SparseTensor Dialect
Reactant.MLIR.Dialects.sparse_tensor.assemble Method
assemble
Assembles the per-level position and coordinate arrays together with the values arrays into a sparse tensor. The order and types of the provided levels must be consistent with the actual storage layout of the returned sparse tensor described below.
levels: [tensor<? x iType>, ...]supplies the sparse tensor position and coordinate arrays of the sparse tensor for the corresponding level as specifed bysparse_tensor::StorageLayout.values : tensor<? x V>supplies the values array for the stored elements in the sparse tensor.
This operation can be used to assemble a sparse tensor from an external source; e.g., by passing numpy arrays from Python. It is the user's responsibility to provide input that can be correctly interpreted by the sparsifier, which does not perform any sanity test to verify data integrity.
Example
%pos = arith.constant dense<[0, 3]> : tensor<2xindex>
%index = arith.constant dense<[[0,0], [1,2], [1,3]]> : tensor<3x2xindex>
%values = arith.constant dense<[ 1.1, 2.2, 3.3 ]> : tensor<3xf64>
%s = sparse_tensor.assemble (%pos, %index), %values
: (tensor<2xindex>, tensor<3x2xindex>), tensor<3xf64> 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|Reactant.MLIR.Dialects.sparse_tensor.binary Method
binary
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.
Due to the possibility of empty regions, i.e. lack of a value for certain cases, the result of this operation may only feed directly into the output of the linalg.generic operation or into into a custom reduction sparse_tensor.reduce operation that follows in the same region.
Example of isEqual applied to intersecting elements only:
%C = tensor.empty(...)
%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 = tensor.empty(...)
%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 = tensor.empty(...)
%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>Reactant.MLIR.Dialects.sparse_tensor.coiterate Method
coiterate
The sparse_tensor.coiterate operation represents a loop (nest) over a set of iteration spaces. The operation can have multiple regions, with each of them defining a case to compute a result at the current iterations. The case condition is defined solely based on the pattern of specified iterators. For example:
%ret = sparse_tensor.coiterate (%sp1, %sp2) at(%coord) iter_args(%arg = %init)
: (!sparse_tensor.iter_space<#CSR, lvls = 0>,
!sparse_tensor.iter_space<#COO, lvls = 0>)
-> index
case %it1, _ {
// %coord is specifed in space %sp1 but *NOT* specified in space %sp2.
}
case %it1, %it2 {
// %coord is specifed in *BOTH* spaces %sp1 and %sp2.
}sparse_tensor.coiterate can also operate on loop-carried variables. It returns the final value for each loop-carried variable after loop termination. The initial values of the variables are passed as additional SSA operands to the iterator SSA value and used coordinate SSA values. Each operation region has variadic arguments for specified (used), one argument for each loop-carried variable, representing the value of the variable at the current iteration, followed by a list of arguments for iterators. The body region must contain exactly one block that terminates with sparse_tensor.yield.
The results of an sparse_tensor.coiterate hold the final values after the last iteration. If the sparse_tensor.coiterate defines any values, a yield must be explicitly present in every region defined in the operation. The number and types of the sparse_tensor.coiterate results must match the initial values in the iter_args binding and the yield operands.
A sparse_tensor.coiterate example that does elementwise addition between two sparse vectors.
%ret = sparse_tensor.coiterate (%sp1, %sp2) at(%coord) iter_args(%arg = %init)
: (!sparse_tensor.iter_space<#CSR, lvls = 0>,
!sparse_tensor.iter_space<#CSR, lvls = 0>)
-> tensor<?xindex, #CSR>
case %it1, _ {
// v = v1 + 0 = v1
%v1 = sparse_tensor.extract_value %t1 at %it1 : index
%yield = sparse_tensor.insert %v1 into %arg[%coord]
sparse_tensor.yield %yield
}
case _, %it2 {
// v = v2 + 0 = v2
%v2 = sparse_tensor.extract_value %t2 at %it2 : index
%yield = sparse_tensor.insert %v1 into %arg[%coord]
sparse_tensor.yield %yield
}
case %it1, %it2 {
// v = v1 + v2
%v1 = sparse_tensor.extract_value %t1 at %it1 : index
%v2 = sparse_tensor.extract_value %t2 at %it2 : index
%v = arith.addi %v1, %v2 : index
%yield = sparse_tensor.insert %v into %arg[%coord]
sparse_tensor.yield %yield
}Reactant.MLIR.Dialects.sparse_tensor.compress Method
compress
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>Reactant.MLIR.Dialects.sparse_tensor.concatenate Method
concatenate
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>Reactant.MLIR.Dialects.sparse_tensor.convert Method
convert
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>Reactant.MLIR.Dialects.sparse_tensor.coordinates Method
coordinates
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>Reactant.MLIR.Dialects.sparse_tensor.coordinates_buffer Method
coordinates_buffer
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>Reactant.MLIR.Dialects.sparse_tensor.crd_translate Method
crd_translate
Performs coordinate translation between level and dimension coordinate space according to the affine maps defined by encoder.
Example
%l0, %l1, %l2, %l3 = sparse_tensor.crd_translate dim_to_lvl [%d0, %d1] as #BSR
: index, index, index, indexReactant.MLIR.Dialects.sparse_tensor.disassemble Method
disassemble
The disassemble operation is the inverse of sparse_tensor::assemble. It copies the per-level position and coordinate arrays together with the values array of the given sparse tensor into the user-supplied buffers along with the actual length of the memory used in each returned buffer.
This operation can be used for returning a disassembled MLIR sparse tensor; e.g., copying the sparse tensor contents into pre-allocated numpy arrays back to Python. It is the user's responsibility to allocate large enough buffers of the appropriate types to hold the sparse tensor contents. The sparsifier simply copies all fields of the sparse tensor into the user-supplied buffers without any sanity test to verify data integrity.
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|
%p, %c, %v, %p_len, %c_len, %v_len =
sparse_tensor.disassemble %s : tensor<3x4xf64, #COO>
out_lvls(%op, %oi : tensor<2xindex>, tensor<3x2xindex>)
out_vals(%od : tensor<3xf64>) ->
(tensor<2xindex>, tensor<3x2xindex>), tensor<3xf64>, (index, index), index
// %p = arith.constant dense<[ 0, 3 ]> : tensor<2xindex>
// %c = arith.constant dense<[[0,0], [1,2], [1,3]]> : tensor<3x2xindex>
// %v = arith.constant dense<[ 1.1, 2.2, 3.3 ]> : tensor<3xf64>
// %p_len = 2
// %c_len = 6 (3x2)
// %v_len = 3Reactant.MLIR.Dialects.sparse_tensor.expand Method
expand
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>Reactant.MLIR.Dialects.sparse_tensor.extract_iteration_space Function
extract_iteration_space
Extracts a !sparse_tensor.iter_space from a sparse tensor between certain (consecutive) levels. For sparse levels, it is usually done by loading a postion range from the underlying sparse tensor storage. E.g., for a compressed level, the iteration space is extracted by [pos[i], pos[i+1]) supposing the the parent iterator points at i.
tensor: the input sparse tensor that defines the iteration space. parentIter: the iterator for the previous level, at which the iteration space at the current levels will be extracted. loLvl, hiLvl: the level range between [loLvl, hiLvl) in the input tensor that the returned iteration space covers. hiLvl - loLvl defines the dimension of the iteration space.
The type of returned the value is must be !sparse_tensor.iter_space<#INPUT_ENCODING, lvls = $loLvl to $hiLvl>. The returned iteration space can then be iterated over by sparse_tensor.iterate operations to visit every stored element (usually nonzeros) in the input sparse tensor.
Example
// Extracts a 1-D iteration space from a COO tensor at level 1.
%space = sparse_tensor.iteration.extract_space %sp at %it1 lvls = 1
: tensor<4x8xf32, #COO>, !sparse_tensor.iterator<#COO, lvls = 0>
->!sparse_tensor.iter_space<#COO, lvls = 1>Reactant.MLIR.Dialects.sparse_tensor.extract_value Method
extract_value
The sparse_tensor.extract_value operation extracts the value pointed to by a sparse iterator from a sparse tensor.
Example
%val = sparse_tensor.extract_value %sp at %it
: tensor<?x?xf32, #CSR>, !sparse_tensor.iterator<#CSR, lvl = 1>Reactant.MLIR.Dialects.sparse_tensor.foreach Method
foreach
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<{
map = (d0, d1) -> (d1 : compressed, d0 : compressed)
}>
// 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<{
map = (d0, d1) -> (d0 : compressed, d1 : 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]
}Reactant.MLIR.Dialects.sparse_tensor.has_runtime_library Method
has_runtime_library
Returns a boolean value that indicates whether the sparsifier runs in runtime library mode or not. For testing only! This operation is useful for writing test cases that require different code depending on runtime/codegen mode.
Example
%has_runtime = sparse_tensor.has_runtime_library
scf.if %has_runtime {
...
}Reactant.MLIR.Dialects.sparse_tensor.iterate Method
iterate
The sparse_tensor.iterate operation represents a loop (nest) over the provided iteration space extracted from a specific sparse tensor. The operation defines an SSA value for a sparse iterator that points to the current stored element in the sparse tensor and SSA values for coordinates of the stored element. The coordinates are always converted to index type despite of the underlying sparse tensor storage. When coordinates are not used, the SSA values can be skipped by _ symbols, which usually leads to simpler generated code after sparsification. For example:
// The coordinate for level 0 is not used when iterating over a 2-D
// iteration space.
%sparse_tensor.iterate %iterator in %space at(_, %crd_1)
: !sparse_tensor.iter_space<#CSR, lvls = 0 to 2>sparse_tensor.iterate can also operate on loop-carried variables. It returns the final values after loop termination. The initial values of the variables are passed as additional SSA operands to the iterator SSA value and used coordinate SSA values mentioned above. The operation region has an argument for the iterator, variadic arguments for specified (used) coordiates and followed by one argument for each loop-carried variable, representing the value of the variable at the current iteration. The body region must contain exactly one block that terminates with sparse_tensor.yield.
The results of an sparse_tensor.iterate hold the final values after the last iteration. If the sparse_tensor.iterate defines any values, a yield must be explicitly present. The number and types of the sparse_tensor.iterate results must match the initial values in the iter_args binding and the yield operands.
A nested sparse_tensor.iterate example that prints all the coordinates stored in the sparse input:
func.func @nested_iterate(%sp : tensor<4x8xf32, #COO>) {
// Iterates over the first level of %sp
%l1 = sparse_tensor.extract_iteration_space %sp lvls = 0
: tensor<4x8xf32, #COO> -> !sparse_tensor.iter_space<#COO, lvls = 0 to 1>
%r1 = sparse_tensor.iterate %it1 in %l1 at (%coord0)
: !sparse_tensor.iter_space<#COO, lvls = 0 to 1> {
// Iterates over the second level of %sp
%l2 = sparse_tensor.extract_iteration_space %sp at %it1 lvls = 1
: tensor<4x8xf32, #COO>, !sparse_tensor.iterator<#COO, lvls = 0 to 1>
-> !sparse_tensor.iter_space<#COO, lvls = 1 to 2>
%r2 = sparse_tensor.iterate %it2 in %l2 at (coord1)
: !sparse_tensor.iter_space<#COO, lvls = 1 to 2> {
vector.print %coord0 : index
vector.print %coord1 : index
}
}
}Reactant.MLIR.Dialects.sparse_tensor.load Method
load
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>Reactant.MLIR.Dialects.sparse_tensor.lvl Method
lvl
The sparse_tensor.lvl behaves similar to tensor.dim operation. It takes a sparse tensor and a level operand of type index and returns the size of the requested level of the given sparse tensor. If the sparse tensor has an identity dimension to level mapping, it returns the same result as tensor.dim. If the level index is out of bounds, the behavior is undefined.
Example
#BSR = #sparse_tensor.encoding<{
map = ( i, j ) ->
( i floordiv 2 : dense,
j floordiv 3 : compressed,
i mod 2 : dense,
j mod 3 : dense
)
}>
// Always returns 2 (4 floordiv 2), can be constant folded:
%c0 = arith.constant 0 : index
%x = sparse_tensor.lvl %A, %c0 : tensor<4x?xf32, #BSR>
// Return the dynamic dimension of %A computed by %j mod 3.
%c1 = arith.constant 1 : index
%y = sparse_tensor.lvl %A, %c1 : tensor<4x?xf32, #BSR>
// Always return 3 (since j mod 3 < 3), can be constant fold
%c3 = arith.constant 3 : index
%y = sparse_tensor.lvl %A, %c3 : tensor<4x?xf32, #BSR>Reactant.MLIR.Dialects.sparse_tensor.new Method
new
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>Reactant.MLIR.Dialects.sparse_tensor.number_of_entries Method
number_of_entries
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>Reactant.MLIR.Dialects.sparse_tensor.out Method
out
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>, !DestReactant.MLIR.Dialects.sparse_tensor.positions Method
positions
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>Reactant.MLIR.Dialects.sparse_tensor.print Method
print
Prints the individual components of a sparse tensors (the positions, coordinates, and values components) to stdout for testing and debugging purposes. This operation lowers to just a few primitives in a light-weight runtime support to simplify supporting this operation on new platforms.
Example
sparse_tensor.print %tensor : tensor<1024x1024xf64, #CSR>Reactant.MLIR.Dialects.sparse_tensor.push_back Function
push_back
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>, f64Reactant.MLIR.Dialects.sparse_tensor.reduce Method
reduce
Defines a computation with a linalg.generic operation that takes two operands and an identity value and reduces all stored 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 reduction operations (add, sub, or, xor) that can be sparsified by merely reducing the stored values. More elaborate reduction operations (mul, and, min, max, etc.) would need to account for implicit zeros as well. They can still be handled using this custom reduction operation. 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 = tensor.empty(...)
%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>Reactant.MLIR.Dialects.sparse_tensor.reinterpret_map Method
reinterpret_map
Reinterprets the dimension-to-level and level-to-dimension map specified in source according to the type of dest. reinterpret_map is a no-op and is introduced merely to resolve type conflicts. It does not make any modification to the source tensor and source/dest tensors are considered to be aliases.
source and dest tensors are "reinterpretable" if and only if they have the exactly same storage at a low level. That is, both source and dest has the same number of levels and level types, and their shape is consistent before and after reinterpret_map.
Example
#CSC = #sparse_tensor.encoding<{
map = (d0, d1) -> (d1: dense, d0: compressed)
}>
#CSR = #sparse_tensor.encoding<{
map = (d0, d1) -> (d0: dense, d1: compressed)
}>
%t1 = sparse_tensor.reinterpret_map %t0 : tensor<3x4xi32, #CSC> to tensor<4x3xi32, #CSR>
#BSR = #sparse_tensor.encoding<{
map = ( i, j ) -> ( i floordiv 2 : dense,
j floordiv 3 : compressed,
i mod 2 : dense,
j mod 3 : dense
)
}>
#DSDD = #sparse_tensor.encoding<{
map = (i, j, k, l) -> (i: dense, j: compressed, k: dense, l: dense)
}>
%t1 = sparse_tensor.reinterpret_map %t0 : tensor<6x12xi32, #BSR> to tensor<3x4x2x3xi32, #DSDD>Reactant.MLIR.Dialects.sparse_tensor.reorder_coo Method
reorder_coo
Reorders the input COO to the same order as specified by the output format. E.g., reorder an unordered COO into an ordered one.
The input and result COO tensor must have the same element type, position type and coordinate type. At the moment, the operation also only supports ordering input and result COO with the same dim2lvl map.
Example
%res = sparse_tensor.reorder_coo quick_sort %coo : tensor<?x?xf64 : #Unordered_COO> to
tensor<?x?xf64 : #Ordered_COO>Reactant.MLIR.Dialects.sparse_tensor.select Method
select
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 = tensor.empty(...)
%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 = tensor.empty(...)
%1 = 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>Reactant.MLIR.Dialects.sparse_tensor.slice_offset Method
slice_offset
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 the sparsifier 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 = %v2Reactant.MLIR.Dialects.sparse_tensor.slice_stride Method
slice_stride
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 the sparsifier 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 = %s2Reactant.MLIR.Dialects.sparse_tensor.sort Method
sort
Sorts the xs values along with some ys values that are put in a single linear buffer xy. The affine map attribute perm_map specifies the permutation to be applied on the xs before comparison, the rank of the permutation map also specifies the number of xs values in xy. 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 * (rank(perm_map) + 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 insertion_sort_stable %n, %x { perm_map = affine_map<(i,j) -> (j,i)> }
: memref<?xindex>Reactant.MLIR.Dialects.sparse_tensor.storage_specifier_get Method
storage_specifier_get
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>Reactant.MLIR.Dialects.sparse_tensor.storage_specifier_init Function
storage_specifier_init
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<{
map = (i, j) -> (i : dense, j : compressed)
}>
#CSR_SLICE = #sparse_tensor.encoding<{
map = (d0 : #sparse_tensor<slice(1, 4, 1)>,
d1 : #sparse_tensor<slice(1, 4, 2)>) ->
(d0 : dense, d1 : compressed)
}>
%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>Reactant.MLIR.Dialects.sparse_tensor.storage_specifier_set Method
storage_specifier_set
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>Reactant.MLIR.Dialects.sparse_tensor.unary Method
unary
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. The absent region may only generate constants or values already computed on entry of the linalg.generic operation.
A region may also be declared empty (i.e. absent={}), indicating that the region does not contribute to the output.
Due to the possibility of empty regions, i.e. lack of a value for certain cases, the result of this operation may only feed directly into the output of the linalg.generic operation or into into a custom reduction sparse_tensor.reduce operation that follows in the same region.
Example of A+1, restricted to existing elements:
%C = tensor.empty(...) : tensor<?xf64, #SparseVector>
%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:
%p1 = arith.constant 1 : i32
%m1 = arith.constant -1 : i32
%C = tensor.empty(...) : tensor<?xi32, #SparseVector>
%1 = linalg.generic #trait
ins(%A: tensor<?xf64, #SparseVector>)
outs(%C: tensor<?xi32, #SparseVector>) {
^bb0(%a: f64, %c: i32) :
%result = sparse_tensor.unary %a : f64 to i32
present={
^bb0(%x: f64):
sparse_tensor.yield %p1 : i32
}
absent={
sparse_tensor.yield %m1 : i32
}
linalg.yield %result : i32
} -> tensor<?xi32, #SparseVector>Example showing a structural inversion (existing values become missing in the output, while missing values are filled with 1):
%c1 = arith.constant 1 : i64
%C = tensor.empty(...) : tensor<?xi64, #SparseVector>
%2 = linalg.generic #trait
ins(%A: tensor<?xf64, #SparseVector>)
outs(%C: tensor<?xi64, #SparseVector>) {
^bb0(%a: f64, %c: i64) :
%result = sparse_tensor.unary %a : f64 to i64
present={}
absent={
sparse_tensor.yield %c1 : i64
}
linalg.yield %result : i64
} -> tensor<?xi64, #SparseVector>Reactant.MLIR.Dialects.sparse_tensor.values Method
values
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>Reactant.MLIR.Dialects.sparse_tensor.yield Method
yield
Yields a value from within a binary, unary, reduce, select or foreach block.
Example
%0 = sparse_tensor.unary %a : i64 to i64 {
present={
^bb0(%arg0: i64):
%cst = arith.constant 1 : i64
%ret = arith.addi %arg0, %cst : i64
sparse_tensor.yield %ret : i64
}
}