'linalg' Dialect - MLIR (original) (raw)

'linalg' Dialect

• Rationale
• Set of Key Transformations
• High-Level Description of Linalg Ops
  • Payload-Carrying Ops
  • Data Representation: Views
  • Metadata Ops
  • Named Payload-Carrying Ops
  • Named Payload Ops Specification
  • YAML Based Named Structured Ops
• Open Issues and Design Alternatives
• Operations
  • linalg.abs (linalg::AbsOp)
  • linalg.add (linalg::AddOp)
  • linalg.batch_matmul (linalg::BatchMatmulOp)
  • linalg.batch_matmul_transpose_a (linalg::BatchMatmulTransposeAOp)
  • linalg.batch_matmul_transpose_b (linalg::BatchMatmulTransposeBOp)
  • linalg.batch_matvec (linalg::BatchMatvecOp)
  • linalg.batch_mmt4d (linalg::BatchMmt4DOp)
  • linalg.batch_reduce_matmul (linalg::BatchReduceMatmulOp)
  • linalg.batch_vecmat (linalg::BatchVecmatOp)
  • linalg.broadcast (linalg::BroadcastOp)
  • linalg.ceil (linalg::CeilOp)
  • linalg.contract (linalg::ContractOp)
  • linalg.conv_1d_ncw_fcw (linalg::Conv1DNcwFcwOp)
  • linalg.conv_1d_nwc_wcf (linalg::Conv1DNwcWcfOp)
  • linalg.conv_1d (linalg::Conv1DOp)
  • linalg.conv_2d_nchw_fchw (linalg::Conv2DNchwFchwOp)
  • linalg.conv_2d_nchw_fchw_q (linalg::Conv2DNchwFchwQOp)
  • linalg.conv_2d_ngchw_fgchw (linalg::Conv2DNgchwFgchwOp)
  • linalg.conv_2d_ngchw_gfchw (linalg::Conv2DNgchwGfchwOp)
  • linalg.conv_2d_ngchw_gfchw_q (linalg::Conv2DNgchwGfchwQOp)
  • linalg.conv_2d_nhwc_fhwc (linalg::Conv2DNhwcFhwcOp)
  • linalg.conv_2d_nhwc_fhwc_q (linalg::Conv2DNhwcFhwcQOp)
  • linalg.conv_2d_nhwc_hwcf (linalg::Conv2DNhwcHwcfOp)
  • linalg.conv_2d_nhwc_hwcf_q (linalg::Conv2DNhwcHwcfQOp)
  • linalg.conv_2d_nhwgc_gfhwc (linalg::Conv2DNhwgcGfhwcOp)
  • linalg.conv_2d_nhwgc_gfhwc_q (linalg::Conv2DNhwgcGfhwcQOp)
  • linalg.conv_2d (linalg::Conv2DOp)
  • linalg.conv_3d_ncdhw_fcdhw (linalg::Conv3DNcdhwFcdhwOp)
  • linalg.conv_3d_ndhwc_dhwcf (linalg::Conv3DNdhwcDhwcfOp)
  • linalg.conv_3d_ndhwc_dhwcf_q (linalg::Conv3DNdhwcDhwcfQOp)
  • linalg.conv_3d (linalg::Conv3DOp)
  • linalg.copy (linalg::CopyOp)
  • linalg.depthwise_conv_1d_ncw_cw (linalg::DepthwiseConv1DNcwCwOp)
  • linalg.depthwise_conv_1d_nwc_wc (linalg::DepthwiseConv1DNwcWcOp)
  • linalg.depthwise_conv_1d_nwc_wcm (linalg::DepthwiseConv1DNwcWcmOp)
  • linalg.depthwise_conv_2d_nchw_chw (linalg::DepthwiseConv2DNchwChwOp)
  • linalg.depthwise_conv_2d_nhwc_hwc (linalg::DepthwiseConv2DNhwcHwcOp)
  • linalg.depthwise_conv_2d_nhwc_hwc_q (linalg::DepthwiseConv2DNhwcHwcQOp)
  • linalg.depthwise_conv_2d_nhwc_hwcm (linalg::DepthwiseConv2DNhwcHwcmOp)
  • linalg.depthwise_conv_2d_nhwc_hwcm_q (linalg::DepthwiseConv2DNhwcHwcmQOp)
  • linalg.depthwise_conv_3d_ncdhw_cdhw (linalg::DepthwiseConv3DNcdhwCdhwOp)
  • linalg.depthwise_conv_3d_ndhwc_dhwc (linalg::DepthwiseConv3DNdhwcDhwcOp)
  • linalg.depthwise_conv_3d_ndhwc_dhwcm (linalg::DepthwiseConv3DNdhwcDhwcmOp)
  • linalg.div (linalg::DivOp)
  • linalg.div_unsigned (linalg::DivUnsignedOp)
  • linalg.dot (linalg::DotOp)
  • linalg.elementwise (linalg::ElementwiseOp)
  • linalg.elemwise_binary (linalg::ElemwiseBinaryOp)
  • linalg.elemwise_unary (linalg::ElemwiseUnaryOp)
  • linalg.erf (linalg::ErfOp)
  • linalg.exp (linalg::ExpOp)
  • linalg.fill (linalg::FillOp)
  • linalg.fill_rng_2d (linalg::FillRng2DOp)
  • linalg.floor (linalg::FloorOp)
  • linalg.generic (linalg::GenericOp)
  • linalg.index (linalg::IndexOp)
  • linalg.pack (linalg::PackOp)
  • linalg.softmax (linalg::SoftmaxOp)
  • linalg.unpack (linalg::UnPackOp)
  • linalg.winograd_filter_transform (linalg::WinogradFilterTransformOp)
  • linalg.winograd_input_transform (linalg::WinogradInputTransformOp)
  • linalg.winograd_output_transform (linalg::WinogradOutputTransformOp)
  • linalg.yield (linalg::YieldOp)
  • linalg.log (linalg::LogOp)
  • linalg.map (linalg::MapOp)
  • linalg.matmul (linalg::MatmulOp)
  • linalg.matmul_transpose_a (linalg::MatmulTransposeAOp)
  • linalg.matmul_transpose_b (linalg::MatmulTransposeBOp)
  • linalg.matvec (linalg::MatvecOp)
  • linalg.max (linalg::MaxOp)
  • linalg.min (linalg::MinOp)
  • linalg.mmt4d (linalg::Mmt4DOp)
  • linalg.mul (linalg::MulOp)
  • linalg.negf (linalg::NegFOp)
  • linalg.pooling_nchw_max (linalg::PoolingNchwMaxOp)
  • linalg.pooling_nchw_sum (linalg::PoolingNchwSumOp)
  • linalg.pooling_ncw_max (linalg::PoolingNcwMaxOp)
  • linalg.pooling_ncw_sum (linalg::PoolingNcwSumOp)
  • linalg.pooling_ndhwc_max (linalg::PoolingNdhwcMaxOp)
  • linalg.pooling_ndhwc_min (linalg::PoolingNdhwcMinOp)
  • linalg.pooling_ndhwc_sum (linalg::PoolingNdhwcSumOp)
  • linalg.pooling_nhwc_max (linalg::PoolingNhwcMaxOp)
  • linalg.pooling_nhwc_max_unsigned (linalg::PoolingNhwcMaxUnsignedOp)
  • linalg.pooling_nhwc_min (linalg::PoolingNhwcMinOp)
  • linalg.pooling_nhwc_min_unsigned (linalg::PoolingNhwcMinUnsignedOp)
  • linalg.pooling_nhwc_sum (linalg::PoolingNhwcSumOp)
  • linalg.pooling_nwc_max (linalg::PoolingNwcMaxOp)
  • linalg.pooling_nwc_max_unsigned (linalg::PoolingNwcMaxUnsignedOp)
  • linalg.pooling_nwc_min (linalg::PoolingNwcMinOp)
  • linalg.pooling_nwc_min_unsigned (linalg::PoolingNwcMinUnsignedOp)
  • linalg.pooling_nwc_sum (linalg::PoolingNwcSumOp)
  • linalg.powf (linalg::PowFOp)
  • linalg.quantized_batch_matmul (linalg::QuantizedBatchMatmulOp)
  • linalg.quantized_matmul (linalg::QuantizedMatmulOp)
  • linalg.reciprocal (linalg::ReciprocalOp)
  • linalg.reduce (linalg::ReduceOp)
  • linalg.round (linalg::RoundOp)
  • linalg.rsqrt (linalg::RsqrtOp)
  • linalg.select (linalg::SelectOp)
  • linalg.sqrt (linalg::SqrtOp)
  • linalg.square (linalg::SquareOp)
  • linalg.sub (linalg::SubOp)
  • linalg.tanh (linalg::TanhOp)
  • linalg.transpose (linalg::TransposeOp)
  • linalg.vecmat (linalg::VecmatOp)

Rationale

Linalg is designed to solve the High-level Hierarchical Optimization (HHO box) in MLIR and to interoperate nicely within a _Mixture Of Expert Compilers_environment (i.e. the CGSel box).

TheRationale Document goes into significantly more design and architectural decision details.

Set of Key Transformations

The following key transformations have been central to driving the design of Linalg. They are all implemented in terms of the properties of thelinalg.generic OpInterface and avoid the pitfall of relying on hardcoded one-off op knowledge.

The textual form description of these transformations is left for future work. Still, it is useful to list the key transformations that are performed on the Linalg IR and that have influenced its design:

1. Progressive Buffer Allocation.
2. Parametric Tiling.
3. Promotion to Temporary Buffer in Fast Memory.
4. Tiled Producer-Consumer Fusion with Parametric Tile-And-Fuse.
5. Map to Parallel and Reduction Loops and Hardware.
6. Vectorization: Rewrite in Vector Form.
7. Lower to Loops (Affine, Generic, and Parallel).
8. Lower to Library Calls or Special Instructions, Intrinsics or ISA.
9. Partially Lower to Iterations Over a Finer-Grained Linalg Op.

High-Level Description of Linalg Ops

Linalg takes at least some inspiration from all previouslylisted prior art. The design enables the definition of CustomOps with generic properties that enablekey transformations, including lowering to scalar load/store and other operations or to external library calls and intrinsics.

These ops can have either tensor or buffer as both input and output operands. Output tensors operands serve the purpose of providing a unifying abstraction and give a shape to the results. Output tensors can come in 2 flavors and are always associated with a corresponding op result:

1. an “init tensor” output value which provides an initial value for a tensor that is created by iteratively updating the result (also called “destructive updates”). Such tensor is always materialized in some form. If enough fusion occurs it may end up being materialized only as a register-level SSA value. It is expected (but not required) that the destructive update pattern can be rewritten as an inplace update on buffers.
2. a “shape-only” tensor output value whose underlying elements are not used in the payload computation and only serves the purpose of carrying shape information to lower levels of abstraction. In the future this will be replaced by an appropriate shape type when it is available as a builtin type (see the discourse discussionLinalg and Shapesfor more details).

Payload-Carrying Ops

Linalg defines a payload carrying operation that implements thestructured opabstraction on tensors and buffers. This linalg.generic operation can express custom operations that optionally have indexing semantics (by accessing the iteration indices using the linalg.index operation). The properties oflinalg.generic are the result of applying the guiding principles described in theRationale Document. They are listed next, with a brief example and discussion for each.

Property 1: Input and Output Operands Define The Iteration Space

A linalg.generic op fully derives the specification of its iteration space from its operands. The property enforces that a localized IR element (the op)has all the information needed to synthesize the control-flow required to iterate over its operands, according to their type. This notion of IR localization bears some resemblance toURUK.

Consider the following fully specified linalg.generic example. Here, the first operand is a memref of f32 scalar elements that has an ordinary identity layout, and the second one is a memref of 4-element vectors with a 2-strided, 1-offset layout.

// File name: example1.mlir
#accesses = [
  affine_map<(m) -> (m)>,
  affine_map<(m) -> (m)>
]

#attrs = {
  indexing_maps = #accesses,
  iterator_types = ["parallel"]
}

func.func @example(%A: memref<?xf32, strided<[1]>>,
              %B: memref<?xvector<4xf32>, strided<[2], offset: 1>>) {
  linalg.generic #attrs
  ins(%A: memref<?xf32, strided<[1]>>)
  outs(%B: memref<?xvector<4xf32>, strided<[2], offset: 1>>) {
  ^bb0(%a: f32, %b: vector<4xf32>):
    %c = "some_compute"(%a, %b): (f32, vector<4xf32>) -> (vector<4xf32>)
    linalg.yield %c: vector<4xf32>
  }
  return
}

The property “_Input and Output Operands Define The Iteration Space_” is materialized by a lowering into a form that will resemble:

// Run: mlir-opt example1.mlir -allow-unregistered-dialect -convert-linalg-to-loops
// This converted representation is in the `scf` dialect.
// It's syntax can be found here: https://mlir.llvm.org/docs/Dialects/SCFDialect/

func.func @example(%arg0: memref<?xf32>,
                   %arg1: memref<?xvector<4xf32>, strided<[2], offset: 1>>) {
  %c0 = arith.constant 0 : index
  %c1 = arith.constant 1 : index
  %0 = memref.dim %arg0, %c0 : memref<?xf32>
  scf.for %arg2 = %c0 to %0 step %c1 {
    %1 = memref.load %arg0[%arg2] : memref<?xf32>
    %2 = memref.load %arg1[%arg2]
       : memref<?xvector<4xf32>, strided<[2], offset: 1>>
    %3 = "some_compute"(%1, %2) : (f32, vector<4xf32>) -> vector<4xf32>
    memref.store %3, %arg1[%arg2]
       : memref<?xvector<4xf32>, strided<[2], offset: 1>>
  }
  return
}

The property participates in simplifying analyses and transformations. For instance, it guarantees no out-of bounds access can occur by construction (assuming dynamic operand dimensions agree with each other, which is the purpose of the assert runtime check).

Before lowering to loop form, loop induction variables and iterators are implicit (i.e. not yet materialized).

The main implications are that:

1. The semantics of the ops are restricted to operate on structured data types, on which we can define an iterator.
2. This does not model arbitrary code with side-effects.

We do not think these are serious limitations in practice because MLIR is all about mixing different levels of abstractions in the same IR. As long as Linalg can progressively lower to the next level of abstraction, it can also be just bypassed for things that do not fit.

At the same time, conditioning op semantics on structured data types is a very promising path towards extensibility to non-dense tensors as experience with LIFT abstractions forsparse andposition-dependent arrays, as well asTACO, has shown.

Property 2: Reversible Mappings Between Control and Data Structures

A linalg.generic defines the mapping between the iteration space (i.e. the loops) and the data.

Consider the following fully specified linalg.generic example. Here, the firstmemref is a 2-strided one on both of its dimensions, and the second memrefuses an identity layout.

// File name: example2.mlir
#indexing_maps = [
  affine_map<(i, j) -> (j, i)>,
  affine_map<(i, j) -> (j)>
]

#attrs = {
  indexing_maps = #indexing_maps,
  iterator_types = ["parallel", "parallel"]
}

func.func @example(%A: memref<8x?xf32, strided<[2, 2], offset: 0>>,
              %B: memref<?xvector<4xf32>>) {
  linalg.generic #attrs
  ins(%A: memref<8x?xf32, strided<[2, 2], offset: 0>>)
  outs(%B: memref<?xvector<4xf32>>) {
  ^bb0(%a: f32, %b: vector<4xf32>):
    %c = "some_compute"(%a, %b): (f32, vector<4xf32>) -> (vector<4xf32>)
    linalg.yield %c: vector<4xf32>
  }
  return
}

The property “_Reversible Mappings Between Control and Data Structures_” is materialized by a lowering into a form that will resemble:

// Run: mlir-opt example2.mlir -allow-unregistered-dialect -convert-linalg-to-loops

func.func @example(%arg0: memref<8x?xf32, strided<[2, 2]>>, %arg1: memref<?xvector<4xf32>>) {
  %c8 = arith.constant 8 : index
  %c0 = arith.constant 0 : index
  %c1 = arith.constant 1 : index
  %0 = memref.dim %arg0, %c1 : memref<8x?xf32, strided<[2, 2]>>
  scf.for %arg2 = %c0 to %0 step %c1 {
    scf.for %arg3 = %c0 to %c8 step %c1 {
      %1 = memref.load %arg0[%arg3, %arg2] : memref<8x?xf32, strided<[2, 2]>>
      %2 = memref.load %arg1[%arg3] : memref<?xvector<4xf32>>
      %3 = "some_compute"(%1, %2) : (f32, vector<4xf32>) -> vector<4xf32>
      memref.store %3, %arg1[%arg3] : memref<?xvector<4xf32>>
    }
  }
  return
}

This mapping needs to be reversible because we want to be able to go back and forth between the two and answer questions such as:

• Given a subset of the iteration space, what subset of data does it read and write?
• Given a subset of data read or written, what subset of the iteration space is responsible for this read or write?

Answering these 2 questions is one of the main analyses that Linalg uses to implement transformations such as tiling, tiled producer-consumer fusion, and promotion to temporary buffers in fast memory.

In the current implementation, linalg.generic uses a list ofAffineMaps (see the#indexing_maps attribute in the previous examples). This is a pragmatic short-term solution, but in the longer term note that this property could be even evaluated dynamically, similarly to inspector-executor algorithms.

Property 3: The Type Of Iterators is Defined Explicitly

A linalg.generic op fully declares the type of its iterators. This information is used in transformations.

These properties are derived from established practice in the field and mirror the properties from Ken Kennedy’sOptimizing Compilers for Modern Architectures. The key idea of legality of loop transformations expressed by Kennedy is that_the lexicographic order of all dependence vectors must be preserved_.

This can be better captured directly at the loop level thanks to specific iterator types, among which: parallel, reduction, partition,permutable/monotonic, sequential, dependence distance, …

These types are traditionally the result of complex dependence analyses and have been referred to as “_bands_” in the polyhedral community (e.g. parallel bands, permutable bands, etc, inISL schedule tree parlance).

Specifying the information declaratively in a linalg.generic allows conveying properties that may be hard (or even impossible) to derive from lower-level information. These properties can be brought all the way to the moment when they are useful for transformations, used and then discarded.

Additionally, these properties may also be viewed as a contract that the frontend/user guarantees and that the compiler may take advantage of. The common example is the use of data-dependent reduction semantics for specifying histogram computations. If the frontend has additional knowledge that proper atomic operations are available, it may be better to specify parallel semantics and use the special atomic in the computation region.

At this time, Linalg only has an explicit use for parallel and _reduction_loops but previous experience shows that the abstraction generalizes.

Property 4: The Compute Payload is Specified With a Region

A linalg.generic op has a compute payload that is fully generic thanks to the use ofRegions.

The region takes as arguments the scalar elemental types of the tensor or buffer operands of the linalg.generic. For flexibility and ability to match library calls, additional special values may be passed. For instance, a linalg.filloperation takes a buffer and an additional scalar value.

At this time there are no additional restrictions to the region semantics. This is meant to allow the exploration of various design tradeoffs at the intersection of regions and iterator types. In particular, the frontend is responsible for the semantics of iterator types to correspond to the operations inside the region: the region can capture buffers arbitrarily and write into them. If this conflicts with some parallel iterator requirement, this is undefined behavior.

Previous examples already elaborate compute payloads with an unregistered function "some_compute". The following code snippet shows what the result will be when using a concrete operation addf:

// File name: example3.mlir
#map = affine_map<(i, j) -> (i, j)>

#attrs = {
  indexing_maps = [#map, #map, #map],
  iterator_types = ["parallel", "parallel"]
}

func.func @example(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
  linalg.generic #attrs
  ins(%A, %B: memref<?x?xf32>, memref<?x?xf32>)
  outs(%C: memref<?x?xf32>) {
    ^bb0(%a: f32, %b: f32, %c: f32):
      %d = arith.addf %a, %b : f32
      linalg.yield %d : f32
  }

  return
}

This function basically element-wise adds up two matrices (%A and %B) and stores the result into another one (%C).

The property “_The Compute Payload is Specified With a Region_” is materialized by a lowering into a form that will resemble:

func.func @example(%arg0: memref<?x?xf32>, %arg1: memref<?x?xf32>, %arg2: memref<?x?xf32>) {
  %c0 = arith.constant 0 : index
  %c1 = arith.constant 1 : index
  %0 = memref.dim %arg0, %c0 : memref<?x?xf32>
  %1 = memref.dim %arg0, %c1 : memref<?x?xf32>
  scf.for %arg3 = %c0 to %0 step %c1 {
    scf.for %arg4 = %c0 to %1 step %c1 {
      %2 = memref.load %arg0[%arg3, %arg4] : memref<?x?xf32>
      %3 = memref.load %arg1[%arg3, %arg4] : memref<?x?xf32>
      %4 = arith.addf %2, %3 : f32
      memref.store %4, %arg2[%arg3, %arg4] : memref<?x?xf32>
    }
  }
  return
}

In the process of lowering to loops and lower-level constructs, similar requirements are encountered, as are discussed in theinlined call op proposal. We expect to be able to reuse the common lower-level infrastructure provided it evolves to support both region arguments and captures.

Property 5: May Map To an External Library Call

A linalg.generic op may map to an external library call by specifying aSymbolAttr. At this level of abstraction, the important glue is the ability to perform transformations that preserve the structure necessary to call the external library after different transformations have been applied.

This involves considerations related to preservation of op semantics and integration at the ABI level. Regardless of whether one wants to use external library calls or a custom ISA, the problem for codegen is similar: preservation of a fixed granularity.

Consider the following example that adds an additional attributelibrary_call="pointwise_add" that specifies the name of an external library call we intend to use:

// File name: example4.mlir
#indexing_maps = [
  affine_map<(i, j) -> (i, j)>,
  affine_map<(i, j) -> (i, j)>,
  affine_map<(i, j) -> (i, j)>
]

#attrs = {
  indexing_maps = #indexing_maps,
  iterator_types = ["parallel", "parallel"],
  library_call = "pointwise_add"
}

func.func @example(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
  linalg.generic #attrs
  ins(%A, %B: memref<?x?xf32>, memref<?x?xf32>)
  outs(%C: memref<?x?xf32>) {
  ^bb0(%a: f32, %b: f32, %c: f32):
    %d = arith.addf %a, %b : f32
    linalg.yield %d : f32
  }
  return
}

The property “_Map To an External Library Call_” is materialized by a lowering into a form that will resemble:

// Run: mlir-opt example4.mlir -convert-linalg-to-std

func.func @example(%arg0: memref<?x?xf32>, %arg1: memref<?x?xf32>, %arg2: memref<?x?xf32>) {
  %0 = memref.cast %arg0 : memref<?x?xf32> to memref<?x?xf32, strided<[?, ?], offset: ?>>
  %1 = memref.cast %arg1 : memref<?x?xf32> to memref<?x?xf32, strided<[?, ?], offset: ?>>
  %2 = memref.cast %arg2 : memref<?x?xf32> to memref<?x?xf32, strided<[?, ?], offset: ?>>
  call @pointwise_add(%0, %1, %2) : (memref<?x?xf32, strided<[?, ?], offset: ?>>,
    memref<?x?xf32, strided<[?, ?], offset: ?>>, memref<?x?xf32, strided<[?, ?], offset: ?>>) -> ()
  return
}
func.func @pointwise_add(memref<?x?xf32, strided<[?, ?], offset: ?>>,
                         memref<?x?xf32, strided<[?, ?], offset: ?>>,
                         memref<?x?xf32, strided<[?, ?], offset: ?>>) attributes {llvm.emit_c_interface}

Which, after lowering to LLVM resembles:

// Run: mlir-opt example4.mlir -convert-linalg-to-std | mlir-opt -convert-func-to-llvm
// Some generated code are omitted here.
func.func @example(%arg0: !llvm<"float*">, ...) {
  ...
  llvm.call @pointwise_add(...) : (!llvm<"float*">, ...) -> ()
  return
}

llvm.func @pointwise_add(%arg0: !llvm<"float*">, ...) attributes {llvm.emit_c_interface} {
  ...
  llvm.call @_mlir_ciface_pointwise_add(%9, %19, %29) : (!llvm."{ float*, float*, i64, [2 x i64], [2 x i64] }*">, !llvm<"{ f32*, f32*, i64, [2 x i64], [2 x i64] }*">, !llvm<"{ float*, float*, i64, [2 x i64], [2 x i64] }
*">) -> ()
  llvm.return
}
llvm.func @_mlir_ciface_pointwise_add(!llvm."{ float*, float*, i64, [2 x i64], [2 x i64] }*">, !llvm<"{ f32*, f32*, i64, [2 x i64], [2 x i64] }*">, !llvm<"{ f32*, f32*, i64, [2 x i64], [2 x i64] }*">) attributes {llvm.emit_c_interface}

Convention For External Library Interoperability

The linalg dialect adopts a convention that is similar to BLAS when offloading operations to fast library implementations: pass a non-owning pointer to input and output data with additional metadata. This convention is also found in libraries such as MKL, OpenBLAS, BLIS, cuBLAS, cuDNN, etc.. and more generally at interface points across language boundaries (e.g. C++ / Python).

Generally, linalg passes non-owning pointers to View data structures to pre-compiled library calls linked externally.

There is anongoing discussionon the topic of extending interoperability in the presence of key attributes.

Property 6: Perfectly Nested Writes To The Whole Output Operands

Perfectly nested loops form a particularly important class of structure that enables key loop transformations such as tiling and mapping to library calls. Unfortunately, this type of structure is easily broken by transformations such as partial loop fusion. Tiling and mapping to library calls become more challenging, or even infeasible. Linalg ops adopt perfect-nestedness as a first-class property: the structure cannot be broken and is transported in the IR by construction.

A linalg.generic op represents a perfectly nested loop nest that writes the entire memory region. This is a structural constraint across regions and loops that has proven to be key in simplifying transformations.

One particular point to mention is that converting imperfectly nested code into perfectly nested code can often be done with enough loop distribution and embedding of conditionals down to the innermost loop level.

Previous experience with Tensor Comprehensions gave us the intuition that forcing innermost control-flow nesting is a lot like writing data-parallel code with arrays of boolean values and predication. This type of trick has also been used before in polyhedral compilers to convert non-affine control into affine compute dependencies.

While it may be possible to automate such rewrites from generic IR,linalg.generic just forces the semantics for now.

The key implication is that this conversion to deep predication needs to be undone once we are done with Linalg transformations. After iterators and induction variables are materialized (i.e. after lowering out oflinalg.generic occurred), the overall performance will be greatly influenced by the quality of canonicalizations, foldings and Loop Independent Code Motion(LICM).

In the grander scheme, the reliance on late LICM was deemed a necessary risk.

Putting it Together

As it stands, the six properties above define the semantics of alinalg.generic op. It is an open question whether all of these semantics are strictly necessary in practice and whether some should or could be derived automatically while still maintaining thecore guiding principles.

For the time being, we have settled on the combination of these properties because of empirical evidence building and working on multiple high-level compilers. As we lay those down and engage more with the community, we expect multiple rounds of discussions and design changes to the original architecture.

Data Representation: Views

The current implementation uses theStrided MemRef (a.k.a View)abstraction. The name View is used interchangeably in linalg to signify_Strided MemRef_. In the future we expect to use other structured data types and support ragged, mixed-sparse and other types. We expect to draw on the experience from existing LIFT abstractions forsparse andposition-dependent arrays.

Metadata Ops

A set of ops that manipulate metadata but do not move memory. These ops takeview operands + extra attributes and return new views. The returned views generally alias the operand view. At the moment the existing ops are:

* `memref.view`,
* `memref.subview`,
* `memref.transpose`.
* `linalg.slice`,
* `linalg.reshape`,

Future ops are added on a per-need basis but should include:

* `linalg.tile`,
* `linalg.intersection`,
* `linalg.convex_union`,
* `linalg.difference` (would need to work on a list of views).

These additional operations correspond to abstractions that have been known to work in the field of large-scale distributed stencil computations.

In a longer-term future, the abstractions fromLegion data-centric programming modelseem generally appealing.

Named Payload-Carrying Ops

Additionally, linalg provides a small subset of commonly named operations:

* `linalg.fill`,
* `linalg.dot`,
* `linalg.matmul`,
* `linalg.conv`.

These named operations adhere to the linalg.generic op interface. Work is in progress to define declarative mechanisms to automatically generate named ops from a description in terms of only the generic op interface.

This is the main reason there are only a small number of ops today: we expect them to be auto-generated from Tablegen soon.

Named Payload Ops Specification

Linalg provides a declarative specification and a generation tool (mlir-linalg-ods-gen) to automatically produce named ops from a notation that is inspired by Einstein notation.

The syntax and semantics used in mlir-linalg-ods-gen are very much in flight and borrow from Tensor Comprehensions (TC) but differ in a few dimensions, to better adapt to Linalg:

1. The input and output tensor parameters are specified as id : type(symbolic-affine-expression-list) (e.g. A : f32(M, N + M)) and each new symbol is discovered eagerly. TC on the other hand does not allow general symbolic affine expressions.
2. The output shapes are specified explicitly, in TC they are always derived from the input shapes.
3. The operations used to specify computations use EDSC intrinsics so that they can easily be parsed and emitted into a simple region builder without resorting to more general MLIR parsing.
4. Reduction dimensions are specified with angle bracket notation on the operation they apply to (e.g. std_add<k> specifies that k is a reduction dimension). In TC, the reduction dimensions are inferred. If one of the operand is not used in any expressions, it will be considered a shape-only operand, and the result of the indexing_map will be reduction dimensions.
5. The parallel and reduction dimension are ordered by the textual program order. For instance, in the comprehension O(i, j) = std_add<k, l>(...),i (resp. j) is a parallel iterator encoded by affine dimension of position 0 (resp. 1); k (resp. l) is a reduction iterator encoded by an affine dimension of position 2 (resp. 3).
6. A list of attributes can be defined for the op with the format of attr( strides: 2xi32) and referenced in comprehension like strides[0]. These attribute uses will be parsed as affine symbols to generate op definition and implementation. For a concrete op instance, the runtime constant values from the attributes will be used to replace the affine symbols and simplify the indexing maps.

These decisions and syntax are subject to evolution and change. In particular, op-specific attributes, dynamic ranks, some form of templating, shape calculation function specification, etc. may be added in the future.

At this time, the following restrictions are imposed on the syntax and semantics:

1. Each def may only contain a single comprehension but each comprehension may perform multiple updates.
2. Each tensor may only be used with a single indexing expression.

A """-wrapped doc string can be attached to the named op. It should contain a oneliner for summary first, followed by lengthy description.

The following specification may be used to define a named batchmatmul op:

def batchmatmul(A: f32(Batch, M, K), B: f32(K, N)) -> (C: f32(Batch, M, N))
"""Batch matrix-multiply operation.

This operation performs batch matrix-multiply over ...
"""
{
  C(b, m, n) = std_addf<k>(std_mulf(A(b, m, k), B(k, n)));
}

When mlir-linalg-ods-gen -gen-ods-decl=1 is called, the following ODS is produced:

def batchmatmulOp : LinalgNamedStructured_Op<"batchmatmul", [
  NInputs<2>,
  NOutputs<1>,
  NamedStructuredOpTrait]> { ... }

When mlir-linalg-ods-gen -gen-impl=1 is called, the following C++ is produced:

std::optional<SmallVector<StringRef, 8>> batchmatmul::referenceIterators() {
  return SmallVector<StringRef, 8>{
    getParallelIteratorTypeName(),
    getParallelIteratorTypeName(),
    getParallelIteratorTypeName(),
    getReductionIteratorTypeName() };
}
std::optional<SmallVector<AffineMap, 8>> batchmatmul::referenceIndexingMaps() {
  MLIRContext *context = getContext();
  AffineExpr d0, d1, d2, d3;
  bindDims(context, d0, d1, d2, d3);
  return SmallVector<AffineMap, 8>{
      AffineMap::get(4, 0, {d0, d1, d3}),
      AffineMap::get(4, 0, {d3, d2}),
      AffineMap::get(4, 0, {d0, d1, d2}) };
}
void batchmatmul::regionBuilder(ArrayRef<BlockArgument> args) {
  using namespace edsc;
  using namespace intrinsics;
  Value _0(args[0]), _1(args[1]), _2(args[2]);
  Value _4 = std_mulf(_0, _1);
  Value _5 = std_addf(_2, _4);
  (linalg_yield(ValueRange{ _5 }));
}

YAML Based Named Structured Ops

Linalg provides a declarative generation tool (mlir-linalg-ods-yaml-gen) to automatically produce named ops from a YAML-based op description format intended to capture the structure of the named ops. The YAML-based op descriptions are generated from a higher levelDSL and are not meant to be edited directly.

This facility is currently in flight and is intended to subsume the above when ready. See the C++ class to YAML mapping traits inmlir-linalg-ods-yaml-gen.cpp as the source of truth for the schema.

Most of the above documentation roughly applies to this path and will be ported as migration continues.

Open Issues and Design Alternatives

Multiple open issues and design alternatives are in flight and it is time to lay them out for the community to discuss and pick apart:

1. Should linalg.generic support nesting?
2. Should linalg.generic regions take views or only scalars?
3. Should we try to solve automatic differentiation at this level of abstraction?
4. Are all the six properties really necessary?
5. Is this relying too much on declarative specification and would we be better off relying more on analyses?
6. Is this general enough for the community’s needs? If not how should this be extended, if at all? …

These key questions (and much more) should be really thought of in the general context of MLIR in which different levels of IR interoperate seamlessly. In practice, it is not necessary (or beneficial) to try and solve all problems in the same IR.

Operations

source

linalg.abs (linalg::AbsOp)

Applies abs(x) elementwise.

No numeric casting is performed on the input operand.

Traits: AttrSizedOperandSegments, RecursiveMemoryEffects, SingleBlockImplicitTerminator<YieldOp>, SingleBlock

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, LinalgStructuredInterface, MemoryEffectOpInterface, ReifyRankedShapedTypeOpInterface

Operands:

Results:

linalg.add (linalg::AddOp)

Adds two tensors elementwise.

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a linalg.broadcast + linalg.add sequence can be lowered to alinalg.generic with different affine maps for the two operands.

Traits: AttrSizedOperandSegments, RecursiveMemoryEffects, SingleBlockImplicitTerminator<YieldOp>, SingleBlock

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, LinalgStructuredInterface, MemoryEffectOpInterface, ReifyRankedShapedTypeOpInterface

Operands:

Results:

linalg.batch_matmul (linalg::BatchMatmulOp)

Performs a batched matrix multiplication of two 3D inputs.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Broadcast and Transpose semantics can be appiled by specifying the explicit attribute
'indexing_maps' as shown below. This is a list attribute, so must include maps for all
arguments if specified.

Example Transpose:
```mlir
linalg.batch_matmul
    indexing_maps = [affine_map<(batch, m, n, k) -> (batch, k, m)>, // transpose
                     affine_map<(batch, m, n, k) -> (batch, k, n)>,
                     affine_map<(batch, m, n, k) -> (batch, m, n)>]
    ins(%arg0, %arg1 : memref<2x5x3xf32>,memref<2x5x7xf32>)
    outs(%arg2: memref<2x3x7xf32>)

Example Broadcast:

linalg.batch_matmul
    indexing_maps = [affine_map<(batch, m, n, k) -> (k)>,           // broadcast
                     affine_map<(batch, m, n, k) -> (batch, k, n)>,
                     affine_map<(batch, m, n, k) -> (batch, m, n)>]
    ins(%arg0, %arg1 : memref<5xf32>, memref<2x5x7xf32>)
    outs(%arg2: memref<2x3x7xf32>)

Example Broadcast and Transpose:

linalg.batch_matmul
    indexing_maps = [affine_map<(batch, m, n, k) -> (m, k)>,        // broadcast
                     affine_map<(batch, m, n, k) -> (batch, n, k)>, // transpose
                     affine_map<(batch, m, n, k) -> (batch, m, n)>]
    ins(%arg0, %arg1 : memref<3x5xf32>, memref<2x7x5xf32>)
    outs(%arg2: memref<2x3x7xf32>)

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute      | MLIR Type                  | Description                                 |
| -------------- | -------------------------- | ------------------------------------------- |
| indexing\_maps | ::mlir::ArrayAttr          | AffineMap array attribute                   |
| cast           | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.batch_matmul_transpose_a` (linalg::BatchMatmulTransposeAOp)

_Performs a batched matrix multiplication of two 3D inputs where lhs operand has its non-batch dimensions transposed._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.batch_matmul_transpose_b` (linalg::BatchMatmulTransposeBOp)

_Performs a batched matrix multiplication of two 3D inputs where rhs operand has its non-batch dimensions transposed._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.batch_matvec` (linalg::BatchMatvecOp)

_Performs a batched matrix-vector multiplication._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.batch_mmt4d` (linalg::BatchMmt4DOp)

_Performs a batched matrix-matrix-transpose multiplication of two batched-4D (5D) inputs._

Besides the outermost batch dimension has the same semantic as linalg.batch\_matmul, the differences from linalg.batch\_matmul in the non-batch dimensions are the same as linalg.mmt4d vs. linalg.matmul. See the description of lingalg.mmt4d.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.batch_reduce_matmul` (linalg::BatchReduceMatmulOp)

_Performs a batch-reduce matrix multiplication on two inputs. The partial multiplication results are reduced into a 2D output._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Broadcast and Transpose semantics can be applied by specifying the explicit attribute ‘indexing\_maps’ as shown below. This is a list attribute, so must include maps for all arguments if specified.

Example Transpose:

linalg.batch_reduce_matmul indexing_maps = [affine_map<(batch, m, n, k) -> (batch, k, m)>, // transpose affine_map<(batch, m, n, k) -> (batch, k, n)>, affine_map<(batch, m, n, k) -> (m, n)>] ins(%arg0, %arg1 : memref<2x5x3xf32>,memref<2x5x7xf32>) outs(%arg2: memref<3x7xf32>)

Example Broadcast:

linalg.batch_reduce_matmul indexing_maps = [affine_map<(batch, m, n, k) -> (k)>, // broadcast affine_map<(batch, m, n, k) -> (batch, k, n)>, affine_map<(batch, m, n, k) -> (m, n)>] ins(%arg0, %arg1 : memref<5xf32>, memref<2x5x7xf32>) outs(%arg2: memref<3x7xf32>)

Example Broadcast and Transpose:

linalg.batch_reduce_matmul indexing_maps = [affine_map<(batch, m, n, k) -> (m, k)>, // broadcast affine_map<(batch, m, n, k) -> (batch, n, k)>, // transpose affine_map<(batch, m, n, k) -> (m, n)>] ins(%arg0, %arg1 : memref<3x5xf32>, memref<2x7x5xf32>) outs(%arg2: memref<3x7xf32>)

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute      | MLIR Type                  | Description                                 |
| -------------- | -------------------------- | ------------------------------------------- |
| indexing\_maps | ::mlir::ArrayAttr          | AffineMap array attribute                   |
| cast           | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.batch_vecmat` (linalg::BatchVecmatOp)

_Performs a batched matrix-vector multiplication._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.broadcast` (linalg::BroadcastOp)

_Static broadcast operator_

Broadcast the input into the given shape by adding `dimensions`.

Example:

%bcast = linalg.broadcast ins(%input:tensor<16xf32>) outs(%init:tensor<16x64xf32>) dimensions = [1]

Traits: `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `OpAsmOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute  | MLIR Type                 | Description               |
| ---------- | ------------------------- | ------------------------- |
| dimensions | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |

#### Operands:

| Operand | Description                                                   |
| ------- | ------------------------------------------------------------- |
| input   | memref of any type values or ranked tensor of any type values |
| init    | memref of any type values or ranked tensor of any type values |

#### Results:

| Result | Description                           |
| ------ | ------------------------------------- |
| result | variadic of tensor of any type values |

### `linalg.ceil` (linalg::CeilOp)

_Applies ceil(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.contract` (linalg::ContractOp)

_Perform a contraction on two inputs, accumulating into the third._

The semantics of contracting inputs `A` and `B` on top of `C` to produce output `D` is given by

`D[H] = (SUM_{(I ∪ J) \ H} A[I] * B[J]) + C[H]`

where `I`, `J`, and `H` are tuples of (pairwise distinct) dimension identifiers - meant to range over valid indices - corresponding to the results of the mandatory (projected permutation) `indexing_maps` for `A`,`B` and `C`. `SUM_{dims}` means reduce over all valid indices for the dimensions in the set `dims` (with `I`, `J`, and `K` treated as _sets_ of dim identifiers).

The iteration space consists of all dimensions in `I`, `J` and `H`, i.e. the domain of each of the `affine_map`s. Like for einsums, the iteration type of each dim is inferred and is either:

* reduction: the dim is used to index into `A` and `B` but not `C`. Per the above semantics, these dims will be contracted, i.e. reduced over.
* parallel: the dim is used to index into `C` and at least one of `A` and`B`, and - deriving from matmul terminology - is either an “M-like” dim (if used on `A` and `C`), an “N-like” dim (if used on `B` and `C`) or a “batch”-dim (if used to index into `A`, `B`, and `C`).

For example, batch-matmul is given by `I = ⟨ b, m, k ⟩`, `J = ⟨ b, k, n ⟩`,`H = ⟨ b, m, n ⟩` (with `k` as a contracting reduction-dimension while `m`,`n` and `b` have parallel iteration-type) and gets represented as:

%D = linalg.contract indexing_maps = [affine_map<(batch, m, n, k) -> (batch, m, k)>, affine_map<(batch, m, n, k) -> (batch, k, n)>, affine_map<(batch, m, n, k) -> (batch, m, n)>] ins(%A, %B: tensor<?x?x?xf32>, tensor<?x?x?xf32>) outs(%C: tensor<?x?x?xf32>) -> tensor<?x?x?xf32>

Note that by permuting dims in the `affine_map`s’ results, accesses to to the inputs and output can be arbitrarily transposed. Similarly, arbitrary broadcasts can be achieved through leaving out dims on either input operand. For example, the following is a variant of batch-matmul with a transposition applied to `A` while `B`’s 2D-matrix gets broadcasted along the batch dim:

linalg.contract indexing_maps = [affine_map<(batch, m, n, k) -> (batch, k, m)>, affine_map<(batch, m, n, k) -> (k, n)>, affine_map<(batch, m, n, k) -> (batch, m, n)>] ins(%A, %B: memref<?x?x?xf32>, memref<?x?xf32>) outs(%C: memref<?x?x?xf32>)

Numeric casting is performed on the operands to the inner multiplication, promoting/truncating them to the same data type as the accumulator/output.

TODO: Allow control over the combining/accumulating op and possibly the multiplication op.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute      | MLIR Type                  | Description                                 |
| -------------- | -------------------------- | ------------------------------------------- |
| indexing\_maps | ::mlir::ArrayAttr          | AffineMap array attribute                   |
| cast           | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                           |
| --------------- | ------------------------------------- |
| result\_tensors | variadic of shaped of any type values |

### `linalg.conv_1d_ncw_fcw` (linalg::Conv1DNcwFcwOp)

_Performs 1-D convolution._

Layout:

* Input: NCW.
* Kernel: FCW.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_1d_nwc_wcf` (linalg::Conv1DNwcWcfOp)

_Performs 1-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_1d` (linalg::Conv1DOp)

_Performs 1-D convolution with no channels._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nchw_fchw` (linalg::Conv2DNchwFchwOp)

_Performs 2-D convolution._

Layout:

* Input: NCHW.
* Kernel: FCHW.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nchw_fchw_q` (linalg::Conv2DNchwFchwQOp)

_Performs 2-D convolution with zero point offsets._

Layout:

* Input: NCHW.
* Kernel: FCHW.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. This includes the zero point offsets common to quantized operations.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_ngchw_fgchw` (linalg::Conv2DNgchwFgchwOp)

_Performs 2-D grouped convolution._

Layout:

* Input: NGCHW.
* Kernel: FGCHW.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_ngchw_gfchw` (linalg::Conv2DNgchwGfchwOp)

_Performs 2-D grouped convolution._

Layout:

* Input: NGCHW.
* Kernel: GFCHW.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_ngchw_gfchw_q` (linalg::Conv2DNgchwGfchwQOp)

_Performs 2-D grouped convolution with zero-point offsets._

Layout:

* Input: NGCHW.
* Kernel: GFCHW.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. This includes the zero point offsets common to quantized operations.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nhwc_fhwc` (linalg::Conv2DNhwcFhwcOp)

_Performs 2-D convolution._

Layout:

* Input: NHWC.
* Kernel: FHWC.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nhwc_fhwc_q` (linalg::Conv2DNhwcFhwcQOp)

_Performs 2-D convolution with zero point offsets._

Layout:

* Input: NHWC.
* Kernel: FHWC.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. This includes the zero point offsets common to quantized operations.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nhwc_hwcf` (linalg::Conv2DNhwcHwcfOp)

_Performs 2-D convolution._

Layout:

* Input: NHWC.
* Kernel: HWCF.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nhwc_hwcf_q` (linalg::Conv2DNhwcHwcfQOp)

_Performs 2-D convolution with zero point offsets._

Layout:

* Input: NHWC.
* Kernel: HWCF.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. This includes the zero point offsets common to quantized operations.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nhwgc_gfhwc` (linalg::Conv2DNhwgcGfhwcOp)

_Performs 2-D grouped convolution._

Layout:

* Input: NHWGC.
* Kernel: GFHWC.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d_nhwgc_gfhwc_q` (linalg::Conv2DNhwgcGfhwcQOp)

_Performs 2-D grouped convolution with zero point offsets._

Layout:

* Input: NHWGC.
* Kernel: GFHWC.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. This includes the zero point offsets common to quantized operations.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_2d` (linalg::Conv2DOp)

_Performs 2-D convolution with no channels._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_3d_ncdhw_fcdhw` (linalg::Conv3DNcdhwFcdhwOp)

_Performs 3-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_3d_ndhwc_dhwcf` (linalg::Conv3DNdhwcDhwcfOp)

_Performs 3-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_3d_ndhwc_dhwcf_q` (linalg::Conv3DNdhwcDhwcfQOp)

_Performs 3-D convolution with zero point offsets._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. This includes the zero point offsets common to quantized operations.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.conv_3d` (linalg::Conv3DOp)

_Performs 3-D convolution with no channels._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.copy` (linalg::CopyOp)

_Copies the tensor elementwise._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                  | Description                                 |
| --------- | -------------------------- | ------------------------------------------- |
| cast      | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_1d_ncw_cw` (linalg::DepthwiseConv1DNcwCwOp)

_Performs depth-wise 1-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. Multiplier is set to 1 which is a special case for most depthwise convolutions.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_1d_nwc_wc` (linalg::DepthwiseConv1DNwcWcOp)

_Performs depth-wise 1-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. Multiplier is set to 1 which is a special case for most depthwise convolutions.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_1d_nwc_wcm` (linalg::DepthwiseConv1DNwcWcmOp)

_Performs depth-wise 1-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_2d_nchw_chw` (linalg::DepthwiseConv2DNchwChwOp)

_Performs depth-wise 2-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. Multiplier is set to 1 which is a special case for most depthwise convolutions.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_2d_nhwc_hwc` (linalg::DepthwiseConv2DNhwcHwcOp)

_Performs depth-wise 2-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. Multiplier is set to 1 which is a special case for most depthwise convolutions.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_2d_nhwc_hwc_q` (linalg::DepthwiseConv2DNhwcHwcQOp)

_Performs depth-wise 2-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_2d_nhwc_hwcm` (linalg::DepthwiseConv2DNhwcHwcmOp)

_Performs depth-wise 2-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_2d_nhwc_hwcm_q` (linalg::DepthwiseConv2DNhwcHwcmQOp)

_Performs depth-wise 2-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_3d_ncdhw_cdhw` (linalg::DepthwiseConv3DNcdhwCdhwOp)

_Performs depth-wise 3-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. Multiplier is set to 1 which is a special case for most depthwise convolutions.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_3d_ndhwc_dhwc` (linalg::DepthwiseConv3DNdhwcDhwcOp)

_Performs depth-wise 3-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. Multiplier is set to 1 which is a special case for most depthwise convolutions.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.depthwise_conv_3d_ndhwc_dhwcm` (linalg::DepthwiseConv3DNdhwcDhwcmOp)

_Performs depth-wise 3-D convolution._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.div` (linalg::DivOp)

_Divides the first tensor by the second tensor, elementwise._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.div` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.div_unsigned` (linalg::DivUnsignedOp)

_Divides the first tensor by the second tensor, elementwise. For integer types, performs an unsigned division._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.div` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.dot` (linalg::DotOp)

_Performs a dot product of two vectors to a scalar result._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.elementwise` (linalg::ElementwiseOp)

_Performs element-wise operation_

The attribute `kind` describes arithmetic operation to perform. The operation kind can be unary (e.g. max), binary (e.g. add) or ternary (e.g. select).

By default, all indexing maps are identities. In the case of default indexing map, all input and output shapes must match. The number of dims in each of the identity maps is equal to the rank of the output type.

Affine-maps for operands and result are required to be provided by the user when a transpose and/or broadcast is needed on any operand. When a map is not provided, default identity maps are inferred for each operand.

Iterator-types are always all `parallel`. Iterator-types are needed for constructing the underlying structured op.

The number of dims of the iterator-types are inferred from the rank of the result type.

Example:

Defining a unary linalg.elementwise with default indexing-map:

%exp = linalg.elementwise kind=#linalg.elementwise_kind ins(%x : tensor<4x16x8xf32>) outs(%y: tensor<4x16x8xf32>) -> tensor<4x16x8xf32>

Defining a binary linalg.elementwise with user-defined indexing-map:

%add = linalg.elementwise kind=#linalg.elementwise_kind indexing_maps = [#transpose, #broadcast, #identity] ins(%exp, %arg1 : tensor<4x16x8xf32>, tensor<4x16xf32>) outs(%arg2: tensor<4x8x16xf32>) -> tensor<4x8x16xf32>

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute      | MLIR Type                           | Description                                                                                                                 |
| -------------- | ----------------------------------- | --------------------------------------------------------------------------------------------------------------------------- |
| kind           | ::mlir::linalg::ElementwiseKindAttr | allowed 32-bit signless integer cases: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 |
| indexing\_maps | ::mlir::ArrayAttr                   | AffineMap array attribute                                                                                                   |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.elemwise_binary` (linalg::ElemwiseBinaryOp)

_Applies the binary function fun elementwise._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                                         |
| --------- | ---------------------------- | ------------------------------------------------------------------- |
| fun       | ::mlir::linalg::BinaryFnAttr | allowed 32-bit signless integer cases: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| cast      | ::mlir::linalg::TypeFnAttr   | allowed 32-bit signless integer cases: 0, 1                         |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.elemwise_unary` (linalg::ElemwiseUnaryOp)

_Applies the unary function fun elementwise._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                   | Description                                                                     |
| --------- | --------------------------- | ------------------------------------------------------------------------------- |
| fun       | ::mlir::linalg::UnaryFnAttr | allowed 32-bit signless integer cases: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 |
| cast      | ::mlir::linalg::TypeFnAttr  | allowed 32-bit signless integer cases: 0, 1                                     |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.erf` (linalg::ErfOp)

_Applies erf(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.exp` (linalg::ExpOp)

_Applies exp(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.fill` (linalg::FillOp)

_Fills the output tensor with the given value._

Works for arbitrary ranked output tensors since the operation performs scalar accesses only and is thus rank polymorphic. Numeric casting is performed on the value operand, promoting it to the same data type as the output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgFillOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.fill_rng_2d` (linalg::FillRng2DOp)

_Fills the output tensor with pseudo random numbers._

The operation generations pseudo random numbers using a linear congruential generator. It provides no guarantees regarding the distribution of the generated random numbers. Instead of generating the random numbers sequentially, it instantiates one random number generator per data element and runs them in parallel. The seed operand and the indices of the data element seed the random number generation. The min and max operands limit the range of the generated random numbers.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.floor` (linalg::FloorOp)

_Applies floor(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.generic` (linalg::GenericOp)

Generic Linalg op form where the key properties of the computation are specified as attributes. In pretty form, a `linalg.generic` op is written as:

linalg.generic #trait_attribute ins(%A, %B : memref<?x?xf32, stride_specification>, memref<?x?xf32, stride_specification>) outs(%C : memref<?x?xf32, stride_specification>) attrs = {other-optional-attributes} {region}

Where #trait\_attributes is an alias of a dictionary attribute containing:

* doc \[optional\]: a documentation string
* indexing\_maps: a list of AffineMapAttr, one AffineMapAttr per each input and output view. Such AffineMapAttr specifies the mapping between the loops and the indexing within each view.
* library\_call \[optional\]: a StringAttr containing the name of an external library function that the linalg.generic operation maps to. The external library is assumed to be dynamically linked and no strong compile-time guarantees are provided. In the absence of such a library call, linalg.generic will always lower to loops.
* iterator\_types: an ArrayAttr specifying the type of the enclosing loops. Each element of the list represents and iterator of one of the following types: parallel, reduction, window

Example: Defining a #matmul\_trait attribute in MLIR can be done as follows:

#matmul_accesses = [ (m, n, k) -> (m, k), (m, n, k) -> (k, n), (m, n, k) -> (m, n) ] #matmul_trait = { doc = "C(m, n) += A(m, k) * B(k, n)", indexing_maps = #matmul_accesses, library_call = "linalg_matmul", iterator_types = ["parallel", "parallel", "reduction"] }

And can be reused in multiple places as:

linalg.generic #matmul_trait ins(%A, %B : memref<?x?xf32, stride_specification>, memref<?x?xf32, stride_specification>) outs(%C : memref<?x?xf32, stride_specification>) {other-optional-attributes} { ^bb0(%a: f32, %b: f32, %c: f32) : %d = arith.mulf %a, %b: f32 %e = arith.addf %c, %d: f32 linalg.yield %e : f32 }

This may lower to either:

call @linalg_matmul(%A, %B, %C) : (memref<?x?xf32, stride_specification>, memref<?x?xf32, stride_specification>, memref<?x?xf32, stride_specification>) -> ()

or IR resembling:

scf.for %m = %c0 to %M step %c1 { scf.for %n = %c0 to %N step %c1 { scf.for %k = %c0 to %K step %c1 { %a = load %A[%m, %k] : memref<?x?xf32, stride_specification> %b = load %B[%k, %n] : memref<?x?xf32, stride_specification> %c = load %C[%m, %n] : memref<?x?xf32, stride_specification> %d = arith.mulf %a, %b: f32 %e = arith.addf %c, %d: f32 store %e, %C[%m, %n] : memref<?x?x?xf32, stride_specification> } } }

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `OpAsmOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute       | MLIR Type          | Description                      |
| --------------- | ------------------ | -------------------------------- |
| indexing\_maps  | ::mlir::ArrayAttr  | AffineMap array attribute        |
| iterator\_types | ::mlir::ArrayAttr  | Iterator type should be an enum. |
| doc             | ::mlir::StringAttr | string attribute                 |
| library\_call   | ::mlir::StringAttr | string attribute                 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.index` (linalg::IndexOp)

_Linalg index operation_

Syntax:

operation ::= linalg.index dimattr−dict‘:‘type(dim attr-dict : type(dimattr−dict‘:‘type(result)

The `linalg.index` operation returns the iteration index of the immediately enclosing linalg structured operation for the iteration dimension `dim`. The`dim` attribute specifies the position of the accessed dimension in the indexing map domain.

Example:

#map = affine_map<(i, j) -> (i, j)> linalg.generic {indexing_maps = [#map, #map], iterator_types = ["parallel", "parallel"]} outs(%I, %J : memref<?x?xindex>, memref<?x?xindex>) { ^bb0(%arg0 : index, %arg1 : index): // Access the outer iteration dimension i %i = linalg.index 0 : index // Access the inner iteration dimension j %j = linalg.index 1 : index linalg.yield %i, %j : index, index }

This may lower to IR resembling:

%0 = dim %I, %c0 : memref<?x?xindex> %1 = dim %I, %c1 : memref<?x?xindex> scf.for %i = %c0 to %0 step %c1 { scf.for %j = %c0 to %1 step %c1 { store %i, %I[%i, %j] : memref<?x?xindex> store %j, %J[%i, %j] : memref<?x?xindex> } }

Traits: `AlwaysSpeculatableImplTrait`

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

Effects: `MemoryEffects::Effect{}`

#### Attributes:

| Attribute | MLIR Type           | Description                                                |
| --------- | ------------------- | ---------------------------------------------------------- |
| dim       | ::mlir::IntegerAttr | 64-bit signless integer attribute whose minimum value is 0 |

#### Results:

| Result | Description |
| ------ | ----------- |
| result | index       |

### `linalg.pack` (linalg::PackOp)

_Linalg.pack operation_

Syntax:

operation ::= linalg.pack $source (padding_value ( paddingvalue‘:‘type(padding_value^ : type(paddingv​alue‘:‘type(padding_value) ))? (outer_dims_perm = $outer_dims_perm^)? inner_dims_pos = $inner_dims_pos inner_tiles = custom($inner_tiles, $static_inner_tiles) into destattr−dict‘:‘type(dest attr-dict : type(destattr−dict‘:‘type(source) -> type($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 = linalg.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 = linalg.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 = linalg.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`, `LinalgRelayoutOpInterface`, `NoMemoryEffect (MemoryEffectOpInterface)`, `OpAsmOpInterface`, `ReifyRankedShapedTypeOpInterface`

Effects: `MemoryEffects::Effect{}`

#### Attributes:

| Attribute            | MLIR Type                 | Description               |
| -------------------- | ------------------------- | ------------------------- |
| outer\_dims\_perm    | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |
| inner\_dims\_pos     | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |
| static\_inner\_tiles | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |

#### Operands:

| Operand        | Description                      |
| -------------- | -------------------------------- |
| source         | ranked tensor of any type values |
| dest           | ranked tensor of any type values |
| padding\_value | any type                         |
| inner\_tiles   | variadic of index                |

#### Results:

| Result | Description                      |
| ------ | -------------------------------- |
| result | ranked tensor of any type values |

### `linalg.softmax` (linalg::SoftmaxOp)

_Softmax operator_

Syntax:

operation ::= linalg.softmax attr-dict dimension ( $dimension ) ins ( input‘:‘type(input : type(input‘:‘type(input) ) outs ( output‘:‘type(output : type(output‘:‘type(output) ) (-> type($result)^)?

linalg.softmax computes a numerically stable version of softmax.

For a given input tensor and a specified dimension `d`, compute:

1. the max `m` along that dimension `d`
2. f(x) = exp(x - m)
3. sum f(x) along dimension d to get l(x).
4. compute the final result f(x) / l(x).

This is an aggregate linalg operation that further reduces to a small DAG of structured operations.

Warning: Regarding the tiling capabilities, the implementation doesn’t check that the provided dimensions make sense. This is the responsability of the transformation calling the tiling to ensure that the provided sizes for each dimension make sense with respect to the semantic of softmax.

Interfaces: `AggregatedOpInterface`, `DestinationStyleOpInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`, `TilingInterface`

#### Attributes:

| Attribute | MLIR Type           | Description                       |
| --------- | ------------------- | --------------------------------- |
| dimension | ::mlir::IntegerAttr | 64-bit signless integer attribute |

#### Operands:

| Operand | Description               |
| ------- | ------------------------- |
| input   | shaped of any type values |
| output  | shaped of any type values |

#### Results:

| Result | Description                                  |
| ------ | -------------------------------------------- |
| result | variadic of ranked tensor of any type values |

### `linalg.unpack` (linalg::UnPackOp)

_Linalg.unpack operation_

Syntax:

operation ::= linalg.unpack $source (outer_dims_perm = $outer_dims_perm^)? inner_dims_pos = $inner_dims_pos inner_tiles = custom($inner_tiles, $static_inner_tiles) into destattr−dict‘:‘type(dest attr-dict : type(destattr−dict‘:‘type(source) -> type($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 = linalg.unpack %source inner_dims_pos = [0, 1] inner_tiles = [8, 32] into %dest : tensor<16x8x8x32xf32> -> tensor<128x256xf32>

// CK to KCck: %0 = linalg.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`, `LinalgRelayoutOpInterface`, `NoMemoryEffect (MemoryEffectOpInterface)`, `OpAsmOpInterface`, `ReifyRankedShapedTypeOpInterface`

Effects: `MemoryEffects::Effect{}`

#### Attributes:

| Attribute            | MLIR Type                 | Description               |
| -------------------- | ------------------------- | ------------------------- |
| outer\_dims\_perm    | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |
| inner\_dims\_pos     | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |
| static\_inner\_tiles | ::mlir::DenseI64ArrayAttr | i64 dense array attribute |

#### Operands:

| Operand      | Description                      |
| ------------ | -------------------------------- |
| source       | ranked tensor of any type values |
| dest         | ranked tensor of any type values |
| inner\_tiles | variadic of index                |

#### Results:

| Result | Description                      |
| ------ | -------------------------------- |
| result | ranked tensor of any type values |

### `linalg.winograd_filter_transform` (linalg::WinogradFilterTransformOp)

_Winograd filter transform operator_

Syntax:

operation ::= linalg.winograd_filter_transform attr-dict m ( $m ) r ( $r ) ins ( filter‘:‘type(filter : type(filter‘:‘type(filter) ) outs ( output‘:‘type(output : type(output‘:‘type(output) ) -> type($result)

Winograd Conv2D algorithm will convert linalg Conv2D operator into batched matrix multiply. Before the matrix multiply, it will convert filter and input into a format suitable for batched matrix multiply. After the matrix multiply, it will convert output to the final result tensor.

The algorithm F(m x m, r x r) is

Y = A^T x \[(G x g x G^T) @ (B^T x d x B)\] x A

The size of output Y is m x m. The size of filter g is r x r. The size of input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are transformation matrices.

This operator is defined to represent the high level concept of filter transformation (G x g x G^T) in the Winograd Conv2D algorithm.

Interfaces: `DestinationStyleOpInterface`, `TilingInterface`

#### Attributes:

| Attribute | MLIR Type           | Description                       |
| --------- | ------------------- | --------------------------------- |
| m         | ::mlir::IntegerAttr | 64-bit signless integer attribute |
| r         | ::mlir::IntegerAttr | 64-bit signless integer attribute |

#### Operands:

| Operand | Description                  |
| ------- | ---------------------------- |
| filter  | 4D tensor of any type values |
| output  | 4D tensor of any type values |

#### Results:

| Result | Description                  |
| ------ | ---------------------------- |
| result | 4D tensor of any type values |

### `linalg.winograd_input_transform` (linalg::WinogradInputTransformOp)

_Winograd input transform operator_

Syntax:

operation ::= linalg.winograd_input_transform attr-dict m ( $m ) r ( $r ) ins ( input‘:‘type(input : type(input‘:‘type(input) ) outs ( output‘:‘type(output : type(output‘:‘type(output) ) -> type($result)

Winograd Conv2D algorithm will convert linalg Conv2D operator into batched matrix multiply. Before the matrix multiply, it will convert filter and input into a format suitable for batched matrix multiply. After the matrix multiply, it will convert output to the final result tensor.

The algorithm F(m x m, r x r) is

Y = A^T x \[(G x g x G^T) @ (B^T x d x B)\] x A

The size of output Y is m x m. The size of filter g is r x r. The size of input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are transformation matrices.

This operator is defined to represent the high level concept of input transformation (B^T x d x B) in the Winograd Conv2D algorithm.

Interfaces: `DestinationStyleOpInterface`, `TilingInterface`

#### Attributes:

| Attribute | MLIR Type           | Description                       |
| --------- | ------------------- | --------------------------------- |
| m         | ::mlir::IntegerAttr | 64-bit signless integer attribute |
| r         | ::mlir::IntegerAttr | 64-bit signless integer attribute |

#### Operands:

| Operand | Description                  |
| ------- | ---------------------------- |
| input   | 4D tensor of any type values |
| output  | 6D tensor of any type values |

#### Results:

| Result | Description                  |
| ------ | ---------------------------- |
| result | 6D tensor of any type values |

### `linalg.winograd_output_transform` (linalg::WinogradOutputTransformOp)

_Winograd output transform operator_

Syntax:

operation ::= linalg.winograd_output_transform attr-dict m ( $m ) r ( $r ) ins ( value‘:‘type(value : type(value‘:‘type(value) ) outs ( output‘:‘type(output : type(output‘:‘type(output) ) -> type($result)

Winograd Conv2D algorithm will convert linalg Conv2D operator into batched matrix multiply. Before the matrix multiply, it will convert filter and input into a format suitable for batched matrix multiply. After the matrix multiply, it will convert output to the final result tensor.

The algorithm F(m x m, r x r) is

Y = A^T x \[(G x g x G^T) @ (B^T x d x B)\] x A

The size of output Y is m x m. The size of filter g is r x r. The size of input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are transformation matrices.

This operator is defined to represent the high level concept of output transformation (A^T x y x A) in the Winograd Conv2D algorithm.

Interfaces: `DestinationStyleOpInterface`, `TilingInterface`

#### Attributes:

| Attribute | MLIR Type           | Description                       |
| --------- | ------------------- | --------------------------------- |
| m         | ::mlir::IntegerAttr | 64-bit signless integer attribute |
| r         | ::mlir::IntegerAttr | 64-bit signless integer attribute |

#### Operands:

| Operand | Description                  |
| ------- | ---------------------------- |
| value   | 6D tensor of any type values |
| output  | 4D tensor of any type values |

#### Results:

| Result | Description                  |
| ------ | ---------------------------- |
| result | 4D tensor of any type values |

### `linalg.yield` (linalg::YieldOp)

_Linalg yield operation_

`linalg.yield` is a special terminator operation for blocks inside regions in `linalg` generic ops. It returns values to the immediately enclosing`linalg` generic op.

Example:

linalg.yield %f0, %f1 : f32, f32

Traits: `AlwaysSpeculatableImplTrait`, `ReturnLike`, `Terminator`

Interfaces: `ConditionallySpeculatable`, `NoMemoryEffect (MemoryEffectOpInterface)`, `RegionBranchTerminatorOpInterface`

Effects: `MemoryEffects::Effect{}`

#### Operands:

| Operand | Description          |
| ------- | -------------------- |
| values  | variadic of any type |

### `linalg.log` (linalg::LogOp)

_Applies log(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.map` (linalg::MapOp)

_Elementwise operations_

Models elementwise operations on tensors in terms of arithmetic operations on the corresponding elements.

Example:

%add = linalg.map ins(%lhs, %rhs : tensor<64xf32>, tensor<64xf32>) outs(%init: tensor<64xf32>) (%lhs_elem: f32, %rhs_elem: f32) { %0 = arith.addf %lhs_elem, %rhs_elem: f32 linalg.yield %0: f32 }

Shortened print form is available. Applies to simple maps with one non-yield operation inside the body.

The example above will be printed as:

%add = linalg.map { arith.addf } ins(%lhs, %rhs : tensor<64xf32>, tensor<64xf32>) outs(%init: tensor<64xf32>)

Traits: `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `OpAsmOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                                                               |
| ------- | ------------------------------------------------------------------------- |
| inputs  | variadic of memref of any type values or ranked tensor of any type values |
| init    | memref of any type values or ranked tensor of any type values             |

#### Results:

| Result | Description                           |
| ------ | ------------------------------------- |
| result | variadic of tensor of any type values |

### `linalg.matmul` (linalg::MatmulOp)

_Performs a matrix multiplication of two 2D inputs without broadcast or transpose._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Broadcast and Transpose semantics can be appiled by specifying the explicit attribute ‘indexing\_maps’ as shown below.This is a list attribute, so the list must include all the maps if specified.

Example Transpose:

linalg.matmul indexing_maps = [affine_map<(m, n, k) -> (k, m)>, // transpose affine_map<(m, n, k) -> (k, n)>, affine_map<(m, n, k) -> (m, n)>] ins(%arg0, %arg1 : memref<5x3xf32>,memref<5x7xf32>) outs(%arg2: memref<3x7xf32>)

Example Broadcast:

linalg.matmul indexing_maps = [affine_map<(m, n, k) -> (k)>, // broadcast affine_map<(m, n, k) -> (k, n)>, affine_map<(m, n, k) -> (m, n)>] ins(%arg0, %arg1 : memref<3xf32>, memref<5x7xf32>) outs(%arg2: memref<3x7xf32>)

Example Broadcast and transpose:

linalg.matmul indexing_maps = [affine_map<(m, n, k) -> (k, m)>, // transpose affine_map<(m, n, k) -> (k)>, // broadcast affine_map<(m, n, k) -> (m, n)>] ins(%arg0, %arg1 : memref<5x3xf32>, memref<7xf32>) outs(%arg2: memref<3x7xf32>)

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute      | MLIR Type                  | Description                                 |
| -------------- | -------------------------- | ------------------------------------------- |
| indexing\_maps | ::mlir::ArrayAttr          | AffineMap array attribute                   |
| cast           | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.matmul_transpose_a` (linalg::MatmulTransposeAOp)

_Performs a matrix multiplication of two 2D inputs with lhs operand transposed._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                  | Description                                 |
| --------- | -------------------------- | ------------------------------------------- |
| cast      | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.matmul_transpose_b` (linalg::MatmulTransposeBOp)

_Performs a matrix multiplication of two 2D inputs with rhs operand transposed._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                  | Description                                 |
| --------- | -------------------------- | ------------------------------------------- |
| cast      | ::mlir::linalg::TypeFnAttr | allowed 32-bit signless integer cases: 0, 1 |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.matvec` (linalg::MatvecOp)

_Performs a matrix-vector multiplication._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.max` (linalg::MaxOp)

_Takes the max (signed) between two inputs, elementwise._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.max` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.min` (linalg::MinOp)

_Takes the min (signed) between two inputs, elementwise._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.min` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.mmt4d` (linalg::Mmt4DOp)

_Performs a matrix-matrix-transpose multiplication of two 4D inputs._

Differences from linalg.matmul:

* The right hand side is transposed, whence the ’t’ in ‘mmt’.
* The input and output tensors have a 4D shape instead of a 2D shape. They are interpreted as 2D matrices with one level of 2D tile subdivision, whence the 2+2=4 dimensions. The inner tile dimensions are identified with ‘0’ suffixes below, for instance the LHS matrix shape (M, K, M0, K0) reads as: MxK tiles, each of shape M0xK0.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgContractionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.mul` (linalg::MulOp)

_Multiplies two tensors elementwise._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.mul` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.negf` (linalg::NegFOp)

_Applies negf(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nchw_max` (linalg::PoolingNchwMaxOp)

_Performs max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nchw_sum` (linalg::PoolingNchwSumOp)

_Performs sum pooling._

Layout:

* Input: NCHW.
* Kernel: HW.

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_ncw_max` (linalg::PoolingNcwMaxOp)

_Performs max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_ncw_sum` (linalg::PoolingNcwSumOp)

_Performs sum pooling._

Layout:

* Input: NCW.
* Kernel: W.

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_ndhwc_max` (linalg::PoolingNdhwcMaxOp)

_Performs 3D max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_ndhwc_min` (linalg::PoolingNdhwcMinOp)

_Performs 3D min pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_ndhwc_sum` (linalg::PoolingNdhwcSumOp)

_Performs 3D sum pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[3\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nhwc_max` (linalg::PoolingNhwcMaxOp)

_Performs max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nhwc_max_unsigned` (linalg::PoolingNhwcMaxUnsignedOp)

_Performs unsigned max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nhwc_min` (linalg::PoolingNhwcMinOp)

_Performs min pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nhwc_min_unsigned` (linalg::PoolingNhwcMinUnsignedOp)

_Performs unsigned min pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nhwc_sum` (linalg::PoolingNhwcSumOp)

_Performs sum pooling._

Layout:

* Input: NHWC.
* Kernel: HW.

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[2\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nwc_max` (linalg::PoolingNwcMaxOp)

_Performs max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nwc_max_unsigned` (linalg::PoolingNwcMaxUnsignedOp)

_Performs unsigned max pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nwc_min` (linalg::PoolingNwcMinOp)

_Performs min pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nwc_min_unsigned` (linalg::PoolingNwcMinUnsignedOp)

_Performs unsigned min pooling._

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.pooling_nwc_sum` (linalg::PoolingNwcSumOp)

_Performs sum pooling._

Layout:

* Input: NWC.
* Kernel: W.

Numeric casting is performed on the input operand, promoting it to the same data type as the accumulator/output.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgConvolutionOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute | MLIR Type                    | Description                                           |
| --------- | ---------------------------- | ----------------------------------------------------- |
| strides   | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |
| dilations | ::mlir::DenseIntElementsAttr | 64-bit signless int elements attribute of shape \[1\] |

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.powf` (linalg::PowFOp)

_Takes the powf(lhs, rhs) between two inputs, elementwise. For powf(arg, 2) use `linalg.square`._

Only applies to floating point values.

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.powf` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.quantized_batch_matmul` (linalg::QuantizedBatchMatmulOp)

_Performs a batched matrix multiplication of two 3D inputs._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. The quantized variant includes zero-point adjustments for the left and right operands of the matmul.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.quantized_matmul` (linalg::QuantizedMatmulOp)

_Performs a matrix multiplication of two 2D inputs._

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output. The quantized variant includes zero-point adjustments for the left and right operands of the matmul.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.reciprocal` (linalg::ReciprocalOp)

_Applies reciprocal(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.reduce` (linalg::ReduceOp)

_Reduce operator_

Executes `combiner` on the `dimensions` of `inputs` and returns the reduced result. The `dimensions` attribute needs to list the reduction dimensions in increasing order.

Example:

%reduce = linalg.reduce ins(%input:tensor<16x32x64xf32>) outs(%init:tensor<16x64xf32>) dimensions = [1] (%in: f32, %out: f32) { %0 = arith.addf %out, %in: f32 linalg.yield %0: f32 }

Shortened print form is available. Applies to simple (not variadic) reduces with one non-yield operation inside the body. Applies only if the operation takes `%out` as the first argument.

The example above will be printed as:

  %reduce = linalg.reduce { arith.addf }
  ins(%input:tensor<16x32x64xf32>)
  outs(%init:tensor<16x64xf32>)
  dimensions = [1]

Traits: `RecursiveMemoryEffects`, `SameVariadicOperandSize`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `OpAsmOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Attributes:

| Attribute  | MLIR Type                 | Description                                             |
| ---------- | ------------------------- | ------------------------------------------------------- |
| dimensions | ::mlir::DenseI64ArrayAttr | i64 dense array attribute should be in increasing order |

#### Operands:

| Operand | Description                                                               |
| ------- | ------------------------------------------------------------------------- |
| inputs  | variadic of memref of any type values or ranked tensor of any type values |
| inits   | variadic of memref of any type values or ranked tensor of any type values |

#### Results:

| Result    | Description                           |
| --------- | ------------------------------------- |
| «unnamed» | variadic of tensor of any type values |

### `linalg.round` (linalg::RoundOp)

_Applies round(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.rsqrt` (linalg::RsqrtOp)

_Applies rsqrt(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.select` (linalg::SelectOp)

_Chooses one value based on a binary condition supplied as its first operand._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.select` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.sqrt` (linalg::SqrtOp)

_Applies sqrt(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.square` (linalg::SquareOp)

_Applies square(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.sub` (linalg::SubOp)

_Subtracts two tensors elementwise._

The shapes and element types must be identical. The appropriate casts, broadcasts and reductions should be done previously to calling this op.

This means reduction/broadcast/element cast semantics is explicit. Further passes can take that into account when lowering this code. For example, a `linalg.broadcast` \+ `linalg.sub` sequence can be lowered to a`linalg.generic` with different affine maps for the two operands.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.tanh` (linalg::TanhOp)

_Applies tanh(x) elementwise._

No numeric casting is performed on the input operand.

Traits: `AttrSizedOperandSegments`, `RecursiveMemoryEffects`, `SingleBlockImplicitTerminator<YieldOp>`, `SingleBlock`

Interfaces: `ConditionallySpeculatable`, `DestinationStyleOpInterface`, `LinalgStructuredInterface`, `MemoryEffectOpInterface`, `ReifyRankedShapedTypeOpInterface`

#### Operands:

| Operand | Description                           |
| ------- | ------------------------------------- |
| inputs  | variadic of any type                  |
| outputs | variadic of shaped of any type values |

#### Results:

| Result          | Description                                  |
| --------------- | -------------------------------------------- |
| result\_tensors | variadic of ranked tensor of any type values |

### `linalg.transpose` (linalg::TransposeOp)

_Transpose operator_

Permutes the dimensions of `input` according to the given `permutation`.`dim(result, i) = dim(input, permutation[i])`

This op actually moves data, unlike `memref.transpose` which is a metadata operation only that produces a transposed “view”.

Example:

%transpose = linalg.transpose ins(%input:tensor<16x64xf32>) outs(%init:tensor<64x16xf32>) permutation = [1, 0]

```

Traits: RecursiveMemoryEffects, SingleBlockImplicitTerminator<YieldOp>, SingleBlock

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, LinalgStructuredInterface, MemoryEffectOpInterface, OpAsmOpInterface, ReifyRankedShapedTypeOpInterface

Attributes:

Operands:

Results:

linalg.vecmat (linalg::VecmatOp)

Performs a vector-matrix multiplication.

Numeric casting is performed on the operands to the inner multiply, promoting them to the same data type as the accumulator/output.

Traits: AttrSizedOperandSegments, RecursiveMemoryEffects, SingleBlockImplicitTerminator<YieldOp>, SingleBlock

Interfaces: ConditionallySpeculatable, DestinationStyleOpInterface, LinalgContractionOpInterface, LinalgStructuredInterface, MemoryEffectOpInterface, ReifyRankedShapedTypeOpInterface

Operands:

Results:

'linalg' Dialect Docs

• Linalg OpDSL