VAL_63]], %[[VAL_60]] : index
-// CHECK:                 %[[VAL_68:.*]] = and %[[VAL_66]], %[[VAL_67]] : i1
-// CHECK:                 scf.if %[[VAL_68]] {
-// CHECK:                   %[[VAL_69:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                   %[[VAL_70:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_57]]] : memref<?xf32>
-// CHECK:                   %[[VAL_71:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_58]]] : memref<?xf32>
-// CHECK:                   %[[VAL_72:.*]] = mulf %[[VAL_70]], %[[VAL_71]] : f32
-// CHECK:                   %[[VAL_73:.*]] = mulf %[[VAL_72]], %[[VAL_37]] : f32
-// CHECK:                   %[[VAL_74:.*]] = mulf %[[VAL_73]], %[[VAL_26]] : f32
-// CHECK:                   %[[VAL_75:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_59]]] : memref<?xf32>
-// CHECK:                   %[[VAL_76:.*]] = addf %[[VAL_74]], %[[VAL_75]] : f32
-// CHECK:                   %[[VAL_77:.*]] = addf %[[VAL_69]], %[[VAL_76]] : f32
-// CHECK:                   store %[[VAL_77]], %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                 } else {
-// CHECK:                   %[[VAL_78:.*]] = cmpi eq, %[[VAL_61]], %[[VAL_60]] : index
-// CHECK:                   %[[VAL_79:.*]] = cmpi eq, %[[VAL_62]], %[[VAL_60]] : index
-// CHECK:                   %[[VAL_80:.*]] = and %[[VAL_78]], %[[VAL_79]] : i1
-// CHECK:                   scf.if %[[VAL_80]] {
-// CHECK:                     %[[VAL_81:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                     %[[VAL_82:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_57]]] : memref<?xf32>
-// CHECK:                     %[[VAL_83:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_58]]] : memref<?xf32>
-// CHECK:                     %[[VAL_84:.*]] = mulf %[[VAL_82]], %[[VAL_83]] : f32
-// CHECK:                     %[[VAL_85:.*]] = mulf %[[VAL_84]], %[[VAL_37]] : f32
-// CHECK:                     %[[VAL_86:.*]] = mulf %[[VAL_85]], %[[VAL_26]] : f32
-// CHECK:                     %[[VAL_87:.*]] = addf %[[VAL_81]], %[[VAL_86]] : f32
-// CHECK:                     store %[[VAL_87]], %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                   } else {
-// CHECK:                     %[[VAL_88:.*]] = cmpi eq, %[[VAL_63]], %[[VAL_60]] : index
-// CHECK:                     scf.if %[[VAL_88]] {
-// CHECK:                       %[[VAL_89:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                       %[[VAL_90:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_59]]] : memref<?xf32>
-// CHECK:                       %[[VAL_91:.*]] = addf %[[VAL_89]], %[[VAL_90]] : f32
-// CHECK:                       store %[[VAL_91]], %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
+// CHECK:               ^bb0(%[[VAL_56:.*]]: index, %[[VAL_57:.*]]: index, %[[VAL_58:.*]]: index, %[[VAL_59:.*]]: index):
+// CHECK:                 %[[VAL_60:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_56]]] : memref<?xindex>
+// CHECK:                 %[[VAL_61:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_57]]] : memref<?xindex>
+// CHECK:                 %[[VAL_62:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_58]]] : memref<?xindex>
+// CHECK:                 %[[VAL_63:.*]] = cmpi eq, %[[VAL_60]], %[[VAL_59]] : index
+// CHECK:                 %[[VAL_64:.*]] = cmpi eq, %[[VAL_61]], %[[VAL_59]] : index
+// CHECK:                 %[[VAL_65:.*]] = and %[[VAL_63]], %[[VAL_64]] : i1
+// CHECK:                 %[[VAL_66:.*]] = cmpi eq, %[[VAL_62]], %[[VAL_59]] : index
+// CHECK:                 %[[VAL_67:.*]] = and %[[VAL_65]], %[[VAL_66]] : i1
+// CHECK:                 scf.if %[[VAL_67]] {
+// CHECK:                   %[[VAL_68:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                   %[[VAL_69:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_56]]] : memref<?xf32>
+// CHECK:                   %[[VAL_70:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_57]]] : memref<?xf32>
+// CHECK:                   %[[VAL_71:.*]] = mulf %[[VAL_69]], %[[VAL_70]] : f32
+// CHECK:                   %[[VAL_72:.*]] = mulf %[[VAL_71]], %[[VAL_36]] : f32
+// CHECK:                   %[[VAL_73:.*]] = mulf %[[VAL_72]], %[[VAL_25]] : f32
+// CHECK:                   %[[VAL_74:.*]] = load %[[VAL_19]]{{\[}}%[[VAL_58]]] : memref<?xf32>
+// CHECK:                   %[[VAL_75:.*]] = addf %[[VAL_73]], %[[VAL_74]] : f32
+// CHECK:                   %[[VAL_76:.*]] = addf %[[VAL_68]], %[[VAL_75]] : f32
+// CHECK:                   store %[[VAL_76]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                 } else {
+// CHECK:                   %[[VAL_77:.*]] = cmpi eq, %[[VAL_60]], %[[VAL_59]] : index
+// CHECK:                   %[[VAL_78:.*]] = cmpi eq, %[[VAL_61]], %[[VAL_59]] : index
+// CHECK:                   %[[VAL_79:.*]] = and %[[VAL_77]], %[[VAL_78]] : i1
+// CHECK:                   scf.if %[[VAL_79]] {
+// CHECK:                     %[[VAL_80:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                     %[[VAL_81:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_56]]] : memref<?xf32>
+// CHECK:                     %[[VAL_82:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_57]]] : memref<?xf32>
+// CHECK:                     %[[VAL_83:.*]] = mulf %[[VAL_81]], %[[VAL_82]] : f32
+// CHECK:                     %[[VAL_84:.*]] = mulf %[[VAL_83]], %[[VAL_36]] : f32
+// CHECK:                     %[[VAL_85:.*]] = mulf %[[VAL_84]], %[[VAL_25]] : f32
+// CHECK:                     %[[VAL_86:.*]] = addf %[[VAL_80]], %[[VAL_85]] : f32
+// CHECK:                     store %[[VAL_86]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                   } else {
+// CHECK:                     %[[VAL_87:.*]] = cmpi eq, %[[VAL_62]], %[[VAL_59]] : index
+// CHECK:                     scf.if %[[VAL_87]] {
+// CHECK:                       %[[VAL_88:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                       %[[VAL_89:.*]] = load %[[VAL_19]]{{\[}}%[[VAL_58]]] : memref<?xf32>
+// CHECK:                       %[[VAL_90:.*]] = addf %[[VAL_88]], %[[VAL_89]] : f32
+// CHECK:                       store %[[VAL_90]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
 // CHECK:                     } else {
 // CHECK:                     }
 // CHECK:                   }
 // CHECK:                 }
-// CHECK:                 %[[VAL_92:.*]] = cmpi eq, %[[VAL_61]], %[[VAL_60]] : index
-// CHECK:                 %[[VAL_93:.*]] = addi %[[VAL_57]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_94:.*]] = select %[[VAL_92]], %[[VAL_93]], %[[VAL_57]] : index
-// CHECK:                 %[[VAL_95:.*]] = cmpi eq, %[[VAL_62]], %[[VAL_60]] : index
-// CHECK:                 %[[VAL_96:.*]] = addi %[[VAL_58]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_97:.*]] = select %[[VAL_95]], %[[VAL_96]], %[[VAL_58]] : index
-// CHECK:                 %[[VAL_98:.*]] = cmpi eq, %[[VAL_63]], %[[VAL_60]] : index
-// CHECK:                 %[[VAL_99:.*]] = addi %[[VAL_59]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_100:.*]] = select %[[VAL_98]], %[[VAL_99]], %[[VAL_59]] : index
-// CHECK:                 %[[VAL_101:.*]] = addi %[[VAL_60]], %[[VAL_9]] : index
-// CHECK:                 scf.yield %[[VAL_94]], %[[VAL_97]], %[[VAL_100]], %[[VAL_101]] : index, index, index, index
-// CHECK:               }
-// CHECK:               %[[VAL_102:.*]]:3 = scf.while (%[[VAL_103:.*]] = %[[VAL_104:.*]]#0, %[[VAL_105:.*]] = %[[VAL_104]]#1, %[[VAL_106:.*]] = %[[VAL_104]]#3) : (index, index, index) -> (index, index, index) {
-// CHECK:                 %[[VAL_107:.*]] = cmpi ult, %[[VAL_103]], %[[VAL_40]] : index
-// CHECK:                 %[[VAL_108:.*]] = cmpi ult, %[[VAL_105]], %[[VAL_43]] : index
-// CHECK:                 %[[VAL_109:.*]] = and %[[VAL_107]], %[[VAL_108]] : i1
-// CHECK:                 scf.condition(%[[VAL_109]]) %[[VAL_103]], %[[VAL_105]], %[[VAL_106]] : index, index, index
+// CHECK:                 %[[VAL_91:.*]] = cmpi eq, %[[VAL_60]], %[[VAL_59]] : index
+// CHECK:                 %[[VAL_92:.*]] = addi %[[VAL_56]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_93:.*]] = select %[[VAL_91]], %[[VAL_92]], %[[VAL_56]] : index
+// CHECK:                 %[[VAL_94:.*]] = cmpi eq, %[[VAL_61]], %[[VAL_59]] : index
+// CHECK:                 %[[VAL_95:.*]] = addi %[[VAL_57]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_96:.*]] = select %[[VAL_94]], %[[VAL_95]], %[[VAL_57]] : index
+// CHECK:                 %[[VAL_97:.*]] = cmpi eq, %[[VAL_62]], %[[VAL_59]] : index
+// CHECK:                 %[[VAL_98:.*]] = addi %[[VAL_58]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_99:.*]] = select %[[VAL_97]], %[[VAL_98]], %[[VAL_58]] : index
+// CHECK:                 %[[VAL_100:.*]] = addi %[[VAL_59]], %[[VAL_8]] : index
+// CHECK:                 scf.yield %[[VAL_93]], %[[VAL_96]], %[[VAL_99]], %[[VAL_100]] : index, index, index, index
+// CHECK:               }
+// CHECK:               %[[VAL_101:.*]]:3 = scf.while (%[[VAL_102:.*]] = %[[VAL_103:.*]]#0, %[[VAL_104:.*]] = %[[VAL_103]]#1, %[[VAL_105:.*]] = %[[VAL_103]]#3) : (index, index, index) -> (index, index, index) {
+// CHECK:                 %[[VAL_106:.*]] = cmpi ult, %[[VAL_102]], %[[VAL_39]] : index
+// CHECK:                 %[[VAL_107:.*]] = cmpi ult, %[[VAL_104]], %[[VAL_42]] : index
+// CHECK:                 %[[VAL_108:.*]] = and %[[VAL_106]], %[[VAL_107]] : i1
+// CHECK:                 scf.condition(%[[VAL_108]]) %[[VAL_102]], %[[VAL_104]], %[[VAL_105]] : index, index, index
 // CHECK:               } do {
-// CHECK:               ^bb0(%[[VAL_110:.*]]: index, %[[VAL_111:.*]]: index, %[[VAL_112:.*]]: index):
-// CHECK:                 %[[VAL_113:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_110]]] : memref<?xindex>
-// CHECK:                 %[[VAL_114:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_111]]] : memref<?xindex>
-// CHECK:                 %[[VAL_115:.*]] = cmpi eq, %[[VAL_113]], %[[VAL_112]] : index
-// CHECK:                 %[[VAL_116:.*]] = cmpi eq, %[[VAL_114]], %[[VAL_112]] : index
-// CHECK:                 %[[VAL_117:.*]] = and %[[VAL_115]], %[[VAL_116]] : i1
-// CHECK:                 scf.if %[[VAL_117]] {
-// CHECK:                   %[[VAL_118:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                   %[[VAL_119:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_110]]] : memref<?xf32>
-// CHECK:                   %[[VAL_120:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_111]]] : memref<?xf32>
-// CHECK:                   %[[VAL_121:.*]] = mulf %[[VAL_119]], %[[VAL_120]] : f32
-// CHECK:                   %[[VAL_122:.*]] = mulf %[[VAL_121]], %[[VAL_37]] : f32
-// CHECK:                   %[[VAL_123:.*]] = mulf %[[VAL_122]], %[[VAL_26]] : f32
-// CHECK:                   %[[VAL_124:.*]] = addf %[[VAL_118]], %[[VAL_123]] : f32
-// CHECK:                   store %[[VAL_124]], %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                 } else {
-// CHECK:                 }
-// CHECK:                 %[[VAL_125:.*]] = cmpi eq, %[[VAL_113]], %[[VAL_112]] : index
-// CHECK:                 %[[VAL_126:.*]] = addi %[[VAL_110]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_127:.*]] = select %[[VAL_125]], %[[VAL_126]], %[[VAL_110]] : index
-// CHECK:                 %[[VAL_128:.*]] = cmpi eq, %[[VAL_114]], %[[VAL_112]] : index
-// CHECK:                 %[[VAL_129:.*]] = addi %[[VAL_111]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_130:.*]] = select %[[VAL_128]], %[[VAL_129]], %[[VAL_111]] : index
-// CHECK:                 %[[VAL_131:.*]] = addi %[[VAL_112]], %[[VAL_9]] : index
-// CHECK:                 scf.yield %[[VAL_127]], %[[VAL_130]], %[[VAL_131]] : index, index, index
-// CHECK:               }
-// CHECK:               %[[VAL_132:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:               %[[VAL_133:.*]] = scf.for %[[VAL_134:.*]] = %[[VAL_135:.*]]#2 to %[[VAL_46]] step %[[VAL_9]] iter_args(%[[VAL_136:.*]] = %[[VAL_132]]) -> (f32) {
-// CHECK:                 %[[VAL_137:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_134]]] : memref<?xf32>
-// CHECK:                 %[[VAL_138:.*]] = addf %[[VAL_136]], %[[VAL_137]] : f32
-// CHECK:                 scf.yield %[[VAL_138]] : f32
-// CHECK:               }
-// CHECK:               store %[[VAL_139:.*]], %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:             } else {
-// CHECK:               scf.if %[[VAL_8]] {
-// CHECK:                 %[[VAL_140:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_34]]] : memref<?xindex>
-// CHECK:                 %[[VAL_141:.*]] = addi %[[VAL_34]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_142:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_141]]] : memref<?xindex>
-// CHECK:                 %[[VAL_143:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:                 %[[VAL_144:.*]] = scf.for %[[VAL_145:.*]] = %[[VAL_140]] to %[[VAL_142]] step %[[VAL_9]] iter_args(%[[VAL_146:.*]] = %[[VAL_143]]) -> (f32) {
-// CHECK:                   %[[VAL_147:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_145]]] : memref<?xf32>
-// CHECK:                   %[[VAL_148:.*]] = addf %[[VAL_146]], %[[VAL_147]] : f32
-// CHECK:                   scf.yield %[[VAL_148]] : f32
-// CHECK:                 }
-// CHECK:                 store %[[VAL_149:.*]], %[[VAL_25]]{{\[}}%[[VAL_34]]] : memref<?xf32>
-// CHECK:               } else {
-// CHECK:               }
-// CHECK:             }
-// CHECK:             %[[VAL_150:.*]] = cmpi eq, %[[VAL_35]], %[[VAL_34]] : index
-// CHECK:             %[[VAL_151:.*]] = addi %[[VAL_33]], %[[VAL_9]] : index
-// CHECK:             %[[VAL_152:.*]] = select %[[VAL_150]], %[[VAL_151]], %[[VAL_33]] : index
-// CHECK:             %[[VAL_153:.*]] = addi %[[VAL_34]], %[[VAL_9]] : index
-// CHECK:             scf.yield %[[VAL_152]], %[[VAL_153]] : index, index
-// CHECK:           }
-// CHECK:           scf.for %[[VAL_154:.*]] = %[[VAL_155:.*]]#1 to %[[VAL_24]] step %[[VAL_9]] {
-// CHECK:             %[[VAL_156:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_154]]] : memref<?xindex>
-// CHECK:             %[[VAL_157:.*]] = addi %[[VAL_154]], %[[VAL_9]] : index
-// CHECK:             %[[VAL_158:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_157]]] : memref<?xindex>
-// CHECK:             %[[VAL_159:.*]] = load %[[VAL_25]]{{\[}}%[[VAL_154]]] : memref<?xf32>
-// CHECK:             %[[VAL_160:.*]] = scf.for %[[VAL_161:.*]] = %[[VAL_156]] to %[[VAL_158]] step %[[VAL_9]] iter_args(%[[VAL_162:.*]] = %[[VAL_159]]) -> (f32) {
-// CHECK:               %[[VAL_163:.*]] = load %[[VAL_20]]{{\[}}%[[VAL_161]]] : memref<?xf32>
-// CHECK:               %[[VAL_164:.*]] = addf %[[VAL_162]], %[[VAL_163]] : f32
-// CHECK:               scf.yield %[[VAL_164]] : f32
+// CHECK:               ^bb0(%[[VAL_109:.*]]: index, %[[VAL_110:.*]]: index, %[[VAL_111:.*]]: index):
+// CHECK:                 %[[VAL_112:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_109]]] : memref<?xindex>
+// CHECK:                 %[[VAL_113:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_110]]] : memref<?xindex>
+// CHECK:                 %[[VAL_114:.*]] = cmpi eq, %[[VAL_112]], %[[VAL_111]] : index
+// CHECK:                 %[[VAL_115:.*]] = cmpi eq, %[[VAL_113]], %[[VAL_111]] : index
+// CHECK:                 %[[VAL_116:.*]] = and %[[VAL_114]], %[[VAL_115]] : i1
+// CHECK:                 scf.if %[[VAL_116]] {
+// CHECK:                   %[[VAL_117:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                   %[[VAL_118:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_109]]] : memref<?xf32>
+// CHECK:                   %[[VAL_119:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_110]]] : memref<?xf32>
+// CHECK:                   %[[VAL_120:.*]] = mulf %[[VAL_118]], %[[VAL_119]] : f32
+// CHECK:                   %[[VAL_121:.*]] = mulf %[[VAL_120]], %[[VAL_36]] : f32
+// CHECK:                   %[[VAL_122:.*]] = mulf %[[VAL_121]], %[[VAL_25]] : f32
+// CHECK:                   %[[VAL_123:.*]] = addf %[[VAL_117]], %[[VAL_122]] : f32
+// CHECK:                   store %[[VAL_123]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                 } else {
+// CHECK:                 }
+// CHECK:                 %[[VAL_124:.*]] = cmpi eq, %[[VAL_112]], %[[VAL_111]] : index
+// CHECK:                 %[[VAL_125:.*]] = addi %[[VAL_109]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_126:.*]] = select %[[VAL_124]], %[[VAL_125]], %[[VAL_109]] : index
+// CHECK:                 %[[VAL_127:.*]] = cmpi eq, %[[VAL_113]], %[[VAL_111]] : index
+// CHECK:                 %[[VAL_128:.*]] = addi %[[VAL_110]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_129:.*]] = select %[[VAL_127]], %[[VAL_128]], %[[VAL_110]] : index
+// CHECK:                 %[[VAL_130:.*]] = addi %[[VAL_111]], %[[VAL_8]] : index
+// CHECK:                 scf.yield %[[VAL_126]], %[[VAL_129]], %[[VAL_130]] : index, index, index
+// CHECK:               }
+// CHECK:               %[[VAL_131:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:               %[[VAL_132:.*]] = scf.for %[[VAL_133:.*]] = %[[VAL_134:.*]]#2 to %[[VAL_45]] step %[[VAL_8]] iter_args(%[[VAL_135:.*]] = %[[VAL_131]]) -> (f32) {
+// CHECK:                 %[[VAL_136:.*]] = load %[[VAL_19]]{{\[}}%[[VAL_133]]] : memref<?xf32>
+// CHECK:                 %[[VAL_137:.*]] = addf %[[VAL_135]], %[[VAL_136]] : f32
+// CHECK:                 scf.yield %[[VAL_137]] : f32
+// CHECK:               }
+// CHECK:               store %[[VAL_138:.*]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:             } else {
+// CHECK:               scf.if %[[VAL_7]] {
+// CHECK:                 %[[VAL_139:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_33]]] : memref<?xindex>
+// CHECK:                 %[[VAL_140:.*]] = addi %[[VAL_33]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_141:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_140]]] : memref<?xindex>
+// CHECK:                 %[[VAL_142:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:                 %[[VAL_143:.*]] = scf.for %[[VAL_144:.*]] = %[[VAL_139]] to %[[VAL_141]] step %[[VAL_8]] iter_args(%[[VAL_145:.*]] = %[[VAL_142]]) -> (f32) {
+// CHECK:                   %[[VAL_146:.*]] = load %[[VAL_19]]{{\[}}%[[VAL_144]]] : memref<?xf32>
+// CHECK:                   %[[VAL_147:.*]] = addf %[[VAL_145]], %[[VAL_146]] : f32
+// CHECK:                   scf.yield %[[VAL_147]] : f32
+// CHECK:                 }
+// CHECK:                 store %[[VAL_148:.*]], %[[VAL_24]]{{\[}}%[[VAL_33]]] : memref<?xf32>
+// CHECK:               } else {
+// CHECK:               }
+// CHECK:             }
+// CHECK:             %[[VAL_149:.*]] = cmpi eq, %[[VAL_34]], %[[VAL_33]] : index
+// CHECK:             %[[VAL_150:.*]] = addi %[[VAL_32]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_151:.*]] = select %[[VAL_149]], %[[VAL_150]], %[[VAL_32]] : index
+// CHECK:             %[[VAL_152:.*]] = addi %[[VAL_33]], %[[VAL_8]] : index
+// CHECK:             scf.yield %[[VAL_151]], %[[VAL_152]] : index, index
+// CHECK:           }
+// CHECK:           scf.for %[[VAL_153:.*]] = %[[VAL_154:.*]]#1 to %[[VAL_22]] step %[[VAL_8]] {
+// CHECK:             %[[VAL_155:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_153]]] : memref<?xindex>
+// CHECK:             %[[VAL_156:.*]] = addi %[[VAL_153]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_157:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_156]]] : memref<?xindex>
+// CHECK:             %[[VAL_158:.*]] = load %[[VAL_24]]{{\[}}%[[VAL_153]]] : memref<?xf32>
+// CHECK:             %[[VAL_159:.*]] = scf.for %[[VAL_160:.*]] = %[[VAL_155]] to %[[VAL_157]] step %[[VAL_8]] iter_args(%[[VAL_161:.*]] = %[[VAL_158]]) -> (f32) {
+// CHECK:               %[[VAL_162:.*]] = load %[[VAL_19]]{{\[}}%[[VAL_160]]] : memref<?xf32>
+// CHECK:               %[[VAL_163:.*]] = addf %[[VAL_161]], %[[VAL_162]] : f32
+// CHECK:               scf.yield %[[VAL_163]] : f32
 // CHECK:             }
-// CHECK:             store %[[VAL_165:.*]], %[[VAL_25]]{{\[}}%[[VAL_154]]] : memref<?xf32>
+// CHECK:             store %[[VAL_164:.*]], %[[VAL_24]]{{\[}}%[[VAL_153]]] : memref<?xf32>
 // CHECK:           }
-// CHECK:           %[[VAL_166:.*]] = tensor_load %[[VAL_25]] : memref<?xf32>
-// CHECK:           return %[[VAL_166]] : tensor<?xf32>
+// CHECK:           %[[VAL_165:.*]] = tensor_load %[[VAL_24]] : memref<?xf32>
+// CHECK:           return %[[VAL_165]] : tensor<?xf32>
 // CHECK:         }
 func @sum_kernel_with_inv(%arga: tensor<?x?xf32>,
                           %argb: tensor<?x?xf32>,
                           %argc: tensor<?x?xf32>,
                           %argd: tensor<?xf32>,
                           %arge: tensor<f32>,
                           %argx: tensor<?xf32>) -> tensor<?xf32> {
   %0 = linalg.generic #trait_sum_kernel_with_inv

mlir/test/Dialect/Linalg/sparse_3d.mlir

 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 16 : index
 // CHECK:           %[[VAL_5:.*]] = constant 8 : index
 // CHECK:           %[[VAL_6:.*]] = constant 0 : index
 // CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
-// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:               scf.for %[[VAL_13:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
-// CHECK:                 %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]], %[[VAL_13]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_11]], %[[VAL_12]], %[[VAL_13]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_16:.*]] = addf %[[VAL_14]], %[[VAL_15]] : f32
-// CHECK:                 store %[[VAL_16]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]], %[[VAL_13]]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_0]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_11:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<32x16x8xf32>, 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:               scf.for %[[VAL_14:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
+// CHECK:                 %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_14]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_14]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_17:.*]] = addf %[[VAL_15]], %[[VAL_16]] : f32
+// CHECK:                 store %[[VAL_17]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_14]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_17:.*]] = tensor_load %[[VAL_10]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_17]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_18:.*]] = tensor_load %[[VAL_11]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_18]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_ddd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_ddd
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_ddd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
 // CHECK:           %[[VAL_3:.*]] = constant 32 : index
 // CHECK:           %[[VAL_4:.*]] = constant 16 : index
 // CHECK:           %[[VAL_5:.*]] = constant 8 : index
 // CHECK:           %[[VAL_6:.*]] = constant 0 : index
 // CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_10:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_11:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_7]] {
-// CHECK:             scf.for %[[VAL_12:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:               scf.for %[[VAL_13:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
-// CHECK:                 %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_11]], %[[VAL_12]], %[[VAL_13]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_11]], %[[VAL_12]], %[[VAL_13]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_16:.*]] = mulf %[[VAL_14]], %[[VAL_15]] : f32
-// CHECK:                 store %[[VAL_16]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_12]], %[[VAL_13]]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_0]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_11:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_10]], %[[VAL_11]]) : memref<32x16x8xf32>, 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:               scf.for %[[VAL_14:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
+// CHECK:                 %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_14]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_14]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_17:.*]] = mulf %[[VAL_15]], %[[VAL_16]] : f32
+// CHECK:                 store %[[VAL_17]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_14]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_17:.*]] = tensor_load %[[VAL_10]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_17]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_18:.*]] = tensor_load %[[VAL_11]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_18]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @mul_ddd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_ddd
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_dds = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_dds(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 32 : index
 // CHECK:           %[[VAL_5:.*]] = constant 16 : index
 // CHECK:           %[[VAL_6:.*]] = constant 8 : index
 // CHECK:           %[[VAL_7:.*]] = constant 0 : index
 // CHECK:           %[[VAL_8:.*]] = constant true
 // CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_9]] {
-// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:               %[[VAL_17:.*]] = muli %[[VAL_15]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_18:.*]] = addi %[[VAL_17]], %[[VAL_16]] : index
-// CHECK:               %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:               %[[VAL_20:.*]] = addi %[[VAL_18]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_21:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<?xindex>
-// CHECK:               %[[VAL_22:.*]]:2 = scf.while (%[[VAL_23:.*]] = %[[VAL_19]], %[[VAL_24:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
-// CHECK:                 %[[VAL_25:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_21]] : index
-// CHECK:                 scf.condition(%[[VAL_25]]) %[[VAL_23]], %[[VAL_24]] : index, index
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_15:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_14]], %[[VAL_15]]) : memref<32x16x8xf32>, 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:.*]] = muli %[[VAL_16]], %[[VAL_5]] : index
+// CHECK:               %[[VAL_19:.*]] = addi %[[VAL_18]], %[[VAL_17]] : index
+// CHECK:               %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:               %[[VAL_21:.*]] = addi %[[VAL_19]], %[[VAL_9]] : index
+// CHECK:               %[[VAL_22:.*]] = 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:.*]] = cmpi ult, %[[VAL_24]], %[[VAL_22]] : index
+// CHECK:                 scf.condition(%[[VAL_26]]) %[[VAL_24]], %[[VAL_25]] : index, index
 // CHECK:               } do {
-// CHECK:               ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
-// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
-// CHECK:                 %[[VAL_29:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
-// CHECK:                 scf.if %[[VAL_29]] {
-// CHECK:                   %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xf32>
-// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_27]]] : memref<32x16x8xf32>
-// CHECK:                   %[[VAL_32:.*]] = addf %[[VAL_30]], %[[VAL_31]] : f32
-// CHECK:                   store %[[VAL_32]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK:               ^bb0(%[[VAL_27:.*]]: index, %[[VAL_28:.*]]: index):
+// CHECK:                 %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:                 %[[VAL_30:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_28]] : index
+// CHECK:                 scf.if %[[VAL_30]] {
+// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xf32>
+// CHECK:                   %[[VAL_32:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
+// CHECK:                   %[[VAL_33:.*]] = addf %[[VAL_31]], %[[VAL_32]] : f32
+// CHECK:                   store %[[VAL_33]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
 // CHECK:                 } else {
 // CHECK:                   scf.if %[[VAL_8]] {
-// CHECK:                     %[[VAL_33:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_27]]] : memref<32x16x8xf32>
-// CHECK:                     store %[[VAL_33]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK:                     %[[VAL_34:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
+// CHECK:                     store %[[VAL_34]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_28]]] : memref<32x16x8xf32>
 // CHECK:                   } else {
 // CHECK:                   }
 // CHECK:                 }
-// CHECK:                 %[[VAL_34:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
-// CHECK:                 %[[VAL_35:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_36:.*]] = select %[[VAL_34]], %[[VAL_35]], %[[VAL_26]] : index
-// CHECK:                 %[[VAL_37:.*]] = addi %[[VAL_27]], %[[VAL_9]] : index
-// CHECK:                 scf.yield %[[VAL_36]], %[[VAL_37]] : index, index
+// CHECK:                 %[[VAL_35:.*]] = cmpi eq, %[[VAL_29]], %[[VAL_28]] : index
+// CHECK:                 %[[VAL_36:.*]] = addi %[[VAL_27]], %[[VAL_9]] : index
+// CHECK:                 %[[VAL_37:.*]] = select %[[VAL_35]], %[[VAL_36]], %[[VAL_27]] : index
+// CHECK:                 %[[VAL_38:.*]] = addi %[[VAL_28]], %[[VAL_9]] : index
+// CHECK:                 scf.yield %[[VAL_37]], %[[VAL_38]] : index, index
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_38:.*]] = %[[VAL_39:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_40:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_38]]] : memref<32x16x8xf32>
-// CHECK:                 store %[[VAL_40]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_38]]] : memref<32x16x8xf32>
+// CHECK:               scf.for %[[VAL_39:.*]] = %[[VAL_40:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
+// CHECK:                 %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_39]]] : memref<32x16x8xf32>
+// CHECK:                 store %[[VAL_41]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_39]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_41:.*]] = tensor_load %[[VAL_14]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_41]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_42:.*]] = tensor_load %[[VAL_15]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_42]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_dds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_dds
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_dds(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 32 : index
 // CHECK:           %[[VAL_5:.*]] = constant 16 : index
 // CHECK:           %[[VAL_6:.*]] = constant 0 : index
 // CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:             scf.for %[[VAL_14:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
-// CHECK:               %[[VAL_15:.*]] = muli %[[VAL_13]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_16:.*]] = addi %[[VAL_15]], %[[VAL_14]] : index
-// CHECK:               %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:               %[[VAL_18:.*]] = addi %[[VAL_16]], %[[VAL_7]] : index
-// CHECK:               %[[VAL_19:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_20:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_7]] {
-// CHECK:                 %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xindex>
-// CHECK:                 %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_20]]] : memref<?xf32>
-// CHECK:                 %[[VAL_23:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]], %[[VAL_14]], %[[VAL_21]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_24:.*]] = mulf %[[VAL_22]], %[[VAL_23]] : f32
-// CHECK:                 store %[[VAL_24]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_14]], %[[VAL_21]]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_12]], %[[VAL_13]]) : memref<32x16x8xf32>, 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:.*]] = muli %[[VAL_14]], %[[VAL_5]] : index
+// CHECK:               %[[VAL_17:.*]] = addi %[[VAL_16]], %[[VAL_15]] : index
+// CHECK:               %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK:               %[[VAL_19:.*]] = addi %[[VAL_17]], %[[VAL_7]] : index
+// CHECK:               %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_7]] {
+// CHECK:                 %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK:                 %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xf32>
+// CHECK:                 %[[VAL_24:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_22]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_25:.*]] = mulf %[[VAL_23]], %[[VAL_24]] : f32
+// CHECK:                 store %[[VAL_25]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_22]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_25:.*]] = tensor_load %[[VAL_12]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_25]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_26:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_26]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @mul_dds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_dds
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_dsd = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_dsd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 16 : index
-// CHECK:           %[[VAL_6:.*]] = constant 8 : index
-// CHECK:           %[[VAL_7:.*]] = constant true
-// CHECK:           %[[VAL_8:.*]] = constant 0 : index
-// CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_8]] to %[[VAL_4]] step %[[VAL_9]] {
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_15]]] : memref<?xindex>
-// CHECK:             %[[VAL_17:.*]] = addi %[[VAL_15]], %[[VAL_9]] : index
-// CHECK:             %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_17]]] : memref<?xindex>
-// CHECK:             %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_16]], %[[VAL_21:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 16 : index
+// CHECK:           %[[VAL_5:.*]] = constant 8 : index
+// CHECK:           %[[VAL_6:.*]] = constant true
+// CHECK:           %[[VAL_7:.*]] = constant 0 : index
+// CHECK:           %[[VAL_8:.*]] = constant 1 : index
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_13]], %[[VAL_14]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_7]] to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             %[[VAL_17:.*]] = addi %[[VAL_15]], %[[VAL_8]] : index
+// CHECK:             %[[VAL_18:.*]] = 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:.*]] = 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:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:               %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xindex>
 // CHECK:               %[[VAL_26:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
 // CHECK:               scf.if %[[VAL_26]] {
-// CHECK:                 scf.for %[[VAL_27:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                   %[[VAL_28:.*]] = muli %[[VAL_23]], %[[VAL_6]] : index
+// CHECK:                 scf.for %[[VAL_27:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK:                   %[[VAL_28:.*]] = muli %[[VAL_23]], %[[VAL_5]] : index
 // CHECK:                   %[[VAL_29:.*]] = addi %[[VAL_28]], %[[VAL_27]] : index
-// CHECK:                   %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_29]]] : memref<?xf32>
-// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK:                   %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_29]]] : memref<?xf32>
+// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
 // CHECK:                   %[[VAL_32:.*]] = addf %[[VAL_30]], %[[VAL_31]] : f32
 // CHECK:                   store %[[VAL_32]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
 // CHECK:                 }
 // CHECK:               } else {
-// CHECK:                 scf.if %[[VAL_7]] {
-// CHECK:                   scf.for %[[VAL_33:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_34:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_33]]] : memref<32x16x8xf32>
+// CHECK:                 scf.if %[[VAL_6]] {
+// CHECK:                   scf.for %[[VAL_33:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK:                     %[[VAL_34:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_33]]] : memref<32x16x8xf32>
 // CHECK:                     store %[[VAL_34]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_24]], %[[VAL_33]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
 // CHECK:               %[[VAL_35:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
-// CHECK:               %[[VAL_36:.*]] = addi %[[VAL_23]], %[[VAL_9]] : index
+// CHECK:               %[[VAL_36:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
 // CHECK:               %[[VAL_37:.*]] = select %[[VAL_35]], %[[VAL_36]], %[[VAL_23]] : index
-// CHECK:               %[[VAL_38:.*]] = addi %[[VAL_24]], %[[VAL_9]] : index
+// CHECK:               %[[VAL_38:.*]] = 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_5]] step %[[VAL_9]] {
-// CHECK:               scf.for %[[VAL_41:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_42:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_15]], %[[VAL_39]], %[[VAL_41]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_39]], %[[VAL_41]]] : memref<32x16x8xf32>
 // CHECK:                 store %[[VAL_42]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_39]], %[[VAL_41]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_43:.*]] = tensor_load %[[VAL_14]] : memref<32x16x8xf32>
 // CHECK:           return %[[VAL_43]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_dsd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_dsd
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_dsd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 8 : index
-// CHECK:           %[[VAL_6:.*]] = constant 0 : index
-// CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_13]]] : memref<?xindex>
-// CHECK:             %[[VAL_15:.*]] = addi %[[VAL_13]], %[[VAL_7]] : index
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_15]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_14]] to %[[VAL_16]] step %[[VAL_7]] {
-// CHECK:               %[[VAL_18:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_17]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_19:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
-// CHECK:                 %[[VAL_20:.*]] = muli %[[VAL_17]], %[[VAL_5]] : index
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 8 : index
+// CHECK:           %[[VAL_5:.*]] = constant 0 : index
+// CHECK:           %[[VAL_6:.*]] = constant 1 : index
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK:             %[[VAL_15:.*]] = addi %[[VAL_13]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_14]] to %[[VAL_16]] step %[[VAL_6]] {
+// CHECK:               %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK:                 %[[VAL_20:.*]] = muli %[[VAL_17]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_21:.*]] = addi %[[VAL_20]], %[[VAL_19]] : index
-// CHECK:                 %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xf32>
-// CHECK:                 %[[VAL_23:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_19]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xf32>
+// CHECK:                 %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_19]]] : memref<32x16x8xf32>
 // CHECK:                 %[[VAL_24:.*]] = mulf %[[VAL_22]], %[[VAL_23]] : f32
 // CHECK:                 store %[[VAL_24]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_19]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_25:.*]] = tensor_load %[[VAL_12]] : memref<32x16x8xf32>
 // CHECK:           return %[[VAL_25]] : tensor<32x16x8xf32>
 // CHECK:         }
#trait_dss = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_dss(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 32 : index
 // CHECK:           %[[VAL_5:.*]] = constant 16 : index
 // CHECK:           %[[VAL_6:.*]] = constant 8 : index
 // CHECK:           %[[VAL_7:.*]] = constant true
 // CHECK:           %[[VAL_8:.*]] = constant 0 : index
 // CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_15:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_8]] to %[[VAL_4]] step %[[VAL_9]] {
-// CHECK:             %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_17]]] : memref<?xindex>
-// CHECK:             %[[VAL_19:.*]] = addi %[[VAL_17]], %[[VAL_9]] : index
-// CHECK:             %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<?xindex>
-// CHECK:             %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_18]], %[[VAL_23:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
-// CHECK:               %[[VAL_24:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_20]] : index
-// CHECK:               scf.condition(%[[VAL_24]]) %[[VAL_22]], %[[VAL_23]] : index, index
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_16:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_17:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_16]], %[[VAL_17]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           scf.for %[[VAL_18:.*]] = %[[VAL_8]] to %[[VAL_4]] step %[[VAL_9]] {
+// CHECK:             %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK:             %[[VAL_20:.*]] = addi %[[VAL_18]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_21:.*]] = 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:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_21]] : index
+// CHECK:               scf.condition(%[[VAL_25]]) %[[VAL_23]], %[[VAL_24]] : index, index
 // CHECK:             } do {
-// CHECK:             ^bb0(%[[VAL_25:.*]]: index, %[[VAL_26:.*]]: index):
-// CHECK:               %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:               %[[VAL_28:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
-// CHECK:               scf.if %[[VAL_28]] {
-// CHECK:                 %[[VAL_29:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:                 %[[VAL_30:.*]] = addi %[[VAL_25]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_30]]] : memref<?xindex>
-// CHECK:                 %[[VAL_32:.*]]:2 = scf.while (%[[VAL_33:.*]] = %[[VAL_29]], %[[VAL_34:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
-// CHECK:                   %[[VAL_35:.*]] = cmpi ult, %[[VAL_33]], %[[VAL_31]] : index
-// CHECK:                   scf.condition(%[[VAL_35]]) %[[VAL_33]], %[[VAL_34]] : index, index
+// CHECK:             ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
+// CHECK:               %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:               %[[VAL_29:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
+// CHECK:               scf.if %[[VAL_29]] {
+// CHECK:                 %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:                 %[[VAL_31:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
+// CHECK:                 %[[VAL_32:.*]] = 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:.*]] = cmpi ult, %[[VAL_34]], %[[VAL_32]] : index
+// CHECK:                   scf.condition(%[[VAL_36]]) %[[VAL_34]], %[[VAL_35]] : index, index
 // CHECK:                 } do {
-// CHECK:                 ^bb0(%[[VAL_36:.*]]: index, %[[VAL_37:.*]]: index):
-// CHECK:                   %[[VAL_38:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_36]]] : memref<?xindex>
-// CHECK:                   %[[VAL_39:.*]] = cmpi eq, %[[VAL_38]], %[[VAL_37]] : index
-// CHECK:                   scf.if %[[VAL_39]] {
-// CHECK:                     %[[VAL_40:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_36]]] : memref<?xf32>
-// CHECK:                     %[[VAL_41:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
-// CHECK:                     %[[VAL_42:.*]] = addf %[[VAL_40]], %[[VAL_41]] : f32
-// CHECK:                     store %[[VAL_42]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK:                 ^bb0(%[[VAL_37:.*]]: index, %[[VAL_38:.*]]: index):
+// CHECK:                   %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:                   %[[VAL_40:.*]] = cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
+// CHECK:                   scf.if %[[VAL_40]] {
+// CHECK:                     %[[VAL_41:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_37]]] : memref<?xf32>
+// CHECK:                     %[[VAL_42:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
+// CHECK:                     %[[VAL_43:.*]] = addf %[[VAL_41]], %[[VAL_42]] : f32
+// CHECK:                     store %[[VAL_43]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
 // CHECK:                   } else {
 // CHECK:                     scf.if %[[VAL_7]] {
-// CHECK:                       %[[VAL_43:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
-// CHECK:                       store %[[VAL_43]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK:                       %[[VAL_44:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
+// CHECK:                       store %[[VAL_44]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
 // CHECK:                     } else {
 // CHECK:                     }
 // CHECK:                   }
-// CHECK:                   %[[VAL_44:.*]] = cmpi eq, %[[VAL_38]], %[[VAL_37]] : index
-// CHECK:                   %[[VAL_45:.*]] = addi %[[VAL_36]], %[[VAL_9]] : index
-// CHECK:                   %[[VAL_46:.*]] = select %[[VAL_44]], %[[VAL_45]], %[[VAL_36]] : index
-// CHECK:                   %[[VAL_47:.*]] = addi %[[VAL_37]], %[[VAL_9]] : index
-// CHECK:                   scf.yield %[[VAL_46]], %[[VAL_47]] : index, index
+// CHECK:                   %[[VAL_45:.*]] = cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
+// CHECK:                   %[[VAL_46:.*]] = addi %[[VAL_37]], %[[VAL_9]] : index
+// CHECK:                   %[[VAL_47:.*]] = select %[[VAL_45]], %[[VAL_46]], %[[VAL_37]] : index
+// CHECK:                   %[[VAL_48:.*]] = addi %[[VAL_38]], %[[VAL_9]] : index
+// CHECK:                   scf.yield %[[VAL_47]], %[[VAL_48]] : index, index
 // CHECK:                 }
-// CHECK:                 scf.for %[[VAL_48:.*]] = %[[VAL_49:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                   %[[VAL_50:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_48]]] : memref<32x16x8xf32>
-// CHECK:                   store %[[VAL_50]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_48]]] : memref<32x16x8xf32>
+// CHECK:                 scf.for %[[VAL_49:.*]] = %[[VAL_50:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
+// CHECK:                   %[[VAL_51:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_49]]] : memref<32x16x8xf32>
+// CHECK:                   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_51:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_52:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_51]]] : memref<32x16x8xf32>
-// CHECK:                     store %[[VAL_52]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_26]], %[[VAL_51]]] : memref<32x16x8xf32>
+// CHECK:                   scf.for %[[VAL_52:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
+// CHECK:                     %[[VAL_53:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_52]]] : memref<32x16x8xf32>
+// CHECK:                     store %[[VAL_53]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_27]], %[[VAL_52]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 } else {
 // CHECK:                 }
 // CHECK:               }
-// CHECK:               %[[VAL_53:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
-// CHECK:               %[[VAL_54:.*]] = addi %[[VAL_25]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_55:.*]] = select %[[VAL_53]], %[[VAL_54]], %[[VAL_25]] : index
-// CHECK:               %[[VAL_56:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
-// CHECK:               scf.yield %[[VAL_55]], %[[VAL_56]] : index, index
+// CHECK:               %[[VAL_54:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
+// CHECK:               %[[VAL_55:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
+// CHECK:               %[[VAL_56:.*]] = select %[[VAL_54]], %[[VAL_55]], %[[VAL_26]] : index
+// CHECK:               %[[VAL_57:.*]] = addi %[[VAL_27]], %[[VAL_9]] : index
+// CHECK:               scf.yield %[[VAL_56]], %[[VAL_57]] : index, index
 // CHECK:             }
-// CHECK:             scf.for %[[VAL_57:.*]] = %[[VAL_58:.*]]#1 to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:               scf.for %[[VAL_59:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_60:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_17]], %[[VAL_57]], %[[VAL_59]]] : memref<32x16x8xf32>
-// CHECK:                 store %[[VAL_60]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_57]], %[[VAL_59]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_18]], %[[VAL_58]], %[[VAL_60]]] : memref<32x16x8xf32>
+// CHECK:                 store %[[VAL_61]], %[[VAL_17]]{{\[}}%[[VAL_18]], %[[VAL_58]], %[[VAL_60]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_61:.*]] = tensor_load %[[VAL_16]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_61]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_62:.*]] = tensor_load %[[VAL_17]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_62]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_dss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_dss
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_dss(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 32 : index
 // CHECK:           %[[VAL_5:.*]] = constant 0 : index
 // CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           scf.for %[[VAL_14:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
-// CHECK:             %[[VAL_16:.*]] = addi %[[VAL_14]], %[[VAL_6]] : index
-// CHECK:             %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_18:.*]] = %[[VAL_15]] to %[[VAL_17]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_19:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:               %[[VAL_20:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:               %[[VAL_21:.*]] = addi %[[VAL_18]], %[[VAL_6]] : index
-// CHECK:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_23:.*]] = %[[VAL_20]] to %[[VAL_22]] step %[[VAL_6]] {
-// CHECK:                 %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:                 %[[VAL_25:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xf32>
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_19]], %[[VAL_24]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_27:.*]] = mulf %[[VAL_25]], %[[VAL_26]] : f32
-// CHECK:                 store %[[VAL_27]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_19]], %[[VAL_24]]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_6]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_13]], %[[VAL_14]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             %[[VAL_17:.*]] = addi %[[VAL_15]], %[[VAL_6]] : index
+// CHECK:             %[[VAL_18:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_19:.*]] = %[[VAL_16]] to %[[VAL_18]] step %[[VAL_6]] {
+// CHECK:               %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:               %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:               %[[VAL_22:.*]] = addi %[[VAL_19]], %[[VAL_6]] : index
+// CHECK:               %[[VAL_23:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_6]] {
+// CHECK:                 %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_15]], %[[VAL_20]], %[[VAL_25]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_28:.*]] = mulf %[[VAL_26]], %[[VAL_27]] : f32
+// CHECK:                 store %[[VAL_28]], %[[VAL_14]]{{\[}}%[[VAL_15]], %[[VAL_20]], %[[VAL_25]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_28:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_28]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_29:.*]] = tensor_load %[[VAL_14]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_29]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @mul_dss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_dss
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_sdd = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_sdd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 16 : index
-// CHECK:           %[[VAL_6:.*]] = constant 8 : index
-// CHECK:           %[[VAL_7:.*]] = constant true
-// CHECK:           %[[VAL_8:.*]] = constant 0 : index
-// CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_15]], %[[VAL_19:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 16 : index
+// CHECK:           %[[VAL_5:.*]] = constant 8 : index
+// CHECK:           %[[VAL_6:.*]] = constant true
+// CHECK:           %[[VAL_7:.*]] = constant 0 : index
+// CHECK:           %[[VAL_8:.*]] = constant 1 : index
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_13]], %[[VAL_14]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = 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:.*]] = 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:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK:             %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xindex>
 // CHECK:             %[[VAL_24:.*]] = cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
 // CHECK:             scf.if %[[VAL_24]] {
-// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_26:.*]] = muli %[[VAL_21]], %[[VAL_5]] : index
+// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK:                 %[[VAL_26:.*]] = muli %[[VAL_21]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_27:.*]] = addi %[[VAL_26]], %[[VAL_25]] : index
-// CHECK:                 scf.for %[[VAL_28:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                   %[[VAL_29:.*]] = muli %[[VAL_27]], %[[VAL_6]] : index
+// CHECK:                 scf.for %[[VAL_28:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK:                   %[[VAL_29:.*]] = muli %[[VAL_27]], %[[VAL_5]] : index
 // CHECK:                   %[[VAL_30:.*]] = addi %[[VAL_29]], %[[VAL_28]] : index
-// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_30]]] : memref<?xf32>
-// CHECK:                   %[[VAL_32:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_25]], %[[VAL_28]]] : memref<32x16x8xf32>
+// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_30]]] : memref<?xf32>
+// CHECK:                   %[[VAL_32:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_22]], %[[VAL_25]], %[[VAL_28]]] : memref<32x16x8xf32>
 // CHECK:                   %[[VAL_33:.*]] = addf %[[VAL_31]], %[[VAL_32]] : f32
 // CHECK:                   store %[[VAL_33]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_25]], %[[VAL_28]]] : memref<32x16x8xf32>
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_7]] {
-// CHECK:                 scf.for %[[VAL_34:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                   scf.for %[[VAL_35:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_36:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_34]], %[[VAL_35]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_22]], %[[VAL_34]], %[[VAL_35]]] : memref<32x16x8xf32>
 // CHECK:                     store %[[VAL_36]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_34]], %[[VAL_35]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_37:.*]] = cmpi eq, %[[VAL_23]], %[[VAL_22]] : index
-// CHECK:             %[[VAL_38:.*]] = addi %[[VAL_21]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_38:.*]] = addi %[[VAL_21]], %[[VAL_8]] : index
 // CHECK:             %[[VAL_39:.*]] = select %[[VAL_37]], %[[VAL_38]], %[[VAL_21]] : index
-// CHECK:             %[[VAL_40:.*]] = addi %[[VAL_22]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_40:.*]] = 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_4]] step %[[VAL_9]] {
-// CHECK:             scf.for %[[VAL_43:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:               scf.for %[[VAL_44:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_45:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_41]], %[[VAL_43]], %[[VAL_44]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_41]], %[[VAL_43]], %[[VAL_44]]] : memref<32x16x8xf32>
 // CHECK:                 store %[[VAL_45]], %[[VAL_14]]{{\[}}%[[VAL_41]], %[[VAL_43]], %[[VAL_44]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_46:.*]] = tensor_load %[[VAL_14]] : memref<32x16x8xf32>
 // CHECK:           return %[[VAL_46]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_sdd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_sdd
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_sdd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 16 : index
-// CHECK:           %[[VAL_5:.*]] = constant 8 : index
-// CHECK:           %[[VAL_6:.*]] = constant 0 : index
-// CHECK:           %[[VAL_7:.*]] = constant 1 : index
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_7]] {
-// CHECK:             %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_15]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
-// CHECK:               %[[VAL_18:.*]] = muli %[[VAL_15]], %[[VAL_4]] : index
+// CHECK:           %[[VAL_3:.*]] = constant 16 : index
+// CHECK:           %[[VAL_4:.*]] = constant 8 : index
+// CHECK:           %[[VAL_5:.*]] = constant 0 : index
+// CHECK:           %[[VAL_6:.*]] = constant 1 : index
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_15:.*]] = %[[VAL_13]] to %[[VAL_14]] step %[[VAL_6]] {
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK:               %[[VAL_18:.*]] = muli %[[VAL_15]], %[[VAL_3]] : index
 // CHECK:               %[[VAL_19:.*]] = addi %[[VAL_18]], %[[VAL_17]] : index
-// CHECK:               scf.for %[[VAL_20:.*]] = %[[VAL_6]] to %[[VAL_5]] step %[[VAL_7]] {
-// CHECK:                 %[[VAL_21:.*]] = muli %[[VAL_19]], %[[VAL_5]] : index
+// CHECK:               scf.for %[[VAL_20:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK:                 %[[VAL_21:.*]] = muli %[[VAL_19]], %[[VAL_4]] : index
 // CHECK:                 %[[VAL_22:.*]] = addi %[[VAL_21]], %[[VAL_20]] : index
-// CHECK:                 %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xf32>
-// CHECK:                 %[[VAL_24:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_20]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_23:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xf32>
+// CHECK:                 %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_20]]] : memref<32x16x8xf32>
 // CHECK:                 %[[VAL_25:.*]] = mulf %[[VAL_23]], %[[VAL_24]] : f32
 // CHECK:                 store %[[VAL_25]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_20]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_26:.*]] = tensor_load %[[VAL_12]] : memref<32x16x8xf32>
 // CHECK:           return %[[VAL_26]] : tensor<32x16x8xf32>
 // CHECK:         }
#trait_sds = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_sds(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 32 : index
 // CHECK:           %[[VAL_5:.*]] = constant 16 : index
 // CHECK:           %[[VAL_6:.*]] = constant 8 : index
 // CHECK:           %[[VAL_7:.*]] = constant true
 // CHECK:           %[[VAL_8:.*]] = constant 0 : index
 // CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_15:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_17]], %[[VAL_21:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
-// CHECK:             %[[VAL_22:.*]] = cmpi ult, %[[VAL_20]], %[[VAL_18]] : index
-// CHECK:             scf.condition(%[[VAL_22]]) %[[VAL_20]], %[[VAL_21]] : index, index
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_16:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_17:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_16]], %[[VAL_17]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
+// CHECK:           %[[VAL_19:.*]] = 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:.*]] = cmpi ult, %[[VAL_21]], %[[VAL_19]] : index
+// CHECK:             scf.condition(%[[VAL_23]]) %[[VAL_21]], %[[VAL_22]] : index, index
 // CHECK:           } do {
-// CHECK:           ^bb0(%[[VAL_23:.*]]: index, %[[VAL_24:.*]]: index):
-// CHECK:             %[[VAL_25:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:             %[[VAL_26:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
-// CHECK:             scf.if %[[VAL_26]] {
-// CHECK:               scf.for %[[VAL_27:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_28:.*]] = muli %[[VAL_23]], %[[VAL_5]] : index
-// CHECK:                 %[[VAL_29:.*]] = addi %[[VAL_28]], %[[VAL_27]] : index
-// CHECK:                 %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_29]]] : memref<?xindex>
-// CHECK:                 %[[VAL_31:.*]] = addi %[[VAL_29]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_32:.*]] = 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:.*]] = cmpi ult, %[[VAL_34]], %[[VAL_32]] : index
-// CHECK:                   scf.condition(%[[VAL_36]]) %[[VAL_34]], %[[VAL_35]] : index, index
+// CHECK:           ^bb0(%[[VAL_24:.*]]: index, %[[VAL_25:.*]]: index):
+// CHECK:             %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK:             %[[VAL_27:.*]] = 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:.*]] = muli %[[VAL_24]], %[[VAL_5]] : index
+// CHECK:                 %[[VAL_30:.*]] = addi %[[VAL_29]], %[[VAL_28]] : index
+// CHECK:                 %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_30]]] : memref<?xindex>
+// CHECK:                 %[[VAL_32:.*]] = addi %[[VAL_30]], %[[VAL_9]] : index
+// CHECK:                 %[[VAL_33:.*]] = 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:.*]] = cmpi ult, %[[VAL_35]], %[[VAL_33]] : index
+// CHECK:                   scf.condition(%[[VAL_37]]) %[[VAL_35]], %[[VAL_36]] : index, index
 // CHECK:                 } do {
-// CHECK:                 ^bb0(%[[VAL_37:.*]]: index, %[[VAL_38:.*]]: index):
-// CHECK:                   %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_37]]] : memref<?xindex>
-// CHECK:                   %[[VAL_40:.*]] = cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
-// CHECK:                   scf.if %[[VAL_40]] {
-// CHECK:                     %[[VAL_41:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_37]]] : memref<?xf32>
-// CHECK:                     %[[VAL_42:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
-// CHECK:                     %[[VAL_43:.*]] = addf %[[VAL_41]], %[[VAL_42]] : f32
-// CHECK:                     store %[[VAL_43]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
+// CHECK:                 ^bb0(%[[VAL_38:.*]]: index, %[[VAL_39:.*]]: index):
+// CHECK:                   %[[VAL_40:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_38]]] : memref<?xindex>
+// CHECK:                   %[[VAL_41:.*]] = cmpi eq, %[[VAL_40]], %[[VAL_39]] : index
+// CHECK:                   scf.if %[[VAL_41]] {
+// CHECK:                     %[[VAL_42:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_38]]] : memref<?xf32>
+// CHECK:                     %[[VAL_43:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
+// CHECK:                     %[[VAL_44:.*]] = addf %[[VAL_42]], %[[VAL_43]] : f32
+// CHECK:                     store %[[VAL_44]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
 // CHECK:                   } else {
 // CHECK:                     scf.if %[[VAL_7]] {
-// CHECK:                       %[[VAL_44:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
-// CHECK:                       store %[[VAL_44]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_27]], %[[VAL_38]]] : memref<32x16x8xf32>
+// CHECK:                       %[[VAL_45:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
+// CHECK:                       store %[[VAL_45]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_39]]] : memref<32x16x8xf32>
 // CHECK:                     } else {
 // CHECK:                     }
 // CHECK:                   }
-// CHECK:                   %[[VAL_45:.*]] = cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
-// CHECK:                   %[[VAL_46:.*]] = addi %[[VAL_37]], %[[VAL_9]] : index
-// CHECK:                   %[[VAL_47:.*]] = select %[[VAL_45]], %[[VAL_46]], %[[VAL_37]] : index
-// CHECK:                   %[[VAL_48:.*]] = addi %[[VAL_38]], %[[VAL_9]] : index
-// CHECK:                   scf.yield %[[VAL_47]], %[[VAL_48]] : index, index
+// CHECK:                   %[[VAL_46:.*]] = cmpi eq, %[[VAL_40]], %[[VAL_39]] : index
+// CHECK:                   %[[VAL_47:.*]] = addi %[[VAL_38]], %[[VAL_9]] : index
+// CHECK:                   %[[VAL_48:.*]] = select %[[VAL_46]], %[[VAL_47]], %[[VAL_38]] : index
+// CHECK:                   %[[VAL_49:.*]] = addi %[[VAL_39]], %[[VAL_9]] : index
+// CHECK:                   scf.yield %[[VAL_48]], %[[VAL_49]] : index, index
 // CHECK:                 }
-// CHECK:                 scf.for %[[VAL_49:.*]] = %[[VAL_50:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                   %[[VAL_51:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_27]], %[[VAL_49]]] : memref<32x16x8xf32>
-// CHECK:                   store %[[VAL_51]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_27]], %[[VAL_49]]] : memref<32x16x8xf32>
+// CHECK:                 scf.for %[[VAL_50:.*]] = %[[VAL_51:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
+// CHECK:                   %[[VAL_52:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_28]], %[[VAL_50]]] : memref<32x16x8xf32>
+// CHECK:                   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_52:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                   scf.for %[[VAL_53:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_54:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_52]], %[[VAL_53]]] : memref<32x16x8xf32>
-// CHECK:                     store %[[VAL_54]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_52]], %[[VAL_53]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_25]], %[[VAL_53]], %[[VAL_54]]] : memref<32x16x8xf32>
+// CHECK:                     store %[[VAL_55]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_53]], %[[VAL_54]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
-// CHECK:             %[[VAL_55:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
-// CHECK:             %[[VAL_56:.*]] = addi %[[VAL_23]], %[[VAL_9]] : index
-// CHECK:             %[[VAL_57:.*]] = select %[[VAL_55]], %[[VAL_56]], %[[VAL_23]] : index
-// CHECK:             %[[VAL_58:.*]] = addi %[[VAL_24]], %[[VAL_9]] : index
-// CHECK:             scf.yield %[[VAL_57]], %[[VAL_58]] : index, index
+// CHECK:             %[[VAL_56:.*]] = cmpi eq, %[[VAL_26]], %[[VAL_25]] : index
+// CHECK:             %[[VAL_57:.*]] = addi %[[VAL_24]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_58:.*]] = select %[[VAL_56]], %[[VAL_57]], %[[VAL_24]] : index
+// CHECK:             %[[VAL_59:.*]] = addi %[[VAL_25]], %[[VAL_9]] : index
+// CHECK:             scf.yield %[[VAL_58]], %[[VAL_59]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_59:.*]] = %[[VAL_60:.*]]#1 to %[[VAL_4]] step %[[VAL_9]] {
-// CHECK:             scf.for %[[VAL_61:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:               scf.for %[[VAL_62:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_63:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_59]], %[[VAL_61]], %[[VAL_62]]] : memref<32x16x8xf32>
-// CHECK:                 store %[[VAL_63]], %[[VAL_16]]{{\[}}%[[VAL_59]], %[[VAL_61]], %[[VAL_62]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_60]], %[[VAL_62]], %[[VAL_63]]] : memref<32x16x8xf32>
+// CHECK:                 store %[[VAL_64]], %[[VAL_17]]{{\[}}%[[VAL_60]], %[[VAL_62]], %[[VAL_63]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_64:.*]] = tensor_load %[[VAL_16]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_64]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_65:.*]] = tensor_load %[[VAL_17]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_65]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_sds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_sds
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_sds(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 16 : index
 // CHECK:           %[[VAL_5:.*]] = constant 0 : index
 // CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_16:.*]] = %[[VAL_14]] to %[[VAL_15]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_18:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_19:.*]] = muli %[[VAL_16]], %[[VAL_4]] : index
-// CHECK:               %[[VAL_20:.*]] = addi %[[VAL_19]], %[[VAL_18]] : index
-// CHECK:               %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_20]]] : memref<?xindex>
-// CHECK:               %[[VAL_22:.*]] = addi %[[VAL_20]], %[[VAL_6]] : index
-// CHECK:               %[[VAL_23:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_6]] {
-// CHECK:                 %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xf32>
-// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_17]], %[[VAL_18]], %[[VAL_25]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_28:.*]] = mulf %[[VAL_26]], %[[VAL_27]] : f32
-// CHECK:                 store %[[VAL_28]], %[[VAL_13]]{{\[}}%[[VAL_17]], %[[VAL_18]], %[[VAL_25]]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_13]], %[[VAL_14]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_15]] to %[[VAL_16]] step %[[VAL_6]] {
+// CHECK:             %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK:               %[[VAL_20:.*]] = muli %[[VAL_17]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_21:.*]] = addi %[[VAL_20]], %[[VAL_19]] : index
+// CHECK:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK:               %[[VAL_23:.*]] = addi %[[VAL_21]], %[[VAL_6]] : index
+// CHECK:               %[[VAL_24:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_22]] to %[[VAL_24]] step %[[VAL_6]] {
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xindex>
+// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_18]], %[[VAL_19]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_29:.*]] = mulf %[[VAL_27]], %[[VAL_28]] : f32
+// CHECK:                 store %[[VAL_29]], %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_19]], %[[VAL_26]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_29:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_29]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_30:.*]] = tensor_load %[[VAL_14]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_30]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @mul_sds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_sds
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_ssd = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_ssd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 32 : index
-// CHECK:           %[[VAL_5:.*]] = constant 16 : index
-// CHECK:           %[[VAL_6:.*]] = constant 8 : index
-// CHECK:           %[[VAL_7:.*]] = constant true
-// CHECK:           %[[VAL_8:.*]] = constant 0 : index
-// CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_15:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_16:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_17:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
-// CHECK:           %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
-// CHECK:           %[[VAL_19:.*]]:2 = scf.while (%[[VAL_20:.*]] = %[[VAL_17]], %[[VAL_21:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
+// CHECK:           %[[VAL_3:.*]] = constant 32 : index
+// CHECK:           %[[VAL_4:.*]] = constant 16 : index
+// CHECK:           %[[VAL_5:.*]] = constant 8 : index
+// CHECK:           %[[VAL_6:.*]] = constant true
+// CHECK:           %[[VAL_7:.*]] = constant 0 : index
+// CHECK:           %[[VAL_8:.*]] = constant 1 : index
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_7]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_14:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_16:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_15]], %[[VAL_16]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = 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:.*]] = 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:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:             %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xindex>
 // CHECK:             %[[VAL_26:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
 // CHECK:             scf.if %[[VAL_26]] {
-// CHECK:               %[[VAL_27:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_23]]] : memref<?xindex>
-// CHECK:               %[[VAL_28:.*]] = addi %[[VAL_23]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_29:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xindex>
-// CHECK:               %[[VAL_30:.*]]:2 = scf.while (%[[VAL_31:.*]] = %[[VAL_27]], %[[VAL_32:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
+// CHECK:               %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:               %[[VAL_28:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
+// CHECK:               %[[VAL_29:.*]] = 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:.*]] = 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:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_34]]] : memref<?xindex>
+// CHECK:                 %[[VAL_36:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_34]]] : memref<?xindex>
 // CHECK:                 %[[VAL_37:.*]] = cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
 // CHECK:                 scf.if %[[VAL_37]] {
-// CHECK:                   scf.for %[[VAL_38:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_39:.*]] = muli %[[VAL_34]], %[[VAL_6]] : index
+// CHECK:                   scf.for %[[VAL_38:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK:                     %[[VAL_39:.*]] = muli %[[VAL_34]], %[[VAL_5]] : index
 // CHECK:                     %[[VAL_40:.*]] = addi %[[VAL_39]], %[[VAL_38]] : index
-// CHECK:                     %[[VAL_41:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_40]]] : memref<?xf32>
-// CHECK:                     %[[VAL_42:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_38]]] : memref<32x16x8xf32>
+// CHECK:                     %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xf32>
+// CHECK:                     %[[VAL_42:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_38]]] : memref<32x16x8xf32>
 // CHECK:                     %[[VAL_43:.*]] = addf %[[VAL_41]], %[[VAL_42]] : f32
 // CHECK:                     store %[[VAL_43]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_38]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 } else {
-// CHECK:                   scf.if %[[VAL_7]] {
-// CHECK:                     scf.for %[[VAL_44:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                       %[[VAL_45:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_44]]] : memref<32x16x8xf32>
+// CHECK:                   scf.if %[[VAL_6]] {
+// CHECK:                     scf.for %[[VAL_44:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK:                       %[[VAL_45:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_44]]] : memref<32x16x8xf32>
 // CHECK:                       store %[[VAL_45]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_35]], %[[VAL_44]]] : memref<32x16x8xf32>
 // CHECK:                     }
 // CHECK:                   } else {
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:                 %[[VAL_46:.*]] = cmpi eq, %[[VAL_36]], %[[VAL_35]] : index
-// CHECK:                 %[[VAL_47:.*]] = addi %[[VAL_34]], %[[VAL_9]] : index
+// CHECK:                 %[[VAL_47:.*]] = addi %[[VAL_34]], %[[VAL_8]] : index
 // CHECK:                 %[[VAL_48:.*]] = select %[[VAL_46]], %[[VAL_47]], %[[VAL_34]] : index
-// CHECK:                 %[[VAL_49:.*]] = addi %[[VAL_35]], %[[VAL_9]] : index
+// CHECK:                 %[[VAL_49:.*]] = 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_5]] step %[[VAL_9]] {
-// CHECK:                 scf.for %[[VAL_52:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                   %[[VAL_53:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_50]], %[[VAL_52]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_50]], %[[VAL_52]]] : memref<32x16x8xf32>
 // CHECK:                   store %[[VAL_53]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_50]], %[[VAL_52]]] : memref<32x16x8xf32>
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             } else {
-// CHECK:               scf.if %[[VAL_7]] {
-// CHECK:                 scf.for %[[VAL_54:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                   scf.for %[[VAL_55:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_56:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_24]], %[[VAL_54]], %[[VAL_55]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_24]], %[[VAL_54]], %[[VAL_55]]] : memref<32x16x8xf32>
 // CHECK:                     store %[[VAL_56]], %[[VAL_16]]{{\[}}%[[VAL_24]], %[[VAL_54]], %[[VAL_55]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
 // CHECK:             %[[VAL_57:.*]] = cmpi eq, %[[VAL_25]], %[[VAL_24]] : index
-// CHECK:             %[[VAL_58:.*]] = addi %[[VAL_23]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_58:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
 // CHECK:             %[[VAL_59:.*]] = select %[[VAL_57]], %[[VAL_58]], %[[VAL_23]] : index
-// CHECK:             %[[VAL_60:.*]] = addi %[[VAL_24]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_60:.*]] = 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_4]] step %[[VAL_9]] {
-// CHECK:             scf.for %[[VAL_63:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:               scf.for %[[VAL_64:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_65:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_61]], %[[VAL_63]], %[[VAL_64]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_61]], %[[VAL_63]], %[[VAL_64]]] : memref<32x16x8xf32>
 // CHECK:                 store %[[VAL_65]], %[[VAL_16]]{{\[}}%[[VAL_61]], %[[VAL_63]], %[[VAL_64]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_66:.*]] = tensor_load %[[VAL_16]] : memref<32x16x8xf32>
 // CHECK:           return %[[VAL_66]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_ssd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_ssd
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_ssd(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 8 : index
-// CHECK:           %[[VAL_5:.*]] = constant 0 : index
-// CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_6]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_16:.*]] = %[[VAL_14]] to %[[VAL_15]] step %[[VAL_6]] {
-// CHECK:             %[[VAL_17:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:             %[[VAL_18:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:             %[[VAL_19:.*]] = addi %[[VAL_16]], %[[VAL_6]] : index
-// CHECK:             %[[VAL_20:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_23:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
-// CHECK:                 %[[VAL_24:.*]] = muli %[[VAL_21]], %[[VAL_4]] : index
+// CHECK:           %[[VAL_3:.*]] = constant 8 : index
+// CHECK:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_13:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_12]], %[[VAL_13]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_16:.*]] = %[[VAL_14]] to %[[VAL_15]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK:             %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK:             %[[VAL_19:.*]] = addi %[[VAL_16]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_5]] {
+// CHECK:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_23:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK:                 %[[VAL_24:.*]] = muli %[[VAL_21]], %[[VAL_3]] : index
 // CHECK:                 %[[VAL_25:.*]] = addi %[[VAL_24]], %[[VAL_23]] : index
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xf32>
-// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_23]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_23]]] : memref<32x16x8xf32>
 // CHECK:                 %[[VAL_28:.*]] = mulf %[[VAL_26]], %[[VAL_27]] : f32
 // CHECK:                 store %[[VAL_28]], %[[VAL_13]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_23]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_29:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
 // CHECK:           return %[[VAL_29]] : tensor<32x16x8xf32>
 // CHECK:         }
#trait_sss = {
   iterator_types = ["parallel", "parallel", "parallel"],
   doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
 }
 
 // CHECK-LABEL:   func @add_sss(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 32 : index
 // CHECK:           %[[VAL_5:.*]] = constant 16 : index
 // CHECK:           %[[VAL_6:.*]] = constant 8 : index
 // CHECK:           %[[VAL_7:.*]] = constant true
 // CHECK:           %[[VAL_8:.*]] = constant 0 : index
 // CHECK:           %[[VAL_9:.*]] = constant 1 : index
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_17:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_18:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
-// CHECK:           %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_9]]] : memref<?xindex>
-// CHECK:           %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_19]], %[[VAL_23:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
-// CHECK:             %[[VAL_24:.*]] = cmpi ult, %[[VAL_22]], %[[VAL_20]] : index
-// CHECK:             scf.condition(%[[VAL_24]]) %[[VAL_22]], %[[VAL_23]] : index, index
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_8]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_13:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_9]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_17:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_18:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_19:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_18]], %[[VAL_19]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_20:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_8]]] : memref<?xindex>
+// CHECK:           %[[VAL_21:.*]] = 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:.*]] = cmpi ult, %[[VAL_23]], %[[VAL_21]] : index
+// CHECK:             scf.condition(%[[VAL_25]]) %[[VAL_23]], %[[VAL_24]] : index, index
 // CHECK:           } do {
-// CHECK:           ^bb0(%[[VAL_25:.*]]: index, %[[VAL_26:.*]]: index):
-// CHECK:             %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:             %[[VAL_28:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
-// CHECK:             scf.if %[[VAL_28]] {
-// CHECK:               %[[VAL_29:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:               %[[VAL_30:.*]] = addi %[[VAL_25]], %[[VAL_9]] : index
-// CHECK:               %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_30]]] : memref<?xindex>
-// CHECK:               %[[VAL_32:.*]]:2 = scf.while (%[[VAL_33:.*]] = %[[VAL_29]], %[[VAL_34:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
-// CHECK:                 %[[VAL_35:.*]] = cmpi ult, %[[VAL_33]], %[[VAL_31]] : index
-// CHECK:                 scf.condition(%[[VAL_35]]) %[[VAL_33]], %[[VAL_34]] : index, index
+// CHECK:           ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
+// CHECK:             %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:             %[[VAL_29:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
+// CHECK:             scf.if %[[VAL_29]] {
+// CHECK:               %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:               %[[VAL_31:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
+// CHECK:               %[[VAL_32:.*]] = 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:.*]] = cmpi ult, %[[VAL_34]], %[[VAL_32]] : index
+// CHECK:                 scf.condition(%[[VAL_36]]) %[[VAL_34]], %[[VAL_35]] : index, index
 // CHECK:               } do {
-// CHECK:               ^bb0(%[[VAL_36:.*]]: index, %[[VAL_37:.*]]: index):
-// CHECK:                 %[[VAL_38:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_36]]] : memref<?xindex>
-// CHECK:                 %[[VAL_39:.*]] = cmpi eq, %[[VAL_38]], %[[VAL_37]] : index
-// CHECK:                 scf.if %[[VAL_39]] {
-// CHECK:                   %[[VAL_40:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_36]]] : memref<?xindex>
-// CHECK:                   %[[VAL_41:.*]] = addi %[[VAL_36]], %[[VAL_9]] : index
-// CHECK:                   %[[VAL_42:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_41]]] : memref<?xindex>
-// CHECK:                   %[[VAL_43:.*]]:2 = scf.while (%[[VAL_44:.*]] = %[[VAL_40]], %[[VAL_45:.*]] = %[[VAL_8]]) : (index, index) -> (index, index) {
-// CHECK:                     %[[VAL_46:.*]] = cmpi ult, %[[VAL_44]], %[[VAL_42]] : index
-// CHECK:                     scf.condition(%[[VAL_46]]) %[[VAL_44]], %[[VAL_45]] : index, index
+// CHECK:               ^bb0(%[[VAL_37:.*]]: index, %[[VAL_38:.*]]: index):
+// CHECK:                 %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:                 %[[VAL_40:.*]] = cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
+// CHECK:                 scf.if %[[VAL_40]] {
+// CHECK:                   %[[VAL_41:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_37]]] : memref<?xindex>
+// CHECK:                   %[[VAL_42:.*]] = addi %[[VAL_37]], %[[VAL_9]] : index
+// CHECK:                   %[[VAL_43:.*]] = 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:.*]] = cmpi ult, %[[VAL_45]], %[[VAL_43]] : index
+// CHECK:                     scf.condition(%[[VAL_47]]) %[[VAL_45]], %[[VAL_46]] : index, index
 // CHECK:                   } do {
-// CHECK:                   ^bb0(%[[VAL_47:.*]]: index, %[[VAL_48:.*]]: index):
-// CHECK:                     %[[VAL_49:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_47]]] : memref<?xindex>
-// CHECK:                     %[[VAL_50:.*]] = cmpi eq, %[[VAL_49]], %[[VAL_48]] : index
-// CHECK:                     scf.if %[[VAL_50]] {
-// CHECK:                       %[[VAL_51:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_47]]] : memref<?xf32>
-// CHECK:                       %[[VAL_52:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_48]]] : memref<32x16x8xf32>
-// CHECK:                       %[[VAL_53:.*]] = addf %[[VAL_51]], %[[VAL_52]] : f32
-// CHECK:                       store %[[VAL_53]], %[[VAL_18]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_48]]] : memref<32x16x8xf32>
+// CHECK:                   ^bb0(%[[VAL_48:.*]]: index, %[[VAL_49:.*]]: index):
+// CHECK:                     %[[VAL_50:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK:                     %[[VAL_51:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_49]] : index
+// CHECK:                     scf.if %[[VAL_51]] {
+// CHECK:                       %[[VAL_52:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK:                       %[[VAL_53:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
+// CHECK:                       %[[VAL_54:.*]] = addf %[[VAL_52]], %[[VAL_53]] : f32
+// CHECK:                       store %[[VAL_54]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
 // CHECK:                     } else {
 // CHECK:                       scf.if %[[VAL_7]] {
-// CHECK:                         %[[VAL_54:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_48]]] : memref<32x16x8xf32>
-// CHECK:                         store %[[VAL_54]], %[[VAL_18]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_48]]] : memref<32x16x8xf32>
+// CHECK:                         %[[VAL_55:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
+// CHECK:                         store %[[VAL_55]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_49]]] : memref<32x16x8xf32>
 // CHECK:                       } else {
 // CHECK:                       }
 // CHECK:                     }
-// CHECK:                     %[[VAL_55:.*]] = cmpi eq, %[[VAL_49]], %[[VAL_48]] : index
-// CHECK:                     %[[VAL_56:.*]] = addi %[[VAL_47]], %[[VAL_9]] : index
-// CHECK:                     %[[VAL_57:.*]] = select %[[VAL_55]], %[[VAL_56]], %[[VAL_47]] : index
-// CHECK:                     %[[VAL_58:.*]] = addi %[[VAL_48]], %[[VAL_9]] : index
-// CHECK:                     scf.yield %[[VAL_57]], %[[VAL_58]] : index, index
+// CHECK:                     %[[VAL_56:.*]] = cmpi eq, %[[VAL_50]], %[[VAL_49]] : index
+// CHECK:                     %[[VAL_57:.*]] = addi %[[VAL_48]], %[[VAL_9]] : index
+// CHECK:                     %[[VAL_58:.*]] = select %[[VAL_56]], %[[VAL_57]], %[[VAL_48]] : index
+// CHECK:                     %[[VAL_59:.*]] = addi %[[VAL_49]], %[[VAL_9]] : index
+// CHECK:                     scf.yield %[[VAL_58]], %[[VAL_59]] : index, index
 // CHECK:                   }
-// CHECK:                   scf.for %[[VAL_59:.*]] = %[[VAL_60:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_61:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_59]]] : memref<32x16x8xf32>
-// CHECK:                     store %[[VAL_61]], %[[VAL_18]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_59]]] : memref<32x16x8xf32>
+// CHECK:                   scf.for %[[VAL_60:.*]] = %[[VAL_61:.*]]#1 to %[[VAL_6]] step %[[VAL_9]] {
+// CHECK:                     %[[VAL_62:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_60]]] : memref<32x16x8xf32>
+// CHECK:                     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_62:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                       %[[VAL_63:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_62]]] : memref<32x16x8xf32>
-// CHECK:                       store %[[VAL_63]], %[[VAL_18]]{{\[}}%[[VAL_26]], %[[VAL_37]], %[[VAL_62]]] : memref<32x16x8xf32>
+// CHECK:                     scf.for %[[VAL_63:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
+// CHECK:                       %[[VAL_64:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_63]]] : memref<32x16x8xf32>
+// CHECK:                       store %[[VAL_64]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_38]], %[[VAL_63]]] : memref<32x16x8xf32>
 // CHECK:                     }
 // CHECK:                   } else {
 // CHECK:                   }
 // CHECK:                 }
-// CHECK:                 %[[VAL_64:.*]] = cmpi eq, %[[VAL_38]], %[[VAL_37]] : index
-// CHECK:                 %[[VAL_65:.*]] = addi %[[VAL_36]], %[[VAL_9]] : index
-// CHECK:                 %[[VAL_66:.*]] = select %[[VAL_64]], %[[VAL_65]], %[[VAL_36]] : index
-// CHECK:                 %[[VAL_67:.*]] = addi %[[VAL_37]], %[[VAL_9]] : index
-// CHECK:                 scf.yield %[[VAL_66]], %[[VAL_67]] : index, index
+// CHECK:                 %[[VAL_65:.*]] = cmpi eq, %[[VAL_39]], %[[VAL_38]] : index
+// CHECK:                 %[[VAL_66:.*]] = addi %[[VAL_37]], %[[VAL_9]] : index
+// CHECK:                 %[[VAL_67:.*]] = select %[[VAL_65]], %[[VAL_66]], %[[VAL_37]] : index
+// CHECK:                 %[[VAL_68:.*]] = addi %[[VAL_38]], %[[VAL_9]] : index
+// CHECK:                 scf.yield %[[VAL_67]], %[[VAL_68]] : index, index
 // CHECK:               }
-// CHECK:               scf.for %[[VAL_68:.*]] = %[[VAL_69:.*]]#1 to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                 scf.for %[[VAL_70:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                   %[[VAL_71:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_26]], %[[VAL_68]], %[[VAL_70]]] : memref<32x16x8xf32>
-// CHECK:                   store %[[VAL_71]], %[[VAL_18]]{{\[}}%[[VAL_26]], %[[VAL_68]], %[[VAL_70]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_69]], %[[VAL_71]]] : memref<32x16x8xf32>
+// CHECK:                   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_72:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:                   scf.for %[[VAL_73:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                     %[[VAL_74:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_26]], %[[VAL_72]], %[[VAL_73]]] : memref<32x16x8xf32>
-// CHECK:                     store %[[VAL_74]], %[[VAL_18]]{{\[}}%[[VAL_26]], %[[VAL_72]], %[[VAL_73]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_27]], %[[VAL_73]], %[[VAL_74]]] : memref<32x16x8xf32>
+// CHECK:                     store %[[VAL_75]], %[[VAL_19]]{{\[}}%[[VAL_27]], %[[VAL_73]], %[[VAL_74]]] : memref<32x16x8xf32>
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:               } else {
 // CHECK:               }
 // CHECK:             }
-// CHECK:             %[[VAL_75:.*]] = cmpi eq, %[[VAL_27]], %[[VAL_26]] : index
-// CHECK:             %[[VAL_76:.*]] = addi %[[VAL_25]], %[[VAL_9]] : index
-// CHECK:             %[[VAL_77:.*]] = select %[[VAL_75]], %[[VAL_76]], %[[VAL_25]] : index
-// CHECK:             %[[VAL_78:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
-// CHECK:             scf.yield %[[VAL_77]], %[[VAL_78]] : index, index
+// CHECK:             %[[VAL_76:.*]] = cmpi eq, %[[VAL_28]], %[[VAL_27]] : index
+// CHECK:             %[[VAL_77:.*]] = addi %[[VAL_26]], %[[VAL_9]] : index
+// CHECK:             %[[VAL_78:.*]] = select %[[VAL_76]], %[[VAL_77]], %[[VAL_26]] : index
+// CHECK:             %[[VAL_79:.*]] = addi %[[VAL_27]], %[[VAL_9]] : index
+// CHECK:             scf.yield %[[VAL_78]], %[[VAL_79]] : index, index
 // CHECK:           }
-// CHECK:           scf.for %[[VAL_79:.*]] = %[[VAL_80:.*]]#1 to %[[VAL_4]] step %[[VAL_9]] {
-// CHECK:             scf.for %[[VAL_81:.*]] = %[[VAL_8]] to %[[VAL_5]] step %[[VAL_9]] {
-// CHECK:               scf.for %[[VAL_82:.*]] = %[[VAL_8]] to %[[VAL_6]] step %[[VAL_9]] {
-// CHECK:                 %[[VAL_83:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_79]], %[[VAL_81]], %[[VAL_82]]] : memref<32x16x8xf32>
-// CHECK:                 store %[[VAL_83]], %[[VAL_18]]{{\[}}%[[VAL_79]], %[[VAL_81]], %[[VAL_82]]] : memref<32x16x8xf32>
+// 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:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_80]], %[[VAL_82]], %[[VAL_83]]] : memref<32x16x8xf32>
+// CHECK:                 store %[[VAL_84]], %[[VAL_19]]{{\[}}%[[VAL_80]], %[[VAL_82]], %[[VAL_83]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_84:.*]] = tensor_load %[[VAL_18]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_84]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_85:.*]] = tensor_load %[[VAL_19]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_85]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @add_sss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_sss
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = addf %a, %b : f32
         linalg.yield %0 : f32
   } -> tensor<32x16x8xf32>
   return %0 : tensor<32x16x8xf32>
 }
 
 // CHECK-LABEL:   func @mul_sss(
 // CHECK-SAME:                  %[[VAL_0:.*0]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_1:.*1]]: tensor<32x16x8xf32>,
 // CHECK-SAME:                  %[[VAL_2:.*2]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
+// CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 0 : index
 // CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_10:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
-// CHECK:           %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_17:.*]] = %[[VAL_15]] to %[[VAL_16]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_18:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
-// CHECK:             %[[VAL_19:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
-// CHECK:             %[[VAL_20:.*]] = addi %[[VAL_17]], %[[VAL_5]] : index
-// CHECK:             %[[VAL_21:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_22:.*]] = %[[VAL_19]] to %[[VAL_21]] step %[[VAL_5]] {
-// CHECK:               %[[VAL_23:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<?xindex>
-// CHECK:               %[[VAL_24:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_22]]] : memref<?xindex>
-// CHECK:               %[[VAL_25:.*]] = addi %[[VAL_22]], %[[VAL_5]] : index
-// CHECK:               %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_27:.*]] = %[[VAL_24]] to %[[VAL_26]] step %[[VAL_5]] {
-// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:                 %[[VAL_29:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xf32>
-// CHECK:                 %[[VAL_30:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_18]], %[[VAL_23]], %[[VAL_28]]] : memref<32x16x8xf32>
-// CHECK:                 %[[VAL_31:.*]] = mulf %[[VAL_29]], %[[VAL_30]] : f32
-// CHECK:                 store %[[VAL_31]], %[[VAL_14]]{{\[}}%[[VAL_18]], %[[VAL_23]], %[[VAL_28]]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_4]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_5]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_10:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_11:.*]] = linalg.sparse_indices %[[VAL_0]], %[[VAL_3]] : tensor<32x16x8xf32> to memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<32x16x8xf32> to memref<?xf32>
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_1]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_14:.*]] = tensor_to_memref %[[VAL_2]] : memref<32x16x8xf32>
+// CHECK:           %[[VAL_15:.*]] = alloc() : memref<32x16x8xf32>
+// CHECK:           linalg.copy(%[[VAL_14]], %[[VAL_15]]) : memref<32x16x8xf32>, memref<32x16x8xf32>
+// CHECK:           %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_5]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_18:.*]] = %[[VAL_16]] to %[[VAL_17]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_19:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK:             %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK:             %[[VAL_21:.*]] = addi %[[VAL_18]], %[[VAL_5]] : index
+// CHECK:             %[[VAL_22:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_23:.*]] = %[[VAL_20]] to %[[VAL_22]] step %[[VAL_5]] {
+// CHECK:               %[[VAL_24:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:               %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK:               %[[VAL_26:.*]] = addi %[[VAL_23]], %[[VAL_5]] : index
+// CHECK:               %[[VAL_27:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK:               scf.for %[[VAL_28:.*]] = %[[VAL_25]] to %[[VAL_27]] step %[[VAL_5]] {
+// CHECK:                 %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK:                 %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_28]]] : memref<?xf32>
+// CHECK:                 %[[VAL_31:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_19]], %[[VAL_24]], %[[VAL_29]]] : memref<32x16x8xf32>
+// CHECK:                 %[[VAL_32:.*]] = mulf %[[VAL_30]], %[[VAL_31]] : f32
+// CHECK:                 store %[[VAL_32]], %[[VAL_15]]{{\[}}%[[VAL_19]], %[[VAL_24]], %[[VAL_29]]] : memref<32x16x8xf32>
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_32:.*]] = tensor_load %[[VAL_14]] : memref<32x16x8xf32>
-// CHECK:           return %[[VAL_32]] : tensor<32x16x8xf32>
+// CHECK:           %[[VAL_33:.*]] = tensor_load %[[VAL_15]] : memref<32x16x8xf32>
+// CHECK:           return %[[VAL_33]] : tensor<32x16x8xf32>
 // CHECK:         }
 func @mul_sss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>, %argx: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
   %0 = linalg.generic #trait_sss
      ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>)
     outs(%argx: tensor<32x16x8xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
#trait_kernel_3d = {
   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>,
 // CHECK-SAME:                    %[[VAL_2:.*2]]: tensor<?x?xf32>,
 // CHECK-SAME:                    %[[VAL_3:.*3]]: tensor<?x?xf32>) -> tensor<?x?xf32> {
-// CHECK:           %[[VAL_4:.*]] = constant 999 : index
+// CHECK:           %[[VAL_4:.*]] = constant 2 : index
 // CHECK:           %[[VAL_5:.*]] = constant 0 : index
 // CHECK:           %[[VAL_6:.*]] = constant 1 : index
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_4]]) : memref<?xindex>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_4]]) : memref<?xf32>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<?x?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<?x?x?xf32> to memref<?xindex>
+// CHECK:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<?x?x?xf32> to memref<?xf32>
 // CHECK:           %[[VAL_10:.*]] = dim %[[VAL_2]], %[[VAL_5]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_11:.*]] = dim %[[VAL_2]], %[[VAL_6]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca(%[[VAL_10]], %[[VAL_11]]) : memref<?x?xf32>
-// CHECK:           %[[VAL_13:.*]] = dim %[[VAL_3]], %[[VAL_5]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_14:.*]] = dim %[[VAL_3]], %[[VAL_6]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_13]], %[[VAL_14]]) : memref<?x?xf32>
-// CHECK:           %[[VAL_16:.*]] = dim %[[VAL_0]], %[[VAL_5]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_17:.*]] = dim %[[VAL_0]], %[[VAL_6]] : tensor<?x?xf32>
-// CHECK:           %[[VAL_18:.*]] = alloca(%[[VAL_16]], %[[VAL_17]]) : memref<?x?xf32>
-// CHECK:           scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_16]] step %[[VAL_6]] {
-// CHECK:             scf.for %[[VAL_20:.*]] = %[[VAL_5]] to %[[VAL_10]] step %[[VAL_6]] {
-// CHECK:               %[[VAL_21:.*]] = muli %[[VAL_10]], %[[VAL_19]] : index
-// CHECK:               %[[VAL_22:.*]] = addi %[[VAL_21]], %[[VAL_20]] : index
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<?x?xf32>
+// CHECK:           %[[VAL_12:.*]] = tensor_to_memref %[[VAL_3]] : memref<?x?xf32>
+// CHECK:           %[[VAL_13:.*]] = dim %[[VAL_0]], %[[VAL_5]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_14:.*]] = dim %[[VAL_0]], %[[VAL_6]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_15:.*]] = tensor_to_memref %[[VAL_0]] : memref<?x?xf32>
+// CHECK:           %[[VAL_16:.*]] = alloc(%[[VAL_13]], %[[VAL_14]]) : memref<?x?xf32>
+// CHECK:           linalg.copy(%[[VAL_15]], %[[VAL_16]]) : memref<?x?xf32>, 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:.*]] = muli %[[VAL_10]], %[[VAL_17]] : index
+// CHECK:               %[[VAL_20:.*]] = addi %[[VAL_19]], %[[VAL_18]] : index
+// CHECK:               %[[VAL_21:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_20]]] : memref<?xindex>
+// CHECK:               %[[VAL_22:.*]] = addi %[[VAL_20]], %[[VAL_6]] : index
 // CHECK:               %[[VAL_23:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_22]]] : memref<?xindex>
-// CHECK:               %[[VAL_24:.*]] = addi %[[VAL_22]], %[[VAL_6]] : index
-// CHECK:               %[[VAL_25:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_24]]] : memref<?xindex>
-// CHECK:               scf.for %[[VAL_26:.*]] = %[[VAL_23]] to %[[VAL_25]] step %[[VAL_6]] {
-// CHECK:                 %[[VAL_27:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_26]]] : memref<?xindex>
-// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_26]]] : memref<?xf32>
-// CHECK:                 scf.for %[[VAL_29:.*]] = %[[VAL_5]] to %[[VAL_17]] step %[[VAL_6]] {
-// CHECK:                   %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_20]], %[[VAL_29]]] : memref<?x?xf32>
-// CHECK:                   %[[VAL_31:.*]] = mulf %[[VAL_28]], %[[VAL_30]] : f32
-// CHECK:                   %[[VAL_32:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_27]], %[[VAL_29]]] : memref<?x?xf32>
-// CHECK:                   %[[VAL_33:.*]] = mulf %[[VAL_31]], %[[VAL_32]] : f32
-// CHECK:                   %[[VAL_34:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_19]], %[[VAL_29]]] : memref<?x?xf32>
-// CHECK:                   %[[VAL_35:.*]] = addf %[[VAL_33]], %[[VAL_34]] : f32
-// CHECK:                   store %[[VAL_35]], %[[VAL_18]]{{\[}}%[[VAL_19]], %[[VAL_29]]] : memref<?x?xf32>
+// CHECK:               scf.for %[[VAL_24:.*]] = %[[VAL_21]] to %[[VAL_23]] step %[[VAL_6]] {
+// CHECK:                 %[[VAL_25:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK:                 scf.for %[[VAL_27:.*]] = %[[VAL_5]] to %[[VAL_14]] step %[[VAL_6]] {
+// CHECK:                   %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_18]], %[[VAL_27]]] : memref<?x?xf32>
+// CHECK:                   %[[VAL_29:.*]] = mulf %[[VAL_26]], %[[VAL_28]] : f32
+// CHECK:                   %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_25]], %[[VAL_27]]] : memref<?x?xf32>
+// CHECK:                   %[[VAL_31:.*]] = mulf %[[VAL_29]], %[[VAL_30]] : f32
+// CHECK:                   %[[VAL_32:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_27]]] : memref<?x?xf32>
+// CHECK:                   %[[VAL_33:.*]] = addf %[[VAL_31]], %[[VAL_32]] : f32
+// CHECK:                   store %[[VAL_33]], %[[VAL_16]]{{\[}}%[[VAL_17]], %[[VAL_27]]] : memref<?x?xf32>
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_36:.*]] = tensor_load %[[VAL_18]] : memref<?x?xf32>
-// CHECK:           return %[[VAL_36]] : tensor<?x?xf32>
+// CHECK:           %[[VAL_34:.*]] = tensor_load %[[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>,
                 %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>, tensor<?x?xf32>, tensor<?x?xf32>)
       outs(%arga: tensor<?x?xf32>) {
#trait_sum_reduction = {
   ],
   iterator_types = ["reduction", "reduction", "reduction"],
   doc = "x += SUM_ijk A(i,j,k)"
 }
 
 // CHECK-LABEL:   func @sum_reduction(
 // CHECK-SAME:                        %[[VAL_0:.*]]: tensor<10x20x30xf32>,
 // CHECK-SAME:                        %[[VAL_1:.*]]: tensor<f32>) -> tensor<f32> {
-// CHECK:           %[[VAL_2:.*]] = constant 999 : index
+// CHECK:           %[[VAL_2:.*]] = constant 2 : index
 // CHECK:           %[[VAL_3:.*]] = constant 0 : index
 // CHECK:           %[[VAL_4:.*]] = constant 1 : index
-// CHECK:           %[[VAL_5:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_6:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_7:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
-// CHECK:           %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca() : memref<f32>
-// CHECK:           %[[VAL_10:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
-// CHECK:           %[[VAL_11:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
-// CHECK:           scf.for %[[VAL_12:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_4]] {
-// CHECK:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
-// CHECK:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_4]] : index
-// CHECK:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
-// CHECK:             scf.for %[[VAL_16:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_4]] {
-// CHECK:               %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_16]]] : memref<?xindex>
-// CHECK:               %[[VAL_18:.*]] = addi %[[VAL_16]], %[[VAL_4]] : index
-// CHECK:               %[[VAL_19:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
-// CHECK:               %[[VAL_20:.*]] = load %[[VAL_9]][] : memref<f32>
-// CHECK:               %[[VAL_21:.*]] = scf.for %[[VAL_22:.*]] = %[[VAL_17]] to %[[VAL_19]] step %[[VAL_4]] iter_args(%[[VAL_23:.*]] = %[[VAL_20]]) -> (f32) {
-// CHECK:                 %[[VAL_24:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_22]]] : memref<?xf32>
-// CHECK:                 %[[VAL_25:.*]] = addf %[[VAL_23]], %[[VAL_24]] : f32
-// CHECK:                 scf.yield %[[VAL_25]] : f32
+// CHECK:           %[[VAL_5:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_3]] : tensor<10x20x30xf32> to memref<?xindex>
+// CHECK:           %[[VAL_6:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_4]] : tensor<10x20x30xf32> to memref<?xindex>
+// CHECK:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_0]], %[[VAL_2]] : tensor<10x20x30xf32> to memref<?xindex>
+// CHECK:           %[[VAL_8:.*]] = linalg.sparse_values %[[VAL_0]] : tensor<10x20x30xf32> to memref<?xf32>
+// CHECK:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<f32>
+// CHECK:           %[[VAL_10:.*]] = alloc() : memref<f32>
+// CHECK:           linalg.copy(%[[VAL_9]], %[[VAL_10]]) : memref<f32>, memref<f32>
+// CHECK:           %[[VAL_11:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK:           %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_11]] to %[[VAL_12]] step %[[VAL_4]] {
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK:             %[[VAL_15:.*]] = addi %[[VAL_13]], %[[VAL_4]] : index
+// CHECK:             %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK:             scf.for %[[VAL_17:.*]] = %[[VAL_14]] to %[[VAL_16]] step %[[VAL_4]] {
+// CHECK:               %[[VAL_18:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK:               %[[VAL_19:.*]] = addi %[[VAL_17]], %[[VAL_4]] : index
+// CHECK:               %[[VAL_20:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK:               %[[VAL_21:.*]] = load %[[VAL_10]][] : memref<f32>
+// CHECK:               %[[VAL_22:.*]] = scf.for %[[VAL_23:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_4]] iter_args(%[[VAL_24:.*]] = %[[VAL_21]]) -> (f32) {
+// CHECK:                 %[[VAL_25:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK:                 %[[VAL_26:.*]] = addf %[[VAL_24]], %[[VAL_25]] : f32
+// CHECK:                 scf.yield %[[VAL_26]] : f32
 // CHECK:               }
-// CHECK:               store %[[VAL_26:.*]], %[[VAL_9]][] : memref<f32>
+// CHECK:               store %[[VAL_27:.*]], %[[VAL_10]][] : memref<f32>
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_27:.*]] = tensor_load %[[VAL_9]] : memref<f32>
-// CHECK:           return %[[VAL_27]] : tensor<f32>
+// CHECK:           %[[VAL_28:.*]] = tensor_load %[[VAL_10]] : memref<f32>
+// CHECK:           return %[[VAL_28]] : tensor<f32>
 // CHECK:         }
 func @sum_reduction(%arga: tensor<10x20x30xf32>, %argx: tensor<f32>) -> tensor<f32> {
   %0 = linalg.generic #trait_sum_reduction
      ins(%arga: tensor<10x20x30xf32>)
     outs(%argx: tensor<f32>) {
       ^bb(%a: f32, %x: f32):
         %0 = addf %x, %a : f32
         linalg.yield %0 : f32

 
 // CHECK-LABEL:   func @sum_reduction_inv(
 // CHECK-SAME:                            %[[VAL_0:.*]]: tensor<?x?x?xf32>,
 // CHECK-SAME:                            %[[VAL_1:.*]]: tensor<?xf32>,
 // CHECK-SAME:                            %[[VAL_2:.*]]: tensor<f32>) -> tensor<f32> {
 // CHECK:           %[[VAL_3:.*]] = constant 2 : index
 // CHECK:           %[[VAL_4:.*]] = constant 0 : index
 // CHECK:           %[[VAL_5:.*]] = constant 1 : index
-// CHECK:           %[[VAL_6:.*]] = dim %[[VAL_0]], %[[VAL_4]] : tensor<?x?x?xf32>
-// CHECK:           %[[VAL_7:.*]] = dim %[[VAL_0]], %[[VAL_5]] : tensor<?x?x?xf32>
-// CHECK:           %[[VAL_8:.*]] = dim %[[VAL_0]], %[[VAL_3]] : tensor<?x?x?xf32>
-// CHECK:           %[[VAL_9:.*]] = alloca(%[[VAL_6]], %[[VAL_7]], %[[VAL_8]]) : memref<?x?x?xf32>
-// CHECK:           %[[VAL_10:.*]] = dim %[[VAL_1]], %[[VAL_4]] : tensor<?xf32>
-// CHECK:           %[[VAL_11:.*]] = alloca(%[[VAL_10]]) : memref<?xf32>
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<f32>
-// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_4]] to %[[VAL_10]] step %[[VAL_5]] {
-// CHECK:             %[[VAL_14:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]]] : memref<?xf32>
-// CHECK:             scf.for %[[VAL_15:.*]] = %[[VAL_4]] to %[[VAL_7]] step %[[VAL_5]] {
+// CHECK:           %[[VAL_6:.*]] = dim %[[VAL_0]], %[[VAL_5]] : tensor<?x?x?xf32>
+// CHECK:           %[[VAL_7:.*]] = dim %[[VAL_0]], %[[VAL_3]] : tensor<?x?x?xf32>
+// CHECK:           %[[VAL_8:.*]] = tensor_to_memref %[[VAL_0]] : memref<?x?x?xf32>
+// CHECK:           %[[VAL_9:.*]] = dim %[[VAL_1]], %[[VAL_4]] : tensor<?xf32>
+// CHECK:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<?xf32>
+// CHECK:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<f32>
+// CHECK:           %[[VAL_12:.*]] = alloc() : memref<f32>
+// CHECK:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<f32>, memref<f32>
+// CHECK:           scf.for %[[VAL_13:.*]] = %[[VAL_4]] to %[[VAL_9]] step %[[VAL_5]] {
+// CHECK:             %[[VAL_14:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_13]]] : memref<?xf32>
+// CHECK:             scf.for %[[VAL_15:.*]] = %[[VAL_4]] to %[[VAL_6]] step %[[VAL_5]] {
 // CHECK:               %[[VAL_16:.*]] = load %[[VAL_12]][] : memref<f32>
-// CHECK:               %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_4]] to %[[VAL_8]] step %[[VAL_5]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f32) {
-// CHECK:                 %[[VAL_20:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_13]], %[[VAL_15]], %[[VAL_18]]] : memref<?x?x?xf32>
+// CHECK:               %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_4]] to %[[VAL_7]] step %[[VAL_5]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f32) {
+// CHECK:                 %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_13]], %[[VAL_15]], %[[VAL_18]]] : memref<?x?x?xf32>
 // CHECK:                 %[[VAL_21:.*]] = mulf %[[VAL_20]], %[[VAL_14]] : f32
 // CHECK:                 %[[VAL_22:.*]] = addf %[[VAL_19]], %[[VAL_21]] : f32
 // CHECK:                 scf.yield %[[VAL_22]] : f32
 // CHECK:               }
 // CHECK:               store %[[VAL_23:.*]], %[[VAL_12]][] : memref<f32>
 // CHECK:             }
 // CHECK:           }
 // CHECK:           %[[VAL_24:.*]] = tensor_load %[[VAL_12]] : memref<f32>

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

mlir/test/Dialect/Linalg/sparse_lower.mlir

+// RUN: mlir-opt %s -test-sparsification | \
+// RUN:   FileCheck %s --check-prefix=CHECK-HIR
+//
+// RUN: mlir-opt %s -test-sparsification="lower" --convert-linalg-to-loops | \
+// RUN:   FileCheck %s --check-prefix=CHECK-MIR
+//
+// RUN: mlir-opt %s -test-sparsification="lower" --convert-linalg-to-loops \
+// RUN:   --func-bufferize --tensor-constant-bufferize \
+// RUN:   --tensor-bufferize --finalizing-bufferize  | \
+// RUN:   FileCheck %s --check-prefix=CHECK-LIR
+//
+// RUN: mlir-opt %s -test-sparsification="lower fast-output" --convert-linalg-to-loops \
+// RUN:   --func-bufferize --tensor-constant-bufferize \
+// RUN:   --tensor-bufferize --finalizing-bufferize  | \
+// RUN:   FileCheck %s --check-prefix=CHECK-FAST
+
+#trait_matvec = {
+  indexing_maps = [
+    affine_map<(i,j) -> (i,j)>,  // A
+    affine_map<(i,j) -> (j)>,    // b
+    affine_map<(i,j) -> (i)>     // x (out)
+  ],
+  iterator_types = ["parallel","reduction"],
+  sparse = [
+    [ "D", "S" ],  // A
+    [ "D" ],       // b
+    [ "D" ]        // x (out)
+  ],
+  sparse_dim_map = [
+    affine_map<(i,j) -> (j,i)>,  // A: column-wise
+    affine_map<(i)   -> (i)>,    // x
+    affine_map<(i)   -> (i)>     // b
+  ],
+  doc = "x(i) += A(i,j) * b(j)"
+}
+
+// CHECK-HIR-LABEL:   func @matvec(
+// CHECK-HIR-SAME:                 %[[VAL_0:.*]]: !llvm.ptr<i8>,
+// CHECK-HIR-SAME:                 %[[VAL_1:.*]]: tensor<64xf64>,
+// CHECK-HIR-SAME:                 %[[VAL_2:.*]]: tensor<64xf64>) -> tensor<64xf64> {
+// CHECK-HIR:           %[[VAL_3:.*]] = constant 64 : index
+// CHECK-HIR:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK-HIR:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK-HIR:           %[[VAL_6:.*]] = linalg.sparse_tensor %[[VAL_0]] : !llvm.ptr<i8> to tensor<64x64xf64>
+// CHECK-HIR:           %[[VAL_7:.*]] = linalg.sparse_pointers %[[VAL_6]], %[[VAL_5]] : tensor<64x64xf64> to memref<?xindex>
+// CHECK-HIR:           %[[VAL_8:.*]] = linalg.sparse_indices %[[VAL_6]], %[[VAL_5]] : tensor<64x64xf64> to memref<?xindex>
+// CHECK-HIR:           %[[VAL_9:.*]] = linalg.sparse_values %[[VAL_6]] : tensor<64x64xf64> to memref<?xf64>
+// CHECK-HIR:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_1]] : memref<64xf64>
+// CHECK-HIR:           %[[VAL_11:.*]] = tensor_to_memref %[[VAL_2]] : memref<64xf64>
+// CHECK-HIR:           %[[VAL_12:.*]] = alloc() : memref<64xf64>
+// CHECK-HIR:           linalg.copy(%[[VAL_11]], %[[VAL_12]]) : memref<64xf64>, memref<64xf64>
+// CHECK-HIR:           scf.for %[[VAL_13:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK-HIR:             %[[VAL_14:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK-HIR:             %[[VAL_15:.*]] = addi %[[VAL_13]], %[[VAL_5]] : index
+// CHECK-HIR:             %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK-HIR:             %[[VAL_17:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_13]]] : memref<64xf64>
+// CHECK-HIR:             %[[VAL_18:.*]] = scf.for %[[VAL_19:.*]] = %[[VAL_14]] to %[[VAL_16]] step %[[VAL_5]] iter_args(%[[VAL_20:.*]] = %[[VAL_17]]) -> (f64) {
+// CHECK-HIR:               %[[VAL_21:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK-HIR:               %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xf64>
+// CHECK-HIR:               %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<64xf64>
+// CHECK-HIR:               %[[VAL_24:.*]] = mulf %[[VAL_22]], %[[VAL_23]] : f64
+// CHECK-HIR:               %[[VAL_25:.*]] = addf %[[VAL_20]], %[[VAL_24]] : f64
+// CHECK-HIR:               scf.yield %[[VAL_25]] : f64
+// CHECK-HIR:             }
+// CHECK-HIR:             store %[[VAL_26:.*]], %[[VAL_12]]{{\[}}%[[VAL_13]]] : memref<64xf64>
+// CHECK-HIR:           }
+// CHECK-HIR:           %[[VAL_27:.*]] = tensor_load %[[VAL_12]] : memref<64xf64>
+// CHECK-HIR:           return %[[VAL_27]] : tensor<64xf64>
+// CHECK-HIR:         }
+
+// CHECK-MIR-LABEL:   func @matvec(
+// CHECK-MIR-SAME:                 %[[VAL_0:.*]]: !llvm.ptr<i8>,
+// CHECK-MIR-SAME:                 %[[VAL_1:.*]]: tensor<64xf64>,
+// CHECK-MIR-SAME:                 %[[VAL_2:.*]]: tensor<64xf64>) -> tensor<64xf64> {
+// CHECK-MIR:           %[[VAL_3:.*]] = constant 64 : index
+// CHECK-MIR:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK-MIR:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK-MIR:           %[[VAL_6:.*]] = call @sparsePtrsI64(%[[VAL_0]], %[[VAL_5]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+// CHECK-MIR:           %[[VAL_7:.*]] = call @sparseIndxsI64(%[[VAL_0]], %[[VAL_5]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+// CHECK-MIR:           %[[VAL_8:.*]] = call @sparseValsF64(%[[VAL_0]]) : (!llvm.ptr<i8>) -> memref<?xf64>
+// CHECK-MIR:           %[[VAL_9:.*]] = tensor_to_memref %[[VAL_1]] : memref<64xf64>
+// CHECK-MIR:           %[[VAL_10:.*]] = tensor_to_memref %[[VAL_2]] : memref<64xf64>
+// CHECK-MIR:           %[[VAL_11:.*]] = alloc() : memref<64xf64>
+// CHECK-MIR:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK-MIR:             %[[VAL_13:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_12]]] : memref<64xf64>
+// CHECK-MIR:             store %[[VAL_13]], %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<64xf64>
+// CHECK-MIR:           }
+// CHECK-MIR:           scf.for %[[VAL_14:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK-MIR:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK-MIR:             %[[VAL_16:.*]] = addi %[[VAL_14]], %[[VAL_5]] : index
+// CHECK-MIR:             %[[VAL_17:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK-MIR:             %[[VAL_18:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_14]]] : memref<64xf64>
+// CHECK-MIR:             %[[VAL_19:.*]] = scf.for %[[VAL_20:.*]] = %[[VAL_15]] to %[[VAL_17]] step %[[VAL_5]] iter_args(%[[VAL_21:.*]] = %[[VAL_18]]) -> (f64) {
+// CHECK-MIR:               %[[VAL_22:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_20]]] : memref<?xindex>
+// CHECK-MIR:               %[[VAL_23:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_20]]] : memref<?xf64>
+// CHECK-MIR:               %[[VAL_24:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_22]]] : memref<64xf64>
+// CHECK-MIR:               %[[VAL_25:.*]] = mulf %[[VAL_23]], %[[VAL_24]] : f64
+// CHECK-MIR:               %[[VAL_26:.*]] = addf %[[VAL_21]], %[[VAL_25]] : f64
+// CHECK-MIR:               scf.yield %[[VAL_26]] : f64
+// CHECK-MIR:             }
+// CHECK-MIR:             store %[[VAL_27:.*]], %[[VAL_11]]{{\[}}%[[VAL_14]]] : memref<64xf64>
+// CHECK-MIR:           }
+// CHECK-MIR:           %[[VAL_28:.*]] = tensor_load %[[VAL_11]] : memref<64xf64>
+// CHECK-MIR:           return %[[VAL_28]] : tensor<64xf64>
+// CHECK-MIR:         }
+
+// CHECK-LIR-LABEL:   func @matvec(
+// CHECK-LIR-SAME:                 %[[VAL_0:.*]]: !llvm.ptr<i8>,
+// CHECK-LIR-SAME:                 %[[VAL_1:.*]]: memref<64xf64>,
+// CHECK-LIR-SAME:                 %[[VAL_2:.*]]: memref<64xf64>) -> memref<64xf64> {
+// CHECK-LIR:           %[[VAL_3:.*]] = constant 64 : index
+// CHECK-LIR:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK-LIR:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK-LIR:           %[[VAL_6:.*]] = call @sparsePtrsI64(%[[VAL_0]], %[[VAL_5]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+// CHECK-LIR:           %[[VAL_7:.*]] = call @sparseIndxsI64(%[[VAL_0]], %[[VAL_5]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+// CHECK-LIR:           %[[VAL_8:.*]] = call @sparseValsF64(%[[VAL_0]]) : (!llvm.ptr<i8>) -> memref<?xf64>
+// CHECK-LIR:           %[[VAL_9:.*]] = alloc() : memref<64xf64>
+// CHECK-LIR:           scf.for %[[VAL_10:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK-LIR:             %[[VAL_11:.*]] = load %[[VAL_2]]{{\[}}%[[VAL_10]]] : memref<64xf64>
+// CHECK-LIR:             store %[[VAL_11]], %[[VAL_9]]{{\[}}%[[VAL_10]]] : memref<64xf64>
+// CHECK-LIR:           }
+// CHECK-LIR:           scf.for %[[VAL_12:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK-LIR:             %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK-LIR:             %[[VAL_14:.*]] = addi %[[VAL_12]], %[[VAL_5]] : index
+// CHECK-LIR:             %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK-LIR:             %[[VAL_16:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_12]]] : memref<64xf64>
+// CHECK-LIR:             %[[VAL_17:.*]] = scf.for %[[VAL_18:.*]] = %[[VAL_13]] to %[[VAL_15]] step %[[VAL_5]] iter_args(%[[VAL_19:.*]] = %[[VAL_16]]) -> (f64) {
+// CHECK-LIR:               %[[VAL_20:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK-LIR:               %[[VAL_21:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_18]]] : memref<?xf64>
+// CHECK-LIR:               %[[VAL_22:.*]] = load %[[VAL_1]]{{\[}}%[[VAL_20]]] : memref<64xf64>
+// CHECK-LIR:               %[[VAL_23:.*]] = mulf %[[VAL_21]], %[[VAL_22]] : f64
+// CHECK-LIR:               %[[VAL_24:.*]] = addf %[[VAL_19]], %[[VAL_23]] : f64
+// CHECK-LIR:               scf.yield %[[VAL_24]] : f64
+// CHECK-LIR:             }
+// CHECK-LIR:             store %[[VAL_25:.*]], %[[VAL_9]]{{\[}}%[[VAL_12]]] : memref<64xf64>
+// CHECK-LIR:           }
+// CHECK-LIR:           return %[[VAL_9]] : memref<64xf64>
+// CHECK-LIR:         }
+
+// CHECK-FAST-LABEL:   func @matvec(
+// CHECK-FAST-SAME:                 %[[VAL_0:.*]]: !llvm.ptr<i8>,
+// CHECK-FAST-SAME:                 %[[VAL_1:.*]]: memref<64xf64>,
+// CHECK-FAST-SAME:                 %[[VAL_2:.*]]: memref<64xf64>) -> memref<64xf64> {
+// CHECK-FAST:           %[[VAL_3:.*]] = constant 64 : index
+// CHECK-FAST:           %[[VAL_4:.*]] = constant 0 : index
+// CHECK-FAST:           %[[VAL_5:.*]] = constant 1 : index
+// CHECK-FAST:           %[[VAL_6:.*]] = call @sparsePtrsI64(%[[VAL_0]], %[[VAL_5]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+// CHECK-FAST:           %[[VAL_7:.*]] = call @sparseIndxsI64(%[[VAL_0]], %[[VAL_5]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+// CHECK-FAST:           %[[VAL_8:.*]] = call @sparseValsF64(%[[VAL_0]]) : (!llvm.ptr<i8>) -> memref<?xf64>
+// CHECK-FAST:           scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK-FAST:             %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]]] : memref<?xindex>
+// CHECK-FAST:             %[[VAL_11:.*]] = addi %[[VAL_9]], %[[VAL_5]] : index
+// CHECK-FAST:             %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xindex>
+// CHECK-FAST:             %[[VAL_13:.*]] = load %[[VAL_2]]{{\[}}%[[VAL_9]]] : memref<64xf64>
+// CHECK-FAST:             %[[VAL_14:.*]] = scf.for %[[VAL_15:.*]] = %[[VAL_10]] to %[[VAL_12]] step %[[VAL_5]] iter_args(%[[VAL_16:.*]] = %[[VAL_13]]) -> (f64) {
+// CHECK-FAST:               %[[VAL_17:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK-FAST:               %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_15]]] : memref<?xf64>
+// CHECK-FAST:               %[[VAL_19:.*]] = load %[[VAL_1]]{{\[}}%[[VAL_17]]] : memref<64xf64>
+// CHECK-FAST:               %[[VAL_20:.*]] = mulf %[[VAL_18]], %[[VAL_19]] : f64
+// CHECK-FAST:               %[[VAL_21:.*]] = addf %[[VAL_16]], %[[VAL_20]] : f64
+// CHECK-FAST:               scf.yield %[[VAL_21]] : f64
+// CHECK-FAST:             }
+// CHECK-FAST:             store %[[VAL_22:.*]], %[[VAL_2]]{{\[}}%[[VAL_9]]] : memref<64xf64>
+// CHECK-FAST:           }
+// CHECK-FAST:           return %[[VAL_2]] : memref<64xf64>
+// CHECK-FAST:         }
+
+!SparseTensor = type !llvm.ptr<i8>
+
+func @matvec(%argA: !SparseTensor, %argb: tensor<64xf64>, %argx: tensor<64xf64>) -> tensor<64xf64> {
+  %arga = linalg.sparse_tensor %argA : !SparseTensor to tensor<64x64xf64>
+  %0 = linalg.generic #trait_matvec
+      ins(%arga, %argb : tensor<64x64xf64>, tensor<64xf64>)
+      outs(%argx: tensor<64xf64>) {
+    ^bb(%A: f64, %b: f64, %x: f64):
+      %0 = mulf %A, %b : f64
+      %1 = addf %x, %0 : f64
+      linalg.yield %1 : f64
+  } -> tensor<64xf64>
+  return %0 : tensor<64xf64>
+}

mlir/test/Dialect/Linalg/sparse_lower_calls.mlir

+// RUN: mlir-opt --test-sparsification="lower" %s | FileCheck %s
+
+!SparseTensor = type !llvm.ptr<i8>
+
+// CHECK-LABEL: func @sparse_pointers(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
+//       CHECK: %[[C:.*]] = constant 1 : index
+//       CHECK: %[[T:.*]] = call @sparsePtrsI64(%[[A]], %[[C]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+//       CHECK: return %[[T]] : memref<?xindex>
+func @sparse_pointers(%arg0: !SparseTensor) -> memref<?xindex> {
+  %a = linalg.sparse_tensor %arg0 : !SparseTensor to tensor<128xf64>
+  %c = constant 1 : index
+  %0 = linalg.sparse_pointers %a, %c : tensor<128xf64> to memref<?xindex>
+  return %0 : memref<?xindex>
+}
+
+// CHECK-LABEL: func @sparse_indices(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
+//       CHECK: %[[C:.*]] = constant 1 : index
+//       CHECK: %[[T:.*]] = call @sparseIndxsI64(%[[A]], %[[C]]) : (!llvm.ptr<i8>, index) -> memref<?xindex>
+//       CHECK: return %[[T]] : memref<?xindex>
+func @sparse_indices(%arg0: !SparseTensor) -> memref<?xindex> {
+  %a = linalg.sparse_tensor %arg0 : !SparseTensor to tensor<128xf64>
+  %c = constant 1 : index
+  %0 = linalg.sparse_indices %a, %c : tensor<128xf64> to memref<?xindex>
+  return %0 : memref<?xindex>
+}
+
+// CHECK-LABEL: func @sparse_values(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
+//       CHECK: %[[T:.*]] = call @sparseValsF64(%[[A]]) : (!llvm.ptr<i8>) -> memref<?xf64>
+//       CHECK: return %[[T]] : memref<?xf64>
+func @sparse_values(%arg0: !SparseTensor) -> memref<?xf64> {
+  %a = linalg.sparse_tensor %arg0 : !SparseTensor to tensor<128xf64>
+  %0 = linalg.sparse_values %a : tensor<128xf64> to memref<?xf64>
+  return %0 : memref<?xf64>
+}

mlir/test/Dialect/Linalg/sparse_nd.mlir

iterator_types = ["parallel", "parallel", "parallel", "parallel",
                     "parallel", "parallel", "parallel", "parallel"],
   doc = "X(i,j,k,l,m,n,o,p) = A(i,j,k,l,m,n,o,p)  * B(p,o,n,m,l,k,j,i)"
 }
 
 // CHECK-LABEL:   func @mul(
 // CHECK-SAME:              %[[VAL_0:.*0]]: tensor<100x200x300x400x500x600x700x800xf32>,
 // CHECK-SAME:              %[[VAL_1:.*1]]: tensor<100x200x300x400x500x600x700x800xf32>,
 // CHECK-SAME:              %[[VAL_2:.*2]]: tensor<100x200x300x400x500x600x700x800xf32>) -> tensor<100x200x300x400x500x600x700x800xf32> {
-// CHECK:           %[[VAL_3:.*]] = constant 999 : index
-// CHECK:           %[[VAL_4:.*]] = constant 100 : index
-// CHECK:           %[[VAL_5:.*]] = constant 200 : index
-// CHECK:           %[[VAL_6:.*]] = constant 300 : index
-// CHECK:           %[[VAL_7:.*]] = constant 600 : index
-// CHECK:           %[[VAL_8:.*]] = constant 700 : index
-// CHECK:           %[[VAL_9:.*]] = constant 800 : index
-// CHECK:           %[[VAL_10:.*]] = constant 0 : index
-// CHECK:           %[[VAL_11:.*]] = constant 1 : index
-// CHECK:           %[[VAL_12:.*]] = alloca() : memref<100x200x300x400x500x600x700x800xf32>
-// CHECK:           %[[VAL_13:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_14:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_15:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_16:.*]] = alloca(%[[VAL_3]]) : memref<?xindex>
-// CHECK:           %[[VAL_17:.*]] = alloca(%[[VAL_3]]) : memref<?xf32>
-// CHECK:           %[[VAL_18:.*]] = alloca() : memref<100x200x300x400x500x600x700x800xf32>
-// CHECK:           scf.for %[[VAL_19:.*]] = %[[VAL_10]] to %[[VAL_9]] step %[[VAL_11]] {
-// CHECK:             scf.for %[[VAL_20:.*]] = %[[VAL_10]] to %[[VAL_8]] step %[[VAL_11]] {
-// CHECK:               %[[VAL_21:.*]] = muli %[[VAL_19]], %[[VAL_8]] : index
-// CHECK:               %[[VAL_22:.*]] = addi %[[VAL_21]], %[[VAL_20]] : index
-// CHECK:               scf.for %[[VAL_23:.*]] = %[[VAL_10]] to %[[VAL_7]] step %[[VAL_11]] {
-// CHECK:                 %[[VAL_24:.*]] = muli %[[VAL_22]], %[[VAL_7]] : index
-// CHECK:                 %[[VAL_25:.*]] = addi %[[VAL_24]], %[[VAL_23]] : index
-// CHECK:                 %[[VAL_26:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_25]]] : memref<?xindex>
-// CHECK:                 %[[VAL_27:.*]] = addi %[[VAL_25]], %[[VAL_11]] : index
-// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_27]]] : memref<?xindex>
-// CHECK:                 scf.for %[[VAL_29:.*]] = %[[VAL_26]] to %[[VAL_28]] step %[[VAL_11]] {
-// CHECK:                   %[[VAL_30:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_29]]] : memref<?xindex>
-// CHECK:                   %[[VAL_31:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_29]]] : memref<?xindex>
-// CHECK:                   %[[VAL_32:.*]] = addi %[[VAL_29]], %[[VAL_11]] : index
-// CHECK:                   %[[VAL_33:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_32]]] : memref<?xindex>
-// CHECK:                   scf.for %[[VAL_34:.*]] = %[[VAL_31]] to %[[VAL_33]] step %[[VAL_11]] {
-// CHECK:                     %[[VAL_35:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_34]]] : memref<?xindex>
-// CHECK:                     scf.for %[[VAL_36:.*]] = %[[VAL_10]] to %[[VAL_6]] step %[[VAL_11]] {
-// CHECK:                       %[[VAL_37:.*]] = muli %[[VAL_34]], %[[VAL_6]] : index
-// CHECK:                       %[[VAL_38:.*]] = addi %[[VAL_37]], %[[VAL_36]] : index
-// CHECK:                       scf.for %[[VAL_39:.*]] = %[[VAL_10]] to %[[VAL_5]] step %[[VAL_11]] {
-// CHECK:                         %[[VAL_40:.*]] = muli %[[VAL_38]], %[[VAL_5]] : index
-// CHECK:                         %[[VAL_41:.*]] = addi %[[VAL_40]], %[[VAL_39]] : index
-// CHECK:                         scf.for %[[VAL_42:.*]] = %[[VAL_10]] to %[[VAL_4]] step %[[VAL_11]] {
-// CHECK:                           %[[VAL_43:.*]] = muli %[[VAL_41]], %[[VAL_4]] : index
-// CHECK:                           %[[VAL_44:.*]] = addi %[[VAL_43]], %[[VAL_42]] : index
-// CHECK:                           %[[VAL_45:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_42]], %[[VAL_39]], %[[VAL_36]], %[[VAL_35]], %[[VAL_30]], %[[VAL_23]], %[[VAL_20]], %[[VAL_19]]] : memref<100x200x300x400x500x600x700x800xf32>
-// CHECK:                           %[[VAL_46:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_44]]] : memref<?xf32>
-// CHECK:                           %[[VAL_47:.*]] = mulf %[[VAL_45]], %[[VAL_46]] : f32
-// CHECK:                           store %[[VAL_47]], %[[VAL_18]]{{\[}}%[[VAL_42]], %[[VAL_39]], %[[VAL_36]], %[[VAL_35]], %[[VAL_30]], %[[VAL_23]], %[[VAL_20]], %[[VAL_19]]] : memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:           %[[VAL_3:.*]] = constant 3 : index
+// CHECK:           %[[VAL_4:.*]] = constant 4 : index
+// CHECK:           %[[VAL_5:.*]] = constant 100 : index
+// CHECK:           %[[VAL_6:.*]] = constant 200 : index
+// CHECK:           %[[VAL_7:.*]] = constant 300 : index
+// CHECK:           %[[VAL_8:.*]] = constant 600 : index
+// CHECK:           %[[VAL_9:.*]] = constant 700 : index
+// CHECK:           %[[VAL_10:.*]] = constant 800 : index
+// CHECK:           %[[VAL_11:.*]] = constant 0 : index
+// CHECK:           %[[VAL_12:.*]] = constant 1 : index
+// CHECK:           %[[VAL_13:.*]] = tensor_to_memref %[[VAL_0]] : memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:           %[[VAL_14:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_3]] : tensor<100x200x300x400x500x600x700x800xf32> to memref<?xindex>
+// CHECK:           %[[VAL_15:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_3]] : tensor<100x200x300x400x500x600x700x800xf32> to memref<?xindex>
+// CHECK:           %[[VAL_16:.*]] = linalg.sparse_pointers %[[VAL_1]], %[[VAL_4]] : tensor<100x200x300x400x500x600x700x800xf32> to memref<?xindex>
+// CHECK:           %[[VAL_17:.*]] = linalg.sparse_indices %[[VAL_1]], %[[VAL_4]] : tensor<100x200x300x400x500x600x700x800xf32> to memref<?xindex>
+// CHECK:           %[[VAL_18:.*]] = linalg.sparse_values %[[VAL_1]] : tensor<100x200x300x400x500x600x700x800xf32> to memref<?xf32>
+// CHECK:           %[[VAL_19:.*]] = tensor_to_memref %[[VAL_2]] : memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:           %[[VAL_20:.*]] = alloc() : memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:           linalg.copy(%[[VAL_19]], %[[VAL_20]]) : memref<100x200x300x400x500x600x700x800xf32>, memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:           scf.for %[[VAL_21:.*]] = %[[VAL_11]] to %[[VAL_10]] step %[[VAL_12]] {
+// CHECK:             scf.for %[[VAL_22:.*]] = %[[VAL_11]] to %[[VAL_9]] step %[[VAL_12]] {
+// CHECK:               %[[VAL_23:.*]] = muli %[[VAL_21]], %[[VAL_9]] : index
+// CHECK:               %[[VAL_24:.*]] = addi %[[VAL_23]], %[[VAL_22]] : index
+// CHECK:               scf.for %[[VAL_25:.*]] = %[[VAL_11]] to %[[VAL_8]] step %[[VAL_12]] {
+// CHECK:                 %[[VAL_26:.*]] = muli %[[VAL_24]], %[[VAL_8]] : index
+// CHECK:                 %[[VAL_27:.*]] = addi %[[VAL_26]], %[[VAL_25]] : index
+// CHECK:                 %[[VAL_28:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK:                 %[[VAL_29:.*]] = addi %[[VAL_27]], %[[VAL_12]] : index
+// CHECK:                 %[[VAL_30:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_29]]] : memref<?xindex>
+// CHECK:                 scf.for %[[VAL_31:.*]] = %[[VAL_28]] to %[[VAL_30]] step %[[VAL_12]] {
+// CHECK:                   %[[VAL_32:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_31]]] : memref<?xindex>
+// CHECK:                   %[[VAL_33:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_31]]] : memref<?xindex>
+// CHECK:                   %[[VAL_34:.*]] = addi %[[VAL_31]], %[[VAL_12]] : index
+// CHECK:                   %[[VAL_35:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_34]]] : memref<?xindex>
+// CHECK:                   scf.for %[[VAL_36:.*]] = %[[VAL_33]] to %[[VAL_35]] step %[[VAL_12]] {
+// CHECK:                     %[[VAL_37:.*]] = load %[[VAL_17]]{{\[}}%[[VAL_36]]] : memref<?xindex>
+// CHECK:                     scf.for %[[VAL_38:.*]] = %[[VAL_11]] to %[[VAL_7]] step %[[VAL_12]] {
+// CHECK:                       %[[VAL_39:.*]] = muli %[[VAL_36]], %[[VAL_7]] : index
+// CHECK:                       %[[VAL_40:.*]] = addi %[[VAL_39]], %[[VAL_38]] : index
+// CHECK:                       scf.for %[[VAL_41:.*]] = %[[VAL_11]] to %[[VAL_6]] step %[[VAL_12]] {
+// CHECK:                         %[[VAL_42:.*]] = muli %[[VAL_40]], %[[VAL_6]] : index
+// CHECK:                         %[[VAL_43:.*]] = addi %[[VAL_42]], %[[VAL_41]] : index
+// CHECK:                         scf.for %[[VAL_44:.*]] = %[[VAL_11]] to %[[VAL_5]] step %[[VAL_12]] {
+// CHECK:                           %[[VAL_45:.*]] = muli %[[VAL_43]], %[[VAL_5]] : index
+// CHECK:                           %[[VAL_46:.*]] = addi %[[VAL_45]], %[[VAL_44]] : index
+// CHECK:                           %[[VAL_47:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_44]], %[[VAL_41]], %[[VAL_38]], %[[VAL_37]], %[[VAL_32]], %[[VAL_25]], %[[VAL_22]], %[[VAL_21]]] : memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:                           %[[VAL_48:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_46]]] : memref<?xf32>
+// CHECK:                           %[[VAL_49:.*]] = mulf %[[VAL_47]], %[[VAL_48]] : f32
+// CHECK:                           store %[[VAL_49]], %[[VAL_20]]{{\[}}%[[VAL_44]], %[[VAL_41]], %[[VAL_38]], %[[VAL_37]], %[[VAL_32]], %[[VAL_25]], %[[VAL_22]], %[[VAL_21]]] : memref<100x200x300x400x500x600x700x800xf32>
 // CHECK:                         }
 // CHECK:                       }
 // CHECK:                     }
 // CHECK:                   }
 // CHECK:                 }
 // CHECK:               }
 // CHECK:             }
 // CHECK:           }
-// CHECK:           %[[VAL_48:.*]] = tensor_load %[[VAL_18]] : memref<100x200x300x400x500x600x700x800xf32>
-// CHECK:           return %[[VAL_48]] : tensor<100x200x300x400x500x600x700x800xf32>
+// CHECK:           %[[VAL_50:.*]] = tensor_load %[[VAL_20]] : memref<100x200x300x400x500x600x700x800xf32>
+// CHECK:           return %[[VAL_50]] : tensor<100x200x300x400x500x600x700x800xf32>
 // CHECK:         }
 func @mul(%arga: tensor<100x200x300x400x500x600x700x800xf32>,
           %argb: tensor<100x200x300x400x500x600x700x800xf32>,
           %argx: tensor<100x200x300x400x500x600x700x800xf32>)
         -> tensor<100x200x300x400x500x600x700x800xf32> {
   %0 = linalg.generic #trait_mul
     ins(%arga, %argb: tensor<100x200x300x400x500x600x700x800xf32>,
                       tensor<100x200x300x400x500x600x700x800xf32>)
     outs(%argx: tensor<100x200x300x400x500x600x700x800xf32>) {
       ^bb(%a: f32, %b: f32, %x: f32):
         %0 = mulf %a, %b : f32
         linalg.yield %0 : f32
     }      -> tensor<100x200x300x400x500x600x700x800xf32>
   return %0 : tensor<100x200x300x400x500x600x700x800xf32>
 }

mlir/test/Dialect/Linalg/sparse_roundtrip.mlir

+// RUN: mlir-opt -split-input-file %s | FileCheck %s
+
+!SparseTensor = type !llvm.ptr<i8>
+
+// CHECK-LABEL: func @sparse_tensor(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
+//       CHECK: %[[T:.*]] = linalg.sparse_tensor %[[A]] : !llvm.ptr<i8> to tensor<128xf64>
+//       CHECK: return %[[T]] : tensor<128xf64>
+func @sparse_tensor(%arg0: !SparseTensor) -> tensor<128xf64> {
+  %0 = linalg.sparse_tensor %arg0 : !SparseTensor to tensor<128xf64>
+  return %0 : tensor<128xf64>
+}
+
+// -----
+
+// CHECK-LABEL: func @sparse_pointers(
+//  CHECK-SAME: %[[A:.*]]: tensor<128xf64>)
+//       CHECK: %[[C:.*]] = constant 1 : index
+//       CHECK: %[[T:.*]] = linalg.sparse_pointers %[[A]], %[[C]] : tensor<128xf64> to memref<?xindex>
+//       CHECK: return %[[T]] : memref<?xindex>
+func @sparse_pointers(%arg0: tensor<128xf64>) -> memref<?xindex> {
+  %c = constant 1 : index
+  %0 = linalg.sparse_pointers %arg0, %c : tensor<128xf64> to memref<?xindex>
+  return %0 : memref<?xindex>
+}
+
+// -----
+
+// CHECK-LABEL: func @sparse_indices(
+//  CHECK-SAME: %[[A:.*]]: tensor<128xf64>)
+//       CHECK: %[[C:.*]] = constant 1 : index
+//       CHECK: %[[T:.*]] = linalg.sparse_indices %[[A]], %[[C]] : tensor<128xf64> to memref<?xindex>
+//       CHECK: return %[[T]] : memref<?xindex>
+func @sparse_indices(%arg0: tensor<128xf64>) -> memref<?xindex> {
+  %c = constant 1 : index
+  %0 = linalg.sparse_indices %arg0, %c : tensor<128xf64> to memref<?xindex>
+  return %0 : memref<?xindex>
+}
+
+// -----
+
+// CHECK-LABEL: func @sparse_values(
+//  CHECK-SAME: %[[A:.*]]: tensor<128xf64>)
+//       CHECK: %[[T:.*]] = linalg.sparse_values %[[A]] : tensor<128xf64> to memref<?xf64>
+//       CHECK: return %[[T]] : memref<?xf64>
+func @sparse_values(%arg0: tensor<128xf64>) -> memref<?xf64> {
+  %0 = linalg.sparse_values %arg0 : tensor<128xf64> to memref<?xf64>
+  return %0 : memref<?xf64>
+}

mlir/test/lib/Transforms/TestSparsification.cpp

 //===- TestSparsification.cpp - Test sparsification of tensors ------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
+#include "mlir/Dialect/LLVMIR/LLVMDialect.h"
 #include "mlir/Dialect/Linalg/Transforms/Transforms.h"
 #include "mlir/Dialect/Vector/VectorOps.h"
 #include "mlir/Pass/Pass.h"
 #include "mlir/Transforms/GreedyPatternRewriteDriver.h"
 
 using namespace mlir;
 
 namespace {
struct TestSparsification
   Option<int32_t> ptrType{*this, "ptr-type",
                           llvm::cl::desc("Set the pointer type"),
                           llvm::cl::init(0)};
 
   Option<int32_t> indType{*this, "ind-type",
                           llvm::cl::desc("Set the index type"),
                           llvm::cl::init(0)};
 
+  Option<bool> fastOutput{*this, "fast-output",
+                          llvm::cl::desc("Allows fast output buffers"),
+                          llvm::cl::init(false)};
+
+  Option<bool> lower{*this, "lower", llvm::cl::desc("Lower sparse primitives"),
+                     llvm::cl::init(false)};
+
   /// Registers all dialects required by testing.
   void getDependentDialects(DialectRegistry &registry) const override {
-    registry.insert<scf::SCFDialect, vector::VectorDialect>();
+    registry
+        .insert<scf::SCFDialect, vector::VectorDialect, LLVM::LLVMDialect>();
   }
 
   /// Returns parallelization strategy given on command line.
   linalg::SparseParallelizationStrategy parallelOption() {
     switch (parallelization) {
     default:
       return linalg::SparseParallelizationStrategy::kNone;
     case 1:
struct TestSparsification
 
   /// Runs the test on a function.
   void runOnFunction() override {
     auto *ctx = &getContext();
     OwningRewritePatternList patterns;
     // Translate strategy flags to strategy options.
     linalg::SparsificationOptions options(parallelOption(), vectorOption(),
                                           vectorLength, typeOption(ptrType),
-                                          typeOption(indType));
+                                          typeOption(indType), fastOutput);
     // Apply rewriting.
     linalg::populateSparsificationPatterns(ctx, patterns, options);
     vector::populateVectorToVectorCanonicalizationPatterns(patterns, ctx);
     (void)applyPatternsAndFoldGreedily(getFunction(), std::move(patterns));
+    // Lower sparse primitives to calls into runtime support library.
+    if (lower) {
+      OwningRewritePatternList conversionPatterns;
+      ConversionTarget target(*ctx);
+      target.addIllegalOp<linalg::SparseTensorFromPointerOp,
+                          linalg::SparseTensorToPointersMemRefOp,
+                          linalg::SparseTensorToIndicesMemRefOp,
+                          linalg::SparseTensorToValuesMemRefOp>();
+      target.addLegalOp<CallOp>();
+      linalg::populateSparsificationConversionPatterns(ctx, conversionPatterns);
+      if (failed(applyPartialConversion(getOperation(), target,
+                                        std::move(conversionPatterns))))
+        signalPassFailure();
+    }
   }
 };
 
 } // end anonymous namespace
 
 namespace mlir {
 namespace test {
 
 void registerTestSparsification() {
   PassRegistration<TestSparsification> sparsificationPass(
       "test-sparsification",
       "Test automatic generation of sparse tensor code");
 }
 
 } // namespace test
 } // namespace mlir