'sparse_tensor' Dialect

The SparseTensor dialect supports all the attributes, types, operations, and passes that are required to make sparse tensor types first class citizens within the MLIR compiler infrastructure. The dialect forms a bridge between high-level operations on sparse tensors types and lower-level operations on the actual sparse storage schemes consisting of positions, coordinates, and values. Lower-level support may consist of fully generated code or may be provided by means of a small sparse runtime support library.

The concept of treating sparsity as a property, not a tedious implementation detail, by letting a sparse compiler generate sparse code automatically was pioneered for linear algebra by [Bik96] in MT1 (see https://www.aartbik.com/sparse.php) and formalized to tensor algebra by [Kjolstad17,Kjolstad20] in the Sparse Tensor Algebra Compiler (TACO) project (see http://tensor-compiler.org).

The MLIR implementation [Biketal22] closely follows the “sparse iteration theory” that forms the foundation of TACO. A rewriting rule is applied to each tensor expression in the Linalg dialect (MLIR’s tensor index notation) where the sparsity of tensors is indicated using the per-level level-types (e.g., dense, compressed, singleton) together with a specification of the order on the levels (see [Chou18] for an in-depth discussions and possible extensions to these level-types). Subsequently, a topologically sorted iteration graph, reflecting the required order on coordinates with respect to the levels of each tensor, is constructed to ensure that all tensors are visited in natural level-coordinate 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 coordinates 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 coordinates are exhausted. As such these iteration lattices drive actual sparse code generation, which consists of a relatively straightforward one-to-one mapping from iteration lattices to combinations of for-loops, while-loops, and if-statements. Sparse tensor outputs that materialize uninitialized are handled with direct insertions if all parallel loops are outermost or insertions that indirectly go through a 1-dimensional access pattern expansion (a.k.a. workspace) where feasible [Gustavson72,Bik96,Kjolstad19].

• [Bik96] Aart J.C. Bik. Compiler Support for Sparse Matrix Computations. PhD thesis, Leiden University, May 1996.
• [Biketal22] Aart J.C. Bik, Penporn Koanantakool, Tatiana Shpeisman, Nicolas Vasilache, Bixia Zheng, and Fredrik Kjolstad. Compiler Support for Sparse Tensor Computations in MLIR. ACM Transactions on Architecture and Code Optimization, June, 2022. See: https://dl.acm.org/doi/10.1145/3544559
• [Chou18] Stephen Chou, Fredrik Berg Kjolstad, and Saman Amarasinghe. Format Abstraction for Sparse Tensor Algebra Compilers. Proceedings of the ACM on Programming Languages, October 2018.
• [Chou20] Stephen Chou, Fredrik Berg Kjolstad, and Saman Amarasinghe. Automatic Generation of Efficient Sparse Tensor Format Conversion Routines. Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, June, 2020.
• [Gustavson72] Fred G. Gustavson. Some basic techniques for solving sparse systems of linear equations. In Sparse Matrices and Their Applications, pages 41–52. Plenum Press, New York, 1972.
• [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.
• [Kjolstad19] Fredrik Berg Kjolstad, Peter Ahrens, Shoaib Ashraf Kamil, and Saman Amarasinghe. Tensor Algebra Compilation with Workspaces, Proceedings of the IEEE/ACM International Symposium on Code Generation and Optimization, 2019.
• [Kjolstad20] Fredrik Berg Kjolstad. Sparse Tensor Algebra Compilation. PhD thesis, MIT, February, 2020.

Operation definition ¶

sparse_tensor.binary (::mlir::sparse_tensor::BinaryOp) ¶

Binary set operation utilized within linalg.generic

Syntax:

operation ::= `sparse_tensor.binary` $x `,` $y `:` attr-dict type($x) `,` type($y) `to` type($output) `\n`
              `overlap` `=` $overlapRegion `\n`
              `left` `=` (`identity` $left_identity^):($leftRegion)? `\n`
              `right` `=` (`identity` $right_identity^):($rightRegion)?

Defines a computation within a linalg.generic operation that takes two operands and executes one of the regions depending on whether both operands or either operand is nonzero (i.e. stored explicitly in the sparse storage format).

Three regions are defined for the operation and must appear in this order:

• overlap (elements present in both sparse tensors)
• left (elements only present in the left sparse tensor)
• right (element only present in the right sparse tensor)

Each region contains a single block describing the computation and result. Every non-empty block must end with a sparse_tensor.yield and the return type must match the type of output. The primary region’s block has two arguments, while the left and right region’s block has only one argument.

A region may also be declared empty (i.e. left={}), indicating that the region does not contribute to the output. For example, setting both left={} and right={} is equivalent to the intersection of the two inputs as only the overlap region will contribute values to the output.

As a convenience, there is also a special token identity which can be used in place of the left or right region. This token indicates that the return value is the input value (i.e. func(%x) => return %x). As a practical example, setting left=identity and right=identity would be equivalent to a union operation where non-overlapping values in the inputs are copied to the output unchanged.

Example of isEqual applied to intersecting elements only:

%C = bufferization.alloc_tensor...
%0 = linalg.generic #trait
  ins(%A: tensor<?xf64, #SparseVector>,
      %B: tensor<?xf64, #SparseVector>)
  outs(%C: tensor<?xi8, #SparseVector>) {
  ^bb0(%a: f64, %b: f64, %c: i8) :
    %result = sparse_tensor.binary %a, %b : f64, f64 to i8
      overlap={
        ^bb0(%arg0: f64, %arg1: f64):
          %cmp = arith.cmpf "oeq", %arg0, %arg1 : f64
          %ret_i8 = arith.extui %cmp : i1 to i8
          sparse_tensor.yield %ret_i8 : i8
      }
      left={}
      right={}
    linalg.yield %result : i8
} -> tensor<?xi8, #SparseVector>

Example of A+B in upper triangle, A-B in lower triangle:

%C = bufferization.alloc_tensor...
%1 = linalg.generic #trait
  ins(%A: tensor<?x?xf64, #CSR>, %B: tensor<?x?xf64, #CSR>
  outs(%C: tensor<?x?xf64, #CSR> {
  ^bb0(%a: f64, %b: f64, %c: f64) :
    %row = linalg.index 0 : index
    %col = linalg.index 1 : index
    %result = sparse_tensor.binary %a, %b : f64, f64 to f64
      overlap={
        ^bb0(%x: f64, %y: f64):
          %cmp = arith.cmpi "uge", %col, %row : index
          %upperTriangleResult = arith.addf %x, %y : f64
          %lowerTriangleResult = arith.subf %x, %y : f64
          %ret = arith.select %cmp, %upperTriangleResult, %lowerTriangleResult : f64
          sparse_tensor.yield %ret : f64
      }
      left=identity
      right={
        ^bb0(%y: f64):
          %cmp = arith.cmpi "uge", %col, %row : index
          %lowerTriangleResult = arith.negf %y : f64
          %ret = arith.select %cmp, %y, %lowerTriangleResult : f64
          sparse_tensor.yield %ret : f64
      }
    linalg.yield %result : f64
} -> tensor<?x?xf64, #CSR>

Example of set difference. Returns a copy of A where its sparse structure is not overlapped by B. The element type of B can be different than A because we never use its values, only its sparse structure:

%C = bufferization.alloc_tensor...
%2 = linalg.generic #trait
  ins(%A: tensor<?x?xf64, #CSR>, %B: tensor<?x?xi32, #CSR>
  outs(%C: tensor<?x?xf64, #CSR> {
  ^bb0(%a: f64, %b: i32, %c: f64) :
    %result = sparse_tensor.binary %a, %b : f64, i32 to f64
      overlap={}
      left=identity
      right={}
    linalg.yield %result : f64
} -> tensor<?x?xf64, #CSR>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.compress (::mlir::sparse_tensor::CompressOp) ¶

Compressed an access pattern for insertion

Syntax:

operation ::= `sparse_tensor.compress` $values `,` $filled `,` $added `,` $count `into` $tensor `[` $lvlCoords `]` attr-dict `:` type($values) `,` type($filled) `,` type($added) `,` type($tensor)

Finishes a single access pattern expansion by moving inserted elements into the sparse storage scheme of the given tensor with the given level-coordinates. The arity of lvlCoords is one less than the level-rank of the tensor, with the coordinate of the innermost level defined through the added array. The values and filled arrays are reset in a sparse fashion by only iterating over set elements through an indirection using the added array, so that the operations are kept proportional to the number of nonzeros. See the sparse_tensor.expand operation for more details.

Note that this operation is “impure” in the sense that even though the result is modeled through an SSA value, the insertion is eventually done “in place”, and referencing the old SSA value is undefined behavior.

Example:

%result = sparse_tensor.compress %values, %filled, %added, %count into %tensor[%i]
  : memref<?xf64>, memref<?xi1>, memref<?xindex>, tensor<4x4xf64, #CSR>

Interfaces: InferTypeOpInterface

Operands: ¶

Results: ¶

sparse_tensor.concatenate (::mlir::sparse_tensor::ConcatenateOp) ¶

Concatenates a list of tensors into a single tensor.

Syntax:

operation ::= `sparse_tensor.concatenate` $inputs attr-dict `:` type($inputs) `to` type($result)

Concatenates a list input tensors and the output tensor with the same dimension-rank. The concatenation happens on the specified dimension (0 <= dimension < dimRank). The resulting dimension size is the sum of all the input sizes for that dimension, while all the other dimensions should have the same size in the input and output tensors.

Only statically-sized input tensors are accepted, while the output tensor can be dynamically-sized.

Example:

%0 = sparse_tensor.concatenate %1, %2 { dimension = 0 : index }
  : tensor<64x64xf64, #CSR>, tensor<64x64xf64, #CSR> to tensor<128x64xf64, #CSR>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.convert (::mlir::sparse_tensor::ConvertOp) ¶

Converts between different tensor types

Syntax:

operation ::= `sparse_tensor.convert` $source attr-dict `:` type($source) `to` type($dest)

Converts one sparse or dense tensor type to another tensor type. The rank of the source and destination types must match exactly, and the dimension sizes must either match exactly or relax from a static to a dynamic size. The sparse encoding of the two types can obviously be completely different. The name convert was preferred over cast, since the operation may incur a non-trivial cost.

When converting between two different sparse tensor types, only explicitly stored values are moved from one underlying sparse storage format to the other. When converting from an unannotated dense tensor type to a sparse tensor type, an explicit test for nonzero values is used. When converting to an unannotated dense tensor type, implicit zeroes in the sparse storage format are made explicit. Note that the conversions can have non-trivial costs associated with them, since they may involve elaborate data structure transformations. Also, conversions from sparse tensor types into dense tensor types may be infeasible in terms of storage requirements.

Trivial dense-to-dense convert will be removed by canonicalization while trivial sparse-to-sparse convert will be removed by the sparse codegen. This is because we use trivial sparse-to-sparse convert to tell bufferization that the sparse codegen will expand the tensor buffer into sparse tensor storage.

Examples:

%0 = sparse_tensor.convert %a : tensor<32x32xf32> to tensor<32x32xf32, #CSR>
%1 = sparse_tensor.convert %a : tensor<32x32xf32> to tensor<?x?xf32, #CSR>
%2 = sparse_tensor.convert %b : tensor<8x8xi32, #CSC> to tensor<8x8xi32, #CSR>
%3 = sparse_tensor.convert %c : tensor<4x8xf64, #CSR> to tensor<4x?xf64, #CSC>

// The following conversion is not allowed (since it would require a
// runtime assertion that the source's dimension size is actually 100).
%4 = sparse_tensor.convert %d : tensor<?xf64> to tensor<100xf64, #SV>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.expand (::mlir::sparse_tensor::ExpandOp) ¶

Expands an access pattern for insertion

Syntax:

operation ::= `sparse_tensor.expand` $tensor attr-dict `:` type($tensor) `to` type($values) `,` type($filled) `,` type($added)

Performs an access pattern expansion for the innermost levels of the given tensor. This operation is useful to implement kernels in which a sparse tensor appears as output. This technique is known under several different names and using several alternative implementations, for example, phase counter [Gustavson72], expanded or switch array [Pissanetzky84], in phase scan [Duff90], access pattern expansion [Bik96], and workspaces [Kjolstad19].

The values and filled arrays must have lengths equal to the level-size of the innermost level (i.e., as if the innermost level were dense). The added array and count are used to store new level-coordinates when a false value is encountered in the filled array. All arrays should be allocated before the loop (possibly even shared between loops in a future optimization) so that their dense initialization can be amortized over many iterations. Setting and resetting the dense arrays in the loop nest itself is kept sparse by only iterating over set elements through an indirection using the added array, so that the operations are kept proportional to the number of nonzeros.

Note that this operation is “impure” in the sense that even though the results are modeled through SSA values, the operation relies on a proper side-effecting context that sets and resets the expanded arrays.

Example:

%values, %filled, %added, %count = sparse_tensor.expand %tensor
  : tensor<4x4xf64, #CSR> to memref<?xf64>, memref<?xi1>, memref<?xindex>

Operands: ¶

Results: ¶

sparse_tensor.foreach (::mlir::sparse_tensor::ForeachOp) ¶

Iterates over elements in a tensor

Syntax:

operation ::= `sparse_tensor.foreach` `in` $tensor (`init``(`$initArgs^`)`)? attr-dict    `:` type($tensor) (`,` type($initArgs)^)?  (`->` type($results)^)?  `do` $region

Iterates over stored elements in a tensor (which are typically, but not always, non-zero for sparse tensors) and executes the block.

tensor: the input tensor to iterate over. initArgs: the initial loop argument to carry and update during each iteration. order: an optional permutation affine map that specifies the order in which the dimensions are visited (e.g., row first or column first). This is only applicable when the input tensor is a non-annotated dense tensor.

For an input tensor with dim-rank n, the block must take n + 1 arguments (plus additional loop-carried variables as described below). The first n arguments provide the dimension-coordinates of the element being visited, and must all have index type. The (n+1)-th argument provides the element’s value, and must have the tensor’s element type.

sparse_tensor.foreach can also operate on loop-carried variables and returns the final values after loop termination. The initial values of the variables are passed as additional SSA operands to the “sparse_tensor.foreach” following the n + 1 SSA values mentioned above (n coordinates and 1 value).

The region must terminate with a “sparse_tensor.yield” that passes the current values of all loop-carried variables to the next iteration, or to the result, if at the last iteration. The number and static types of loop-carried variables may not change with iterations.

For example:

%c0 = arith.constant 0 : i32
%ret = sparse_tensor.foreach in %0 init(%c0): tensor<?x?xi32, #DCSR>, i32 -> i32 do {
 ^bb0(%arg1: index, %arg2: index, %arg3: i32, %iter: i32):
   %sum = arith.add %iter, %arg3
   sparse_tensor.yield %sum
}

It is important to note that the generated loop iterates over elements in their storage order. However, regardless of the storage scheme used by the tensor, the block is always given the dimension-coordinates.

For example:

#COL_MAJOR = #sparse_tensor.encoding<{
  dimLevelType = [ "compressed", "compressed" ],
  dimOrdering = affine_map<(i,j) -> (j,i)>
}>

// foreach on a column-major sparse tensor
sparse_tensor.foreach in %0 : tensor<2x3xf64, #COL_MAJOR> do {
 ^bb0(%row: index, %col: index, %arg3: f64):
    // [%row, %col] -> [0, 0], [1, 0], [2, 0], [0, 1], [1, 1], [2, 1]
}

#ROW_MAJOR = #sparse_tensor.encoding<{
  dimLevelType = [ "compressed", "compressed" ],
}>

// foreach on a row-major sparse tensor
sparse_tensor.foreach in %0 : tensor<2x3xf64, #ROW_MAJOR> do {
 ^bb0(%row: index, %col: index, %arg3: f64):
    // [%row, %col] -> [0, 0], [0, 1], [1, 0], [1, 1], [2, 0], [2, 1]
}

// foreach on a row-major dense tensor but visit column first
sparse_tensor.foreach in %0 {order=affine_map<(i,j)->(j,i)>}: tensor<2x3xf64> do {
 ^bb0(%row: index, %col: index, %arg3: f64):
    // [%row, %col] -> [0, 0], [1, 0], [2, 0], [0, 1], [1, 1], [2, 1]
}

Traits: SingleBlockImplicitTerminator

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.storage_specifier.get (::mlir::sparse_tensor::GetStorageSpecifierOp) ¶

Syntax:

operation ::= `sparse_tensor.storage_specifier.get` $specifier $specifierKind (`at` $level^)? attr-dict`:` qualified(type($specifier))

Returns the requested field of the given storage_specifier.

Example of querying the size of the coordinates array for level 0:

%0 = sparse_tensor.storage_specifier.get %arg0 crd_mem_sz at 0
     : !sparse_tensor.storage_specifier<#COO>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.insert (::mlir::sparse_tensor::InsertOp) ¶

Inserts a value into the sparse tensor

Syntax:

operation ::= `sparse_tensor.insert` $value `into` $tensor `[` $lvlCoords `]` attr-dict`:` type($tensor)

Inserts the value into the underlying storage of the tensor at the given level-coordinates. The arity of lvlCoords must match the level-rank of the tensor. This operation can only be applied when the tensor materializes unintialized from a bufferization.alloc_tensor operation and the final tensor is constructed with a load operation which has the hasInserts attribute set.

The level-properties of the sparse tensor type fully describe what kind of insertion order is allowed. When all levels have “unique” and “ordered” properties, for example, insertions should occur in strict lexicographical level-coordinate order. Other properties define different insertion regimens. Inserting in a way contrary to these properties results in undefined behavior.

Note that this operation is “impure” in the sense that even though the result is modeled through an SSA value, the insertion is eventually done “in place”, and referencing the old SSA value is undefined behavior. This operation is scheduled to be unified with the dense counterpart tensor.insert that has pure SSA semantics.

Example:

%result = sparse_tensor.insert %val into %tensor[%i,%j] : tensor<1024x1024xf64, #CSR>

Interfaces: InferTypeOpInterface

Operands: ¶

Results: ¶

sparse_tensor.load (::mlir::sparse_tensor::LoadOp) ¶

Rematerializes tensor from underlying sparse storage format

Syntax:

operation ::= `sparse_tensor.load` $tensor (`hasInserts` $hasInserts^)? attr-dict `:` type($tensor)

Rematerializes a tensor from the underlying sparse storage format of the given tensor. This is similar to the bufferization.to_tensor operation in the sense that it provides a bridge between a bufferized world view and a tensor world view. Unlike the bufferization.to_tensor operation, however, this sparse operation is used only temporarily to maintain a correctly typed intermediate representation during progressive bufferization.

The hasInserts attribute denote whether insertions to the underlying sparse storage format may have occurred, in which case the underlying sparse storage format needs to be finalized. Otherwise, the operation simply folds away.

Note that this operation is “impure” in the sense that even though the result is modeled through an SSA value, the operation relies on a proper context of materializing and inserting the tensor value.

Examples:

%result = sparse_tensor.load %tensor : tensor<8xf64, #SV>

%1 = sparse_tensor.load %0 hasInserts : tensor<16x32xf32, #CSR>

Traits: SameOperandsAndResultType

Interfaces: InferTypeOpInterface

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.new (::mlir::sparse_tensor::NewOp) ¶

Materializes a new sparse tensor from given source

Syntax:

operation ::= `sparse_tensor.new` $source attr-dict `:` type($source) `to` type($result)

Materializes a sparse tensor with contents taken from an opaque pointer provided by source. For targets that have access to a file system, for example, this pointer may be a filename (or file) of a sparse tensor in a particular external storage format. The form of the operation is kept deliberately very general to allow for alternative implementations in the future, such as pointers to buffers or runnable initialization code. The operation is provided as an anchor that materializes a properly typed sparse tensor with inital contents into a computation.

Reading in a symmetric matrix will result in just the lower/upper triangular part of the matrix (so that only relevant information is stored). Proper symmetry support for operating on symmetric matrices is still TBD.

Example:

sparse_tensor.new %source : !Source to tensor<1024x1024xf64, #CSR>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.number_of_entries (::mlir::sparse_tensor::NumberOfEntriesOp) ¶

Returns the number of entries that are stored in the tensor.

Syntax:

operation ::= `sparse_tensor.number_of_entries` $tensor attr-dict `:` type($tensor)

Returns the number of entries that are stored in the given sparse tensor. Note that this is typically the number of nonzero elements in the tensor, but since explicit zeros may appear in the storage formats, the more accurate nomenclature is used.

Example:

%noe = sparse_tensor.number_of_entries %tensor : tensor<64x64xf64, #CSR>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.out (::mlir::sparse_tensor::OutOp) ¶

Outputs a sparse tensor to the given destination

Syntax:

operation ::= `sparse_tensor.out` $tensor `,` $dest attr-dict `:` type($tensor) `,` type($dest)

Outputs the contents of a sparse tensor to the destination defined by an opaque pointer provided by dest. For targets that have access to a file system, for example, this pointer may specify a filename (or file) for output. The form of the operation is kept deliberately very general to allow for alternative implementations in the future, such as sending the contents to a buffer defined by a pointer.

Note that this operation is “impure” in the sense that its behavior is solely defined by side-effects and not SSA values.

Example:

sparse_tensor.out %t, %dest : tensor<1024x1024xf64, #CSR>, !Dest

Operands: ¶

sparse_tensor.pack (::mlir::sparse_tensor::PackOp) ¶

Returns a sparse tensor from the given (values, coordinates) pair

Syntax:

operation ::= `sparse_tensor.pack` $values `,` $coordinates attr-dict`:` type($values) `,` type($coordinates) `to` type($result)

Packs the values/coordinates into a COO sparse tensor. The length of values must match the outer-length of coordinates, since these two tensors are “zipped” together. The coordinates argument provides level-coords for each value, therefore, the inner-length of coordinates must match the level-rank of the returned tensor, and each level-coords must be valid for the level-sizes of the returned tensor. Note that the returned tensor must be statically shaped because it is impossible to infer the dimension-shape from level-coordinates alone.

TODO: The returned tensor is allowed (in principle) to have non-identity dimOrdering/higherOrdering mappings. However, the current implementation does not yet support them.

• coordinates : tensor<NSE x lvlRank x iType> supplies the level-coords for each element in values.
• values : tensor<NSE x V> supplies the corresponding values for each entry in coordinates.

This operation can be used to materialize a sparse tensor from external sources; e.g., when passing two numpy arrays from Python.

Example:

%values      = arith.constant dense<[ 1.1,   2.2,   3.3 ]> : tensor<3xf64>
%coordinates = arith.constant dense<[[0,0], [1,2], [1,3]]> : tensor<3x2xindex>
%st = sparse_tensor.pack %values, %coordinates
    : tensor<3xf64>, tensor<3x2xindex> to tensor<3x4xf64, #COO>
// yields COO format |1.1, 0.0, 0.0, 0.0|
//     of 3x4 matrix |0.0, 0.0, 2.2, 3.3|
//                   |0.0, 0.0, 0.0, 0.0|

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.push_back (::mlir::sparse_tensor::PushBackOp) ¶

Pushes a value to the back of a given buffer

Syntax:

operation ::= `sparse_tensor.push_back` (`inbounds` $inbounds^)? $curSize `,` $inBuffer `,` $value (`,` $n^ )?  attr-dict `:` type($curSize) `,` type($inBuffer) `,` type($value) (`,` type($n)^ )?

Pushes value to the end of the given sparse tensor storage buffer inBuffer as indicated by the value of curSize and returns the new size of the buffer in newSize (newSize = curSize + n). The capacity of the buffer is recorded in the memref type of inBuffer. If the current buffer is full, then inBuffer.realloc is called before pushing the data to the buffer. This is similar to std::vector push_back.

The optional input n specifies the number of times to repeately push the value to the back of the tensor. When n is a compile-time constant, its value can’t be less than 1. If n is a runtime value that is less than 1, the behavior is undefined. Although using input n is semantically equivalent to calling push_back n times, it gives compiler more chances to to optimize the memory reallocation and the filling of the memory with the same value.

The inbounds attribute tells the compiler that the insertion won’t go beyond the current storage buffer. This allows the compiler to not generate the code for capacity check and reallocation. The typical usage will be for “dynamic” sparse tensors for which a capacity can be set beforehand.

Note that this operation is “impure” in the sense that even though the result is modeled through an SSA value, referencing the memref through the old SSA value after this operation is undefined behavior.

Example:

%buf, %newSize = sparse_tensor.push_back %curSize, %buffer, %val
   : index, memref<?xf64>, f64

%buf, %newSize = sparse_tensor.push_back inbounds %curSize, %buffer, %val
   : xindex, memref<?xf64>, f64

%buf, %newSize = sparse_tensor.push_back inbounds %curSize, %buffer, %val, %n
   : xindex, memref<?xf64>, f64

Interfaces: InferTypeOpInterface

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.reduce (::mlir::sparse_tensor::ReduceOp) ¶

Custom reduction operation utilized within linalg.generic

Syntax:

operation ::= `sparse_tensor.reduce` $x `,` $y `,` $identity attr-dict `:` type($output) $region

Defines a computation with a linalg.generic operation that takes two operands and an identity value and reduces all values down to a single result based on the computation in the region.

The region must contain exactly one block taking two arguments. The block must end with a sparse_tensor.yield and the output must match the input argument types.

Note that this operation is only required for custom reductions beyond the standard operations (add, mul, and, or, etc). The linalg.generic iterator_types defines which indices are being reduced. When the associated operands are used in an operation, a reduction will occur. The use of this explicit reduce operation is not required in most cases.

Example of Matrix->Vector reduction using max(product(x_i), 100):

%cf1 = arith.constant 1.0 : f64
%cf100 = arith.constant 100.0 : f64
%C = bufferization.alloc_tensor...
%0 = linalg.generic #trait
   ins(%A: tensor<?x?xf64, #SparseMatrix>)
  outs(%C: tensor<?xf64, #SparseVector>) {
  ^bb0(%a: f64, %c: f64) :
    %result = sparse_tensor.reduce %c, %a, %cf1 : f64 {
        ^bb0(%arg0: f64, %arg1: f64):
          %0 = arith.mulf %arg0, %arg1 : f64
          %cmp = arith.cmpf "ogt", %0, %cf100 : f64
          %ret = arith.select %cmp, %cf100, %0 : f64
          sparse_tensor.yield %ret : f64
      }
    linalg.yield %result : f64
} -> tensor<?xf64, #SparseVector>

Traits: AlwaysSpeculatableImplTrait, SameOperandsAndResultType

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.select (::mlir::sparse_tensor::SelectOp) ¶

Select operation utilized within linalg.generic

Syntax:

operation ::= `sparse_tensor.select` $x attr-dict `:` type($x) $region

Defines an evaluation within a linalg.generic operation that takes a single operand and decides whether or not to keep that operand in the output.

A single region must contain exactly one block taking one argument. The block must end with a sparse_tensor.yield and the output type must be boolean.

Value threshold is an obvious usage of the select operation. However, by using linalg.index, other useful selection can be achieved, such as selecting the upper triangle of a matrix.

Example of selecting A >= 4.0:

%C = bufferization.alloc_tensor...
%0 = linalg.generic #trait
   ins(%A: tensor<?xf64, #SparseVector>)
  outs(%C: tensor<?xf64, #SparseVector>) {
  ^bb0(%a: f64, %c: f64) :
    %result = sparse_tensor.select %a : f64 {
        ^bb0(%arg0: f64):
          %cf4 = arith.constant 4.0 : f64
          %keep = arith.cmpf "uge", %arg0, %cf4 : f64
          sparse_tensor.yield %keep : i1
      }
    linalg.yield %result : f64
} -> tensor<?xf64, #SparseVector>

Example of selecting lower triangle of a matrix:

%C = bufferization.alloc_tensor...
%0 = linalg.generic #trait
   ins(%A: tensor<?x?xf64, #CSR>)
  outs(%C: tensor<?x?xf64, #CSR>) {
  ^bb0(%a: f64, %c: f64) :
    %row = linalg.index 0 : index
    %col = linalg.index 1 : index
    %result = sparse_tensor.select %a : f64 {
        ^bb0(%arg0: f64):
          %keep = arith.cmpf "olt", %col, %row : f64
          sparse_tensor.yield %keep : i1
      }
    linalg.yield %result : f64
} -> tensor<?x?xf64, #CSR>

Traits: AlwaysSpeculatableImplTrait, SameOperandsAndResultType

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.storage_specifier.set (::mlir::sparse_tensor::SetStorageSpecifierOp) ¶

Syntax:

operation ::= `sparse_tensor.storage_specifier.set` $specifier $specifierKind (`at` $level^)? `with` $value attr-dict `:` qualified(type($result))

Set the field of the storage specifier to the given input value. Returns the updated storage_specifier as a new SSA value.

Example of updating the sizes of the coordinates array for level 0:

%0 = sparse_tensor.storage_specifier.set %arg0 crd_mem_sz at 0 with %new_sz
   : !sparse_tensor.storage_specifier<#COO>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.sort_coo (::mlir::sparse_tensor::SortCooOp) ¶

Sorts the arrays in xs and ys lexicographically on the integral values found in the xs list

Syntax:

operation ::= `sparse_tensor.sort_coo` $algorithm $n`,`$xy (`jointly` $ys^)? attr-dict`:` type($xy) (`jointly` type($ys)^)?

Sparse_tensor.sort_coo is similar to sparse_tensor.sort, except that all the xs values and some ys values are put in the linear buffer xy. The optional index attribute nx provides the number of xs values in xy. When nx is not explicitly specified, its value is 1. The optional index attribute ny provides the number of ys values in xy. When ny is not explicitly specified, its value is 0. This instruction supports a more efficient way to store the COO definition in sparse tensor type.

The buffer xy should have a dimension not less than n * (nx + ny) while the buffers in ys should have a dimension not less than n. The behavior of the operator is undefined if this condition is not met.

Example:

sparse_tensor.sort_coo insertion_sort_stable %n, %x { nx = 2 : index}
  : memref<?xindex>

sparse_tensor.sort hybrid_quick_sort %n, %xy jointly %y1
  { nx = 2 : index, ny = 2 : index}
  : memref<?xi64> jointly memref<?xf32>

Attributes: ¶

Operands: ¶

sparse_tensor.sort (::mlir::sparse_tensor::SortOp) ¶

Sorts the arrays in xs and ys lexicographically on the integral values found in the xs list

Syntax:

operation ::= `sparse_tensor.sort` $algorithm $n `,` $xs (`jointly` $ys^)? attr-dict`:` type($xs) (`jointly` type($ys)^)?

Lexicographically sort the first n values in xs along with the values in ys. Conceptually, the values being sorted are tuples produced by zip(zip(xs), zip(ys)). In particular, values in ys needed to be sorted along with values in xs, but values in ys don’t affect the lexicographical order. The order in which arrays appear in xs affects the sorting result. The operator updates xs and ys in place with the result of the sorting.

For example, assume x1=[4, 3], x2=[1, 2], y1=[10, 5], then the output of “sort 2, x1, x2 jointly y1” are x1=[3, 4], x2=[2, 1], y1=[5, 10] while the output of “sort 2, x2, x1, jointly y1” are x2=[1, 2], x1=[4, 3], y1=[10, 5].

Buffers in xs needs to have the same integral element type while buffers in ys can have different numeric element types. All buffers in xs and ys should have a dimension not less than n. The behavior of the operator is undefined if this condition is not met. The operator requires at least one buffer in xs while ys can be empty.

The enum attribute algorithm indicates the sorting algorithm used to implement the operator: hybrid_quick_sort, insertion_sort_stable, quick_sort, or heap_sort.

Note that this operation is “impure” in the sense that its behavior is solely defined by side-effects and not SSA values.

Example:

sparse_tensor.sort insertion_sort_stable %n, %x1, %x2 jointly y1, %y2
  : memref<?xindex>, memref<?xindex> jointly memref<?xindex>, memref<?xf32>

sparse_tensor.sort hybrid_quick_sort %n, %x1, %x2 jointly y1, %y2
  { alg=1 : index}
  : memref<?xindex>, memref<?xindex> jointly memref<?xindex>, memref<?xf32>

Traits: AttrSizedOperandSegments

Attributes: ¶

Operands: ¶

sparse_tensor.storage_specifier.init (::mlir::sparse_tensor::StorageSpecifierInitOp) ¶

Syntax:

operation ::= `sparse_tensor.storage_specifier.init` attr-dict (`with` $source^)? `:` (`from` qualified(type($source))^ `to`)? qualified(type($result))

Returns an initial storage specifier value. A storage specifier value holds the level-sizes, position arrays, coordinate arrays, and the value array. If this is a specifier for slices, it also holds the extra strides/offsets for each tensor dimension.

TODO: The sparse tensor slice support is currently in a unstable state, and is subject to change in the future.

Example:

#CSR = #sparse_tensor.encoding<{ dimLevelType = [ "dense", "compressed" ]}>
#CSR_SLICE = #sparse_tensor.encoding<{
  dimLevelType = [ "dense", "compressed" ],
  slice = [ (1, 4, 1), (1, 4, 2) ]
}>

%0 = sparse_tensor.storage_specifier.init :  !sparse_tensor.storage_specifier<#CSR>
%1 = sparse_tensor.storage_specifier.init with %src
     : !sparse_tensor.storage_specifier<#CSR> to
       !sparse_tensor.storage_specifier<#CSR_SLICE>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.coordinates_buffer (::mlir::sparse_tensor::ToCoordinatesBufferOp) ¶

Extracts the linear coordinates array from a tensor

Syntax:

operation ::= `sparse_tensor.coordinates_buffer` $tensor attr-dict `:` type($tensor) `to` type($result)

Returns the linear coordinates array for a sparse tensor with a trailing COO region with at least two levels. It is an error if the tensor doesn’t contain such a COO region. This is similar to the bufferization.to_memref operation in the sense that it provides a bridge between a tensor world view and a bufferized world view. Unlike the bufferization.to_memref operation, however, this operation actually lowers into code that extracts the linear coordinates array from the sparse storage scheme that stores the coordinates for the COO region as an array of structures. For example, a 2D COO sparse tensor with two non-zero elements at coordinates (1, 3) and (4, 6) are stored in a linear buffer as (1, 4, 3, 6) instead of two buffer as (1, 4) and (3, 6).

Writing into the result of this operation is undefined behavior.

Example:

%1 = sparse_tensor.coordinates_buffer %0
   : tensor<64x64xf64, #COO> to memref<?xindex>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.coordinates (::mlir::sparse_tensor::ToCoordinatesOp) ¶

Extracts the level-th coordinates array of the tensor

Syntax:

operation ::= `sparse_tensor.coordinates` $tensor attr-dict `:` type($tensor) `to` type($result)

Returns the coordinates array of the tensor’s storage at the given level. This is similar to the bufferization.to_memref operation in the sense that it provides a bridge between a tensor world view and a bufferized world view. Unlike the bufferization.to_memref operation, however, this sparse operation actually lowers into code that extracts the coordinates array from the sparse storage itself (either by calling a support library or through direct code).

Writing into the result of this operation is undefined behavior.

Example:

%1 = sparse_tensor.coordinates %0 { level = 1 : index }
   : tensor<64x64xf64, #CSR> to memref<?xindex>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.positions (::mlir::sparse_tensor::ToPositionsOp) ¶

Extracts the level-th positions array of the tensor

Syntax:

operation ::= `sparse_tensor.positions` $tensor attr-dict `:` type($tensor) `to` type($result)

Returns the positions array of the tensor’s storage at the given level. This is similar to the bufferization.to_memref operation in the sense that it provides a bridge between a tensor world view and a bufferized world view. Unlike the bufferization.to_memref operation, however, this sparse operation actually lowers into code that extracts the positions array from the sparse storage itself (either by calling a support library or through direct code).

Writing into the result of this operation is undefined behavior.

Example:

%1 = sparse_tensor.positions %0 { level = 1 : index }
   : tensor<64x64xf64, #CSR> to memref<?xindex>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.slice.offset (::mlir::sparse_tensor::ToSliceOffsetOp) ¶

Extracts the offset of the sparse tensor slice at the given dimension

Syntax:

operation ::= `sparse_tensor.slice.offset` $slice `at` $dim attr-dict `:` type($slice)

Extracts the offset of the sparse tensor slice at the given dimension.

Currently, sparse tensor slices are still a work in progress, and only works when runtime library is disabled (i.e., running sparse compiler with enable-runtime-library=false).

Example:

%0 = tensor.extract_slice %s[%v1, %v2][64, 64][1, 1] : tensor<128x128xf64, #DCSR>
                                                    to tensor<64x64xf64, #Slice>

%1 = sparse_tensor.slice.offset %0 at 0 : tensor<64x64xf64, #Slice>
%2 = sparse_tensor.slice.offset %0 at 1 : tensor<64x64xf64, #Slice>
// %1 = %v1
// %2 = %v2

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.slice.stride (::mlir::sparse_tensor::ToSliceStrideOp) ¶

Extracts the stride of the sparse tensor slice at the given dimension

Syntax:

operation ::= `sparse_tensor.slice.stride` $slice `at` $dim attr-dict `:` type($slice)

Extracts the stride of the sparse tensor slice at the given dimension.

Currently, sparse tensor slices are still a work in progress, and only works when runtime library is disabled (i.e., running sparse compiler with enable-runtime-library=false).

Example:

%0 = tensor.extract_slice %s[%v1, %v2][64, 64][%s1, %s2] : tensor<128x128xf64, #DCSR>
                                                        to tensor<64x64xf64, #Slice>

%1 = sparse_tensor.slice.stride %0 at 0 : tensor<64x64xf64, #Slice>
%2 = sparse_tensor.slice.stride %0 at 1 : tensor<64x64xf64, #Slice>
// %1 = %s1
// %2 = %s2

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes: ¶

Operands: ¶

Results: ¶

sparse_tensor.values (::mlir::sparse_tensor::ToValuesOp) ¶

Extracts numerical values array from a tensor

Syntax:

operation ::= `sparse_tensor.values` $tensor attr-dict `:` type($tensor) `to` type($result)

Returns the values array of the sparse storage format for the given sparse tensor, independent of the actual dimension. This is similar to the bufferization.to_memref operation in the sense that it provides a bridge between a tensor world view and a bufferized world view. Unlike the bufferization.to_memref operation, however, this sparse operation actually lowers into code that extracts the values array from the sparse storage scheme (either by calling a support library or through direct code).

Writing into the result of this operation is undefined behavior.

Example:

%1 = sparse_tensor.values %0 : tensor<64x64xf64, #CSR> to memref<?xf64>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.unary (::mlir::sparse_tensor::UnaryOp) ¶

Unary set operation utilized within linalg.generic

Syntax:

operation ::= `sparse_tensor.unary` $x attr-dict `:` type($x) `to` type($output) `\n`
              `present` `=` $presentRegion `\n`
              `absent` `=` $absentRegion

Defines a computation with a linalg.generic operation that takes a single operand and executes one of two regions depending on whether the operand is nonzero (i.e. stored explicitly in the sparse storage format).

Two regions are defined for the operation must appear in this order:

• present (elements present in the sparse tensor)
• absent (elements not present in the sparse tensor)

Each region contains a single block describing the computation and result. A non-empty block must end with a sparse_tensor.yield and the return type must match the type of output. The primary region’s block has one argument, while the missing region’s block has zero arguments.

A region may also be declared empty (i.e. absent={}), indicating that the region does not contribute to the output.

Example of A+1, restricted to existing elements:

%C = bufferization.alloc_tensor...
%0 = linalg.generic #trait
   ins(%A: tensor<?xf64, #SparseVector>)
  outs(%C: tensor<?xf64, #SparseVector>) {
  ^bb0(%a: f64, %c: f64) :
    %result = sparse_tensor.unary %a : f64 to f64
      present={
        ^bb0(%arg0: f64):
          %cf1 = arith.constant 1.0 : f64
          %ret = arith.addf %arg0, %cf1 : f64
          sparse_tensor.yield %ret : f64
      }
      absent={}
    linalg.yield %result : f64
} -> tensor<?xf64, #SparseVector>

Example returning +1 for existing values and -1 for missing values:

%result = sparse_tensor.unary %a : f64 to i32
  present={
    ^bb0(%x: f64):
      %ret = arith.constant 1 : i32
      sparse_tensor.yield %ret : i32
  }
  absent={
    %ret = arith.constant -1 : i32
    sparse_tensor.yield %ret : i32
  }

Example showing a structural inversion (existing values become missing in the output, while missing values are filled with 1):

%result = sparse_tensor.unary %a : f64 to i64
  present={}
  absent={
    %ret = arith.constant 1 : i64
    sparse_tensor.yield %ret : i64
  }

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.unpack (::mlir::sparse_tensor::UnpackOp) ¶

Returns the (values, coordinates) pair unpacked from the input tensor

Syntax:

operation ::= `sparse_tensor.unpack` $tensor attr-dict `:` type($tensor)`to` type($values) `,` type($coordinates) `,` type($nse)

The unpack operation is the inverse of sparse_tensor::pack. It returns the values, level-coordinates, and number-of-stored-entries extracted from the sparse tensor. The source tensor is allowed (in principle) to have non-identity dimOrdering/higherOrdering mappings. Regardless of the mappings, the returned coordinates are always level-coordinates, because this is what we mean by “unpacking” as opposed to other forms of exposing sparse tensors to external clients. This operation can be used for returning an unpacked MLIR sparse tensor to frontend; e.g., returning two numpy arrays to Python.

TODO: the current implementation does not yet support non-identity mappings.

This operation ends the lifetime of the sparse tensor, and using the tensor after the unpack is undefined behavior.

Example:

// input COO format |1.1, 0.0, 0.0, 0.0|
//    of 3x4 matrix |0.0, 0.0, 2.2, 3.3|
//                  |0.0, 0.0, 0.0, 0.0|
%values, %coordinates, %nse
  = sparse_tensor.unpack %st
  : tensor<3x4xf64, #COO> to tensor<2xf64>, tensor<2x2xindex>, index
// %values      = arith.constant dense<[ 1.1,   2.2,   3.3 ]> : tensor<3xf64>
// %coordinates = arith.constant dense<[[0,0], [1,2], [1,3]]> : tensor<3x2xindex>
// %nse = 3

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Results: ¶

sparse_tensor.yield (::mlir::sparse_tensor::YieldOp) ¶

Yield from sparse_tensor set-like operations

Syntax:

operation ::= `sparse_tensor.yield` $result attr-dict `:` type($result)

Yields a value from within a binary, unary, reduce, select or foreach block.

Example:

%0 = sparse_tensor.unary %a : i64 to i64 {
  ^bb0(%arg0: i64):
    %cst = arith.constant 1 : i64
    %ret = arith.addi %arg0, %cst : i64
    sparse_tensor.yield %ret : i64
}

Traits: AlwaysSpeculatableImplTrait, Terminator

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: ¶

Attribute definition ¶

SparseTensorDimSliceAttr ¶

An attribute to encode slice information of a sparse tensor on a particular dimension (a tuple of offset, size, stride).

Parameters: ¶

SparseTensorEncodingAttr ¶

An attribute to encode TACO-style information on sparsity properties of tensors. The encoding is eventually used by a sparse compiler pass to generate sparse code fully automatically for all tensor expressions that involve tensors with a sparse encoding. Compiler passes that run before this sparse compiler pass need to be aware of the semantics of tensor types with such an encoding.

The attribute consists of the following fields.

• Level-type for each level of a tensor type:

  • dense : all entries along this level are stored.
  • compressed : only nonzeros along this level are stored.
  • singleton : a variant of the compressed level-format, for when coordinates are guaranteed to have no siblings at this level. By default, each level-type has the property of being unique (no duplicates at that level) and ordered (coordinates appear sorted at that level). The following two suffixes can be used to specify that the level should instead be non-unique (duplicates may appear) and/or non-ordered (coordinates may appear unsorted).
  • -nu : not unique
  • -no : not ordered Currently, these suffixes (if present) must appear in this order. In the future, we may introduce additional level-types and properties, and split up how the level-format and properties are specified rather than using this suffix mechanism.

  TODO: This field is called “dimLevelType” for historical reasons, even though the types are per-level rather than per-dimension. (This will be corrected in an upcoming change that completely overhauls the syntax of this attribute.)

• An optional permutation which maps (higher-ordering)-coordinates to level-coordinates; defaulting to the identity permutation. For example, given a 2-d tensor with the default higher-ordering, (i, j) -> (i, j) specifies row-wise storage and (i, j) -> (j, i) specifies column-wise storage.

  TODO: this field is called “dimOrdering” for historical reasons, even though it actually operates on level-coordinates rather than dimension-coordinates. (This will be corrected in an upcoming change that completely overhauls the syntax of this attribute.)

• An optional higher-order mapping from dimension-coordinates to a higher-order coordinate space; defaulting to the identity map. This is applied before the dimOrdering, thus we have the composite: dimCoords –higherOrdering–> hoCoords –dimOrdering–> lvlCoords. The higher-order mapping is used to define block-sparse storage, jagged-diagonal (JDS/ELL/ITPACK) storage, etc.

  For example, given a 2-d tensor, the mapping (i, j) -> (i floordiv 2, j floordiv 3, i mod 2, j mod 3) imposes an higher-order partitioning into 2x3 blocks along the matrix layout. For block-sparsity, blocks are typically stored with compression while dense storage is used within each block (although hybrid schemes are possible as well).

  TODO: the following example is out-of-date and will be implemented in a different manner than described here. (This will be corrected in an upcoming change that completely overhauls the syntax of this attribute.)

  The higher-order mapping also provides a notion of “counting a dimension”, where every stored element with the same coordinate is mapped to a new slice. For instance, ELL storage of a 2-d tensor can be defined with the mapping (i, j) -> (#i, i, j) using the notation of [Chou20]. Lacking the # symbol in MLIR’s affine mapping, we use a free symbol c to define such counting, together with a constant that denotes the number of resulting slices. For example, the mapping (i, j)[c] -> (c * 3 * i, i, j) with the level-types ["dense", "dense", "compressed"] denotes ELL storage with three jagged diagonals that count the dimension i.

• The required bitwidth for “position” storage (integral offsets into the sparse storage scheme). A narrow width reduces the memory footprint of overhead storage, as long as the width suffices to define the total required range (viz. the maximum number of stored entries over all indirection levels). The choices are 8, 16, 32, 64, or, the default, 0 to indicate the native bitwidth.

• The required bitwidth for “coordinate” storage (the coordinates of stored entries). A narrow width reduces the memory footprint of overhead storage, as long as the width suffices to define the total required range (viz. the maximum value of each tensor coordinate over all levels). The choices are 8, 16, 32, 64, or, the default, 0 to indicate a native bitwidth.

• An optional array of SparseTensorDimSliceAttr, which specifies how the sparse tensor is partitioned on each dimension.

Examples:

// Sparse vector.
#SparseVector = #sparse_tensor.encoding<{
  dimLevelType = [ "compressed" ]
}>
... tensor<?xf32, #SparseVector> ...

// Sorted Coordinate Scheme.
#SortedCOO = #sparse_tensor.encoding<{
  dimLevelType = [ "compressed-nu", "singleton" ]
}>
... tensor<?x?xf64, #SortedCOO> ...

// Doubly compressed sparse column storage with specific bitwidths.
#DCSC = #sparse_tensor.encoding<{
  dimLevelType = [ "compressed", "compressed" ],
  dimOrdering = affine_map<(i, j) -> (j, i)>,
  posWidth = 32,
  crdWidth = 8
}>
... tensor<8x8xf64, #DCSC> ...

// Block sparse row storage (2x3 blocks).
#BCSR = #sparse_tensor.encoding<{
  dimLevelType = [ "compressed", "compressed", "dense", "dense" ],
  dimOrdering  = affine_map<(ii, jj, i, j) -> (ii, jj, i, j)>,
  higherOrdering = affine_map<(i, j) -> (i floordiv 2, j floordiv 3, i mod 2, j mod 3)>
}>
... tensor<20x30xf32, #BCSR> ...

// ELL storage (4 jagged diagonals, i.e., at most 4 nonzeros per row).
#ELL = #sparse_tensor.encoding<{
  dimLevelType = [ "dense", "dense", "compressed" ],
  dimOrdering  = affine_map<(ii, i, j) -> (ii, i, j)>,
  higherOrdering = affine_map<(i, j)[c] -> (c * 4 * i, i, j)>
}>
... tensor<?x?xf64, #ELL> ...

// CSR slice (offset = 0, size = 4, stride = 1 on the first dimension;
// offset = 0, size = 8, and a dynamic stride on the second dimension).
#CSR_SLICE = #sparse_tensor.encoding<{
  dimLevelType = [ "dense", "compressed" ],
  slice = [ (0, 4, 1), (0, 8, ?) ]
}>
... tensor<?x?xf64, #CSC_SLICE> ...

Parameters: ¶

SparseTensorSortKindAttr ¶

sparse tensor sort algorithm

Syntax:

#sparse_tensor.SparseTensorSortAlgorithm<
  ::mlir::sparse_tensor::SparseTensorSortKind   # value
>

Parameters: ¶

StorageSpecifierKindAttr ¶

sparse tensor storage specifier kind

Syntax:

#sparse_tensor.kind<
  ::mlir::sparse_tensor::StorageSpecifierKind   # value
>

Parameters: ¶

Type definition ¶

StorageSpecifierType ¶

Structured metadata for sparse tensor low-level storage scheme

Syntax:

!sparse_tensor.storage_specifier<
  ::mlir::sparse_tensor::SparseTensorEncodingAttr   # encoding
>

Syntax:

storage_specifier-type ::= `!storage_specifier` `<` encoding `>`
encoding ::= attribute-value

Values with storage_specifier types represent aggregated storage scheme metadata for the given sparse tensor encoding. It currently holds a set of values for level-sizes, coordinate arrays, position arrays, and value array. Note that the type is not yet stable and subject to change in the near future.

Examples:

// A storage specifier that can be used to store storage scheme metadata from CSR matrix.
!storage_specifier<#CSR>

Parameters: ¶