[Mlir-commits] [mlir] eced4a8 - [mlir] [sparse] start of sparse tensor compiler support
Aart Bik
llvmlistbot at llvm.org
Tue Nov 17 13:10:56 PST 2020
Author: Aart Bik
Date: 2020-11-17T13:10:42-08:00
New Revision: eced4a8e6fe3041b699bd22b5b89bea47c84c51a
URL: https://github.com/llvm/llvm-project/commit/eced4a8e6fe3041b699bd22b5b89bea47c84c51a
DIFF: https://github.com/llvm/llvm-project/commit/eced4a8e6fe3041b699bd22b5b89bea47c84c51a.diff
LOG: [mlir] [sparse] start of sparse tensor compiler support
As discussed in https://llvm.discourse.group/t/mlir-support-for-sparse-tensors/2020
this CL is the start of sparse tensor compiler support in MLIR. Starting with a
"dense" kernel expressed in the Linalg dialect together with per-dimension
sparsity annotations on the tensors, the compiler automatically lowers the
kernel to sparse code using the methods described in Fredrik Kjolstad's thesis.
Many details are still TBD. For example, the sparse "bufferization" is purely
done locally since we don't have a global solution for propagating sparsity
yet. Furthermore, code to input and output the sparse tensors is missing.
Nevertheless, with some hand modifications, the generated MLIR can be
easily converted into runnable code already.
Reviewed By: nicolasvasilache, ftynse
Differential Revision: https://reviews.llvm.org/D90994
Added:
mlir/lib/Dialect/Linalg/Transforms/Sparsification.cpp
mlir/test/Dialect/Linalg/sparse_1d.mlir
mlir/test/Dialect/Linalg/sparse_2d.mlir
mlir/test/Dialect/Linalg/sparse_3d.mlir
mlir/test/lib/Transforms/TestSparsification.cpp
Modified:
mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
mlir/test/lib/Transforms/CMakeLists.txt
mlir/tools/mlir-opt/mlir-opt.cpp
Removed:
################################################################################
diff --git a/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h b/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
index 54357940b250..523a34e3f613 100644
--- a/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
+++ b/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
@@ -771,6 +771,12 @@ LogicalResult applyStagedPatterns(
const FrozenRewritePatternList &stage2Patterns,
function_ref<LogicalResult(Operation *)> stage3Lambda = nullptr);
+//===----------------------------------------------------------------------===//
+// Support for sparse tensor code generation.
+//===----------------------------------------------------------------------===//
+void populateSparsificationPatterns(MLIRContext *context,
+ OwningRewritePatternList &patterns);
+
} // namespace linalg
} // namespace mlir
diff --git a/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt b/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
index 73df73e83d82..11a48894d9d8 100644
--- a/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
+++ b/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
@@ -9,6 +9,7 @@ add_mlir_dialect_library(MLIRLinalgTransforms
Interchange.cpp
Loops.cpp
Promotion.cpp
+ Sparsification.cpp
Tiling.cpp
Transforms.cpp
Vectorization.cpp
diff --git a/mlir/lib/Dialect/Linalg/Transforms/Sparsification.cpp b/mlir/lib/Dialect/Linalg/Transforms/Sparsification.cpp
new file mode 100644
index 000000000000..44d1e40e3453
--- /dev/null
+++ b/mlir/lib/Dialect/Linalg/Transforms/Sparsification.cpp
@@ -0,0 +1,887 @@
+//===- Sparsification.cpp - Implementation of linalg sparsification -------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+//
+// This file implements lowering annotated linalg dialect to sparse code.
+//
+// The concept of letting a compiler generate sparse code automatically was
+// pioneered for dense linear algebra code in Fortran by [Bik96] in MT1 and
+// formalized to tensor algebra by [Kjolstad17,20] for the Sparse Tensor
+// Algebra Compiler (TACO). The implementation in this file closely follows
+// the "sparse iteration theory" that forms the foundation of TACO. A rewriting
+// rule is applied to each tensor expression in linalg (MLIR's tensor index
+// notation) where the sparsity of tensors is indicated with annotation using
+// a per-dimension specification of sparse/dense storage together with a
+// specification of the order on the dimensions. Subsequently, a topologically
+// sorted iteration graph, reflecting the required order on indices with respect
+// to the dimensions of each tensor, is constructed to ensure that all tensors
+// are visited in natural index order. Next, iteration lattices are constructed
+// for the tensor expression for every index in topological order. Each
+// iteration lattice point consists of a conjunction of tensor indices together
+// with a tensor (sub)expression that needs to be evaluated for that
+// conjunction. Within the lattice, iteration points are ordered according to
+// the way indices are exhausted. As such these iteration lattices drive actual
+// sparse code generation, which consists of a tedious but relatively
+// straightforward one-to-one mapping from iteration lattices to combinations
+// of for-loops, while-loops, and if-statements.
+//
+// [Bik96] Aart J.C. Bik. Compiler Support for Sparse Matrix Computations.
+// PhD thesis, Leiden University, May 1996 (aartbik.com/sparse.php).
+// [Kjolstad17] Fredrik Berg Kjolstad, Shoaib Ashraf Kamil, Stephen Chou,
+// David Lugato, and Saman Amarasinghe. The Tensor Algebra Compiler.
+// Proceedings of the ACM on Programming Languages, October 2017.
+// [Kjolstad20] Fredrik Berg Kjolstad. Sparse Tensor Algebra Compilation.
+// PhD thesis, MIT, February, 2020 (tensor-compiler.org).
+//
+// Implementation detail: We use llvm::SmallVector for vectors with
+// variable lengths and std::vector for vectors with fixed lengths.
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Dialect/Linalg/IR/LinalgOps.h"
+#include "mlir/Dialect/Linalg/Transforms/Transforms.h"
+#include "mlir/Dialect/Linalg/Utils/Utils.h"
+#include "mlir/Dialect/SCF/SCF.h"
+#include "mlir/Dialect/StandardOps/IR/Ops.h"
+
+using namespace mlir;
+
+namespace {
+
+enum class Kind { kTensor, kInvariant, kMulF, kMulI, kAddF, kAddI };
+
+/// Tensor expression. Represents a MLIR expression in tensor index notation.
+/// For tensors and invariants, e0 denotes the tensor index. For all binary
+/// operations, e0 and e1 denote the index of the children tensor expressions.
+struct TensorExp {
+ TensorExp(Kind k, unsigned x, unsigned y) : kind(k), e0(x), e1(y) {}
+ Kind kind;
+ unsigned e0;
+ unsigned e1;
+};
+
+/// Lattice point. Each lattice point consist of a conjunction of tensor
+/// loop indices (encoded in a bitvector) and the index of the corresponding
+/// tensor expression.
+struct LatPoint {
+ LatPoint(unsigned n, unsigned e, unsigned b) : bits(n, false), exp(e) {
+ bits.set(b);
+ }
+ LatPoint(const llvm::BitVector &b, unsigned e) : bits(b), exp(e) {}
+ llvm::BitVector bits;
+ unsigned exp;
+};
+
+/// A class to handle all iteration lattice operations. This class abstracts
+/// away from some implementation details of storing iteration lattices and
+/// tensor expressions. This allows for fine-tuning performance characteristics
+/// independently from the basic algorithm if bottlenecks are identified.
+class Merger {
+public:
+ Merger(unsigned t, unsigned l)
+ : numTensors(t), numLoops(l), isSparse(t, std::vector<bool>(l, false)) {}
+
+ /// Adds a tensor expression. Returns its index.
+ unsigned addExp(Kind k, unsigned e0, unsigned e1 = -1u) {
+ unsigned e = tensorExps.size();
+ tensorExps.push_back(TensorExp(k, e0, e1));
+ return e;
+ }
+
+ /// Adds an iteration lattice point. Returns its index.
+ unsigned addLat(unsigned t, unsigned i, unsigned e) {
+ assert(t < numTensors && i < numLoops);
+ unsigned p = latPoints.size();
+ latPoints.push_back(LatPoint(numLoops * numTensors, e, numTensors * i + t));
+ return p;
+ }
+
+ /// Adds a new, initially empty, set. Returns its index.
+ unsigned addSet() {
+ unsigned s = latSets.size();
+ latSets.emplace_back(SmallVector<unsigned, 16>());
+ return s;
+ }
+
+ /// Computes a single conjunction of two lattice points by taking the "union"
+ /// of loop indices (effectively constucting a larger "intersection" of those
+ /// indices) with a newly constructed tensor (sub)expression of given kind.
+ /// Returns the index of the new lattice point.
+ unsigned conjLatPoint(Kind kind, unsigned p0, unsigned p1) {
+ unsigned p = latPoints.size();
+ llvm::BitVector nb = llvm::BitVector(latPoints[p0].bits);
+ nb |= latPoints[p1].bits;
+ unsigned e = addExp(kind, latPoints[p0].exp, latPoints[p1].exp);
+ latPoints.push_back(LatPoint(nb, e));
+ return p;
+ }
+
+ /// Conjunctive merge of L1 and L2 is conjunction of cartesian product.
+ /// Returns the index of the new set.
+ unsigned takeConj(Kind kind, unsigned s0, unsigned s1) {
+ unsigned s = addSet();
+ for (unsigned p0 : latSets[s0])
+ for (unsigned p1 : latSets[s1])
+ latSets[s].push_back(conjLatPoint(kind, p0, p1));
+ return s;
+ }
+
+ /// Disjunctive merge of L0 and L1 is (L0 /\_op L1, L0, L1).
+ /// Returns the index of the new set.
+ unsigned takeDisj(Kind kind, unsigned s0, unsigned s1) {
+ unsigned s = takeConj(kind, s0, s1);
+ for (unsigned p : latSets[s0])
+ latSets[s].push_back(p);
+ for (unsigned p : latSets[s1])
+ latSets[s].push_back(p);
+ return s;
+ }
+
+ /// Optimizes the iteration lattice points in the given set.
+ unsigned optimize(unsigned s0) {
+ unsigned s = addSet();
+ assert(latSets[s0].size() != 0);
+ unsigned p0 = latSets[s0][0];
+ for (unsigned p1 : latSets[s0]) {
+ bool add = true;
+ if (p0 != p1) {
+ llvm::BitVector tmp = latPoints[p1].bits;
+ tmp ^= latPoints[p0].bits;
+ if (hasAnyOf(tmp, false))
+ continue; // dense exhausted?
+ for (unsigned p2 : latSets[s]) {
+ tmp = latPoints[p1].bits;
+ tmp ^= latPoints[p2].bits;
+ if (tmp.count() == 0) {
+ add = false; // direct dup?
+ break;
+ }
+ }
+ assert(!add || latGT(p0, p1));
+ }
+ if (add)
+ latSets[s].push_back(p1);
+ }
+ return s;
+ }
+
+ // Returns true if Li > Lj.
+ bool latGT(unsigned i, unsigned j) const {
+ const llvm::BitVector &bitsi = latPoints[i].bits;
+ const llvm::BitVector &bitsj = latPoints[j].bits;
+ assert(bitsi.size() == bitsj.size());
+ if (bitsi.count() > bitsj.count()) {
+ for (unsigned b = 0, be = bitsj.size(); b < be; b++)
+ if (bitsj[b] && !bitsi[b])
+ return false;
+ return true;
+ }
+ return false;
+ }
+
+ // Bit translation.
+ unsigned tensor(unsigned b) const { return b % numTensors; }
+ unsigned index(unsigned b) const { return b / numTensors; }
+
+ // Returns true if bit corresponds to sparse access.
+ bool isSparseBit(unsigned b) const {
+ return isSparseAccess(tensor(b), index(b));
+ }
+
+ // Returns true if tensor access at given index is sparse.
+ bool isSparseAccess(unsigned t, unsigned i) const {
+ assert(t < numTensors && i < numLoops);
+ return isSparse[t][i];
+ }
+
+ // Returns true if any set bit corresponds to sparse/dense access.
+ bool hasAnyOf(const llvm::BitVector &bits, bool sparse) const {
+ for (unsigned b = 0, be = bits.size(); b < be; b++)
+ if (bits[b] && isSparseBit(b) == sparse)
+ return true;
+ return false;
+ }
+
+ // Getters.
+ std::vector<std::vector<bool>> &sparse() { return isSparse; }
+ TensorExp &exp(unsigned e) { return tensorExps[e]; }
+ LatPoint &lat(unsigned l) { return latPoints[l]; }
+ SmallVector<unsigned, 16> &set(unsigned s) { return latSets[s]; }
+
+private:
+ const unsigned numTensors;
+ const unsigned numLoops;
+
+ std::vector<std::vector<bool>> isSparse;
+ llvm::SmallVector<TensorExp, 32> tensorExps;
+ llvm::SmallVector<LatPoint, 16> latPoints;
+ llvm::SmallVector<SmallVector<unsigned, 16>, 8> latSets;
+};
+
+// Code generation.
+struct CodeGen {
+ CodeGen(unsigned numTensors, unsigned numLoops)
+ : loops(numLoops), sizes(numLoops), buffers(numTensors),
+ pointers(numTensors, std::vector<Value>(numLoops)),
+ indices(numTensors, std::vector<Value>(numLoops)),
+ highs(numTensors, std::vector<Value>(numLoops)),
+ pidxs(numTensors, std::vector<Value>(numLoops)),
+ idxs(numTensors, std::vector<Value>(numLoops)) {}
+ // Universal dense indices and upper bounds (by index).
+ std::vector<Value> loops;
+ std::vector<Value> sizes;
+ // Buffers for storing dense and sparse numerical values (by tensor).
+ std::vector<Value> buffers;
+ // Sparse storage schemes (1-D): pointers and indices (by tensor and index).
+ std::vector<std::vector<Value>> pointers;
+ std::vector<std::vector<Value>> indices;
+ // Sparse iteration information (by tensor and index).
+ std::vector<std::vector<Value>> highs;
+ std::vector<std::vector<Value>> pidxs;
+ std::vector<std::vector<Value>> idxs;
+};
+
+} // namespace
+
+/// Helper method to inspect sparse annotations in the linalg operation.
+/// Fills the per-dimension sparsity information for all tensors.
+static void findSparseAnnotations(linalg::GenericOp op,
+ std::vector<std::vector<bool>> &isSparse) {
+ unsigned numTensors = op.getNumInputsAndOutputs();
+ ArrayAttr sparseAttr = op.sparseAttr();
+ for (unsigned t = 0; t < numTensors; t++) {
+ auto map = op.getIndexingMap(t);
+ auto dimAttr = sparseAttr[t].cast<ArrayAttr>();
+ // For each tensor, we accept a per-dimension Sparse or Dense annotation.
+ // This is translated to the loop index that indexes that dimension.
+ unsigned rank = op.getShapedType(t).getRank();
+ for (unsigned d = 0; d < rank; d++)
+ if (isSparseDim(dimAttr[d])) {
+ unsigned idx = map.getDimPosition(d);
+ isSparse[t][idx] = true;
+ } else {
+ assert(isDenseDim(dimAttr[d]));
+ }
+ }
+}
+
+/// A DFS helper to compute a topological sort. Note that recursion is
+/// bounded by the number of implicit loops, which is always small.
+/// Returns false when a cycle is detected.
+static bool topSortDFS(unsigned i, std::vector<unsigned> &visit,
+ std::vector<unsigned> &topSort,
+ std::vector<std::vector<bool>> &adjM) {
+ if (visit[i] != 0)
+ return visit[i] != 1; // 1 denotes cycle!
+ visit[i] = 1;
+ for (unsigned j = 0, e = visit.size(); j < e; j++)
+ if (adjM[i][j])
+ if (!topSortDFS(j, visit, topSort, adjM))
+ return false;
+ visit[i] = 2;
+ topSort.push_back(i);
+ return true;
+}
+
+/// Computes a topologically sorted iteration graph for the linalg operation.
+/// Ensures all tensors are visited in natural index order. This is essential
+/// for sparse storage formats since these only support access along fixed
+/// dimensions. Even for dense storage formats, however, the natural index
+/// order yields innermost unit-stride access with better spatial locality.
+static bool computeIterationGraph(linalg::GenericOp op,
+ std::vector<unsigned> &topSort) {
+ // Set up an n x n from/to adjacency matrix of the iteration graph
+ // for the implicit loop indices i_0 .. i_n-1.
+ unsigned n = op.getNumLoops();
+ std::vector<std::vector<bool>> adjM(n, std::vector<bool>(n, false));
+
+ // Iterate over the indexing maps of every tensor in the tensor expression.
+ for (auto imap : llvm::enumerate(op.indexing_maps())) {
+ auto map = imap.value().template cast<AffineMapAttr>().getValue();
+ assert(map.getNumDims() == n);
+ // At the moment, we take the index variables in the tensor access
+ // expression in the order in which they appear (conceptually a
+ // "row-major" layout of every tensor). So, a tensor access A_ijk
+ // forces the ordering i < j < k on the loop indices.
+ // TODO: support affine map to define alternative dimension orders.
+ for (unsigned d = 1, e = map.getNumResults(); d < e; d++) {
+ unsigned f = map.getDimPosition(d - 1);
+ unsigned t = map.getDimPosition(d);
+ adjM[f][t] = true;
+ }
+ }
+
+ // Topologically sort the iteration graph to determine loop order.
+ // Report failure for a cyclic iteration graph.
+ topSort.reserve(n);
+ std::vector<unsigned> visit(n, 0);
+ for (unsigned i = 0; i < n; i++)
+ if (visit[i] == 0)
+ if (!topSortDFS(i, visit, topSort, adjM))
+ return false; // cycle!
+ std::reverse(std::begin(topSort), std::end(topSort));
+ return true;
+}
+
+/// Traverses the SSA tree (possibly a DAG) to build a tensor expression.
+/// This simplifies constructing (sub)expressions during iteration lattice
+/// building (compared to using the SSA representation everywhere).
+static Optional<unsigned> buildTensorExp(Merger &merger, linalg::GenericOp op,
+ Value val) {
+ Operation *def = val.getDefiningOp();
+ if (auto arg = val.dyn_cast<BlockArgument>()) {
+ unsigned argN = arg.getArgNumber();
+ if (arg.getOwner()->getParentOp() == op) {
+ // Any parameter of the generic op is considered a tensor,
+ // indexed by the implicit loop bounds.
+ auto map = op.getIndexingMap(argN);
+ if (map.isProjectedPermutation())
+ return merger.addExp(Kind::kTensor, argN);
+ } else {
+ // Any parameter of a higher op is invariant in the tensor expression.
+ return merger.addExp(Kind::kInvariant, argN);
+ }
+ } else if (def->getNumOperands() == 2) {
+ // Construct binary operations if subexpressions could be built.
+ auto x = buildTensorExp(merger, op, def->getOperand(0));
+ auto y = buildTensorExp(merger, op, def->getOperand(1));
+ if (x.hasValue() && y.hasValue()) {
+ unsigned e0 = x.getValue();
+ unsigned e1 = y.getValue();
+ if (isa<MulFOp>(def))
+ return merger.addExp(Kind::kMulF, e0, e1);
+ if (isa<MulIOp>(def))
+ return merger.addExp(Kind::kMulI, e0, e1);
+ if (isa<AddFOp>(def))
+ return merger.addExp(Kind::kAddF, e0, e1);
+ if (isa<AddIOp>(def))
+ return merger.addExp(Kind::kAddI, e0, e1);
+ }
+ }
+ // Cannot build (yet).
+ return None;
+}
+
+/// Builds the iteration lattices in a bottom-up traversal given the remaining
+/// tensor (sub)expression and the next loop index in the iteration graph.
+static unsigned buildLattices(Merger &merger, linalg::GenericOp op,
+ unsigned exp, unsigned idx) {
+ Kind kind = merger.exp(exp).kind;
+ if (kind == Kind::kTensor || kind == Kind::kInvariant) {
+ // Either the index is really used in the tensor expression, or it it
+ // set to the "non-existing dense index" in that dimension.
+ unsigned s = merger.addSet();
+ merger.set(s).push_back(merger.addLat(merger.exp(exp).e0, idx, exp));
+ return s;
+ }
+ unsigned s0 = buildLattices(merger, op, merger.exp(exp).e0, idx);
+ unsigned s1 = buildLattices(merger, op, merger.exp(exp).e1, idx);
+ switch (kind) {
+ case Kind::kTensor:
+ case Kind::kInvariant:
+ llvm_unreachable("handled above");
+ case Kind::kMulF:
+ case Kind::kMulI:
+ return merger.takeConj(kind, s0, s1);
+ case Kind::kAddF:
+ case Kind::kAddI:
+ return merger.takeDisj(kind, s0, s1);
+ }
+}
+
+/// 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
+void genBuffers(Merger &merger, CodeGen &codegen, PatternRewriter &rewriter,
+ linalg::GenericOp op) {
+ Location loc = op.getLoc();
+ unsigned numTensors = op.getNumInputsAndOutputs();
+ unsigned numInputs = op.getNumInputs();
+ assert(numTensors == numInputs + 1);
+ Type indexType = rewriter.getIndexType();
+
+ // 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).
+ SmallVector<Value, 4> args;
+ for (unsigned t = 0; t < numTensors; t++) {
+ auto tensorType = op.getShapedType(t);
+ auto shape = tensorType.getShape();
+ auto map = op.getIndexingMap(t);
+ // Scan all dimensions of current tensor.
+ bool allDense = true;
+ args.clear();
+ for (unsigned d = 0, rank = shape.size(); d < rank; d++) {
+ unsigned i = map.getDimPosition(d);
+ // Handle sparse storage schemes.
+ if (merger.isSparseAccess(t, i)) {
+ allDense = false;
+ auto dynTp = MemRefType::get({ShapedType::kDynamicSize}, indexType);
+ codegen.pointers[t][i] = rewriter.create<AllocaOp>(loc, dynTp, unknown);
+ codegen.indices[t][i] = rewriter.create<AllocaOp>(loc, dynTp, unknown);
+ }
+ // Find lower and upper bound in current dimension.
+ Value up;
+ if (shape[d] == TensorType::kDynamicSize) {
+ // For the output tensor, we may need to infer the upper bound.
+ // For all others, we look at the incoming argument.
+ if (t == numInputs && !op.getNumInitTensors()) {
+ up = codegen.sizes[i];
+ assert(up); // TODO: what else?
+ } else {
+ Value arg = t < numInputs ? op.getInput(t) : op.getInitTensor(0);
+ up = rewriter.create<DimOp>(loc, arg, 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) {
+ auto denseTp = MemRefType::get(shape, tensorType.getElementType());
+ codegen.buffers[t] = rewriter.create<AllocaOp>(loc, denseTp, args);
+ } else {
+ auto sparseTp = MemRefType::get({ShapedType::kDynamicSize},
+ tensorType.getElementType());
+ codegen.buffers[t] = rewriter.create<AllocaOp>(loc, sparseTp, unknown);
+ }
+ }
+}
+
+/// Generates a load on a dense or sparse tensor.
+static Value genTensorLoad(Merger &merger, CodeGen &codegen,
+ PatternRewriter &rewriter, linalg::GenericOp op,
+ unsigned tensor) {
+ SmallVector<Value, 4> args;
+ auto map = op.getIndexingMap(tensor);
+ bool sparse = false;
+ 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.isSparseAccess(tensor, idx)) {
+ sparse = true;
+ args.clear();
+ args.push_back(codegen.pidxs[tensor][idx]); // position index
+ }
+ }
+ return rewriter.create<LoadOp>(op.getLoc(), codegen.buffers[tensor], args);
+}
+
+/// Generates a store on a dense tensor.
+static void genTensorStore(Merger &merger, CodeGen &codegen,
+ PatternRewriter &rewriter, linalg::GenericOp op,
+ unsigned tensor, Value rhs) {
+ SmallVector<Value, 4> args;
+ auto map = op.getIndexingMap(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
+ }
+ rewriter.create<StoreOp>(op.getLoc(), rhs, codegen.buffers[tensor], args);
+}
+
+/// Recursively generates tensor expression.
+static Value genExp(Merger &merger, CodeGen &codegen, PatternRewriter &rewriter,
+ linalg::GenericOp op, unsigned exp) {
+ if (merger.exp(exp).kind == Kind::kTensor)
+ return genTensorLoad(merger, codegen, rewriter, op, merger.exp(exp).e0);
+ else if (merger.exp(exp).kind == Kind::kInvariant)
+ return op.getParentRegion()->front().getArgument(merger.exp(exp).e0);
+ Value v0 = genExp(merger, codegen, rewriter, op, merger.exp(exp).e0);
+ Value v1 = genExp(merger, codegen, rewriter, op, merger.exp(exp).e1);
+ switch (merger.exp(exp).kind) {
+ case Kind::kTensor:
+ case Kind::kInvariant:
+ llvm_unreachable("handled above");
+ case Kind::kMulF:
+ return rewriter.create<MulFOp>(op.getLoc(), v0, v1);
+ case Kind::kMulI:
+ return rewriter.create<MulIOp>(op.getLoc(), v0, v1);
+ case Kind::kAddF:
+ return rewriter.create<AddFOp>(op.getLoc(), v0, v1);
+ case Kind::kAddI:
+ return rewriter.create<AddIOp>(op.getLoc(), v0, v1);
+ }
+}
+
+/// Generates initialization code for the subsequent loop sequence at
+/// current index level. Returns true if the loop sequence needs to
+/// maintain the universal index.
+static bool genInit(Merger &merger, CodeGen &codegen, PatternRewriter &rewriter,
+ linalg::GenericOp op, std::vector<unsigned> &topSort,
+ unsigned at, llvm::BitVector &inits) {
+ bool needsUniv = false;
+ Location loc = op.getLoc();
+ unsigned idx = topSort[at];
+
+ // Initialize sparse positions.
+ Value one = rewriter.create<ConstantIndexOp>(loc, 1);
+ for (unsigned b = 0, be = inits.size(); b < be; b++) {
+ if (inits[b]) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ if (merger.isSparseBit(b)) {
+ // Initialize sparse index.
+ unsigned pat = at;
+ for (; pat != 0; pat--) {
+ if (codegen.pidxs[tensor][topSort[pat - 1]])
+ break;
+ }
+ Value ptr = codegen.pointers[tensor][idx];
+ Value p = (pat == 0) ? rewriter.create<ConstantIndexOp>(loc, 0)
+ : codegen.pidxs[tensor][topSort[pat - 1]];
+ codegen.pidxs[tensor][idx] = rewriter.create<LoadOp>(loc, ptr, p);
+ p = rewriter.create<AddIOp>(loc, p, one);
+ codegen.highs[tensor][idx] = rewriter.create<LoadOp>(loc, ptr, p);
+ } else {
+ // Dense index still in play.
+ needsUniv = true;
+ }
+ }
+ }
+
+ // Initialize the universal dense index.
+ codegen.loops[idx] = rewriter.create<ConstantIndexOp>(loc, 0);
+ return needsUniv;
+}
+
+/// Generates a for-loop or a while-loop, depending on whether it implements
+/// singleton iteration or co-iteration over the given conjunction.
+static void genLoop(Merger &merger, CodeGen &codegen, PatternRewriter &rewriter,
+ linalg::GenericOp op, unsigned idx, bool needsUniv,
+ llvm::BitVector &indices, scf::ForOp &forOp,
+ scf::WhileOp &whileOp) {
+ Location loc = op.getLoc();
+
+ // Emit a for-loop for a single index.
+ if (indices.count() == 1) {
+ unsigned fb = indices.find_first();
+ unsigned tensor = merger.tensor(fb);
+ assert(idx == merger.index(fb));
+ // Emit a sparse for-loop or a dense for-loop.
+ Value one = rewriter.create<ConstantIndexOp>(loc, 1);
+ if (merger.isSparseBit(fb)) {
+ forOp = rewriter.create<scf::ForOp>(loc, codegen.pidxs[tensor][idx],
+ codegen.highs[tensor][idx], one);
+ codegen.pidxs[tensor][idx] = forOp.getInductionVar();
+ } else {
+ forOp = rewriter.create<scf::ForOp>(loc, codegen.loops[idx],
+ codegen.sizes[idx], one);
+ codegen.loops[idx] = forOp.getInductionVar();
+ }
+ rewriter.setInsertionPointToStart(forOp.getBody());
+ return;
+ }
+
+ // Otherwise, emit a while-loop for co-iteration.
+ Type indexType = rewriter.getIndexType();
+ SmallVector<Type, 4> types;
+ SmallVector<Value, 4> operands;
+ for (unsigned b = 0, be = indices.size(); b < be; b++) {
+ if (indices[b] && merger.isSparseBit(b)) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ types.push_back(indexType);
+ operands.push_back(codegen.pidxs[tensor][idx]);
+ }
+ }
+ if (needsUniv) {
+ types.push_back(indexType);
+ operands.push_back(codegen.loops[idx]);
+ }
+ whileOp = rewriter.create<scf::WhileOp>(loc, types, operands);
+ Block *before = rewriter.createBlock(&whileOp.before(), {}, types);
+ Block *after = rewriter.createBlock(&whileOp.after(), {}, types);
+ // Build the "before" region, which effectively consists
+ // of a conjunction of "i < upper" tests on all induction.
+ rewriter.setInsertionPointToStart(&whileOp.before().front());
+ Value cond;
+ unsigned o = 0;
+ for (unsigned b = 0, be = indices.size(); b < be; b++) {
+ if (indices[b] && merger.isSparseBit(b)) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ Value op1 = before->getArgument(o);
+ Value op2 = codegen.highs[tensor][idx];
+ Value opc = rewriter.create<CmpIOp>(loc, CmpIPredicate::ult, op1, op2);
+ cond = cond ? rewriter.create<AndOp>(loc, cond, opc) : opc;
+ codegen.pidxs[tensor][idx] = after->getArgument(o++);
+ }
+ }
+ if (needsUniv)
+ codegen.loops[idx] = after->getArgument(o++);
+ assert(o == operands.size());
+ rewriter.create<scf::ConditionOp>(loc, cond, before->getArguments());
+ rewriter.setInsertionPointToStart(&whileOp.after().front());
+}
+
+/// Generates the local variables for this loop, consisting of the sparse
+/// indices, restored universal dense index, and dense positions.
+static void genLocals(Merger &merger, CodeGen &codegen,
+ PatternRewriter &rewriter, linalg::GenericOp op,
+ std::vector<unsigned> &topSort, unsigned at,
+ bool needsUniv, llvm::BitVector &locals) {
+ Location loc = op.getLoc();
+ unsigned idx = topSort[at];
+
+ // Initialize sparse indices.
+ Value min;
+ for (unsigned b = 0, be = locals.size(); b < be; b++) {
+ if (locals[b] && merger.isSparseBit(b)) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ Value ld = rewriter.create<LoadOp>(loc, codegen.indices[tensor][idx],
+ codegen.pidxs[tensor][idx]);
+ codegen.idxs[tensor][idx] = ld;
+ if (!needsUniv) {
+ if (min) {
+ Value cmp = rewriter.create<CmpIOp>(loc, CmpIPredicate::ult, ld, min);
+ min = rewriter.create<SelectOp>(loc, cmp, ld, min);
+ } else {
+ min = ld;
+ }
+ }
+ }
+ }
+
+ // Merge dense universal index over minimum.
+ if (min) {
+ assert(!needsUniv);
+ codegen.loops[idx] = min;
+ }
+
+ // Initialize dense positions.
+ for (unsigned b = 0, be = locals.size(); b < be; b++) {
+ if (locals[b] && !merger.isSparseBit(b)) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ if (!codegen.highs[tensor][idx])
+ continue; // unused dimension
+ unsigned pat = at;
+ for (; pat != 0; pat--)
+ if (codegen.pidxs[tensor][topSort[pat - 1]])
+ break;
+ Value p = (pat == 0) ? rewriter.create<ConstantIndexOp>(loc, 0)
+ : codegen.pidxs[tensor][topSort[pat - 1]];
+ Value m = rewriter.create<MulIOp>(loc, codegen.sizes[idx], p);
+ codegen.pidxs[tensor][idx] =
+ rewriter.create<AddIOp>(loc, m, codegen.loops[idx]);
+ }
+ }
+}
+
+/// Generates the induction structure for a while-loop.
+static void genWhileInduction(Merger &merger, CodeGen &codegen,
+ PatternRewriter &rewriter, linalg::GenericOp op,
+ unsigned idx, bool needsUniv,
+ llvm::BitVector &induction, ResultRange results) {
+ Location loc = op.getLoc();
+ unsigned o = 0;
+ SmallVector<Value, 4> operands;
+ Value one = rewriter.create<ConstantIndexOp>(loc, 1);
+ for (unsigned b = 0, be = induction.size(); b < be; b++)
+ if (induction[b] && merger.isSparseBit(b)) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ Value op1 = codegen.idxs[tensor][idx];
+ Value op2 = codegen.loops[idx];
+ Value op3 = codegen.pidxs[tensor][idx];
+ Value cmp = rewriter.create<CmpIOp>(loc, CmpIPredicate::eq, op1, op2);
+ Value add = rewriter.create<AddIOp>(loc, op3, one);
+ operands.push_back(rewriter.create<SelectOp>(loc, cmp, add, op3));
+ codegen.pidxs[tensor][idx] = results[o++];
+ }
+ if (needsUniv) {
+ operands.push_back(rewriter.create<AddIOp>(loc, codegen.loops[idx], one));
+ codegen.loops[idx] = results[o++];
+ }
+ assert(o == operands.size());
+ rewriter.create<scf::YieldOp>(loc, operands);
+}
+
+/// Generates a single if-statement within a while-loop.
+static void genIf(Merger &merger, CodeGen &codegen, PatternRewriter &rewriter,
+ linalg::GenericOp op, unsigned idx,
+ llvm::BitVector &conditions, scf::IfOp &ifOp) {
+ Location loc = op.getLoc();
+ if (ifOp)
+ rewriter.setInsertionPointToStart(&ifOp.elseRegion().front());
+ Value cond;
+ for (unsigned b = 0, be = conditions.size(); b < be; b++) {
+ if (conditions[b]) {
+ unsigned tensor = merger.tensor(b);
+ assert(idx == merger.index(b));
+ Value clause;
+ if (merger.isSparseBit(b)) {
+ Value op1 = codegen.idxs[tensor][idx];
+ Value op2 = codegen.loops[idx];
+ clause = rewriter.create<CmpIOp>(loc, CmpIPredicate::eq, op1, op2);
+ } else {
+ clause = rewriter.create<ConstantIntOp>(loc, 1, 1); // true
+ }
+ cond = cond ? rewriter.create<AndOp>(loc, cond, clause) : clause;
+ }
+ }
+ ifOp = rewriter.create<scf::IfOp>(loc, cond, /*else*/ true);
+ rewriter.setInsertionPointToStart(&ifOp.thenRegion().front());
+}
+
+/// Optimize the loop indices of Li with two rules rules:
+/// (1) convert multiple dense to single dense, and
+/// (2) convert singleton sparse/dense to sparse/random access.
+static void optimizeIndices(Merger merger, unsigned lsize,
+ llvm::BitVector &indices) {
+ if (merger.hasAnyOf(indices, false)) {
+ bool reset = lsize == 1 && merger.hasAnyOf(indices, true);
+ for (unsigned b = 0, be = indices.size(); b < be; b++) {
+ if (indices[b] && !merger.isSparseBit(b)) {
+ if (reset)
+ indices.reset(b);
+ reset = true;
+ }
+ }
+ }
+}
+
+/// Recursively generates code while computing iteration lattices in order
+/// to manage the complexity of implementing co-iteration over unions
+/// and intersections of sparse iterations spaces.
+static void genStmt(Merger &merger, CodeGen &codegen, PatternRewriter &rewriter,
+ linalg::GenericOp op, std::vector<unsigned> &topSort,
+ unsigned exp, unsigned at) {
+ // At each leaf, assign remaining tensor (sub)expression to output tensor.
+ if (at == topSort.size()) {
+ unsigned lhs = op.getNumInputsAndOutputs() - 1;
+ Value rhs = genExp(merger, codegen, rewriter, op, exp);
+ genTensorStore(merger, codegen, rewriter, op, lhs, rhs);
+ return;
+ }
+
+ // Construct iteration lattices for current loop index, with L0 at top.
+ // Then emit initialization code for the loop sequence at this level.
+ // We maintain the universal dense index if dense indices are still
+ // in play for a non-singleton loop sequence.
+ unsigned idx = topSort[at];
+ unsigned lts = merger.optimize(buildLattices(merger, op, exp, idx));
+ unsigned lsize = merger.set(lts).size();
+ assert(lsize != 0);
+ unsigned l0 = merger.set(lts)[0];
+ LatPoint lat0 = merger.lat(l0);
+ bool needsUniv =
+ genInit(merger, codegen, rewriter, op, topSort, at, lat0.bits) &&
+ lsize > 1;
+
+ // Emit a loop for every lattice point L0 >= Li.
+ for (unsigned li : merger.set(lts)) {
+ LatPoint lati = merger.lat(li);
+
+ // Emit loop.
+ scf::ForOp forOp;
+ scf::WhileOp whileOp;
+ llvm::BitVector indices = lati.bits;
+ optimizeIndices(merger, lsize, indices);
+ genLoop(merger, codegen, rewriter, op, idx, needsUniv, indices, forOp,
+ whileOp);
+ genLocals(merger, codegen, rewriter, op, topSort, at, needsUniv, lati.bits);
+
+ // Visit all lattices points with Li >= Lj to generate the
+ // loop-body, possibly with if statements for coiteration.
+ scf::IfOp ifOp;
+ for (unsigned lj : merger.set(lts)) {
+ if (li == lj || merger.latGT(li, lj)) {
+ LatPoint latj = merger.lat(lj);
+ llvm::BitVector tmp = latj.bits;
+ tmp ^= lati.bits;
+ if (merger.hasAnyOf(tmp, false))
+ continue; // dense exhausted within if/else
+ // Recurse into body of each branch.
+ if (whileOp)
+ genIf(merger, codegen, rewriter, op, idx, latj.bits, ifOp);
+ genStmt(merger, codegen, rewriter, op, topSort, latj.exp, at + 1);
+ }
+ }
+
+ // Wrap-up induction and restore insertion point.
+ if (forOp) {
+ needsUniv = false;
+ rewriter.setInsertionPointAfter(forOp);
+ } else {
+ rewriter.setInsertionPointToEnd(&whileOp.after().front());
+ genWhileInduction(merger, codegen, rewriter, op, idx, needsUniv,
+ lati.bits, whileOp.results());
+ rewriter.setInsertionPointAfter(whileOp);
+ }
+ }
+}
+
+namespace {
+
+/// Sparse rewriting rule for generic Lingalg operation.
+struct GenericOpSparsifier : public OpRewritePattern<linalg::GenericOp> {
+ using OpRewritePattern<linalg::GenericOp>::OpRewritePattern;
+
+ LogicalResult matchAndRewrite(linalg::GenericOp op,
+ PatternRewriter &rewriter) const override {
+ unsigned numTensors = op.getNumInputsAndOutputs();
+ unsigned numLoops = op.iterator_types().getValue().size();
+ Merger merger(numTensors, numLoops);
+
+ // Detects sparse annotations and translate the per-dimension sparsity
+ // information for all tensors to loop indices in the kernel.
+ if (!op.hasSparseSemantics())
+ return failure();
+ findSparseAnnotations(op, merger.sparse());
+
+ // Accept only single, dense result.
+ if (op.getNumOutputs() != 1 ||
+ std::any_of(merger.sparse().back().begin(),
+ merger.sparse().back().end(), [](bool b) { return b; }))
+ return failure();
+
+ // Computes a topologically sorted iteration graph to ensure
+ // tensors are visited in natural index order. Fails on cycles.
+ // This assumes that higher-level passes have already put the
+ // tensors in each tensor expression in a feasible order.
+ // TODO: try again without *dense* constraints on failure or
+ // even try to insert sparse reorderings to resolve cycles
+ std::vector<unsigned> topSort;
+ if (!computeIterationGraph(op, topSort))
+ return failure();
+
+ // Finds the terminating yield statement and builds the tensor
+ // expression for the Linalg operation in SSA form.
+ auto ®ion = op.region();
+ if (!llvm::hasSingleElement(region))
+ return failure(); // single block only
+ Operation *yield = region.front().getTerminator();
+ Optional<unsigned> exp = buildTensorExp(merger, op, yield->getOperand(0));
+ if (!exp.hasValue())
+ return failure(); // build failure
+
+ // Recursively generates code.
+ CodeGen codegen(numTensors, numLoops);
+ genBuffers(merger, codegen, rewriter, op);
+ genStmt(merger, codegen, rewriter, op, topSort, exp.getValue(), 0);
+ Value result =
+ rewriter.create<TensorLoadOp>(op.getLoc(), codegen.buffers.back());
+ rewriter.replaceOp(op, result);
+ return success();
+ }
+};
+
+} // namespace
+
+/// Populates the given patterns list with rewriting rules required for
+/// the sparsification of linear algebra operations.
+void mlir::linalg::populateSparsificationPatterns(
+ MLIRContext *context, OwningRewritePatternList &patterns) {
+ patterns.insert<GenericOpSparsifier>(context);
+}
diff --git a/mlir/test/Dialect/Linalg/sparse_1d.mlir b/mlir/test/Dialect/Linalg/sparse_1d.mlir
new file mode 100644
index 000000000000..b0f8f8d5c676
--- /dev/null
+++ b/mlir/test/Dialect/Linalg/sparse_1d.mlir
@@ -0,0 +1,637 @@
+// NOTE: Assertions have been autogenerated by utils/generate-test-checks.py
+// RUN: mlir-opt %s -test-sparsification | FileCheck %s
+
+#trait_d = {
+ indexing_maps = [
+ affine_map<(i) -> (i)>, // a
+ affine_map<(i) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "D" ], // a
+ [ "D" ] // x
+ ],
+ iterator_types = ["parallel"],
+ doc = "x(i) = a(i) OP b"
+}
+
+// CHECK-LABEL: func @add_d(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: f32) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : index
+// CHECK: %[[VAL_3:.*]] = constant 0 : index
+// CHECK: %[[VAL_4:.*]] = constant 1 : index
+// CHECK: %[[VAL_5:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_6:.*]] = alloca() : memref<32xf32>
+// CHECK: scf.for %[[VAL_7:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] {
+// CHECK: %[[VAL_8:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_7]]] : memref<32xf32>
+// CHECK: %[[VAL_9:.*]] = addf %[[VAL_8]], %[[VAL_1]] : f32
+// CHECK: store %[[VAL_9]], %[[VAL_6]]{{\[}}%[[VAL_7]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_10:.*]] = tensor_load %[[VAL_6]] : memref<32xf32>
+// CHECK: return %[[VAL_10]] : tensor<32xf32>
+// CHECK: }
+func @add_d(%arga: tensor<32xf32>, %argb: f32) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_d
+ ins(%arga: tensor<32xf32>) {
+ ^bb(%a: 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) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : index
+// CHECK: %[[VAL_3:.*]] = constant 0 : index
+// CHECK: %[[VAL_4:.*]] = constant 1 : index
+// CHECK: %[[VAL_5:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_6:.*]] = alloca() : memref<32xf32>
+// CHECK: scf.for %[[VAL_7:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] {
+// CHECK: %[[VAL_8:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_7]]] : memref<32xf32>
+// CHECK: %[[VAL_9:.*]] = mulf %[[VAL_8]], %[[VAL_1]] : f32
+// CHECK: store %[[VAL_9]], %[[VAL_6]]{{\[}}%[[VAL_7]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_10:.*]] = tensor_load %[[VAL_6]] : memref<32xf32>
+// CHECK: return %[[VAL_10]] : tensor<32xf32>
+// CHECK: }
+func @mul_d(%arga: tensor<32xf32>, %argb: f32) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_d
+ ins(%arga: tensor<32xf32>) {
+ ^bb(%a: f32):
+ %0 = mulf %a, %argb : f32
+ linalg.yield %0 : f32
+ } -> tensor<32xf32>
+ return %0 : tensor<32xf32>
+}
+
+#trait_s = {
+ indexing_maps = [
+ affine_map<(i) -> (i)>, // a
+ affine_map<(i) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "S" ], // a
+ [ "D" ] // x
+ ],
+ 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) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : 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_6]]] : memref<?xindex>
+// CHECK: %[[VAL_13:.*]]:2 = scf.while (%[[VAL_14:.*]] = %[[VAL_11]], %[[VAL_15:.*]] = %[[VAL_4]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_16:.*]] = cmpi "ult", %[[VAL_14]], %[[VAL_12]] : index
+// CHECK: scf.condition(%[[VAL_16]]) %[[VAL_14]], %[[VAL_15]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_17:.*]]: index, %[[VAL_18:.*]]: index):
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]] = cmpi "eq", %[[VAL_19]], %[[VAL_18]] : index
+// CHECK: scf.if %[[VAL_20]] {
+// CHECK: %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_17]]] : memref<?xf32>
+// CHECK: %[[VAL_22:.*]] = addf %[[VAL_21]], %[[VAL_1]] : f32
+// CHECK: store %[[VAL_22]], %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_5]] {
+// CHECK: store %[[VAL_1]], %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_23:.*]] = cmpi "eq", %[[VAL_19]], %[[VAL_18]] : index
+// CHECK: %[[VAL_24:.*]] = addi %[[VAL_17]], %[[VAL_6]] : index
+// CHECK: %[[VAL_25:.*]] = select %[[VAL_23]], %[[VAL_24]], %[[VAL_17]] : index
+// CHECK: %[[VAL_26:.*]] = addi %[[VAL_18]], %[[VAL_6]] : index
+// CHECK: scf.yield %[[VAL_25]], %[[VAL_26]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_27:.*]] = %[[VAL_28:.*]]#1 to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK: store %[[VAL_1]], %[[VAL_10]]{{\[}}%[[VAL_27]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_29:.*]] = tensor_load %[[VAL_10]] : memref<32xf32>
+// CHECK: return %[[VAL_29]] : tensor<32xf32>
+// CHECK: }
+func @add_s(%arga: tensor<32xf32>, %argb: f32) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_s
+ ins(%arga: tensor<32xf32>) {
+ ^bb(%a: 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>) -> tensor<32xf32> {
+// CHECK: %[[VAL_1:.*]] = constant 999 : index
+// CHECK: %[[VAL_2:.*]] = constant 0 : index
+// CHECK: %[[VAL_3:.*]] = constant 1 : index
+// CHECK: %[[VAL_4:.*]] = alloca(%[[VAL_1]]) : memref<?xindex>
+// CHECK: %[[VAL_5:.*]] = alloca(%[[VAL_1]]) : memref<?xindex>
+// CHECK: %[[VAL_6:.*]] = alloca(%[[VAL_1]]) : memref<?xf32>
+// CHECK: %[[VAL_7:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_8:.*]] = load %[[VAL_4]]{{\[}}%[[VAL_2]]] : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = load %[[VAL_4]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_10:.*]] = %[[VAL_8]] to %[[VAL_9]] step %[[VAL_3]] {
+// CHECK: %[[VAL_11:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_10]]] : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_10]]] : memref<?xf32>
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_10]]] : memref<?xf32>
+// CHECK: %[[VAL_14:.*]] = addf %[[VAL_12]], %[[VAL_13]] : f32
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_10]]] : memref<?xf32>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_10]]] : memref<?xf32>
+// CHECK: %[[VAL_17:.*]] = addf %[[VAL_15]], %[[VAL_16]] : f32
+// CHECK: %[[VAL_18:.*]] = addf %[[VAL_14]], %[[VAL_17]] : f32
+// CHECK: store %[[VAL_18]], %[[VAL_7]]{{\[}}%[[VAL_11]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_19:.*]] = tensor_load %[[VAL_7]] : memref<32xf32>
+// CHECK: return %[[VAL_19]] : tensor<32xf32>
+// CHECK: }
+func @repeated_add_s(%arga: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_s
+ ins(%arga: tensor<32xf32>) {
+ ^bb(%a: 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) -> 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:.*]] = mulf %[[VAL_13]], %[[VAL_1]] : f32
+// CHECK: store %[[VAL_14]], %[[VAL_8]]{{\[}}%[[VAL_12]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_15:.*]] = tensor_load %[[VAL_8]] : memref<32xf32>
+// CHECK: return %[[VAL_15]] : tensor<32xf32>
+// CHECK: }
+func @mul_s(%arga: tensor<32xf32>, %argb: f32) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_s
+ ins(%arga: tensor<32xf32>) {
+ ^bb(%a: f32):
+ %0 = mulf %a, %argb : f32
+ linalg.yield %0 : f32
+ } -> tensor<32xf32>
+ return %0 : tensor<32xf32>
+}
+
+#trait_dd = {
+ indexing_maps = [
+ affine_map<(i) -> (i)>, // a
+ affine_map<(i) -> (i)>, // b
+ affine_map<(i) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "D" ], // a
+ [ "D" ], // b
+ [ "D" ] // x
+ ],
+ iterator_types = ["parallel"],
+ doc = "x(i) = a(i) OP b(i)"
+}
+
+// CHECK-LABEL: func @add_dd(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32xf32>) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : index
+// CHECK: %[[VAL_3:.*]] = constant 0 : index
+// CHECK: %[[VAL_4:.*]] = constant 1 : index
+// CHECK: %[[VAL_5:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_6:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_7:.*]] = alloca() : memref<32xf32>
+// CHECK: scf.for %[[VAL_8:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] {
+// CHECK: %[[VAL_9:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK: %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK: %[[VAL_11:.*]] = addf %[[VAL_9]], %[[VAL_10]] : f32
+// CHECK: store %[[VAL_11]], %[[VAL_7]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_12:.*]] = tensor_load %[[VAL_7]] : memref<32xf32>
+// CHECK: return %[[VAL_12]] : tensor<32xf32>
+// CHECK: }
+func @add_dd(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_dd
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32xf32>) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : index
+// CHECK: %[[VAL_3:.*]] = constant 0 : index
+// CHECK: %[[VAL_4:.*]] = constant 1 : index
+// CHECK: %[[VAL_5:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_6:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_7:.*]] = alloca() : memref<32xf32>
+// CHECK: scf.for %[[VAL_8:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] {
+// CHECK: %[[VAL_9:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK: %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK: %[[VAL_11:.*]] = mulf %[[VAL_9]], %[[VAL_10]] : f32
+// CHECK: store %[[VAL_11]], %[[VAL_7]]{{\[}}%[[VAL_8]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_12:.*]] = tensor_load %[[VAL_7]] : memref<32xf32>
+// CHECK: return %[[VAL_12]] : tensor<32xf32>
+// CHECK: }
+func @mul_dd(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_dd
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32xf32>
+ return %0 : tensor<32xf32>
+}
+
+#trait_ds = {
+ indexing_maps = [
+ affine_map<(i) -> (i)>, // a
+ affine_map<(i) -> (i)>, // b
+ affine_map<(i) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "D" ], // a
+ [ "S" ], // b
+ [ "D" ] // x
+ ],
+ iterator_types = ["parallel"],
+ doc = "x(i) = a(i) OP b(i)"
+}
+
+// CHECK-LABEL: func @add_ds(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32xf32>) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[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_21:.*]] = cmpi "eq", %[[VAL_20]], %[[VAL_19]] : index
+// CHECK: scf.if %[[VAL_21]] {
+// CHECK: %[[VAL_22:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_18]]] : memref<?xf32>
+// CHECK: %[[VAL_24:.*]] = addf %[[VAL_22]], %[[VAL_23]] : f32
+// CHECK: store %[[VAL_24]], %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_5]] {
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: store %[[VAL_25]], %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_26:.*]] = cmpi "eq", %[[VAL_20]], %[[VAL_19]] : index
+// CHECK: %[[VAL_27:.*]] = addi %[[VAL_18]], %[[VAL_6]] : index
+// CHECK: %[[VAL_28:.*]] = select %[[VAL_26]], %[[VAL_27]], %[[VAL_18]] : index
+// CHECK: %[[VAL_29:.*]] = addi %[[VAL_19]], %[[VAL_6]] : index
+// CHECK: scf.yield %[[VAL_28]], %[[VAL_29]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_30:.*]] = %[[VAL_31:.*]]#1 to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK: %[[VAL_32:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_30]]] : memref<32xf32>
+// CHECK: store %[[VAL_32]], %[[VAL_11]]{{\[}}%[[VAL_30]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_33:.*]] = tensor_load %[[VAL_11]] : memref<32xf32>
+// CHECK: return %[[VAL_33]] : tensor<32xf32>
+// CHECK: }
+func @add_ds(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_ds
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: 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() : memref<32xf32>
+// 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<32xf32>
+// CHECK: %[[VAL_10:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_12:.*]] = %[[VAL_10]] to %[[VAL_11]] step %[[VAL_4]] {
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_12]]] : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_13]]] : memref<32xf32>
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_12]]] : memref<?xf32>
+// CHECK: %[[VAL_16:.*]] = mulf %[[VAL_14]], %[[VAL_15]] : f32
+// CHECK: store %[[VAL_16]], %[[VAL_9]]{{\[}}%[[VAL_13]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_17:.*]] = tensor_load %[[VAL_9]] : memref<32xf32>
+// CHECK: return %[[VAL_17]] : tensor<32xf32>
+// CHECK: }
+func @mul_ds(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_ds
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32xf32>
+ return %0 : tensor<32xf32>
+}
+
+#trait_sd = {
+ indexing_maps = [
+ affine_map<(i) -> (i)>, // a
+ affine_map<(i) -> (i)>, // b
+ affine_map<(i) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "S" ], // a
+ [ "D" ], // b
+ [ "D" ] // x
+ ],
+ iterator_types = ["parallel"],
+ doc = "x(i) = a(i) OP b(i)"
+}
+
+// CHECK-LABEL: func @add_sd(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32xf32>) -> tensor<32xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : 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_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_9]]{{\[}}%[[VAL_18]]] : memref<?xf32>
+// CHECK: %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: %[[VAL_24:.*]] = addf %[[VAL_22]], %[[VAL_23]] : f32
+// CHECK: store %[[VAL_24]], %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_5]] {
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: store %[[VAL_25]], %[[VAL_11]]{{\[}}%[[VAL_19]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_26:.*]] = cmpi "eq", %[[VAL_20]], %[[VAL_19]] : index
+// CHECK: %[[VAL_27:.*]] = addi %[[VAL_18]], %[[VAL_6]] : index
+// CHECK: %[[VAL_28:.*]] = select %[[VAL_26]], %[[VAL_27]], %[[VAL_18]] : index
+// CHECK: %[[VAL_29:.*]] = addi %[[VAL_19]], %[[VAL_6]] : index
+// CHECK: scf.yield %[[VAL_28]], %[[VAL_29]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_30:.*]] = %[[VAL_31:.*]]#1 to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK: %[[VAL_32:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_30]]] : memref<32xf32>
+// CHECK: store %[[VAL_32]], %[[VAL_11]]{{\[}}%[[VAL_30]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_33:.*]] = tensor_load %[[VAL_11]] : memref<32xf32>
+// CHECK: return %[[VAL_33]] : tensor<32xf32>
+// CHECK: }
+func @add_sd(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_sd
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: 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:.*]] = alloca() : 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:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_13]]] : memref<32xf32>
+// CHECK: %[[VAL_16:.*]] = mulf %[[VAL_14]], %[[VAL_15]] : f32
+// CHECK: store %[[VAL_16]], %[[VAL_9]]{{\[}}%[[VAL_13]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_17:.*]] = tensor_load %[[VAL_9]] : memref<32xf32>
+// CHECK: return %[[VAL_17]] : tensor<32xf32>
+// CHECK: }
+func @mul_sd(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_sd
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32xf32>
+ return %0 : tensor<32xf32>
+}
+
+#trait_ss = {
+ indexing_maps = [
+ affine_map<(i) -> (i)>, // a
+ affine_map<(i) -> (i)>, // b
+ affine_map<(i) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "S" ], // a
+ [ "S" ], // b
+ [ "D" ] // x
+ ],
+ iterator_types = ["parallel"],
+ doc = "x(i) = a(i) OP b(i)"
+}
+
+// CHECK-LABEL: func @add_ss(
+// 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(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_16:.*]]:2 = scf.while (%[[VAL_17:.*]] = %[[VAL_12]], %[[VAL_18:.*]] = %[[VAL_14]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_19:.*]] = cmpi "ult", %[[VAL_17]], %[[VAL_13]] : index
+// CHECK: %[[VAL_20:.*]] = cmpi "ult", %[[VAL_18]], %[[VAL_15]] : index
+// CHECK: %[[VAL_21:.*]] = and %[[VAL_19]], %[[VAL_20]] : i1
+// CHECK: scf.condition(%[[VAL_21]]) %[[VAL_17]], %[[VAL_18]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
+// CHECK: %[[VAL_24:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_22]]] : memref<?xindex>
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK: %[[VAL_26:.*]] = cmpi "ult", %[[VAL_25]], %[[VAL_24]] : index
+// CHECK: %[[VAL_27:.*]] = select %[[VAL_26]], %[[VAL_25]], %[[VAL_24]] : index
+// CHECK: %[[VAL_28:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_27]] : index
+// CHECK: %[[VAL_29:.*]] = cmpi "eq", %[[VAL_25]], %[[VAL_27]] : index
+// CHECK: %[[VAL_30:.*]] = and %[[VAL_28]], %[[VAL_29]] : i1
+// CHECK: scf.if %[[VAL_30]] {
+// CHECK: %[[VAL_31:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_22]]] : memref<?xf32>
+// CHECK: %[[VAL_32:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK: %[[VAL_33:.*]] = addf %[[VAL_31]], %[[VAL_32]] : f32
+// CHECK: store %[[VAL_33]], %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: %[[VAL_34:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_27]] : index
+// CHECK: scf.if %[[VAL_34]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_22]]] : memref<?xf32>
+// CHECK: store %[[VAL_35]], %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: %[[VAL_36:.*]] = cmpi "eq", %[[VAL_25]], %[[VAL_27]] : index
+// CHECK: scf.if %[[VAL_36]] {
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK: store %[[VAL_37]], %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_38:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_27]] : index
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_22]], %[[VAL_4]] : index
+// CHECK: %[[VAL_40:.*]] = select %[[VAL_38]], %[[VAL_39]], %[[VAL_22]] : index
+// CHECK: %[[VAL_41:.*]] = cmpi "eq", %[[VAL_25]], %[[VAL_27]] : index
+// CHECK: %[[VAL_42:.*]] = addi %[[VAL_23]], %[[VAL_4]] : index
+// CHECK: %[[VAL_43:.*]] = select %[[VAL_41]], %[[VAL_42]], %[[VAL_23]] : index
+// CHECK: scf.yield %[[VAL_40]], %[[VAL_43]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_44:.*]] = %[[VAL_45:.*]]#0 to %[[VAL_13]] step %[[VAL_4]] {
+// CHECK: %[[VAL_46:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_44]]] : memref<?xindex>
+// CHECK: %[[VAL_47:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_44]]] : memref<?xf32>
+// CHECK: store %[[VAL_47]], %[[VAL_11]]{{\[}}%[[VAL_46]]] : memref<32xf32>
+// CHECK: }
+// CHECK: scf.for %[[VAL_48:.*]] = %[[VAL_49:.*]]#1 to %[[VAL_15]] step %[[VAL_4]] {
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK: %[[VAL_51:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: store %[[VAL_51]], %[[VAL_11]]{{\[}}%[[VAL_50]]] : memref<32xf32>
+// CHECK: }
+// CHECK: %[[VAL_52:.*]] = tensor_load %[[VAL_11]] : memref<32xf32>
+// CHECK: return %[[VAL_52]] : tensor<32xf32>
+// CHECK: }
+func @add_ss(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_ss
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: 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(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32xf32>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_16:.*]]:2 = scf.while (%[[VAL_17:.*]] = %[[VAL_12]], %[[VAL_18:.*]] = %[[VAL_14]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_19:.*]] = cmpi "ult", %[[VAL_17]], %[[VAL_13]] : index
+// CHECK: %[[VAL_20:.*]] = cmpi "ult", %[[VAL_18]], %[[VAL_15]] : index
+// CHECK: %[[VAL_21:.*]] = and %[[VAL_19]], %[[VAL_20]] : i1
+// CHECK: scf.condition(%[[VAL_21]]) %[[VAL_17]], %[[VAL_18]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_22:.*]]: index, %[[VAL_23:.*]]: index):
+// CHECK: %[[VAL_24:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_22]]] : memref<?xindex>
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_23]]] : memref<?xindex>
+// CHECK: %[[VAL_26:.*]] = cmpi "ult", %[[VAL_25]], %[[VAL_24]] : index
+// CHECK: %[[VAL_27:.*]] = select %[[VAL_26]], %[[VAL_25]], %[[VAL_24]] : index
+// CHECK: %[[VAL_28:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_27]] : index
+// CHECK: %[[VAL_29:.*]] = cmpi "eq", %[[VAL_25]], %[[VAL_27]] : index
+// CHECK: %[[VAL_30:.*]] = and %[[VAL_28]], %[[VAL_29]] : i1
+// CHECK: scf.if %[[VAL_30]] {
+// CHECK: %[[VAL_31:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_22]]] : memref<?xf32>
+// CHECK: %[[VAL_32:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_23]]] : memref<?xf32>
+// CHECK: %[[VAL_33:.*]] = mulf %[[VAL_31]], %[[VAL_32]] : f32
+// CHECK: store %[[VAL_33]], %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<32xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: %[[VAL_34:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_27]] : index
+// CHECK: %[[VAL_35:.*]] = addi %[[VAL_22]], %[[VAL_4]] : index
+// CHECK: %[[VAL_36:.*]] = select %[[VAL_34]], %[[VAL_35]], %[[VAL_22]] : index
+// CHECK: %[[VAL_37:.*]] = cmpi "eq", %[[VAL_25]], %[[VAL_27]] : index
+// CHECK: %[[VAL_38:.*]] = addi %[[VAL_23]], %[[VAL_4]] : index
+// CHECK: %[[VAL_39:.*]] = select %[[VAL_37]], %[[VAL_38]], %[[VAL_23]] : index
+// CHECK: scf.yield %[[VAL_36]], %[[VAL_39]] : index, index
+// CHECK: }
+// CHECK: %[[VAL_40:.*]] = tensor_load %[[VAL_11]] : memref<32xf32>
+// CHECK: return %[[VAL_40]] : tensor<32xf32>
+// CHECK: }
+func @mul_ss(%arga: tensor<32xf32>, %argb: tensor<32xf32>) -> tensor<32xf32> {
+ %0 = linalg.generic #trait_ss
+ ins(%arga, %argb: tensor<32xf32>, tensor<32xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32xf32>
+ return %0 : tensor<32xf32>
+}
diff --git a/mlir/test/Dialect/Linalg/sparse_2d.mlir b/mlir/test/Dialect/Linalg/sparse_2d.mlir
new file mode 100644
index 000000000000..38d55ef69c4e
--- /dev/null
+++ b/mlir/test/Dialect/Linalg/sparse_2d.mlir
@@ -0,0 +1,1058 @@
+// NOTE: Assertions have been autogenerated by utils/generate-test-checks.py
+// RUN: mlir-opt %s -test-sparsification | FileCheck %s
+
+#trait_dd = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (i,j)>, // B
+ affine_map<(i,j) -> (i,j)> // X (out)
+ ],
+ sparse = [
+ [ "D", "D" ], // A
+ [ "D", "D" ], // B
+ [ "D", "D" ] // X
+ ],
+ iterator_types = ["parallel", "parallel"],
+ doc = "X(i,j) = A(i,j) OP B(i,j)"
+}
+
+// CHECK-LABEL: func @add_dd(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : index
+// CHECK: %[[VAL_3:.*]] = constant 16 : index
+// CHECK: %[[VAL_4:.*]] = constant 0 : index
+// CHECK: %[[VAL_5:.*]] = constant 1 : index
+// CHECK: %[[VAL_6:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_7:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_8:.*]] = alloca() : memref<32x16xf32>
+// CHECK: scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_2]] step %[[VAL_5]] {
+// CHECK: scf.for %[[VAL_10:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]], %[[VAL_10]]] : memref<32x16xf32>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_9]], %[[VAL_10]]] : memref<32x16xf32>
+// CHECK: %[[VAL_13:.*]] = addf %[[VAL_11]], %[[VAL_12]] : f32
+// CHECK: store %[[VAL_13]], %[[VAL_8]]{{\[}}%[[VAL_9]], %[[VAL_10]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_14:.*]] = tensor_load %[[VAL_8]] : memref<32x16xf32>
+// CHECK: return %[[VAL_14]] : tensor<32x16xf32>
+// CHECK: }
+func @add_dd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_dd
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : index
+// CHECK: %[[VAL_3:.*]] = constant 16 : index
+// CHECK: %[[VAL_4:.*]] = constant 0 : index
+// CHECK: %[[VAL_5:.*]] = constant 1 : index
+// CHECK: %[[VAL_6:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_7:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_8:.*]] = alloca() : memref<32x16xf32>
+// CHECK: scf.for %[[VAL_9:.*]] = %[[VAL_4]] to %[[VAL_2]] step %[[VAL_5]] {
+// CHECK: scf.for %[[VAL_10:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_11:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_9]], %[[VAL_10]]] : memref<32x16xf32>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_9]], %[[VAL_10]]] : memref<32x16xf32>
+// CHECK: %[[VAL_13:.*]] = mulf %[[VAL_11]], %[[VAL_12]] : f32
+// CHECK: store %[[VAL_13]], %[[VAL_8]]{{\[}}%[[VAL_9]], %[[VAL_10]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_14:.*]] = tensor_load %[[VAL_8]] : memref<32x16xf32>
+// CHECK: return %[[VAL_14]] : tensor<32x16xf32>
+// CHECK: }
+func @mul_dd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_dd
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16xf32>
+ return %0 : tensor<32x16xf32>
+}
+
+#trait_ds = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (i,j)>, // B
+ affine_map<(i,j) -> (i,j)> // X (out)
+ ],
+ sparse = [
+ [ "D", "S" ], // A
+ [ "D", "D" ], // B
+ [ "D", "D" ] // X
+ ],
+ iterator_types = ["parallel", "parallel"],
+ doc = "X(i,j) = A(i,j) OP B(i,j)"
+}
+
+// CHECK-LABEL: func @add_ds(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16xf32>
+// CHECK: scf.for %[[VAL_13:.*]] = %[[VAL_5]] to %[[VAL_3]] 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: %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_14]], %[[VAL_19:.*]] = %[[VAL_5]]) : (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_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK: %[[VAL_24:.*]] = cmpi "eq", %[[VAL_23]], %[[VAL_22]] : index
+// CHECK: scf.if %[[VAL_24]] {
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xf32>
+// CHECK: %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]], %[[VAL_22]]] : memref<32x16xf32>
+// CHECK: %[[VAL_27:.*]] = addf %[[VAL_25]], %[[VAL_26]] : f32
+// CHECK: store %[[VAL_27]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_22]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]], %[[VAL_22]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_28]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_22]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_29:.*]] = cmpi "eq", %[[VAL_23]], %[[VAL_22]] : index
+// CHECK: %[[VAL_30:.*]] = addi %[[VAL_21]], %[[VAL_7]] : index
+// CHECK: %[[VAL_31:.*]] = select %[[VAL_29]], %[[VAL_30]], %[[VAL_21]] : index
+// CHECK: %[[VAL_32:.*]] = addi %[[VAL_22]], %[[VAL_7]] : index
+// CHECK: scf.yield %[[VAL_31]], %[[VAL_32]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_33:.*]] = %[[VAL_34:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]], %[[VAL_33]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_35]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_33]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_36:.*]] = tensor_load %[[VAL_12]] : memref<32x16xf32>
+// CHECK: return %[[VAL_36]] : tensor<32x16xf32>
+// CHECK: }
+func @add_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ds
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// CHECK: %[[VAL_3:.*]] = constant 32 : 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_9:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32x16xf32>
+// CHECK: scf.for %[[VAL_11:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_11]]] : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = addi %[[VAL_11]], %[[VAL_5]] : index
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_15:.*]] = %[[VAL_12]] 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<?xf32>
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_11]], %[[VAL_16]]] : memref<32x16xf32>
+// CHECK: %[[VAL_19:.*]] = mulf %[[VAL_17]], %[[VAL_18]] : f32
+// CHECK: store %[[VAL_19]], %[[VAL_10]]{{\[}}%[[VAL_11]], %[[VAL_16]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_20:.*]] = tensor_load %[[VAL_10]] : memref<32x16xf32>
+// CHECK: return %[[VAL_20]] : tensor<32x16xf32>
+// CHECK: }
+func @mul_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ds
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16xf32>
+ return %0 : tensor<32x16xf32>
+}
+
+#trait_sd = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (i,j)>, // B
+ affine_map<(i,j) -> (i,j)> // X (out)
+ ],
+ sparse = [
+ [ "S", "D" ], // A
+ [ "D", "D" ], // B
+ [ "D", "D" ] // X
+ ],
+ iterator_types = ["parallel", "parallel"],
+ doc = "X(i,j) = A(i,j) OP B(i,j)"
+}
+
+// CHECK-LABEL: func @add_sd(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_6]]] : 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_6]]) : (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_22:.*]] = cmpi "eq", %[[VAL_21]], %[[VAL_20]] : index
+// CHECK: scf.if %[[VAL_22]] {
+// CHECK: scf.for %[[VAL_23:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_24:.*]] = muli %[[VAL_19]], %[[VAL_4]] : index
+// CHECK: %[[VAL_25:.*]] = addi %[[VAL_24]], %[[VAL_23]] : index
+// CHECK: %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK: %[[VAL_27:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_20]], %[[VAL_23]]] : memref<32x16xf32>
+// CHECK: %[[VAL_28:.*]] = addf %[[VAL_26]], %[[VAL_27]] : f32
+// CHECK: store %[[VAL_28]], %[[VAL_12]]{{\[}}%[[VAL_20]], %[[VAL_23]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_5]] {
+// CHECK: scf.for %[[VAL_29:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_20]], %[[VAL_29]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_30]], %[[VAL_12]]{{\[}}%[[VAL_20]], %[[VAL_29]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_31:.*]] = cmpi "eq", %[[VAL_21]], %[[VAL_20]] : index
+// CHECK: %[[VAL_32:.*]] = addi %[[VAL_19]], %[[VAL_7]] : index
+// CHECK: %[[VAL_33:.*]] = select %[[VAL_31]], %[[VAL_32]], %[[VAL_19]] : index
+// CHECK: %[[VAL_34:.*]] = addi %[[VAL_20]], %[[VAL_7]] : index
+// CHECK: scf.yield %[[VAL_33]], %[[VAL_34]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_35:.*]] = %[[VAL_36:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
+// CHECK: scf.for %[[VAL_37:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_38:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_35]], %[[VAL_37]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_38]], %[[VAL_12]]{{\[}}%[[VAL_35]], %[[VAL_37]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_39:.*]] = tensor_load %[[VAL_12]] : memref<32x16xf32>
+// CHECK: return %[[VAL_39]] : tensor<32x16xf32>
+// CHECK: }
+func @add_sd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_sd
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// CHECK: %[[VAL_3:.*]] = constant 16 : 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_9:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32x16xf32>
+// 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: scf.for %[[VAL_15:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_16:.*]] = muli %[[VAL_13]], %[[VAL_3]] : index
+// CHECK: %[[VAL_17:.*]] = addi %[[VAL_16]], %[[VAL_15]] : index
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_17]]] : memref<?xf32>
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_14]], %[[VAL_15]]] : memref<32x16xf32>
+// CHECK: %[[VAL_20:.*]] = mulf %[[VAL_18]], %[[VAL_19]] : f32
+// CHECK: store %[[VAL_20]], %[[VAL_10]]{{\[}}%[[VAL_14]], %[[VAL_15]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_21:.*]] = tensor_load %[[VAL_10]] : memref<32x16xf32>
+// CHECK: return %[[VAL_21]] : tensor<32x16xf32>
+// CHECK: }
+func @mul_sd(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_sd
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16xf32>
+ return %0 : tensor<32x16xf32>
+}
+
+#trait_ss = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (i,j)>, // B
+ affine_map<(i,j) -> (i,j)> // X (out)
+ ],
+ sparse = [
+ [ "S", "S" ], // A
+ [ "D", "D" ], // B
+ [ "D", "D" ] // X
+ ],
+ iterator_types = ["parallel", "parallel"],
+ doc = "X(i,j) = A(i,j) OP B(i,j)"
+}
+
+// CHECK-LABEL: func @add_ss(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_13:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_14:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_6]]] : memref<?xindex>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK: %[[VAL_17:.*]]:2 = scf.while (%[[VAL_18:.*]] = %[[VAL_15]], %[[VAL_19:.*]] = %[[VAL_6]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_20:.*]] = 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_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK: %[[VAL_24:.*]] = cmpi "eq", %[[VAL_23]], %[[VAL_22]] : index
+// CHECK: scf.if %[[VAL_24]] {
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK: %[[VAL_26:.*]] = addi %[[VAL_21]], %[[VAL_7]] : index
+// CHECK: %[[VAL_27:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_28:.*]]:2 = scf.while (%[[VAL_29:.*]] = %[[VAL_25]], %[[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_32:.*]]: index, %[[VAL_33:.*]]: index):
+// CHECK: %[[VAL_34:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_32]]] : memref<?xindex>
+// CHECK: %[[VAL_35:.*]] = cmpi "eq", %[[VAL_34]], %[[VAL_33]] : index
+// CHECK: scf.if %[[VAL_35]] {
+// CHECK: %[[VAL_36:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_32]]] : memref<?xf32>
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_33]]] : memref<32x16xf32>
+// CHECK: %[[VAL_38:.*]] = addf %[[VAL_36]], %[[VAL_37]] : f32
+// CHECK: store %[[VAL_38]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_33]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_5]] {
+// CHECK: %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_33]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_39]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_33]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_40:.*]] = cmpi "eq", %[[VAL_34]], %[[VAL_33]] : index
+// CHECK: %[[VAL_41:.*]] = addi %[[VAL_32]], %[[VAL_7]] : index
+// CHECK: %[[VAL_42:.*]] = select %[[VAL_40]], %[[VAL_41]], %[[VAL_32]] : index
+// CHECK: %[[VAL_43:.*]] = addi %[[VAL_33]], %[[VAL_7]] : index
+// CHECK: scf.yield %[[VAL_42]], %[[VAL_43]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_44:.*]] = %[[VAL_45:.*]]#1 to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_46:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_44]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_46]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_44]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_5]] {
+// CHECK: scf.for %[[VAL_47:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_48:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_22]], %[[VAL_47]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_48]], %[[VAL_14]]{{\[}}%[[VAL_22]], %[[VAL_47]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_49:.*]] = cmpi "eq", %[[VAL_23]], %[[VAL_22]] : index
+// CHECK: %[[VAL_50:.*]] = addi %[[VAL_21]], %[[VAL_7]] : index
+// CHECK: %[[VAL_51:.*]] = select %[[VAL_49]], %[[VAL_50]], %[[VAL_21]] : index
+// CHECK: %[[VAL_52:.*]] = addi %[[VAL_22]], %[[VAL_7]] : index
+// CHECK: scf.yield %[[VAL_51]], %[[VAL_52]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_53:.*]] = %[[VAL_54:.*]]#1 to %[[VAL_3]] step %[[VAL_7]] {
+// CHECK: scf.for %[[VAL_55:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_7]] {
+// CHECK: %[[VAL_56:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_53]], %[[VAL_55]]] : memref<32x16xf32>
+// CHECK: store %[[VAL_56]], %[[VAL_14]]{{\[}}%[[VAL_53]], %[[VAL_55]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_57:.*]] = tensor_load %[[VAL_14]] : memref<32x16xf32>
+// CHECK: return %[[VAL_57]] : tensor<32x16xf32>
+// CHECK: }
+func @add_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ss
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_12:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_14:.*]] = %[[VAL_12]] to %[[VAL_13]] step %[[VAL_4]] {
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_14]]] : memref<?xindex>
+// CHECK: %[[VAL_17:.*]] = addi %[[VAL_14]], %[[VAL_4]] : index
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_19:.*]] = %[[VAL_16]] to %[[VAL_18]] step %[[VAL_4]] {
+// CHECK: %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK: %[[VAL_21:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xf32>
+// CHECK: %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_15]], %[[VAL_20]]] : memref<32x16xf32>
+// CHECK: %[[VAL_23:.*]] = mulf %[[VAL_21]], %[[VAL_22]] : f32
+// CHECK: store %[[VAL_23]], %[[VAL_11]]{{\[}}%[[VAL_15]], %[[VAL_20]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_24:.*]] = tensor_load %[[VAL_11]] : memref<32x16xf32>
+// CHECK: return %[[VAL_24]] : tensor<32x16xf32>
+// CHECK: }
+func @mul_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ss
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16xf32>
+ return %0 : tensor<32x16xf32>
+}
+
+#trait_ss_ss = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (i,j)>, // B
+ affine_map<(i,j) -> (i,j)> // X (out)
+ ],
+ sparse = [
+ [ "S", "S" ], // A
+ [ "S", "S" ], // B
+ [ "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_16]], %[[VAL_22:.*]] = %[[VAL_18]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_23:.*]] = cmpi "ult", %[[VAL_21]], %[[VAL_17]] : index
+// CHECK: %[[VAL_24:.*]] = cmpi "ult", %[[VAL_22]], %[[VAL_19]] : index
+// CHECK: %[[VAL_25:.*]] = and %[[VAL_23]], %[[VAL_24]] : i1
+// CHECK: scf.condition(%[[VAL_25]]) %[[VAL_21]], %[[VAL_22]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_30:.*]] = cmpi "ult", %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_31:.*]] = select %[[VAL_30]], %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_32:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_33:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_34:.*]] = and %[[VAL_32]], %[[VAL_33]] : i1
+// CHECK: scf.if %[[VAL_34]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_36:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_36]]] : memref<?xindex>
+// CHECK: %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_39]]] : memref<?xindex>
+// CHECK: %[[VAL_41:.*]]:2 = scf.while (%[[VAL_42:.*]] = %[[VAL_35]], %[[VAL_43:.*]] = %[[VAL_38]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_44:.*]] = cmpi "ult", %[[VAL_42]], %[[VAL_37]] : index
+// CHECK: %[[VAL_45:.*]] = cmpi "ult", %[[VAL_43]], %[[VAL_40]] : index
+// CHECK: %[[VAL_46:.*]] = and %[[VAL_44]], %[[VAL_45]] : i1
+// CHECK: scf.condition(%[[VAL_46]]) %[[VAL_42]], %[[VAL_43]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_47:.*]]: index, %[[VAL_48:.*]]: index):
+// CHECK: %[[VAL_49:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_47]]] : memref<?xindex>
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK: %[[VAL_51:.*]] = cmpi "ult", %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_52:.*]] = select %[[VAL_51]], %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_53:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_54:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_55:.*]] = and %[[VAL_53]], %[[VAL_54]] : i1
+// CHECK: scf.if %[[VAL_55]] {
+// CHECK: %[[VAL_56:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_47]]] : memref<?xf32>
+// CHECK: %[[VAL_57:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: %[[VAL_58:.*]] = addf %[[VAL_56]], %[[VAL_57]] : f32
+// CHECK: store %[[VAL_58]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: %[[VAL_59:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: scf.if %[[VAL_59]] {
+// CHECK: %[[VAL_60:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_47]]] : memref<?xf32>
+// CHECK: store %[[VAL_60]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: %[[VAL_61:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: scf.if %[[VAL_61]] {
+// CHECK: %[[VAL_62:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: store %[[VAL_62]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_63:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_64:.*]] = addi %[[VAL_47]], %[[VAL_4]] : index
+// CHECK: %[[VAL_65:.*]] = select %[[VAL_63]], %[[VAL_64]], %[[VAL_47]] : index
+// CHECK: %[[VAL_66:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_67:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
+// CHECK: %[[VAL_68:.*]] = select %[[VAL_66]], %[[VAL_67]], %[[VAL_48]] : index
+// CHECK: scf.yield %[[VAL_65]], %[[VAL_68]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_69:.*]] = %[[VAL_70:.*]]#0 to %[[VAL_37]] step %[[VAL_4]] {
+// CHECK: %[[VAL_71:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_69]]] : memref<?xindex>
+// CHECK: %[[VAL_72:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_69]]] : memref<?xf32>
+// CHECK: store %[[VAL_72]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_71]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: scf.for %[[VAL_73:.*]] = %[[VAL_74:.*]]#1 to %[[VAL_40]] step %[[VAL_4]] {
+// CHECK: %[[VAL_75:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_73]]] : memref<?xindex>
+// CHECK: %[[VAL_76:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_73]]] : memref<?xf32>
+// CHECK: store %[[VAL_76]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_75]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: %[[VAL_77:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: scf.if %[[VAL_77]] {
+// CHECK: %[[VAL_78:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_79:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_80:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_79]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_81:.*]] = %[[VAL_78]] to %[[VAL_80]] step %[[VAL_4]] {
+// CHECK: %[[VAL_82:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_81]]] : memref<?xindex>
+// CHECK: %[[VAL_83:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_81]]] : memref<?xf32>
+// CHECK: store %[[VAL_83]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_82]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: %[[VAL_84:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: scf.if %[[VAL_84]] {
+// CHECK: %[[VAL_85:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_86:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_87:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_86]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_88:.*]] = %[[VAL_85]] to %[[VAL_87]] step %[[VAL_4]] {
+// CHECK: %[[VAL_89:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_88]]] : memref<?xindex>
+// CHECK: %[[VAL_90:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_88]]] : memref<?xf32>
+// CHECK: store %[[VAL_90]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_89]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_91:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_92:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_93:.*]] = select %[[VAL_91]], %[[VAL_92]], %[[VAL_26]] : index
+// CHECK: %[[VAL_94:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_95:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_96:.*]] = select %[[VAL_94]], %[[VAL_95]], %[[VAL_27]] : index
+// CHECK: scf.yield %[[VAL_93]], %[[VAL_96]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_97:.*]] = %[[VAL_98:.*]]#0 to %[[VAL_17]] step %[[VAL_4]] {
+// CHECK: %[[VAL_99:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_97]]] : memref<?xindex>
+// CHECK: %[[VAL_100:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_97]]] : memref<?xindex>
+// CHECK: %[[VAL_101:.*]] = addi %[[VAL_97]], %[[VAL_4]] : index
+// CHECK: %[[VAL_102:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_101]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_103:.*]] = %[[VAL_100]] to %[[VAL_102]] step %[[VAL_4]] {
+// CHECK: %[[VAL_104:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_103]]] : memref<?xindex>
+// CHECK: %[[VAL_105:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_103]]] : memref<?xf32>
+// CHECK: store %[[VAL_105]], %[[VAL_15]]{{\[}}%[[VAL_99]], %[[VAL_104]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: scf.for %[[VAL_106:.*]] = %[[VAL_107:.*]]#1 to %[[VAL_19]] step %[[VAL_4]] {
+// CHECK: %[[VAL_108:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_106]]] : memref<?xindex>
+// CHECK: %[[VAL_109:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_106]]] : memref<?xindex>
+// CHECK: %[[VAL_110:.*]] = addi %[[VAL_106]], %[[VAL_4]] : index
+// CHECK: %[[VAL_111:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_110]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_112:.*]] = %[[VAL_109]] to %[[VAL_111]] step %[[VAL_4]] {
+// CHECK: %[[VAL_113:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_112]]] : memref<?xindex>
+// CHECK: %[[VAL_114:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_112]]] : memref<?xf32>
+// CHECK: store %[[VAL_114]], %[[VAL_15]]{{\[}}%[[VAL_108]], %[[VAL_113]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_115:.*]] = tensor_load %[[VAL_15]] : memref<32x16xf32>
+// CHECK: return %[[VAL_115]] : tensor<32x16xf32>
+// CHECK: }
+func @add_ss_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ss_ss
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_16]], %[[VAL_22:.*]] = %[[VAL_18]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_23:.*]] = cmpi "ult", %[[VAL_21]], %[[VAL_17]] : index
+// CHECK: %[[VAL_24:.*]] = cmpi "ult", %[[VAL_22]], %[[VAL_19]] : index
+// CHECK: %[[VAL_25:.*]] = and %[[VAL_23]], %[[VAL_24]] : i1
+// CHECK: scf.condition(%[[VAL_25]]) %[[VAL_21]], %[[VAL_22]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_30:.*]] = cmpi "ult", %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_31:.*]] = select %[[VAL_30]], %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_32:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_33:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_34:.*]] = and %[[VAL_32]], %[[VAL_33]] : i1
+// CHECK: scf.if %[[VAL_34]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_36:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_36]]] : memref<?xindex>
+// CHECK: %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_39]]] : memref<?xindex>
+// CHECK: %[[VAL_41:.*]]:2 = scf.while (%[[VAL_42:.*]] = %[[VAL_35]], %[[VAL_43:.*]] = %[[VAL_38]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_44:.*]] = cmpi "ult", %[[VAL_42]], %[[VAL_37]] : index
+// CHECK: %[[VAL_45:.*]] = cmpi "ult", %[[VAL_43]], %[[VAL_40]] : index
+// CHECK: %[[VAL_46:.*]] = and %[[VAL_44]], %[[VAL_45]] : i1
+// CHECK: scf.condition(%[[VAL_46]]) %[[VAL_42]], %[[VAL_43]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_47:.*]]: index, %[[VAL_48:.*]]: index):
+// CHECK: %[[VAL_49:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_47]]] : memref<?xindex>
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK: %[[VAL_51:.*]] = cmpi "ult", %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_52:.*]] = select %[[VAL_51]], %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_53:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_54:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_55:.*]] = and %[[VAL_53]], %[[VAL_54]] : i1
+// CHECK: scf.if %[[VAL_55]] {
+// CHECK: %[[VAL_56:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_47]]] : memref<?xf32>
+// CHECK: %[[VAL_57:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: %[[VAL_58:.*]] = mulf %[[VAL_56]], %[[VAL_57]] : f32
+// CHECK: store %[[VAL_58]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: %[[VAL_59:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_60:.*]] = addi %[[VAL_47]], %[[VAL_4]] : index
+// CHECK: %[[VAL_61:.*]] = select %[[VAL_59]], %[[VAL_60]], %[[VAL_47]] : index
+// CHECK: %[[VAL_62:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_63:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
+// CHECK: %[[VAL_64:.*]] = select %[[VAL_62]], %[[VAL_63]], %[[VAL_48]] : index
+// CHECK: scf.yield %[[VAL_61]], %[[VAL_64]] : index, index
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: %[[VAL_65:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_66:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_67:.*]] = select %[[VAL_65]], %[[VAL_66]], %[[VAL_26]] : index
+// CHECK: %[[VAL_68:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_69:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_70:.*]] = select %[[VAL_68]], %[[VAL_69]], %[[VAL_27]] : index
+// CHECK: scf.yield %[[VAL_67]], %[[VAL_70]] : index, index
+// CHECK: }
+// CHECK: %[[VAL_71:.*]] = tensor_load %[[VAL_15]] : memref<32x16xf32>
+// CHECK: return %[[VAL_71]] : tensor<32x16xf32>
+// CHECK: }
+func @mul_ss_ss(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ss_ss
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16xf32>
+ return %0 : tensor<32x16xf32>
+}
+
+#trait_sd_ds = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (i,j)>, // B
+ affine_map<(i,j) -> (i,j)> // X (out)
+ ],
+ sparse = [
+ [ "S", "D" ], // A
+ [ "D", "S" ], // B
+ [ "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_16]], %[[VAL_22:.*]] = %[[VAL_18]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_23:.*]] = cmpi "ult", %[[VAL_21]], %[[VAL_17]] : index
+// CHECK: %[[VAL_24:.*]] = cmpi "ult", %[[VAL_22]], %[[VAL_19]] : index
+// CHECK: %[[VAL_25:.*]] = and %[[VAL_23]], %[[VAL_24]] : i1
+// CHECK: scf.condition(%[[VAL_25]]) %[[VAL_21]], %[[VAL_22]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_30:.*]] = cmpi "ult", %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_31:.*]] = select %[[VAL_30]], %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_32:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_33:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_34:.*]] = and %[[VAL_32]], %[[VAL_33]] : i1
+// CHECK: scf.if %[[VAL_34]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_36:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_36]]] : memref<?xindex>
+// CHECK: %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_39]]] : memref<?xindex>
+// CHECK: %[[VAL_41:.*]]:2 = scf.while (%[[VAL_42:.*]] = %[[VAL_35]], %[[VAL_43:.*]] = %[[VAL_38]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_44:.*]] = cmpi "ult", %[[VAL_42]], %[[VAL_37]] : index
+// CHECK: %[[VAL_45:.*]] = cmpi "ult", %[[VAL_43]], %[[VAL_40]] : index
+// CHECK: %[[VAL_46:.*]] = and %[[VAL_44]], %[[VAL_45]] : i1
+// CHECK: scf.condition(%[[VAL_46]]) %[[VAL_42]], %[[VAL_43]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_47:.*]]: index, %[[VAL_48:.*]]: index):
+// CHECK: %[[VAL_49:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_47]]] : memref<?xindex>
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK: %[[VAL_51:.*]] = cmpi "ult", %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_52:.*]] = select %[[VAL_51]], %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_53:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_54:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_55:.*]] = and %[[VAL_53]], %[[VAL_54]] : i1
+// CHECK: scf.if %[[VAL_55]] {
+// CHECK: %[[VAL_56:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_47]]] : memref<?xf32>
+// CHECK: %[[VAL_57:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: %[[VAL_58:.*]] = addf %[[VAL_56]], %[[VAL_57]] : f32
+// CHECK: store %[[VAL_58]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: %[[VAL_59:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: scf.if %[[VAL_59]] {
+// CHECK: %[[VAL_60:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_47]]] : memref<?xf32>
+// CHECK: store %[[VAL_60]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: %[[VAL_61:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: scf.if %[[VAL_61]] {
+// CHECK: %[[VAL_62:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: store %[[VAL_62]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_63:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_64:.*]] = addi %[[VAL_47]], %[[VAL_4]] : index
+// CHECK: %[[VAL_65:.*]] = select %[[VAL_63]], %[[VAL_64]], %[[VAL_47]] : index
+// CHECK: %[[VAL_66:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_67:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
+// CHECK: %[[VAL_68:.*]] = select %[[VAL_66]], %[[VAL_67]], %[[VAL_48]] : index
+// CHECK: scf.yield %[[VAL_65]], %[[VAL_68]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_69:.*]] = %[[VAL_70:.*]]#0 to %[[VAL_37]] step %[[VAL_4]] {
+// CHECK: %[[VAL_71:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_69]]] : memref<?xindex>
+// CHECK: %[[VAL_72:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_69]]] : memref<?xf32>
+// CHECK: store %[[VAL_72]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_71]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: scf.for %[[VAL_73:.*]] = %[[VAL_74:.*]]#1 to %[[VAL_40]] step %[[VAL_4]] {
+// CHECK: %[[VAL_75:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_73]]] : memref<?xindex>
+// CHECK: %[[VAL_76:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_73]]] : memref<?xf32>
+// CHECK: store %[[VAL_76]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_75]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: %[[VAL_77:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: scf.if %[[VAL_77]] {
+// CHECK: %[[VAL_78:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_79:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_80:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_79]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_81:.*]] = %[[VAL_78]] to %[[VAL_80]] step %[[VAL_4]] {
+// CHECK: %[[VAL_82:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_81]]] : memref<?xindex>
+// CHECK: %[[VAL_83:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_81]]] : memref<?xf32>
+// CHECK: store %[[VAL_83]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_82]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: %[[VAL_84:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: scf.if %[[VAL_84]] {
+// CHECK: %[[VAL_85:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_86:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_87:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_86]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_88:.*]] = %[[VAL_85]] to %[[VAL_87]] step %[[VAL_4]] {
+// CHECK: %[[VAL_89:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_88]]] : memref<?xindex>
+// CHECK: %[[VAL_90:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_88]]] : memref<?xf32>
+// CHECK: store %[[VAL_90]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_89]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_91:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_92:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_93:.*]] = select %[[VAL_91]], %[[VAL_92]], %[[VAL_26]] : index
+// CHECK: %[[VAL_94:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_95:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_96:.*]] = select %[[VAL_94]], %[[VAL_95]], %[[VAL_27]] : index
+// CHECK: scf.yield %[[VAL_93]], %[[VAL_96]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_97:.*]] = %[[VAL_98:.*]]#0 to %[[VAL_17]] step %[[VAL_4]] {
+// CHECK: %[[VAL_99:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_97]]] : memref<?xindex>
+// CHECK: %[[VAL_100:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_97]]] : memref<?xindex>
+// CHECK: %[[VAL_101:.*]] = addi %[[VAL_97]], %[[VAL_4]] : index
+// CHECK: %[[VAL_102:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_101]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_103:.*]] = %[[VAL_100]] to %[[VAL_102]] step %[[VAL_4]] {
+// CHECK: %[[VAL_104:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_103]]] : memref<?xindex>
+// CHECK: %[[VAL_105:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_103]]] : memref<?xf32>
+// CHECK: store %[[VAL_105]], %[[VAL_15]]{{\[}}%[[VAL_99]], %[[VAL_104]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: scf.for %[[VAL_106:.*]] = %[[VAL_107:.*]]#1 to %[[VAL_19]] step %[[VAL_4]] {
+// CHECK: %[[VAL_108:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_106]]] : memref<?xindex>
+// CHECK: %[[VAL_109:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_106]]] : memref<?xindex>
+// CHECK: %[[VAL_110:.*]] = addi %[[VAL_106]], %[[VAL_4]] : index
+// CHECK: %[[VAL_111:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_110]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_112:.*]] = %[[VAL_109]] to %[[VAL_111]] step %[[VAL_4]] {
+// CHECK: %[[VAL_113:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_112]]] : memref<?xindex>
+// CHECK: %[[VAL_114:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_112]]] : memref<?xf32>
+// CHECK: store %[[VAL_114]], %[[VAL_15]]{{\[}}%[[VAL_108]], %[[VAL_113]]] : memref<32x16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_115:.*]] = tensor_load %[[VAL_15]] : memref<32x16xf32>
+// CHECK: return %[[VAL_115]] : tensor<32x16xf32>
+// CHECK: }
+func @add_sd_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ss_ss
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16xf32>) -> tensor<32x16xf32> {
+// 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16xf32>
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_17:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_16]], %[[VAL_22:.*]] = %[[VAL_18]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_23:.*]] = cmpi "ult", %[[VAL_21]], %[[VAL_17]] : index
+// CHECK: %[[VAL_24:.*]] = cmpi "ult", %[[VAL_22]], %[[VAL_19]] : index
+// CHECK: %[[VAL_25:.*]] = and %[[VAL_23]], %[[VAL_24]] : i1
+// CHECK: scf.condition(%[[VAL_25]]) %[[VAL_21]], %[[VAL_22]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_26:.*]]: index, %[[VAL_27:.*]]: index):
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_30:.*]] = cmpi "ult", %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_31:.*]] = select %[[VAL_30]], %[[VAL_29]], %[[VAL_28]] : index
+// CHECK: %[[VAL_32:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_33:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_34:.*]] = and %[[VAL_32]], %[[VAL_33]] : i1
+// CHECK: scf.if %[[VAL_34]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_36:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_36]]] : memref<?xindex>
+// CHECK: %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_27]]] : memref<?xindex>
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_39]]] : memref<?xindex>
+// CHECK: %[[VAL_41:.*]]:2 = scf.while (%[[VAL_42:.*]] = %[[VAL_35]], %[[VAL_43:.*]] = %[[VAL_38]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_44:.*]] = cmpi "ult", %[[VAL_42]], %[[VAL_37]] : index
+// CHECK: %[[VAL_45:.*]] = cmpi "ult", %[[VAL_43]], %[[VAL_40]] : index
+// CHECK: %[[VAL_46:.*]] = and %[[VAL_44]], %[[VAL_45]] : i1
+// CHECK: scf.condition(%[[VAL_46]]) %[[VAL_42]], %[[VAL_43]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_47:.*]]: index, %[[VAL_48:.*]]: index):
+// CHECK: %[[VAL_49:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_47]]] : memref<?xindex>
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_48]]] : memref<?xindex>
+// CHECK: %[[VAL_51:.*]] = cmpi "ult", %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_52:.*]] = select %[[VAL_51]], %[[VAL_50]], %[[VAL_49]] : index
+// CHECK: %[[VAL_53:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_54:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_55:.*]] = and %[[VAL_53]], %[[VAL_54]] : i1
+// CHECK: scf.if %[[VAL_55]] {
+// CHECK: %[[VAL_56:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_47]]] : memref<?xf32>
+// CHECK: %[[VAL_57:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_48]]] : memref<?xf32>
+// CHECK: %[[VAL_58:.*]] = mulf %[[VAL_56]], %[[VAL_57]] : f32
+// CHECK: store %[[VAL_58]], %[[VAL_15]]{{\[}}%[[VAL_31]], %[[VAL_52]]] : memref<32x16xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: %[[VAL_59:.*]] = cmpi "eq", %[[VAL_49]], %[[VAL_52]] : index
+// CHECK: %[[VAL_60:.*]] = addi %[[VAL_47]], %[[VAL_4]] : index
+// CHECK: %[[VAL_61:.*]] = select %[[VAL_59]], %[[VAL_60]], %[[VAL_47]] : index
+// CHECK: %[[VAL_62:.*]] = cmpi "eq", %[[VAL_50]], %[[VAL_52]] : index
+// CHECK: %[[VAL_63:.*]] = addi %[[VAL_48]], %[[VAL_4]] : index
+// CHECK: %[[VAL_64:.*]] = select %[[VAL_62]], %[[VAL_63]], %[[VAL_48]] : index
+// CHECK: scf.yield %[[VAL_61]], %[[VAL_64]] : index, index
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: %[[VAL_65:.*]] = cmpi "eq", %[[VAL_28]], %[[VAL_31]] : index
+// CHECK: %[[VAL_66:.*]] = addi %[[VAL_26]], %[[VAL_4]] : index
+// CHECK: %[[VAL_67:.*]] = select %[[VAL_65]], %[[VAL_66]], %[[VAL_26]] : index
+// CHECK: %[[VAL_68:.*]] = cmpi "eq", %[[VAL_29]], %[[VAL_31]] : index
+// CHECK: %[[VAL_69:.*]] = addi %[[VAL_27]], %[[VAL_4]] : index
+// CHECK: %[[VAL_70:.*]] = select %[[VAL_68]], %[[VAL_69]], %[[VAL_27]] : index
+// CHECK: scf.yield %[[VAL_67]], %[[VAL_70]] : index, index
+// CHECK: }
+// CHECK: %[[VAL_71:.*]] = tensor_load %[[VAL_15]] : memref<32x16xf32>
+// CHECK: return %[[VAL_71]] : tensor<32x16xf32>
+// CHECK: }
+func @mul_sd_ds(%arga: tensor<32x16xf32>, %argb: tensor<32x16xf32>) -> tensor<32x16xf32> {
+ %0 = linalg.generic #trait_ss_ss
+ ins(%arga, %argb: tensor<32x16xf32>, tensor<32x16xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16xf32>
+ return %0 : tensor<32x16xf32>
+}
+
+#trait_matvec = {
+ indexing_maps = [
+ affine_map<(i,j) -> (i,j)>, // A
+ affine_map<(i,j) -> (j)>, // b
+ affine_map<(i,j) -> (i)> // x (out)
+ ],
+ sparse = [
+ [ "D", "S" ], // A
+ [ "D" ], // b
+ [ "D" ] // x
+ ],
+ iterator_types = ["parallel", "reduction"],
+ doc = "x(i) += A(i,j) * b(j)"
+}
+
+// CHECK-LABEL: func @matvec(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<16x32xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32xf32>,
+// CHECK-SAME: %[[VAL_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: 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_17]]] : memref<32xf32>
+// CHECK: %[[VAL_20:.*]] = mulf %[[VAL_18]], %[[VAL_19]] : f32
+// CHECK: %[[VAL_21:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
+// CHECK: %[[VAL_22:.*]] = addf %[[VAL_20]], %[[VAL_21]] : f32
+// CHECK: store %[[VAL_22]], %[[VAL_11]]{{\[}}%[[VAL_12]]] : memref<16xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_23:.*]] = tensor_load %[[VAL_11]] : memref<16xf32>
+// CHECK: return %[[VAL_23]] : tensor<16xf32>
+// CHECK: }
+func @matvec(%argA: tensor<16x32xf32>, %argb: tensor<32xf32>, %argx: tensor<16xf32>) -> tensor<16xf32> {
+ %0 = linalg.generic #trait_matvec
+ ins(%argA, %argb : tensor<16x32xf32>, tensor<32xf32>)
+ init(%argx : tensor<16xf32>) {
+ ^bb(%A: f32, %b: f32, %x: f32):
+ %0 = mulf %A, %b : f32
+ %1 = addf %0, %x : f32
+ linalg.yield %1 : f32
+ } -> tensor<16xf32>
+ return %0 : tensor<16xf32>
+}
diff --git a/mlir/test/Dialect/Linalg/sparse_3d.mlir b/mlir/test/Dialect/Linalg/sparse_3d.mlir
new file mode 100644
index 000000000000..a253ea4557c3
--- /dev/null
+++ b/mlir/test/Dialect/Linalg/sparse_3d.mlir
@@ -0,0 +1,1225 @@
+// NOTE: Assertions have been autogenerated by utils/generate-test-checks.py
+// RUN: mlir-opt %s -test-sparsification | FileCheck %s
+
+#trait_ddd = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "D", "D", "D" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ iterator_types = ["parallel", "parallel", "parallel"],
+ doc = "X(i,j,k) = A(i,j,k) OP B(i,j,k)"
+}
+
+// CHECK-LABEL: func @add_ddd(
+// CHECK-SAME: %[[VAL_0:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : 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:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_8:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_9:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_10:.*]] = %[[VAL_5]] to %[[VAL_2]] step %[[VAL_6]] {
+// 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_10]], %[[VAL_11]], %[[VAL_12]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_10]], %[[VAL_11]], %[[VAL_12]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_15:.*]] = addf %[[VAL_13]], %[[VAL_14]] : f32
+// CHECK: store %[[VAL_15]], %[[VAL_9]]{{\[}}%[[VAL_10]], %[[VAL_11]], %[[VAL_12]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_16:.*]] = tensor_load %[[VAL_9]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_16]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_ddd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_ddd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 32 : 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:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_8:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_9:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_10:.*]] = %[[VAL_5]] to %[[VAL_2]] step %[[VAL_6]] {
+// 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_10]], %[[VAL_11]], %[[VAL_12]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_10]], %[[VAL_11]], %[[VAL_12]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_15:.*]] = mulf %[[VAL_13]], %[[VAL_14]] : f32
+// CHECK: store %[[VAL_15]], %[[VAL_9]]{{\[}}%[[VAL_10]], %[[VAL_11]], %[[VAL_12]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_16:.*]] = tensor_load %[[VAL_9]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_16]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_ddd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_ddd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_dds = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "D", "D", "S" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// 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 true
+// CHECK: %[[VAL_8:.*]] = constant 1 : index
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_14:.*]] = %[[VAL_6]] to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_15:.*]] = %[[VAL_6]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: %[[VAL_16:.*]] = muli %[[VAL_14]], %[[VAL_4]] : index
+// CHECK: %[[VAL_17:.*]] = addi %[[VAL_16]], %[[VAL_15]] : index
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_17]]] : memref<?xindex>
+// CHECK: %[[VAL_19:.*]] = addi %[[VAL_17]], %[[VAL_8]] : index
+// CHECK: %[[VAL_20:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK: %[[VAL_21:.*]]:2 = scf.while (%[[VAL_22:.*]] = %[[VAL_18]], %[[VAL_23:.*]] = %[[VAL_6]]) : (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: } do {
+// CHECK: ^bb0(%[[VAL_25:.*]]: index, %[[VAL_26:.*]]: index):
+// CHECK: %[[VAL_27:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_25]]] : memref<?xindex>
+// CHECK: %[[VAL_28:.*]] = cmpi "eq", %[[VAL_27]], %[[VAL_26]] : index
+// CHECK: scf.if %[[VAL_28]] {
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_25]]] : memref<?xf32>
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_31:.*]] = addf %[[VAL_29]], %[[VAL_30]] : f32
+// CHECK: store %[[VAL_31]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_7]] {
+// CHECK: %[[VAL_32:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_32]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_33:.*]] = cmpi "eq", %[[VAL_27]], %[[VAL_26]] : index
+// CHECK: %[[VAL_34:.*]] = addi %[[VAL_25]], %[[VAL_8]] : index
+// CHECK: %[[VAL_35:.*]] = select %[[VAL_33]], %[[VAL_34]], %[[VAL_25]] : index
+// CHECK: %[[VAL_36:.*]] = addi %[[VAL_26]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_35]], %[[VAL_36]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_37:.*]] = %[[VAL_38:.*]]#1 to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_39:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_39]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_15]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_40:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_40]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_dds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_dds
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// 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(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_3]] step %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_13:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK: %[[VAL_14:.*]] = muli %[[VAL_12]], %[[VAL_4]] : index
+// CHECK: %[[VAL_15:.*]] = addi %[[VAL_14]], %[[VAL_13]] : index
+// 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<?xf32>
+// CHECK: %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_20]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_23:.*]] = mulf %[[VAL_21]], %[[VAL_22]] : f32
+// CHECK: store %[[VAL_23]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_13]], %[[VAL_20]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_24:.*]] = tensor_load %[[VAL_11]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_24]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_dds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_dds
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_dsd = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "D", "S", "D" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_14:.*]] = %[[VAL_7]] to %[[VAL_3]] 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_7]]) : (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_25:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_23]] : index
+// CHECK: scf.if %[[VAL_25]] {
+// CHECK: scf.for %[[VAL_26:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_27:.*]] = muli %[[VAL_22]], %[[VAL_5]] : index
+// CHECK: %[[VAL_28:.*]] = addi %[[VAL_27]], %[[VAL_26]] : index
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xf32>
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_23]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_31:.*]] = addf %[[VAL_29]], %[[VAL_30]] : f32
+// CHECK: store %[[VAL_31]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]], %[[VAL_26]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_32:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_33:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_23]], %[[VAL_32]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_33]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_23]], %[[VAL_32]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_34:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_23]] : index
+// CHECK: %[[VAL_35:.*]] = addi %[[VAL_22]], %[[VAL_8]] : index
+// CHECK: %[[VAL_36:.*]] = select %[[VAL_34]], %[[VAL_35]], %[[VAL_22]] : index
+// CHECK: %[[VAL_37:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_36]], %[[VAL_37]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_38:.*]] = %[[VAL_39:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_40:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_41:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_14]], %[[VAL_38]], %[[VAL_40]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_41]], %[[VAL_13]]{{\[}}%[[VAL_14]], %[[VAL_38]], %[[VAL_40]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_42:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_42]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_dsd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_dsd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_12:.*]] = %[[VAL_5]] to %[[VAL_3]] 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: 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<?xf32>
+// CHECK: %[[VAL_22:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_12]], %[[VAL_17]], %[[VAL_18]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_23:.*]] = mulf %[[VAL_21]], %[[VAL_22]] : f32
+// CHECK: store %[[VAL_23]], %[[VAL_11]]{{\[}}%[[VAL_12]], %[[VAL_17]], %[[VAL_18]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_24:.*]] = tensor_load %[[VAL_11]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_24]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_dsd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_dsd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_dss = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "D", "S", "S" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_16:.*]] = %[[VAL_7]] to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK: %[[VAL_17:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_16]]] : memref<?xindex>
+// CHECK: %[[VAL_18:.*]] = addi %[[VAL_16]], %[[VAL_8]] : index
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_18]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_17]], %[[VAL_22:.*]] = %[[VAL_7]]) : (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_24:.*]]: index, %[[VAL_25:.*]]: index):
+// CHECK: %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK: %[[VAL_27:.*]] = cmpi "eq", %[[VAL_26]], %[[VAL_25]] : index
+// CHECK: scf.if %[[VAL_27]] {
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK: %[[VAL_29:.*]] = addi %[[VAL_24]], %[[VAL_8]] : index
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_29]]] : memref<?xindex>
+// CHECK: %[[VAL_31:.*]]:2 = scf.while (%[[VAL_32:.*]] = %[[VAL_28]], %[[VAL_33:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_34:.*]] = cmpi "ult", %[[VAL_32]], %[[VAL_30]] : index
+// CHECK: scf.condition(%[[VAL_34]]) %[[VAL_32]], %[[VAL_33]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_35:.*]]: index, %[[VAL_36:.*]]: index):
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_35]]] : memref<?xindex>
+// CHECK: %[[VAL_38:.*]] = cmpi "eq", %[[VAL_37]], %[[VAL_36]] : index
+// CHECK: scf.if %[[VAL_38]] {
+// CHECK: %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_35]]] : memref<?xf32>
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_36]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_41:.*]] = addf %[[VAL_39]], %[[VAL_40]] : f32
+// CHECK: store %[[VAL_41]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_36]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: %[[VAL_42:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_36]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_42]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_36]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_43:.*]] = cmpi "eq", %[[VAL_37]], %[[VAL_36]] : index
+// CHECK: %[[VAL_44:.*]] = addi %[[VAL_35]], %[[VAL_8]] : index
+// CHECK: %[[VAL_45:.*]] = select %[[VAL_43]], %[[VAL_44]], %[[VAL_35]] : index
+// CHECK: %[[VAL_46:.*]] = addi %[[VAL_36]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_45]], %[[VAL_46]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_47:.*]] = %[[VAL_48:.*]]#1 to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_49:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_47]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_49]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_47]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_50:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_51:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_50]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_51]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_25]], %[[VAL_50]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_52:.*]] = cmpi "eq", %[[VAL_26]], %[[VAL_25]] : index
+// CHECK: %[[VAL_53:.*]] = addi %[[VAL_24]], %[[VAL_8]] : index
+// CHECK: %[[VAL_54:.*]] = select %[[VAL_52]], %[[VAL_53]], %[[VAL_24]] : index
+// CHECK: %[[VAL_55:.*]] = addi %[[VAL_25]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_54]], %[[VAL_55]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_56:.*]] = %[[VAL_57:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_58:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_59:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_16]], %[[VAL_56]], %[[VAL_58]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_59]], %[[VAL_15]]{{\[}}%[[VAL_16]], %[[VAL_56]], %[[VAL_58]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_60:.*]] = tensor_load %[[VAL_15]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_60]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_dss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_dss
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// CHECK: %[[VAL_3:.*]] = constant 32 : 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: scf.for %[[VAL_13:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_13]]] : memref<?xindex>
+// CHECK: %[[VAL_15:.*]] = addi %[[VAL_13]], %[[VAL_5]] : index
+// CHECK: %[[VAL_16:.*]] = load %[[VAL_6]]{{\[}}%[[VAL_15]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_17:.*]] = %[[VAL_14]] 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<?xf32>
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_23]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_26:.*]] = mulf %[[VAL_24]], %[[VAL_25]] : f32
+// CHECK: store %[[VAL_26]], %[[VAL_12]]{{\[}}%[[VAL_13]], %[[VAL_18]], %[[VAL_23]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_27:.*]] = tensor_load %[[VAL_12]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_27]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_dss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_dss
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_sdd = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "S", "D", "D" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
+// 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_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_23:.*]] = cmpi "eq", %[[VAL_22]], %[[VAL_21]] : index
+// CHECK: scf.if %[[VAL_23]] {
+// CHECK: scf.for %[[VAL_24:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: %[[VAL_25:.*]] = muli %[[VAL_20]], %[[VAL_4]] : index
+// CHECK: %[[VAL_26:.*]] = addi %[[VAL_25]], %[[VAL_24]] : index
+// CHECK: scf.for %[[VAL_27:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_28:.*]] = muli %[[VAL_26]], %[[VAL_5]] : index
+// CHECK: %[[VAL_29:.*]] = addi %[[VAL_28]], %[[VAL_27]] : index
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_29]]] : memref<?xf32>
+// CHECK: %[[VAL_31:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_21]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_32:.*]] = addf %[[VAL_30]], %[[VAL_31]] : f32
+// CHECK: store %[[VAL_32]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_24]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_33:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_34:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_35:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_21]], %[[VAL_33]], %[[VAL_34]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_35]], %[[VAL_13]]{{\[}}%[[VAL_21]], %[[VAL_33]], %[[VAL_34]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_36:.*]] = cmpi "eq", %[[VAL_22]], %[[VAL_21]] : index
+// CHECK: %[[VAL_37:.*]] = addi %[[VAL_20]], %[[VAL_8]] : index
+// CHECK: %[[VAL_38:.*]] = select %[[VAL_36]], %[[VAL_37]], %[[VAL_20]] : index
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_21]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_38]], %[[VAL_39]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_40:.*]] = %[[VAL_41:.*]]#1 to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_42:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_43:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_44:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_40]], %[[VAL_42]], %[[VAL_43]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_44]], %[[VAL_13]]{{\[}}%[[VAL_40]], %[[VAL_42]], %[[VAL_43]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_45:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_45]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_sdd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_sdd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_10:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
+// 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_3]] step %[[VAL_6]] {
+// CHECK: %[[VAL_17:.*]] = muli %[[VAL_14]], %[[VAL_3]] : index
+// CHECK: %[[VAL_18:.*]] = addi %[[VAL_17]], %[[VAL_16]] : index
+// CHECK: scf.for %[[VAL_19:.*]] = %[[VAL_5]] to %[[VAL_4]] step %[[VAL_6]] {
+// CHECK: %[[VAL_20:.*]] = muli %[[VAL_18]], %[[VAL_4]] : index
+// CHECK: %[[VAL_21:.*]] = addi %[[VAL_20]], %[[VAL_19]] : index
+// CHECK: %[[VAL_22:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xf32>
+// CHECK: %[[VAL_23:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_19]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_24:.*]] = mulf %[[VAL_22]], %[[VAL_23]] : f32
+// CHECK: store %[[VAL_24]], %[[VAL_11]]{{\[}}%[[VAL_15]], %[[VAL_16]], %[[VAL_19]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_25:.*]] = tensor_load %[[VAL_11]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_25]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_sdd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_sdd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_sds = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "S", "D", "S" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16x8xf32>
+// 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_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_25:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_23]] : index
+// CHECK: scf.if %[[VAL_25]] {
+// CHECK: scf.for %[[VAL_26:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: %[[VAL_27:.*]] = muli %[[VAL_22]], %[[VAL_4]] : index
+// CHECK: %[[VAL_28:.*]] = addi %[[VAL_27]], %[[VAL_26]] : index
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_28]]] : memref<?xindex>
+// CHECK: %[[VAL_30:.*]] = addi %[[VAL_28]], %[[VAL_8]] : index
+// CHECK: %[[VAL_31:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_30]]] : memref<?xindex>
+// CHECK: %[[VAL_32:.*]]:2 = scf.while (%[[VAL_33:.*]] = %[[VAL_29]], %[[VAL_34:.*]] = %[[VAL_7]]) : (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: } do {
+// CHECK: ^bb0(%[[VAL_36:.*]]: index, %[[VAL_37:.*]]: index):
+// CHECK: %[[VAL_38:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_36]]] : memref<?xindex>
+// CHECK: %[[VAL_39:.*]] = cmpi "eq", %[[VAL_38]], %[[VAL_37]] : index
+// CHECK: scf.if %[[VAL_39]] {
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_36]]] : memref<?xf32>
+// CHECK: %[[VAL_41:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_42:.*]] = addf %[[VAL_40]], %[[VAL_41]] : f32
+// CHECK: store %[[VAL_42]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: %[[VAL_43:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_43]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_26]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_44:.*]] = cmpi "eq", %[[VAL_38]], %[[VAL_37]] : index
+// CHECK: %[[VAL_45:.*]] = addi %[[VAL_36]], %[[VAL_8]] : index
+// CHECK: %[[VAL_46:.*]] = select %[[VAL_44]], %[[VAL_45]], %[[VAL_36]] : index
+// CHECK: %[[VAL_47:.*]] = addi %[[VAL_37]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_46]], %[[VAL_47]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_48:.*]] = %[[VAL_49:.*]]#1 to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_26]], %[[VAL_48]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_50]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_26]], %[[VAL_48]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_51:.*]] = %[[VAL_7]] 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_23]], %[[VAL_51]], %[[VAL_52]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_53]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_51]], %[[VAL_52]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_54:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_23]] : index
+// CHECK: %[[VAL_55:.*]] = addi %[[VAL_22]], %[[VAL_8]] : index
+// CHECK: %[[VAL_56:.*]] = select %[[VAL_54]], %[[VAL_55]], %[[VAL_22]] : index
+// CHECK: %[[VAL_57:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_56]], %[[VAL_57]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_58:.*]] = %[[VAL_59:.*]]#1 to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_60:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_61:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_62:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_58]], %[[VAL_60]], %[[VAL_61]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_62]], %[[VAL_15]]{{\[}}%[[VAL_58]], %[[VAL_60]], %[[VAL_61]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_63:.*]] = tensor_load %[[VAL_15]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_63]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_sds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_sds
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// CHECK: %[[VAL_3:.*]] = constant 16 : 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// 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: scf.for %[[VAL_17:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_18:.*]] = muli %[[VAL_15]], %[[VAL_3]] : index
+// CHECK: %[[VAL_19:.*]] = addi %[[VAL_18]], %[[VAL_17]] : index
+// CHECK: %[[VAL_20:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK: %[[VAL_21:.*]] = addi %[[VAL_19]], %[[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<?xf32>
+// CHECK: %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_24]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_27:.*]] = mulf %[[VAL_25]], %[[VAL_26]] : f32
+// CHECK: store %[[VAL_27]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_17]], %[[VAL_24]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_28:.*]] = tensor_load %[[VAL_12]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_28]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_sds(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_sds
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_ssd = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "S", "S", "D" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_14:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_15:.*]] = alloca() : memref<32x16x8xf32>
+// 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_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_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_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_36:.*]] = cmpi "eq", %[[VAL_35]], %[[VAL_34]] : index
+// CHECK: scf.if %[[VAL_36]] {
+// CHECK: scf.for %[[VAL_37:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_38:.*]] = muli %[[VAL_33]], %[[VAL_5]] : index
+// CHECK: %[[VAL_39:.*]] = addi %[[VAL_38]], %[[VAL_37]] : index
+// CHECK: %[[VAL_40:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_39]]] : memref<?xf32>
+// CHECK: %[[VAL_41:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_34]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_42:.*]] = addf %[[VAL_40]], %[[VAL_41]] : f32
+// CHECK: store %[[VAL_42]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]], %[[VAL_37]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_43:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_44:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_34]], %[[VAL_43]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_44]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_34]], %[[VAL_43]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_45:.*]] = cmpi "eq", %[[VAL_35]], %[[VAL_34]] : index
+// CHECK: %[[VAL_46:.*]] = addi %[[VAL_33]], %[[VAL_8]] : index
+// CHECK: %[[VAL_47:.*]] = select %[[VAL_45]], %[[VAL_46]], %[[VAL_33]] : index
+// CHECK: %[[VAL_48:.*]] = addi %[[VAL_34]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_47]], %[[VAL_48]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_49:.*]] = %[[VAL_50:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_51:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_52:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_49]], %[[VAL_51]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_52]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_49]], %[[VAL_51]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_53:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_54:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_55:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_23]], %[[VAL_53]], %[[VAL_54]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_55]], %[[VAL_15]]{{\[}}%[[VAL_23]], %[[VAL_53]], %[[VAL_54]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_56:.*]] = cmpi "eq", %[[VAL_24]], %[[VAL_23]] : index
+// CHECK: %[[VAL_57:.*]] = addi %[[VAL_22]], %[[VAL_8]] : index
+// CHECK: %[[VAL_58:.*]] = select %[[VAL_56]], %[[VAL_57]], %[[VAL_22]] : index
+// CHECK: %[[VAL_59:.*]] = addi %[[VAL_23]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_58]], %[[VAL_59]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_60:.*]] = %[[VAL_61:.*]]#1 to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_62:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_63:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_64:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_60]], %[[VAL_62]], %[[VAL_63]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_64]], %[[VAL_15]]{{\[}}%[[VAL_60]], %[[VAL_62]], %[[VAL_63]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_65:.*]] = tensor_load %[[VAL_15]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_65]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_ssd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_ssd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : index
+// CHECK: %[[VAL_3:.*]] = constant 8 : 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_11:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// 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: scf.for %[[VAL_22:.*]] = %[[VAL_4]] to %[[VAL_3]] step %[[VAL_5]] {
+// CHECK: %[[VAL_23:.*]] = muli %[[VAL_20]], %[[VAL_3]] : index
+// CHECK: %[[VAL_24:.*]] = addi %[[VAL_23]], %[[VAL_22]] : index
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xf32>
+// CHECK: %[[VAL_26:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_16]], %[[VAL_21]], %[[VAL_22]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_27:.*]] = mulf %[[VAL_25]], %[[VAL_26]] : f32
+// CHECK: store %[[VAL_27]], %[[VAL_12]]{{\[}}%[[VAL_16]], %[[VAL_21]], %[[VAL_22]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_28:.*]] = tensor_load %[[VAL_12]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_28]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_ssd(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_ssd
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_sss = {
+ indexing_maps = [
+ affine_map<(i,j,k) -> (i,j,k)>, // A
+ affine_map<(i,j,k) -> (i,j,k)>, // B
+ affine_map<(i,j,k) -> (i,j,k)> // X (out)
+ ],
+ sparse = [
+ [ "S", "S", "S" ], // A
+ [ "D", "D", "D" ], // B
+ [ "D", "D", "D" ] // X
+ ],
+ 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// CHECK: %[[VAL_2:.*]] = constant 999 : 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:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_12:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_13:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_14:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_15:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_16:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_17:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_18:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_7]]] : memref<?xindex>
+// CHECK: %[[VAL_19:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_8]]] : memref<?xindex>
+// CHECK: %[[VAL_20:.*]]:2 = scf.while (%[[VAL_21:.*]] = %[[VAL_18]], %[[VAL_22:.*]] = %[[VAL_7]]) : (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_24:.*]]: index, %[[VAL_25:.*]]: index):
+// CHECK: %[[VAL_26:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK: %[[VAL_27:.*]] = cmpi "eq", %[[VAL_26]], %[[VAL_25]] : index
+// CHECK: scf.if %[[VAL_27]] {
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK: %[[VAL_29:.*]] = addi %[[VAL_24]], %[[VAL_8]] : index
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_29]]] : memref<?xindex>
+// CHECK: %[[VAL_31:.*]]:2 = scf.while (%[[VAL_32:.*]] = %[[VAL_28]], %[[VAL_33:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_34:.*]] = cmpi "ult", %[[VAL_32]], %[[VAL_30]] : index
+// CHECK: scf.condition(%[[VAL_34]]) %[[VAL_32]], %[[VAL_33]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_35:.*]]: index, %[[VAL_36:.*]]: index):
+// CHECK: %[[VAL_37:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_35]]] : memref<?xindex>
+// CHECK: %[[VAL_38:.*]] = cmpi "eq", %[[VAL_37]], %[[VAL_36]] : index
+// CHECK: scf.if %[[VAL_38]] {
+// CHECK: %[[VAL_39:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_35]]] : memref<?xindex>
+// CHECK: %[[VAL_40:.*]] = addi %[[VAL_35]], %[[VAL_8]] : index
+// CHECK: %[[VAL_41:.*]] = load %[[VAL_13]]{{\[}}%[[VAL_40]]] : memref<?xindex>
+// CHECK: %[[VAL_42:.*]]:2 = scf.while (%[[VAL_43:.*]] = %[[VAL_39]], %[[VAL_44:.*]] = %[[VAL_7]]) : (index, index) -> (index, index) {
+// CHECK: %[[VAL_45:.*]] = cmpi "ult", %[[VAL_43]], %[[VAL_41]] : index
+// CHECK: scf.condition(%[[VAL_45]]) %[[VAL_43]], %[[VAL_44]] : index, index
+// CHECK: } do {
+// CHECK: ^bb0(%[[VAL_46:.*]]: index, %[[VAL_47:.*]]: index):
+// CHECK: %[[VAL_48:.*]] = load %[[VAL_14]]{{\[}}%[[VAL_46]]] : memref<?xindex>
+// CHECK: %[[VAL_49:.*]] = cmpi "eq", %[[VAL_48]], %[[VAL_47]] : index
+// CHECK: scf.if %[[VAL_49]] {
+// CHECK: %[[VAL_50:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_46]]] : memref<?xf32>
+// CHECK: %[[VAL_51:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_47]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_52:.*]] = addf %[[VAL_50]], %[[VAL_51]] : f32
+// CHECK: store %[[VAL_52]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_47]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: %[[VAL_53:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_47]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_53]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_47]]] : memref<32x16x8xf32>
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_54:.*]] = cmpi "eq", %[[VAL_48]], %[[VAL_47]] : index
+// CHECK: %[[VAL_55:.*]] = addi %[[VAL_46]], %[[VAL_8]] : index
+// CHECK: %[[VAL_56:.*]] = select %[[VAL_54]], %[[VAL_55]], %[[VAL_46]] : index
+// CHECK: %[[VAL_57:.*]] = addi %[[VAL_47]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_56]], %[[VAL_57]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_58:.*]] = %[[VAL_59:.*]]#1 to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_60:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_58]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_60]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_58]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_61:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_62:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_61]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_62]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_36]], %[[VAL_61]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_63:.*]] = cmpi "eq", %[[VAL_37]], %[[VAL_36]] : index
+// CHECK: %[[VAL_64:.*]] = addi %[[VAL_35]], %[[VAL_8]] : index
+// CHECK: %[[VAL_65:.*]] = select %[[VAL_63]], %[[VAL_64]], %[[VAL_35]] : index
+// CHECK: %[[VAL_66:.*]] = addi %[[VAL_36]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_65]], %[[VAL_66]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_67:.*]] = %[[VAL_68:.*]]#1 to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_69:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_70:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_25]], %[[VAL_67]], %[[VAL_69]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_70]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_67]], %[[VAL_69]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: scf.if %[[VAL_6]] {
+// CHECK: scf.for %[[VAL_71:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_72:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_73:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_25]], %[[VAL_71]], %[[VAL_72]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_73]], %[[VAL_17]]{{\[}}%[[VAL_25]], %[[VAL_71]], %[[VAL_72]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: } else {
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_74:.*]] = cmpi "eq", %[[VAL_26]], %[[VAL_25]] : index
+// CHECK: %[[VAL_75:.*]] = addi %[[VAL_24]], %[[VAL_8]] : index
+// CHECK: %[[VAL_76:.*]] = select %[[VAL_74]], %[[VAL_75]], %[[VAL_24]] : index
+// CHECK: %[[VAL_77:.*]] = addi %[[VAL_25]], %[[VAL_8]] : index
+// CHECK: scf.yield %[[VAL_76]], %[[VAL_77]] : index, index
+// CHECK: }
+// CHECK: scf.for %[[VAL_78:.*]] = %[[VAL_79:.*]]#1 to %[[VAL_3]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_80:.*]] = %[[VAL_7]] to %[[VAL_4]] step %[[VAL_8]] {
+// CHECK: scf.for %[[VAL_81:.*]] = %[[VAL_7]] to %[[VAL_5]] step %[[VAL_8]] {
+// CHECK: %[[VAL_82:.*]] = load %[[VAL_16]]{{\[}}%[[VAL_78]], %[[VAL_80]], %[[VAL_81]]] : memref<32x16x8xf32>
+// CHECK: store %[[VAL_82]], %[[VAL_17]]{{\[}}%[[VAL_78]], %[[VAL_80]], %[[VAL_81]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_83:.*]] = tensor_load %[[VAL_17]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_83]] : tensor<32x16x8xf32>
+// CHECK: }
+func @add_sss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_sss
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: 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:.*]]: tensor<32x16x8xf32>,
+// CHECK-SAME: %[[VAL_1:.*]]: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+// 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<?xindex>
+// CHECK: %[[VAL_8:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_9:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_10:.*]] = alloca(%[[VAL_2]]) : memref<?xindex>
+// CHECK: %[[VAL_11:.*]] = alloca(%[[VAL_2]]) : memref<?xf32>
+// CHECK: %[[VAL_12:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_13:.*]] = alloca() : memref<32x16x8xf32>
+// CHECK: %[[VAL_14:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_3]]] : memref<?xindex>
+// CHECK: %[[VAL_15:.*]] = load %[[VAL_5]]{{\[}}%[[VAL_4]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_16:.*]] = %[[VAL_14]] 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<?xindex>
+// CHECK: %[[VAL_19:.*]] = addi %[[VAL_16]], %[[VAL_4]] : index
+// CHECK: %[[VAL_20:.*]] = load %[[VAL_7]]{{\[}}%[[VAL_19]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_21:.*]] = %[[VAL_18]] to %[[VAL_20]] step %[[VAL_4]] {
+// CHECK: %[[VAL_22:.*]] = load %[[VAL_8]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK: %[[VAL_23:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_21]]] : memref<?xindex>
+// CHECK: %[[VAL_24:.*]] = addi %[[VAL_21]], %[[VAL_4]] : index
+// CHECK: %[[VAL_25:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_24]]] : memref<?xindex>
+// CHECK: scf.for %[[VAL_26:.*]] = %[[VAL_23]] to %[[VAL_25]] step %[[VAL_4]] {
+// CHECK: %[[VAL_27:.*]] = load %[[VAL_10]]{{\[}}%[[VAL_26]]] : memref<?xindex>
+// CHECK: %[[VAL_28:.*]] = load %[[VAL_11]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK: %[[VAL_30:.*]] = mulf %[[VAL_28]], %[[VAL_29]] : f32
+// CHECK: store %[[VAL_30]], %[[VAL_13]]{{\[}}%[[VAL_17]], %[[VAL_22]], %[[VAL_27]]] : memref<32x16x8xf32>
+// CHECK: }
+// CHECK: }
+// CHECK: }
+// CHECK: %[[VAL_31:.*]] = tensor_load %[[VAL_13]] : memref<32x16x8xf32>
+// CHECK: return %[[VAL_31]] : tensor<32x16x8xf32>
+// CHECK: }
+func @mul_sss(%arga: tensor<32x16x8xf32>, %argb: tensor<32x16x8xf32>) -> tensor<32x16x8xf32> {
+ %0 = linalg.generic #trait_sss
+ ins(%arga, %argb: tensor<32x16x8xf32>, tensor<32x16x8xf32>) {
+ ^bb(%a: f32, %b: f32):
+ %0 = mulf %a, %b : f32
+ linalg.yield %0 : f32
+ } -> tensor<32x16x8xf32>
+ return %0 : tensor<32x16x8xf32>
+}
+
+#trait_kernel_3d = {
+ indexing_maps = [
+ affine_map<(i,j,k,l) -> (i,k,l)>, // B
+ affine_map<(i,j,k,l) -> (k,j)>, // C
+ affine_map<(i,j,k,l) -> (l,j)>, // D
+ affine_map<(i,j,k,l) -> (i,j)> // A (out)
+ ],
+ sparse = [
+ [ "D", "D", "S" ], // B
+ [ "D", "D" ], // C
+ [ "D", "D" ], // D
+ [ "D", "D" ] // A
+ ],
+ iterator_types = ["parallel", "parallel", "reduction", "reduction"],
+ doc = "A(i,j) = SUM_k,l B(i,k,l) * C(k,j) * D(l,j)"
+}
+
+// CHECK-LABEL: func @kernel_3d(
+// CHECK-SAME: %[[VAL_0:.*0]]: tensor<?x?xf32>,
+// CHECK-SAME: %[[VAL_1:.*1]]: tensor<?x?x?xf32>,
+// 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<?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_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: scf.for %[[VAL_28:.*]] = %[[VAL_5]] to %[[VAL_17]] step %[[VAL_6]] {
+// CHECK: %[[VAL_29:.*]] = load %[[VAL_9]]{{\[}}%[[VAL_26]]] : memref<?xf32>
+// CHECK: %[[VAL_30:.*]] = load %[[VAL_12]]{{\[}}%[[VAL_20]], %[[VAL_28]]] : memref<?x?xf32>
+// CHECK: %[[VAL_31:.*]] = mulf %[[VAL_29]], %[[VAL_30]] : f32
+// CHECK: %[[VAL_32:.*]] = load %[[VAL_15]]{{\[}}%[[VAL_27]], %[[VAL_28]]] : memref<?x?xf32>
+// CHECK: %[[VAL_33:.*]] = mulf %[[VAL_31]], %[[VAL_32]] : f32
+// CHECK: %[[VAL_34:.*]] = load %[[VAL_18]]{{\[}}%[[VAL_19]], %[[VAL_28]]] : memref<?x?xf32>
+// CHECK: %[[VAL_35:.*]] = addf %[[VAL_33]], %[[VAL_34]] : f32
+// CHECK: store %[[VAL_35]], %[[VAL_18]]{{\[}}%[[VAL_19]], %[[VAL_28]]] : 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: }
+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>)
+ init(%arga : tensor<?x?xf32>) {
+ ^bb(%b: f32, %c: f32, %d : f32, %a : f32):
+ %0 = mulf %b, %c : f32
+ %1 = mulf %0, %d : f32
+ %2 = addf %1, %a : f32
+ linalg.yield %2 : f32
+ } -> tensor<?x?xf32>
+ return %0 : tensor<?x?xf32>
+}
diff --git a/mlir/test/lib/Transforms/CMakeLists.txt b/mlir/test/lib/Transforms/CMakeLists.txt
index 5dfe1e82c75a..b753928241f0 100644
--- a/mlir/test/lib/Transforms/CMakeLists.txt
+++ b/mlir/test/lib/Transforms/CMakeLists.txt
@@ -30,6 +30,7 @@ add_mlir_library(MLIRTestTransforms
TestMemRefDependenceCheck.cpp
TestMemRefStrideCalculation.cpp
TestSCFUtils.cpp
+ TestSparsification.cpp
TestVectorTransforms.cpp
EXCLUDE_FROM_LIBMLIR
diff --git a/mlir/test/lib/Transforms/TestSparsification.cpp b/mlir/test/lib/Transforms/TestSparsification.cpp
new file mode 100644
index 000000000000..038d7fab0656
--- /dev/null
+++ b/mlir/test/lib/Transforms/TestSparsification.cpp
@@ -0,0 +1,42 @@
+//===- 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/Linalg/Transforms/Transforms.h"
+#include "mlir/Pass/Pass.h"
+#include "mlir/Transforms/GreedyPatternRewriteDriver.h"
+
+using namespace mlir;
+
+namespace {
+
+struct TestSparsification
+ : public PassWrapper<TestSparsification, FunctionPass> {
+ void getDependentDialects(DialectRegistry ®istry) const override {
+ registry.insert<scf::SCFDialect>();
+ }
+ void runOnFunction() override {
+ auto *ctx = &getContext();
+ OwningRewritePatternList patterns;
+ linalg::populateSparsificationPatterns(ctx, patterns);
+ applyPatternsAndFoldGreedily(getFunction(), std::move(patterns));
+ }
+};
+
+} // end anonymous namespace
+
+namespace mlir {
+namespace test {
+
+void registerTestSparsification() {
+ PassRegistration<TestSparsification> sparsificationPass(
+ "test-sparsification",
+ "Test automatic geneneration of sparse tensor code");
+}
+
+} // namespace test
+} // namespace mlir
diff --git a/mlir/tools/mlir-opt/mlir-opt.cpp b/mlir/tools/mlir-opt/mlir-opt.cpp
index 0b4a66e37987..4771b11b20e4 100644
--- a/mlir/tools/mlir-opt/mlir-opt.cpp
+++ b/mlir/tools/mlir-opt/mlir-opt.cpp
@@ -87,6 +87,7 @@ void registerTestOpaqueLoc();
void registerTestPreparationPassWithAllowedMemrefResults();
void registerTestRecursiveTypesPass();
void registerTestSCFUtilsPass();
+void registerTestSparsification();
void registerTestVectorConversions();
} // namespace test
} // namespace mlir
@@ -152,6 +153,7 @@ void registerTestPasses() {
test::registerTestOpaqueLoc();
test::registerTestRecursiveTypesPass();
test::registerTestSCFUtilsPass();
+ test::registerTestSparsification();
test::registerTestVectorConversions();
}
#endif
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