# MLIR

Multi-Level IR Compiler Framework

# 'linalg' Dialect

## 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).

The Rationale 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 the linalg.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 previously listed prior art . The design enables the definition of CustomOps with generic properties that enable key 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 discussion Linalg and Shapes for more details).

### Payload-Carrying Ops

Linalg defines a payload carrying operation that implements the structured op abstraction 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 of linalg.generic are the result of applying the guiding principles described in the Rationale 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 to URUK .

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"]
}

// memory layouts
#identity = affine_map<(d0) -> (d0)>

func @example(%A: memref<?xf32, #identity>,
%B: memref<?xvector<4xf32>, offset: 1, strides: [2]>) {
linalg.generic #attrs
ins(%A: memref<?xf32, #identity>)
outs(%B: memref<?xvector<4xf32>, offset: 1, strides: [2]>) {
^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/
#map0 = affine_map<(d0) -> (d0 * 2 + 1)>

func @example(%arg0: memref<?xf32>, %arg1: memref<?xvector<4xf32>, #map0>) {
%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>, #map0>
%3 = "some_compute"(%1, %2) : (f32, vector<4xf32>) -> vector<4xf32>
memref.store %3, %arg1[%arg2] : memref<?xvector<4xf32>, #map0>
}
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 for sparse and position-dependent arrays , as well as TACO , 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 first memref is a 2-strided one on both of its dimensions, and the second memref uses 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 @example(%A: memref<8x?xf32, offset: 0, strides: [2, 2]>,
%B: memref<?xvector<4xf32>>) {
linalg.generic #attrs
ins(%A: memref<8x?xf32, offset: 0, strides: [2, 2]>)
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
#map0 = affine_map<(d0, d1) -> (d0 * 2 + d1 * 2)>

func @example(%arg0: memref<8x?xf32, #map0>, %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, #map0>
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, #map0>
%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 of AffineMaps (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’s Optimizing 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, in ISL 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 of Regions .

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.fill operation 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 @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 @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 the inlined 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 a SymbolAttr. 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 attribute library_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 @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
// Note that we lower the Linalg dialect directly to the Standard dialect.
// See this doc: https://mlir.llvm.org/docs/Dialects/Standard/

#map0 = affine_map<(d0, d1)[s0, s1, s2] -> (d0 * s1 + s0 + d1 * s2)>

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, #map0>
%1 = memref.cast %arg1 : memref<?x?xf32> to memref<?x?xf32, #map0>
%2 = memref.cast %arg2 : memref<?x?xf32> to memref<?x?xf32, #map0>
call @pointwise_add(%0, %1, %2) : (memref<?x?xf32, #map0>, memref<?x?xf32, #map0>, memref<?x?xf32, #map0>) -> ()
return
}
func @pointwise_add(memref<?x?xf32, #map0>, memref<?x?xf32, #map0>, memref<?x?xf32, #map0>) attributes {llvm.emit_c_interface}


Which, after lowering to LLVM resembles:

// Run: mlir-opt example4.mlir -convert-linalg-to-std | mlir-opt -convert-std-to-llvm
// Some generated code are omitted here.
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 an ongoing discussion on 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 of linalg.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 a linalg.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 the core 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 the Strided 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 for sparse and position-dependent arrays .

### Metadata Ops

A set of ops that manipulate metadata but do not move memory. These ops take view 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.range,
* 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 from Legion data-centric programming model seem generally appealing.

### Named Payload-Carrying Ops

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

* linalg.copy,
* 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:

llvm::Optional<SmallVector<StringRef, 8>> batchmatmul::referenceIterators() {
return SmallVector<StringRef, 8>{
getParallelIteratorTypeName(),
getParallelIteratorTypeName(),
getParallelIteratorTypeName(),
getReductionIteratorTypeName() };
}
llvm::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 level DSL 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 in mlir-mlinalg-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

### linalg.batch_matmul (::mlir::linalg::BatchMatmulOp)

Performs a batched matrix multiplication of two 3D inputs.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs a batched matrix-vector multiplication.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 1-D convolution.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [1]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [1]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 1-D convolution with no channels.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 2-D convolution.

Layout: Input: NCHW. Kernel: FCHW.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 2-D convolution.

Layout: Input: NHWC. Kernel: HWCF.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 2-D convolution with zero point offsets.

Layout: Input: NHWC. Kernel: HWCF.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 2-D convolution with no channels.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 3-D convolution.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 3-D convolution with no channels.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Syntax:

operation ::= linalg.copy ( $input ,$output ) attr-dict :
type($input) , type($output)
custom<FillOpRegion>($region, ref(type($value)), ref(type($output)))  #### Operands: OperandDescription valuecomplex-type or floating-point or signless integer or vector of any type values outputshaped of any type values #### Results: ResultDescription resultranked tensor of any type values ### linalg.fill_rng_2d (::mlir::linalg::FillRng2DOp) Fills the output tensor with pseudo random numbers. The operation generations pseudo random numbers using a linear congruential rator. It provides no guarantees regarding the distribution of the rated random numbers. Instead of generating the random numbers entially, it instantiates one random number generator per data element runs them in parallel. The seed operand and the indices of the data ent seed the random number generation. The min and max operands limit range of the generated random numbers. #### Operands: OperandDescription inputsany type outputsshaped of any type values #### Results: ResultDescription result_tensorsranked tensor of any type values ### linalg.generic (::mlir::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> } } }  To allow progressive lowering from the value world (a.k.a tensor values) to the buffer world (a.k.a memref values), a linalg.generic op allows mixing tensors and buffers operands and tensor results. %C = linalg.generic #trait_attribute ins(%A, %B : tensor<?x?xf32>, memref<?x?xf32, stride_specification>) outs(%C : tensor<?x?xf32>) {other-optional-attributes} {region} -> (tensor<?x?xf32>)  #### Attributes: AttributeMLIR TypeDescription indexing_maps::mlir::ArrayAttrAffineMap array attribute iterator_types::mlir::ArrayAttrarray attribute doc::mlir::StringAttrstring attribute library_call::mlir::StringAttrstring attribute #### Operands: OperandDescription inputsany type outputsshaped of any type values #### Results: ResultDescription result_tensorsranked tensor of any type values ### linalg.index (::mlir::linalg::IndexOp) linalg index operation Syntax: operation ::= linalg.index$dim attr-dict : type($result)  The linalg.index operation returns the iteration index of the immediately enclosing linalg structured operation for the iteration dimension dim. The dim attribute specifies the position of the accessed dimension in the indexing map domain. Example: #map = affine_map<(i, j) -> (i, j)> linalg.generic {indexing_maps = [#map, #map], iterator_types = ["parallel", "parallel"]} outs(%I, %J : memref<?x?xindex>, memref<?x?xindex>) { ^bb0(%arg0 : index, %arg1 : index): // Access the outer iteration dimension i %i = linalg.index 0 : index // Access the inner iteration dimension j %j = linalg.index 1 : index linalg.yield %i, %j : index, index }  This may lower to IR resembling: %0 = dim %I, %c0 : memref<?x?xindex> %1 = dim %I, %c1 : memref<?x?xindex> scf.for %i = %c0 to %0 step %c1 { scf.for %j = %c0 to %1 step %c1 { store %i, %I[%i, %j] : memref<?x?xindex> store %j, %J[%i, %j] : memref<?x?xindex> } }  #### Attributes: AttributeMLIR TypeDescription dim::mlir::IntegerAttr64-bit signless integer attribute whose minimum value is 0 #### Results: ResultDescription resultindex ### linalg.init_tensor (::mlir::linalg::InitTensorOp) operation to define a tensor of particular value Syntax: operation ::= linalg.init_tensor custom<OperandsOrIntegersSizesList>($sizes, $static_sizes) attr-dict : type($result)


linalg.init_tensor is an operation that materializes a tensor of a given shape. The shape could be dynamic or static.

#### Attributes:

AttributeMLIR TypeDescription
static_sizes::mlir::ArrayAttr64-bit integer array attribute

#### Operands:

OperandDescription
sizesindex

#### Results:

ResultDescription
resulttensor of any type values

### linalg.pad_tensor (::mlir::linalg::PadTensorOp)

tensor pad operation

Syntax:

operation ::= linalg.pad_tensor $source (nofold$nofold^)?
low  custom<OperandsOrIntegersSizesList>($low,$static_low)
high  custom<OperandsOrIntegersSizesList>($high,$static_high)
$region attr-dict : type($source) to type($result)  linalg.pad_tensor is an operation that pads the source tensor with given low and high padding config. The PadTensor operation supports the following arguments: • source: the “base” tensor on which to pad. • low: A list contains the padding along the start of each dimension, i.e low. • high: A list contains the padding along the end of each dimension, i.e. high. • nofold: indicates that the operation should not be folded when source and result types are equal. The result tensor dimensions are low + dim + high along that dimension. The number of elements of low and high must match the rank of the input tensor. They can be either a constant or a dynamic value. The region of the pad_tensor operation returns the value to use for the padding. The arguments of the region represent the index of the source being accessed. There should be as many arguments as the rank of the source tensor. The value yield-ed by the region is used as the value of the view at the given position. If nofold is set, the padding operation will not be folded away even if the source type and the padded type have the same static shape. This can be used, e.g., for packing or promotion to faster memory. Example 1:  %pad_value = ... : f32 %0 = linalg.pad_tensor %0 low[1, 2] high[2, 3] { ^bb0(%arg0 : index, %arg1 : index): linalg.yield %pad_value : f32 } : tensor<?x?xf32> to tensor<?x?xf32>  Example 2:  %pad_value = ... : f32 %0 = linalg.pad_tensor %arg0 low[2, %arg1, 3, 3] high[3, 3, %arg1, 2] { ^bb0(%arg2: index, %arg3: index, %arg4: index, %arg5: index): linalg.yield %pad_value : f32 } : tensor<1x2x2x?xf32> to tensor<6x?x?x?xf32>  Example 3:  %pad_value = ... : f32 %0 = linalg.pad_tensor %arg0 low[0, 0] high[%ub0, %ub1] { ^bb0(%arg1: index, %arg2: index): linalg.yield %pad_value : f32 } : tensor<2x3xf32> to tensor<?x?xf32>  Example 4:  // Force a padded value to be always exist with nofold. %pad_value = ... : f32 %0 = linalg.pad_tensor %arg0 nofold low[0, 0] high[0, 0] { ^bb0(%arg1: index, %arg2: index): linalg.yield %pad_value : f32 } : tensor<2x3xf32> to tensor<2x3xf32>  #### Attributes: AttributeMLIR TypeDescription static_low::mlir::ArrayAttr64-bit integer array attribute static_high::mlir::ArrayAttr64-bit integer array attribute nofold::mlir::UnitAttrunit attribute #### Operands: OperandDescription sourcetensor of any type values lowindex highindex #### Results: ResultDescription resulttensor of any type values ### linalg.range (::mlir::linalg::RangeOp) Create a range type value, used to create views Syntax: operation ::= linalg.range$min : $max :$step attr-dict : type(results)


The linalg.range op creates a !linalg.range from 3 values of type index that represent the min, max and step values of the range. This type does not pass function boundaries at the moment.

Example:

%3 = linalg.range %0:%1:%2 : !linalg.range


#### Operands:

OperandDescription
minindex
maxindex
stepindex

#### Results:

ResultDescription
«unnamed»range

### linalg.tensor_collapse_shape (::mlir::linalg::TensorCollapseShapeOp)

operation to produce a tensor with a smaller rank

The linalg.tensor_collapse_shape op produces a new tensor with a smaller rank whose sizes are a reassociation of the original src.

A reassociation is defined as a continuous grouping of dimensions and is represented with an array of I64ArrayAttr attribute.

The verification rule is that the reassociation maps are applied to the operand tensor with the higher rank to obtain the result tensor with the smaller rank.

The result tensor type of a reshape can be zero-ranked if the operand tensor type is statically shaped with all dimensions being unit extent. In such case the reassociation map is empty.

Examples:

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


#### Attributes:

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

#### Operands:

OperandDescription
srctensor of any type values

#### Results:

ResultDescription
resulttensor of any type values

### linalg.tensor_expand_shape (::mlir::linalg::TensorExpandShapeOp)

operation to produce a tensor with a higher rank

The linalg.tensor_expand_shape op produces a new tensor with a higher rank whose sizes are a reassociation of the original src.

A reassociation is defined as a continuous grouping of dimensions and is represented with an array of I64ArrayAttr attribute.

The verification rule is that the reassociation maps are applied to the result tensor with the higher rank to obtain the operand tensor with the smaller rank.

The operand tensor type of a reshape can be zero-ranked if the result tensor type is statically shaped with all dimensions being unit extent. In such cases the reassociation map is empty.

Examples:

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


#### Attributes:

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

#### Operands:

OperandDescription
srctensor of any type values

#### Results:

ResultDescription
resulttensor of any type values

### linalg.tiled_loop (::mlir::linalg::TiledLoopOp)

Linalg tiled loop operation

This is a loop-like operation with additional properties. The arguments also include the input and the output tensors or memrefs and the attributes to specify the iterator types.

Parsing TiledLoopOp will set all elements of the iterator_types attribute to “parallel” type, when it is absent from the custom format.

Tensor-based version:

The body region of the loop contains extract_slice operations applied to every tensor argument of TiledLoopOp.

The body region must contain exactly one block that terminates with linalg.yield with the operands resulting from insert_slice operations.

Example:

%0 = linalg.tiled_loop (%i) = (%c0) to (%c24) step (%c4)
ins(%lhs, %rhs : tensor<24x64xi8>, tensor<24x64xi8>)
outs(%out : tensor<24x64xi8>)
iterators("parallel")
distribution("block_x") {
%lhs_sub = tensor.extract_slice %lhs[%i, 0] [%c4, %c64] [1, 1]
: tensor<24x64xi8> to tensor<?x?xi8>
%rhs_sub = tensor.extract_slice %rhs[%i, 0] [%c4, %c64] [1, 1]
: tensor<24x64xi8> to tensor<?x?xi8>
%out_sub = tensor.extract_slice %out[%i, 0] [%c4, %c64] [1, 1]
: tensor<24x64xi8> to tensor<?x?xi8>

%result_sub = linalg.generic ...

%result = tensor.insert_slice %result_sub into %out[%i, 0][%c4, %c64][1, 1]
: tensor<?x?xi8> into tensor<24x64xi8>
linalg.yield %result : tensor<24x64xi8>
}


MemRef-based version:

The body region of the loop contains subview operations applied to every memref argument of TiledLoopOp.

The body region must contain exactly one block that terminates with linalg.yield with no operands.

Example:

linalg.tiled_loop (%i) = (%c0) to (%c24) step (%c4)
ins(%lhs, %rhs : memref<24x64xi8>, memref<24x64xi8>)
outs(%out : memref<24x64xi8>)
iterators("parallel")
distribution("block_x") {
%lhs_sub = subview %lhs[%i, 0] [%c4, %c64] [1, 1]
: memref<24x64xi8> to memref<?x?xi8>
%rhs_sub = subview %rhs[%i, 0] [%c4, %c64] [1, 1]
: memref<24x64xi8> to memref<?x?xi8>
%out_sub = subview %out[%i, 0] [%c4, %c64] [1, 1]
: memref<24x64xi8> to memref<?x?xi8>

%result_sub = linalg.generic ...
linalg.yield
}


#### Attributes:

AttributeMLIR TypeDescription
iterator_types::mlir::ArrayAttrarray attribute
distribution_types::mlir::ArrayAttrarray attribute

#### Operands:

OperandDescription
lowerBoundindex
upperBoundindex
stepindex
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
resultsranked tensor of any type values

### linalg.yield (::mlir::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


#### Operands:

OperandDescription
valuesany type

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

Performs a matrix multiplication of two 2D inputs.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

### linalg.matmul_unsigned (::mlir::linalg::MatmulUnsignedOp)

Performs a unsigned matrix multiplication of two 2D inputs.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs a matrix-vector multiplication.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs a matrix-matrix-transpose multiplication of two 4D inputs.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs max pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 3D max pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 3D min pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs 3D sum pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [3]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs max pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs unsigned max pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs min pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs unsigned min pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs sum pooling.

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

#### Attributes:

AttributeMLIR TypeDescription
strides::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]
dilations::mlir::DenseIntElementsAttr64-bit signless int elements attribute of shape [2]

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs a batched matrix multiplication of two 3D inputs.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

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

Performs a matrix multiplication of two 2D inputs.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

### linalg.soft_plus_2d (::mlir::linalg::SoftPlus2DOp)

Implements the soft plus operator.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values

### linalg.vecmat (::mlir::linalg::VecmatOp)

Performs a vector-matrix multiplication.

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

#### Operands:

OperandDescription
inputsany type
outputsshaped of any type values

#### Results:

ResultDescription
result_tensorsranked tensor of any type values