MLIR

Multi-Level IR Compiler Framework

'tensor' Dialect

The tensor dialect is intended to hold core tensor creation and manipulation ops, which are not strongly associated with any particular other dialect or domain abstraction. The aim for ops in this dialect is that they make sense for any tensor element type. When this is not the case, the op is left to live in other dialects. Examples of element types that could be supported by the tensor dialect include:

  • representing large, dense aggregations of primitive types, suitable for high-performance numerical computing.
  • representing shapes in the shape dialect, which consist of small 1D tensors of index data type.
  • representing aggregations of strings or “variant” types.
  • representing large, sparse aggregations of primitive types, suitable for high-performance numerical computing.

Because of this broad element type support and because of the existence of more dedicated dialects, such as the sparse_tensor and linalg dialects, we prefer for now to keep the tensor dialect as small as possible. The expectation is that at some point in the future, the tensor dialect’s scope may be broadened through a careful discussion of the tradeoffs.

On the tensor type itself, note that it is actually a builtin type (it lives in the builtin dialect), and does not live in this dialect. Furthermore, a tensor is an immutable object. For example, this means that a copy will always be made of the tensor object when it is passed to the dest operand used by some ops in this dialect. As an optimization, an implementation can eliminate these copies during lowering when they are redundant and perform in-place mutation, see the Destination-Passing Style documentation for more information.

Operations 

source

tensor.bitcast (tensor::BitcastOp) 

Tensor bitcast operation

Syntax:

operation ::= `tensor.bitcast` $source attr-dict `:` type($source) `to` type($dest)

Bitcast a tensor from one type to another type of equivalent element width. If both are ranked, then the rank should be the same and static dimensions should match.

Example:

// Bitcast from unsigned to signed or signless integer.
%2 = tensor.bitcast %1 : tensor<4xui32> to tensor<4xi32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: CastOpInterface, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
sourcetensor of any type values

Results: 

ResultDescription
desttensor of any type values

tensor.cast (tensor::CastOp) 

Tensor cast operation

Syntax:

operation ::= `tensor.cast` $source attr-dict `:` type($source) `to` type($dest)

Convert a tensor from one type to an equivalent type without changing any data elements. The source and destination types must both be tensor types with the same element type. If both are ranked, then the rank should be the same and static dimensions should match. The operation is invalid if converting to a mismatching constant dimension.

Example:

// Convert from unknown rank to rank 2 with unknown dimension sizes.
%2 = tensor.cast %1 : tensor<*xf32> to tensor<?x?xf32>

// Convert to a type with more known dimensions.
%3 = tensor.cast %2 : tensor<?x?xf32> to tensor<4x?xf32>

// Discard static dimension and rank information.
%4 = tensor.cast %3 : tensor<4x?xf32> to tensor<?x?xf32>
%5 = tensor.cast %4 : tensor<?x?xf32> to tensor<*xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: CastOpInterface, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
sourcetensor of any type values

Results: 

ResultDescription
desttensor of any type values

tensor.collapse_shape (tensor::CollapseShapeOp) 

Operation to produce a tensor with a smaller rank

Syntax:

operation ::= `tensor.collapse_shape` $src $reassociation attr-dict `:` type($src) `into` type($result)

The tensor.collapse_shape op produces a new tensor of lower (or equal) rank whose dimension sizes are a reassociation of the original src dimensions.

A reassociation is defined as a continuous grouping of dimensions and is represented by an array of DenseI64ArrayAttr attribute. The reassociation maps are applied to the operand shape to obtain the result shape.

Example:

// Dimension collapse (i, j) -> i' and k -> k'
%b = tensor.collapse_shape %a [[0, 1], [2]]
    : tensor<?x?x?xf32> into tensor<?x?xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
reassociation::mlir::ArrayAttrArray of 64-bit integer array attributes

Operands: 

OperandDescription
srcranked tensor of any type values

Results: 

ResultDescription
resultranked tensor of any type values

tensor.concat (tensor::ConcatOp) 

Tensor concatenation operation

Syntax:

operation ::= `tensor.concat` `dim` `(` $dim `)` $inputs attr-dict
              `:` functional-type(operands, results)

The “concat” operation constructs a tensor out of a variadic list of input tensors, concatenated along a static dimension number. All inputs and the result type must share the same rank.

dim specifies the dimension along which to concatenate. The size of the concatenated dimension in the result must be equal to the sum of the sizes of the inputs along that dimension. All other dimensions in both the inputs and result must be the same size.

Example:

%0 = tensor.concat dim(0) %0, %1, %2 :
    (tensor<3x6xf32>, tensor<3x6xf32>, tensor<1x6xf32) -> tensor<7x6xf32>

// Dynamic + dynamic -> static
%0 = tensor.concat dim(1) %0, %1, %2 :
    (tensor<3x?xf32>, tensor<3x2xf32>, tensor<3x?xf32) -> tensor<3x10xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
dim::mlir::IntegerAttr64-bit signless integer attribute

Operands: 

OperandDescription
inputsvariadic of ranked tensor of any type values

Results: 

ResultDescription
resultranked tensor of any type values

tensor.dim (tensor::DimOp) 

Dimension index operation

Syntax:

operation ::= `tensor.dim` attr-dict $source `,` $index `:` type($source)

The tensor.dim operation takes a tensor and a dimension operand of type index. It returns the size of the requested dimension of the given tensor. If the dimension index is out of bounds, the behavior is undefined.

The specified tensor type is that of the first operand.

Example:

// Always returns 4, can be constant folded:
%c0 = arith.constant 0 : index
%x = tensor.dim %A, %c0 : tensor<4x?xf32>

// Return the dynamic dimension of %A.
%c1 = arith.constant 1 : index
%y = tensor.dim %A, %c1 : memref<4x?xf32>

// Equivalent generic form:
%x = "tensor.dim"(%A, %c0) : (memref<4x?xf32>, index) -> index
%y = "tensor.dim"(%A, %c1) : (memref<4x?xf32>, index) -> index

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface, ShapedDimOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
sourcenon-0-ranked or unranked tensor
indexindex

Results: 

ResultDescription
resultindex

tensor.empty (tensor::EmptyOp) 

Empty tensor operation

Syntax:

operation ::= `tensor.empty` `(`$dynamicSizes`)` attr-dict `:` type($result)

tensor.empty is an operation that defines a tensor of a particular shape. The shape could be dynamic or static. The contents of the tensor are unspecified and the only purpose of the op result is to materialize the specified shape in IR and make it available to other transformations.

tensor.empty is useful in transformations that expect destination style ops. I.e., ops that implement DestinationStyleOpInterface. Ops that are not in destination style can be made compatible with such transformations with a tensor.empty destination.

Note: This op can be lowered to a bufferization.alloc_tensor, at which point it turns into an explicit buffer allocation.

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
dynamicSizesvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.expand_shape (tensor::ExpandShapeOp) 

Operation to produce a tensor with a higher rank

Syntax:

operation ::= `tensor.expand_shape` $src $reassociation attr-dict `:` type($src) `into` type($result)

The tensor.expand_shape op produces a tensor of higher (or equal) rank than the operand src whose dimension sizes are a reassociation of src.

A reassociation is defined as a continuous grouping of dimensions. It is represented with an array of DenseI64ArrayAttr attribute. Entries in the array are referred to as reassociation maps.

The reassociation maps are applied to the result shape to obtain the operand shape.

Example:

// Dimension expansion i -> (i', j') and (k) -> (k')
%b = tensor.expand_shape %a [[0, 1], [2]]
    : tensor<?x?xf32> into tensor<?x?x?xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
reassociation::mlir::ArrayAttrArray of 64-bit integer array attributes

Operands: 

OperandDescription
srcranked tensor of any type values

Results: 

ResultDescription
resultranked tensor of any type values

tensor.extract (tensor::ExtractOp) 

Element extraction operation

Syntax:

operation ::= `tensor.extract` $tensor `[` $indices `]` attr-dict `:` type($tensor)

The tensor.extract op reads a ranked tensor and returns one element as specified by the given indices. The result of the op is a value with the same type as the elements of the tensor. The arity of indices must match the rank of the accessed value. All indices should all be of index type.

Example:

%4 = tensor.extract %t[%1, %2] : tensor<4x4xi32>
%5 = tensor.extract %rt[%1, %2] : tensor<?x?xi32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
tensorranked tensor of any type values
indicesvariadic of index

Results: 

ResultDescription
resultany type

tensor.extract_slice (tensor::ExtractSliceOp) 

Extract slice operation

Syntax:

operation ::= `tensor.extract_slice` $source ``
              custom<DynamicIndexList>($offsets, $static_offsets)
              custom<DynamicIndexList>($sizes, $static_sizes)
              custom<DynamicIndexList>($strides, $static_strides)
              attr-dict `:` type($source) `to` type($result)

The “extract_slice” operation extract a tensor from another tensor as specified by the operation’s offsets, sizes and strides arguments.

The extract_slice operation supports the following arguments:

  • source: the “base” tensor from which to extract a slice.
  • offsets: tensor-rank number of offsets into the “base” tensor from which to extract the slice.
  • sizes: tensor-rank number of sizes which specify the sizes of the result tensor type.
  • strides: tensor-rank number of strides specifying subsampling in each dimension.

The representation based on offsets, sizes and strides support a partially-static specification via attributes specified through the static_offsets, static_sizes and static_strides arguments. A special sentinel value ShapedType::kDynamic encodes that the corresponding entry has a dynamic value.

After buffer allocation, the “extract_slice” op is expected to lower into a memref.subview op.

An extract_slice operation may additionally reduce the rank of the resulting tensor by removing dimensions that are statically known to be of size 1. This rank-reduction behavior is not required by the op semantics: this flexibility allows to progressively drop unit dimensions while lowering between different flavors of ops on that operate on tensors.

Verification vs Inference in the rank-reduced case 

Note that there may be multiple ways to infer a resulting rank-reduced type. e.g. 1x6x1 could potentially rank-reduce to either 1x6 or 6x1 2-D shapes.

To disambiguate, the inference helpers inferCanonicalRankReducedResultType only drop the first unit dimensions, in order: e.g. 1x6x1 rank-reduced to 2-D will infer the 6x1 2-D shape, but not 1x6.

Verification however has access to result type and does not need to infer. The verifier calls isRankReducedType(getSource(), getResult()) to determine whether the result type is rank-reduced from the source type. This computes a so-called rank-reduction mask, consisting of dropped unit dims, to map the rank-reduced type to the source type by dropping ones: e.g. 1x6 is a rank-reduced version of 1x6x1 by mask {2} 6x1 is a rank-reduced version of 1x6x1 by mask {0} 1x2x1x4 is a rank-reduced version of 1x1x2x1x1x4x1 by mask {1, 4, 6} (remaining common 1 dimensions are matched eagerly)

Example:

// Rank-reducing extract_slice.
%1 = tensor.extract_slice %0[0, 0, 0][1, 16, 4][1, 1, 1] :
  tensor<8x16x4xf32> to tensor<16x4xf32>
%3 = tensor.extract_slice %2[%o0, 4, %o2][1, %sz1, 1][1, %st1, 1] :
  tensor<8x16x4xf32> to tensor<1x?xf32>

Traits: AlwaysSpeculatableImplTrait, AttrSizedOperandSegments

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OffsetSizeAndStrideOpInterface, OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
static_offsets::mlir::DenseI64ArrayAttri64 dense array attribute
static_sizes::mlir::DenseI64ArrayAttri64 dense array attribute
static_strides::mlir::DenseI64ArrayAttri64 dense array attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
offsetsvariadic of index
sizesvariadic of index
stridesvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.from_elements (tensor::FromElementsOp) 

Tensor from elements operation.

Syntax:

operation ::= `tensor.from_elements` $elements attr-dict `:` type($result)

Create a N-D tensor from a range of same-type arguments. The number of provided elements should equal to the number of the elements in the result type. The elements correspond to a flattened tensor.

Example:

tensor.from_elements %a, %b, %c, %d, %e, %f :  tensor<2x3xindex>

will result in a tensor

[[%a, %b, %c] [%d, %e, %f]]

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
elementsvariadic of any type

Results: 

ResultDescription
resultstatically shaped tensor of any type values

tensor.gather (tensor::GatherOp) 

Gather a subset of a tensor at specified indices

Syntax:

operation ::= `tensor.gather` $source `[` $indices `]`
              `gather_dims` `(` $gather_dims `)`
              (`unique` $unique^)?
              attr-dict
              `:` functional-type(operands, results)

The gather operation extracts a subset of the elements from a source tensor at the given indices.

In its most general form, the tensor of indices specifies all the coordinates of every element to extract (i.e. COO format, without the payload). The indices are expected to be confined to coordinate values that fit the range of the source tensor, otherwise the behavior is undefined.

The leading dimensions of the index tensor give the result tensor its leading dimensions. The trailing dimensions of the result tensor are obtained from the source tensor by omitting the dimensions specified in gather_dims (rank-reducing semantics) or setting them to 1 (rank-preserving semantics) (see examples). The trailing dimension of the index tensor contains the coordinates and is expected to have its size equal to the number of dimensions being gathered. This convention allows an idiomatic specification and lowering of “gathering multiple N-D slices from the source tensor”.

Note: in the examples below, we separate out the indexing part of the tensor type by a whitespace for readability purposes.

Example:

    // For each 1x2 triple of coordinates in %indices, extract the
    // element (i.e. 0-D subset) at the coordinates triple in %source.
    //
    %out = tensor.gather %source[%indices] gather_dims([0, 1, 2]) :
      (tensor<4x4x4xf32>, tensor<1x2x 3xindex>) -> tensor<1x2x 1x1x1xf32>

    // Note: result type may be further rank-reduced to tensor<1x2x f32>.

A slice variant is provided to allow specifying whole slices of the source tensor.

Example:

    // For each 5x6 singleton of coordinates in %indices, extract the 2-D
    // slice %source[*, %indices[...]:%indices[...] + 1, *] with the indices
    // corresponding to the `gather_dims` attribute specified by %indices.
    //
    %out = tensor.gather %source[%indices] gather_dims([1]) :
      (tensor<3x4x5xf32>, tensor<6x7x 1xindex>) -> tensor<6x7x 3x1x5xf32>

    // Note: result type may be further rank-reduced to tensor<6x7x 3x5xf32>.

The dimensions specified in the gather_dims attribute are ones for which the result tensor has size 1. I.e. if the source type is axbxcxd and the coordinates are [1, 3], then the shape suffix is ax1xcx1. Gather also allows rank-reducing semantics where the shape ax1xcx1 can be further simplified to axc.

The elemental type of the indices tensor can be any integer type. In the absence of target-specific or problem specific information the default type one should use is index.

This operation does not support unranked tensors.

An optional unique unit attribute may be specified to indicate that the coordinates in indices are statically guaranteed to be unique at runtime. Incorrectly setting the unique attribute when the coordinates are not truly unique is undefined behavior.

Only full slices are meant to be supported by this op, if one desires partial slices (e.g. strided windows) one should compose this op with other tensor ops (e.g. tensor.extract_slice). This is to avoid a slippery slope of complexity that would make the op unusable in practice.

At the tensor-level, the index tensor is specified in an AoS form (i.e. coordinate tuple is the most minor). It is the responsibility of further lowerings and bufferiation to implement various concrete layouts.

Note: As currently specified, the operation must lower to an abstraction that performs copies to the output tensor. This is because the buffer type system is currently not rich enough to allow multiple non-contiguous views in the same type. This is visible more clearly in a notional buffer version of the op:

    // memref<?x4x1xf32> is a contiguous buffer of ?x4x1 elements.
    // gather from random source slices must copy to the contiguous output.
    %out = memref.gather %source[%indices] gather_dims([1]) :
      (memref<4x4xf32>, memref<?x 1xindex>) -> memref<?x 4x1xf32>

    // Nested buffer support would allow gather to directly index into the
    // source buffer (i.e. represent a jagged view into the source).
    %out = memref.gather %source[%indices] gather_dims([1]) :
      (memref<4x4xf32>, memref<?x 1xindex>) -> memref<? x memref<4x1xf32>>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
gather_dims::mlir::DenseI64ArrayAttri64 dense array attribute
unique::mlir::UnitAttrunit attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
indicesranked tensor of signless integer or index values

Results: 

ResultDescription
resultranked tensor of any type values

tensor.generate (tensor::GenerateOp) 

Creates a dynamically sized tensor from elements

Syntax:

operation ::= `tensor.generate` $dynamicExtents $body attr-dict `:` type($result)

This operation creates a dynamically sized tensor with elements of any type. It expects one index operand per dynamic extent of the result tensor.

The body region defines the tensor’s elements. It takes index operands as its region arguments that span the index space. The element at the given position is yielded with the yield operation (see YieldOp). There is no defined ordering to the invocations of the body. It is conceptually a “parallel map” operation.

Example:

  %tnsr = tensor.generate %m, %n {
  ^bb0(%i : index, %j : index, %k : index):
    ...
    yield %elem : f32
  } : tensor<?x3x?f32>

Traits: RecursiveMemoryEffects, SingleBlockImplicitTerminator<mlir::tensor::YieldOp>, SingleBlock

Interfaces: OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Operands: 

OperandDescription
dynamicExtentsvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.insert (tensor::InsertOp) 

Element insertion operation

Syntax:

operation ::= `tensor.insert` $scalar `into` $dest `[` $indices `]` attr-dict `:` type($dest)

The tensor.insert op inserts a scalar into a ranked tensor dest as specified by the operation’s indices.

It returns a copy of dest with the indexed position updated to the value of scalar.

The arity of indices must match the rank of the tensor dest. All indices should be of index type.

Example:

%4 = tensor.insert %t into %dest[%1, %2] : tensor<4x4xi32>
%5 = tensor.insert %rt into %dest[%1, %2] : tensor<?x?xi32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
scalarany type
destranked tensor of any type values
indicesvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.insert_slice (tensor::InsertSliceOp) 

Insert_slice operation

Syntax:

operation ::= `tensor.insert_slice` $source `into` $dest ``
              custom<DynamicIndexList>($offsets, $static_offsets)
              custom<DynamicIndexList>($sizes, $static_sizes)
              custom<DynamicIndexList>($strides, $static_strides)
              attr-dict `:` type($source) `into` type($dest)

The “insert_slice” operation insert a tensor source into another tensor dest as specified by the operation’s offsets, sizes and strides arguments.

It returns a copy of dest with the proper slice updated with the value of source.

The insert_slice operation supports the following arguments:

  • source: the tensor that is inserted.
  • dest: the tensor into which the source tensor is inserted.
  • offsets: tensor-rank number of offsets into the dest tensor into which the slice is inserted.
  • sizes: tensor-rank number of sizes which specify the sizes of the source tensor type.
  • strides: tensor-rank number of strides that specify subsampling in each dimension.

The representation based on offsets, sizes and strides support a partially-static specification via attributes specified through the static_offsets, static_sizes and static_strides arguments. A special sentinel value ShapedType::kDynamic encodes that the corresponding entry has a dynamic value.

After buffer allocation, the “insert_slice” op is expected to lower into a memref.subview op.

An insert_slice operation may additionally specify insertion into a tensor of higher rank than the source tensor, along dimensions that are statically known to be of size 1. This rank-altering behavior is not required by the op semantics: this flexibility allows to progressively drop unit dimensions while lowering between different flavors of ops on that operate on tensors. The rank-altering behavior of tensor.insert_slice matches the rank-reducing behavior of tensor.extract_slice.

Verification in the rank-reduced case 

The same verification discussion and mechanisms apply as for ExtractSliceOp. Unlike ExtractSliceOp however, there is no need for a specific inference.

Example:

// Rank-altering insert_slice.
%1 = tensor.insert_slice %t into %0[0, 0, 0][1, 16, 4][1, 1, 1] :
  tensor<16x4xf32> into tensor<8x16x4xf32>
%3 = tensor.insert_slice %tt into %2[%o0, 4, %o2][1, %sz1, 1][1, %st1, 1] :
  tensor<1x?xf32> into tensor<8x16x4xf32>

Traits: AlwaysSpeculatableImplTrait, AttrSizedOperandSegments

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OffsetSizeAndStrideOpInterface, OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
static_offsets::mlir::DenseI64ArrayAttri64 dense array attribute
static_sizes::mlir::DenseI64ArrayAttri64 dense array attribute
static_strides::mlir::DenseI64ArrayAttri64 dense array attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
destranked tensor of any type values
offsetsvariadic of index
sizesvariadic of index
stridesvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.pack (tensor::PackOp) 

Tensor pack operation

Syntax:

operation ::= `tensor.pack` $source
              (`padding_value` `(` $padding_value^ `:` type($padding_value) `)`)?
              (`outer_dims_perm` `=` $outer_dims_perm^)?
              `inner_dims_pos` `=` $inner_dims_pos
              `inner_tiles` `=`
              custom<DynamicIndexList>($inner_tiles, $static_inner_tiles)
              `into` $dest attr-dict `:` type($source) `->` type($dest)

The “pack” operation converts a source tensor of rank n into a result tensor of rank n + k with a tiled and packed layout (maybe with padding) and optionally transposes the tiled source tensor dimensions.

inner_dims_pos (mandatory) specifies k source tensor dimensions that are being tiled, where 0 < k <= n. The order of the dimensions matters:

  • The tiled dimensions (of size inner_tiles) are added to the end of the result tensor in the order in which they appear in inner_dims_pos.
  • inner_dims_pos[i] specifies the source tensor dimension tiled by inner_tiles[i].

inner_tiles (mandatory) specifies k tile sizes. These tile sizes correspond to the least significant (“inner”) result tensor dimension sizes, in the same order. Tile sizes can be static or dynamic.

Example: If inner_tiles = [16, 32], the result tensor has a shape of ...x16x32. If inner_dims_pos = [0, 1], the 0th source dimension is tiled by 16 and the 1st source dimension is tiled by 32. Other source dimensions (if any) are not tiled. If inner_dims_pos = [1, 0], the 1st dimension is tiled by 16 and the 0th dimension is tiled by 32.

Example:

// NC to NCnc
%0 = tensor.pack %source inner_dims_pos = [0, 1] inner_tiles = [8, 32]
    into %dest : tensor<128x256xf32> -> tensor<16x8 x 8x32 xf32>
//                                             \  /   \  /
//                                       outer dims  inner dims

outer_dims_perm (optional) specifies a permutation for the outer dimensions. If specified, it must have n elements.

Example:

// CK to KCck
%0 = tensor.pack %source outer_dims_perm = [1, 0] inner_dims_pos = [0, 1]
    inner_tiles = [8, 32] into %dest
    : tensor<128x256xf32> -> tensor<8x16 x 8x32 xf32>
//                                  \  /
//            compare with "NC to NCnc": outer dims are transposed

padding_value specifies a padding value at the boundary on non-perfectly divisible dimensions. Padding is optional:

  • If absent, it is UB if the tile does not perfectly divide the dimension.
  • If present, it will pad along high dimensions (high-padding) to make the tile complete.

Example:

%0 = tensor.pack %arg0 padding_value(%pad : f32) outer_dims_perm = [2, 1, 0]
    inner_dims_pos = [1] inner_tiles = [2] into %arg1
    : tensor<200x127x256xf32> -> tensor<256x64x200x2xf32>
//                 \
//                padded and tiled dim
//
// Source dimension 1 is tiled. 64 does not divide 127 evenly, so 1 padded
// element is added at the end.
//
// Note: Only tiled dimensions can be padded.

Traits: AttrSizedOperandSegments

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
outer_dims_perm::mlir::DenseI64ArrayAttri64 dense array attribute
inner_dims_pos::mlir::DenseI64ArrayAttri64 dense array attribute
static_inner_tiles::mlir::DenseI64ArrayAttri64 dense array attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
destranked tensor of any type values
padding_valueany type
inner_tilesvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.pad (tensor::PadOp) 

Tensor pad operation

Syntax:

operation ::= `tensor.pad` $source
              (`nofold` $nofold^)?
              `low` `` custom<DynamicIndexList>($low, $static_low)
              `high` `` custom<DynamicIndexList>($high, $static_high)
              $region attr-dict `:` type($source) `to` type($result)

tensor.pad is an operation that pads the source tensor with given low and high padding config.

The PadOp operation supports the following arguments:

  • source: the “base” tensor on which to pad.
  • low: A list contains the padding along the start of each dimension, i.e., how many padded values are prepended to the beginning of the tensor in each dimension.
  • high: A list contains the padding along the end of each dimension, i.e., how many padded values are appended to the end of the tensor in each dimension.
  • nofold: indicates that the operation should not be folded when source and result types are equal.

The result tensor dimensions are low[i] + dim[i] + high[i] for each dimension i. The number of elements of low and high must match the rank of the input tensor. They can be either a constant or a dynamic value.

The region of the tensor.pad operation returns the value to use for the padding. The arguments of the region represent the index of the source being accessed. There should be as many arguments as the rank of the source tensor. The value yield-ed by the region is used as the value of the view at the given position.

If nofold is set, the padding operation will not be folded away even if the source type and the padded type have the same static shape. This can be used, e.g., for packing or promotion to faster memory.

Example 1: add 3 zeros to the beginning and 5 zeros to the end of a 1D tensor.

  %arg0 = ... : tensor<10xi32>
  %c0_i32 = arith.constant 0 : i32
  %padded = tensor.pad %arg0 low[3] high[5] {
  ^bb0(%arg1: index):
    tensor.yield %c0_i32 : i32
  } : tensor<10xi32> to tensor<18xi32>

Example 2: add 1 value to the beginning of dimension 0, 2 values to the end of dimension 0, 2 values to the start of dimension 1, and 3 values to the end of dimension 1.

  %pad_value = ... : f32
  %0 = tensor.pad %0 low[1, 2] high[2, 3] {
  ^bb0(%arg0 : index, %arg1 : index):
    tensor.yield %pad_value : f32
  } : tensor<?x?xf32> to tensor<?x?xf32>

Example 3:

  %pad_value = ... : f32
  %0 = tensor.pad %arg0 low[2, %arg1, 3, 3] high[3, 3, %arg1, 2] {
  ^bb0(%arg2: index, %arg3: index, %arg4: index, %arg5: index):
      tensor.yield %pad_value : f32
  } : tensor<1x2x2x?xf32> to tensor<6x?x?x?xf32>

Example 4:

  %pad_value = ... : f32
  %0 = tensor.pad %arg0 low[0, 0] high[%ub0, %ub1] {
  ^bb0(%arg1: index, %arg2: index):
    tensor.yield %pad_value : f32
  } : tensor<2x3xf32> to tensor<?x?xf32>

Example 5: Force a padded value to be always exist with nofold, even though the padding config specifies that no new elements will be added to the tensor.

  %pad_value = ... : f32
  %0 = tensor.pad %arg0 nofold low[0, 0] high[0, 0] {
  ^bb0(%arg1: index, %arg2: index):
    tensor.yield %pad_value : f32
  } : tensor<2x3xf32> to tensor<2x3xf32>

Traits: AlwaysSpeculatableImplTrait, AttrSizedOperandSegments, SingleBlockImplicitTerminator<mlir::tensor::YieldOp>, SingleBlock

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
static_low::mlir::DenseI64ArrayAttri64 dense array attribute
static_high::mlir::DenseI64ArrayAttri64 dense array attribute
nofold::mlir::UnitAttrunit attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
lowvariadic of index
highvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.parallel_insert_slice (tensor::ParallelInsertSliceOp) 

Specify the tensor slice update of a single thread of a parent ParallelCombiningOpInterface op.

Syntax:

operation ::= `tensor.parallel_insert_slice` $source `into` $dest ``
              custom<DynamicIndexList>($offsets, $static_offsets)
              custom<DynamicIndexList>($sizes, $static_sizes)
              custom<DynamicIndexList>($strides, $static_strides)
              attr-dict `:` type($source) `into` type($dest)

The parallel_insert_slice yields a subset tensor value to its parent ParallelCombiningOpInterface. These subset tensor values are aggregated to in some unspecified order into a full tensor value returned by the parent parallel iterating op. The parallel_insert_slice is one such op allowed in the ParallelCombiningOpInterface op.

Conflicting writes result in undefined semantics, in that the indices written to by multiple parallel updates might contain data from any of the updates, or even a malformed bit pattern.

If an index is updated exactly once, the value contained at that index in the resulting tensor will be equal to the value at a corresponding index of a slice that was used for the updated. If an index is not updated at all, its value will be equal to the one in the original tensor.

This op does not create a new value, which allows maintaining a clean separation between the subset and full tensor.

Note that we cannot mark this operation as pure (Pures), even though it has no side effects, because it will get DCEd during canonicalization.

The parallel_insert_slice operation supports the following arguments:

  • source: the tensor that is inserted.
  • dest: the tensor into which the source tensor is inserted.
  • offsets: tensor-rank number of offsets into the dest tensor into which the slice is inserted.
  • sizes: tensor-rank number of sizes which specify the sizes of the source tensor type.
  • strides: tensor-rank number of strides that specify subsampling in each dimension.

The representation based on offsets, sizes and strides support a partially-static specification via attributes specified through the static_offsets, static_sizes and static_strides arguments. A special sentinel value ShapedType::kDynamic encodes that the corresponding entry has a dynamic value.

After buffer allocation, the “parallel_insert_slice” op is expected to lower into a memref.subview op.

A parallel_insert_slice operation may additionally specify insertion into a tensor of higher rank than the source tensor, along dimensions that are statically known to be of size 1. This rank-altering behavior is not required by the op semantics: this flexibility allows to progressively drop unit dimensions while lowering between different flavors of ops on that operate on tensors. The rank-altering behavior of tensor.parallel_insert_slice matches the rank-reducing behavior of tensor.insert_slice and tensor.extract_slice.

Verification in the rank-reduced case 

The same verification discussion and mechanisms apply as for ExtractSliceOp. Unlike ExtractSliceOp however, there is no need for a specific inference.

Traits: AttrSizedOperandSegments

Interfaces: OffsetSizeAndStrideOpInterface

Attributes: 

AttributeMLIR TypeDescription
static_offsets::mlir::DenseI64ArrayAttri64 dense array attribute
static_sizes::mlir::DenseI64ArrayAttri64 dense array attribute
static_strides::mlir::DenseI64ArrayAttri64 dense array attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
destranked tensor of any type values
offsetsvariadic of index
sizesvariadic of index
stridesvariadic of index

tensor.rank (tensor::RankOp) 

Rank operation

Syntax:

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

The tensor.rank operation takes a tensor operand and returns its rank.

Example:

%0 = tensor.rank %arg0 : tensor<*xf32>
%1 = tensor.rank %arg1 : tensor<?x?xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
tensortensor of any type values

Results: 

ResultDescription
«unnamed»index

tensor.reshape (tensor::ReshapeOp) 

Tensor reshape operation

Syntax:

operation ::= `tensor.reshape` $source `(` $shape `)` attr-dict `:` functional-type(operands, results)

The reshape operation converts a tensor from one type to an equivalent type with a provided shape. The source and destination types are compatible if both have the same element type, same number of elements. The following combinations are possible:

a. Source type is ranked or unranked. Shape argument has static size. Result type is ranked.

// Reshape statically-shaped tensor.
%dst = tensor.reshape %src(%shape)
         : (tensor<4x1xf32>, tensor<1xi32>) -> tensor<4xf32>
%dst0 = tensor.reshape %src(%shape0)
         : (tensor<4x1xf32>, tensor<2xi32>) -> tensor<2x2xf32>
// Flatten unranked tensor.
%dst = tensor.reshape %src(%shape)
         : (tensor<*xf32>, tensor<1xi32>) -> tensor<?xf32>

b. Source type is ranked or unranked. Shape argument has dynamic size. Result type is unranked.

// Reshape dynamically-shaped 1D tensor.
%dst = tensor.reshape %src(%shape)
         : (tensor<?xf32>, tensor<?xi32>) -> tensor<*xf32>
// Reshape unranked tensor.
%dst = tensor.reshape %src(%shape)
         : (tensor<*xf32>, tensor<?xi32>) -> tensor<*xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
sourcetensor of any type values
shape1D tensor of signless integer or index values

Results: 

ResultDescription
resulttensor of any type values

tensor.scatter (tensor::ScatterOp) 

Scatter a tensor into a destination tensor at specified indices

Syntax:

operation ::= `tensor.scatter` $source `into` $dest `[` $indices `]`
              `scatter_dims` `(` $scatter_dims `)`
              (`unique` $unique^)?
              attr-dict
              `:` functional-type(operands, results)

The scatter operation inserts a source tensor into a dest tensor at the given indices.

In its most general form, the tensor of indices specifies all the coordinates of every element to insert (i.e. COO format, without the payload). The indices are expected to be confined to coordinate values that fit the range of the dest tensor, otherwise the behavior is undefined.

The leading dimensions of the index tensor must match that of the dest tensor. The trailing dimensions of the dest tensor must match those of the source tensor by omitting the dimensions specified in scatter_dims (rank-reducing semantics) or setting them to 1 (rank-preserving semantics) (see examples). This convention allows an idiomatic specification and lowering of “scattering multiple N-D slices into the dest tensor”. The result type must match the type of the dest tensor.

Note: in the examples below, we separate out the indexing part of the tensor type by a whitespace for readability purposes.

Example:

    // For each 1x2 triple of coordinates in %indices, insert the
    // element (i.e. 0-D subset) at the coordinates triple in %dest.
    //
    %out = tensor.scatter %source into %dest[%indices]
        scatter_dims([0, 1, 2]) unique :
      (tensor<1x2x 1x1x1xf32>, tensor<4x4x4xf32>, tensor<1x2x 3xindex>)
        -> tensor<4x4x4xf32>

    // Note: source type may be further rank-reduced to tensor<1x2x f32>.

A slice variant is provided to allow specifying insertion of whole tensor slices into the dest tensor.

Example:

    // For each 3 singleton of coordinates in %indices, insert the 2-D
    // slice into %dest[*, %indices[...]:%indices[...] + 1, *] with the
    // indices corresponding to the scatter_dims attribute specified by
    // %indices.
    //
    %out = tensor.scatter %source into %dest[%indices] scatter_dims([1]) unique :
      (tensor<3x 4x1x6xf32>, tensor<4x5x6xf32>, tensor<3x 1xindex>)
        -> tensor<4x5x6xf32>

The dimensions specified in the scatter_dims attribute are ones for which the source tensor has size 1. I.e. if the dest type is axbxcxd and the coordinates are [1, 3], then the source type suffix is ax1xcx1. Sactter also allows rank-reducing semantics where the shape ax1xcx1 can be further simplified to axc.

The elemental type of the indices tensor can be any integer type. In the absence of target-specific or problem specific information the default type one should use is index.

This operation does not support unranked tensors.

A unique unit attribute must be be specified to indicate that the coordinates are statically guaranteed to be unique at runtime. If coordinates are not truly unique at runtime, the behavior is undefined.

Only full slices are meant to be supported by this op, if one desires partial slices (e.g. strided windows) one should compose this op with other tensor ops (e.g. tensor.insert_slice). This is to avoid a slippery slope of complexity that would make the op unusable in practice.

At the tensor-level, the index tensor is specified in an AoS form (i.e. coordinate tuple is the most minor). It is the responsibility of further lowerings and bufferiation to implement various concrete layouts.

Note: As currently specified, the operation must lower to an abstraction that performs copies to the output tensor. This is because the buffer type system is currently not rich enough to allow multiple non-contiguous views in the same type. This is visible more clearly in a notional buffer version of the op:

    // memref<?x 4xf32> is a contiguous buffer of ?x4 elements, scatter into
    // random dest slices must copy to the contiguous dest.
    //
    some_side_effecting_op_writing_into %source, ...: memref<3x 4xf32>
    memref.scatter %source into %dest[%indices] scatter_dims([1]) unique :
      (memref<3x 4xf32>, memref<?x 4xf32>, memref<?x 1xindex>)

    // Nested buffer support in the producing op would allow writing directly
    // into the dest buffer.
    %v = some_nested_buffer_view_op %dest[%indices] scatter_dims([1]) unique :
      memref<? x memref<4xf32>>
    some_side_effecting_op_writing_into %v, ...: memref<? x memref<4xf32>>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
scatter_dims::mlir::DenseI64ArrayAttri64 dense array attribute
unique::mlir::UnitAttrunit attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
destranked tensor of any type values
indicesranked tensor of signless integer or index values

Results: 

ResultDescription
resultranked tensor of any type values

tensor.splat (tensor::SplatOp) 

Tensor splat or broadcast operation

Syntax:

operation ::= `tensor.splat` $input (`[` $dynamicSizes^ `]`)? attr-dict `:` type($aggregate)

Broadcast the operand to all elements of the result tensor. The operand is required to be of integer/index/float type.

An additional argument of type index must be provided for each dynamic dimension present in the result type.

Example for a statically shaped tensor:

%s = arith.constant 1.0 : f32
%t = tensor.splat %s : tensor<8x16xf32>

Example for a tensor containing dynamic dimensions:

// Broadcasts %s to a 3D dynamically shaped tensor, with %m and %n binding
// to dimensions 0 and 2 of the resulting tensor, respectively.
%m = arith.constant 10 : index
%n = arith.constant 30 : index
%t = tensor.splat %s[%m, %n] : tensor<?x20x?xf32>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
inputinteger/index/float type
dynamicSizesvariadic of index

Results: 

ResultDescription
aggregateranked tensor of any type values

tensor.unpack (tensor::UnPackOp) 

Tensor unpack operation

Syntax:

operation ::= `tensor.unpack` $source
              (`outer_dims_perm` `=` $outer_dims_perm^)?
              `inner_dims_pos` `=` $inner_dims_pos
              `inner_tiles` `=`
              custom<DynamicIndexList>($inner_tiles, $static_inner_tiles)
              `into` $dest attr-dict `:` type($source) `->` type($dest)

The “unpack” operation converts a source tensor of rank n with a tiled and packed layout to a result tensor of rank n - k.

inner_dims_pos (mandatory) specifies k source tensor dimensions with which the last k source tensor dimensions are combined, where 0 < k <= n/2. Each inner_dims_pos element must be >= 0 and < n - k. The order of the dimensions in inner_dims_pos matters: dimension inner_dims_pos[i] is combined with dimension n - k + i (assuming that outer_dims_perm is not specified).

inner_tiles (mandatory) specifies k tile sizes. These tile sizes correspond to the least significant (“inner”) source tensor dimension sizes. The behavior of this op is undefined if:

  • inner_tiles do not exactly match with the corresponding source tensor dimension sizes.
  • Or, inner_tiles[i] does not divide the size of dimension inner_dims_pos[i] (assuming that outer_dims_perm is not specified) evenly.

outer_dims_perm (optional) specifies a permutation for the outer dimensions. If specified, it must have n - k elements. If specified, this permutation is applied before combining any dimensions.

Example:

// NCnc to NC:
%0 = tensor.unpack %source inner_dims_pos = [0, 1] inner_tiles = [8, 32]
    into %dest : tensor<16x8x8x32xf32> -> tensor<128x256xf32>

// CK to KCck:
%0 = tensor.unpack %source outer_dims_perm = [1, 0] inner_dims_pos = [0, 1]
    inner_tiles = [8, 32] into %dest
    : tensor<8x16x8x32xf32> -> tensor<128x256xf32>

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface), OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Effects: MemoryEffects::Effect{}

Attributes: 

AttributeMLIR TypeDescription
outer_dims_perm::mlir::DenseI64ArrayAttri64 dense array attribute
inner_dims_pos::mlir::DenseI64ArrayAttri64 dense array attribute
static_inner_tiles::mlir::DenseI64ArrayAttri64 dense array attribute

Operands: 

OperandDescription
sourceranked tensor of any type values
destranked tensor of any type values
inner_tilesvariadic of index

Results: 

ResultDescription
resultranked tensor of any type values

tensor.yield (tensor::YieldOp) 

Yield a value from a region

Syntax:

operation ::= `tensor.yield` $value attr-dict `:` type($value)

This operation is used to yield a single value from a within a region. It is used to create dynamically sized tensors (see tensor.generate and tensor.pad ops).

Traits: AlwaysSpeculatableImplTrait, HasParent<::mlir::tensor::GenerateOp, ::mlir::tensor::PadOp>, ReturnLike, Terminator

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), RegionBranchTerminatorOpInterface

Effects: MemoryEffects::Effect{}

Operands: 

OperandDescription
valueany type