[Mlir-commits] [mlir] b88ed4e - [mlir][Linlag] Reflow Linalg.md - NFC
Nicolas Vasilache
llvmlistbot at llvm.org
Fri Dec 18 08:16:10 PST 2020
Author: Nicolas Vasilache
Date: 2020-12-18T16:15:58Z
New Revision: b88ed4ec8e7d35f786a59de527989316ba9c5f48
URL: https://github.com/llvm/llvm-project/commit/b88ed4ec8e7d35f786a59de527989316ba9c5f48
DIFF: https://github.com/llvm/llvm-project/commit/b88ed4ec8e7d35f786a59de527989316ba9c5f48.diff
LOG: [mlir][Linlag] Reflow Linalg.md - NFC
Markdown formatting seems to now be available, reflowing the doc without changing any content.
Added:
Modified:
mlir/docs/Dialects/Linalg.md
Removed:
################################################################################
diff --git a/mlir/docs/Dialects/Linalg.md b/mlir/docs/Dialects/Linalg.md
index c6681a93e53e..02508a81b63a 100644
--- a/mlir/docs/Dialects/Linalg.md
+++ b/mlir/docs/Dialects/Linalg.md
@@ -6,12 +6,12 @@
<img width="90" align="left" alt="MLIR Codegen Flow" src="https://user-images.githubusercontent.com/10148468/73613629-c5586580-45c5-11ea-94b7-074aeea94c7b.png">
-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).
+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](../Rationale/RationaleLinalgDialect.md)
-goes into significantly more design and architectural decision details.
+The [Rationale Document](../Rationale/RationaleLinalgDialect.md) goes into
+significantly more design and architectural decision details.
## Set of Key Transformations<a name="key_transformations"></a>
@@ -20,51 +20,56 @@ 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 at least the key transformations that are
-performed on the Linalg IR and that have influenced its design:
-1. Progressive Buffer Allocation.
-1. Parametric Tiling.
-1. Promotion to Temporary Buffer in Fast Memory.
-1. Tiled Producer-Consumer Fusion with Parametric Tile-And-Fuse.
-1. Map to Parallel and Reduction Loops and Hardware.
-1. Vectorization: Rewrite in Vector Form.
-1. Lower to Loops (Affine, Generic, and Parallel).
-1. Lower to Library Calls or Special Instructions, Intrinsics or ISA.
-1. Partially Lower to Iterations Over a Finer-Grained Linalg Op.
+The textual form description of these transformations is left for future work.
+Still, it is useful to at least the key transformations that are performed on
+the Linalg IR and that have influenced its design:
+
+1. Progressive Buffer Allocation.
+1. Parametric Tiling.
+1. Promotion to Temporary Buffer in Fast Memory.
+1. Tiled Producer-Consumer Fusion with Parametric Tile-And-Fuse.
+1. Map to Parallel and Reduction Loops and Hardware.
+1. Vectorization: Rewrite in Vector Form.
+1. Lower to Loops (Affine, Generic, and Parallel).
+1. Lower to Library Calls or Special Instructions, Intrinsics or ISA.
+1. Partially Lower to Iterations Over a Finer-Grained Linalg Op.
## High-Level Description of Linalg Ops<a name="linalg_ops"></a>
-Linalg takes at least some inspiration from all previously [listed prior
-art](#prior_art). The design enables the definition of ***CustomOps*** with
-generic properties that enable [key transformations](#key_transformations),
-including lowering to scalar load/store and other operations or to external
-library calls and intrinsics.
+
+Linalg takes at least some inspiration from all previously
+[listed prior art](#prior_art). The design enables the definition of
+***CustomOps*** with generic properties that enable
+[key transformations](#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 operands***, subject to
[conventions and limitations](#tensors_and_buffers).
### Payload-Carrying Ops<a name="payload_ops"></a>
-Linalg defines two payload carrying operations that implement the [structured ops](
-https://docs.google.com/presentation/d/1P-j1GrH6Q5gLBjao0afQ-GfvcAeF-QU4GXXeSy0eJ9I/edit#slide=id.p
-) abstraction on tensors and buffers. This is architected as two generic operations
-`linalg.generic` (resp. `linalg.indexed_generic`) that can express custom
-operations with *index-free semantics* (resp. *indexing semantics*).
-The properties of these generic ops are the result of applying the
-guiding principles described in the [Rationale Document](../Rationale/RationaleLinalgDialect.md).
-They are listed next, with a brief example and discussion for each.
+
+Linalg defines two payload carrying operations that implement the
+[structured ops](https://docs.google.com/presentation/d/1P-j1GrH6Q5gLBjao0afQ-GfvcAeF-QU4GXXeSy0eJ9I/edit#slide=id.p)
+abstraction on tensors and buffers. This is architected as two generic
+operations `linalg.generic` (resp. `linalg.indexed_generic`) that can express
+custom operations with *index-free semantics* (resp. *indexing semantics*). The
+properties of these generic ops are the result of applying the guiding
+principles described in the
+[Rationale Document](../Rationale/RationaleLinalgDialect.md). They are listed
+next, with a brief example and discussion for each.
#### Property 1: Input and Output Operands Define The Iteration Space<a name="prop1"></a>
+
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](http://icps.u-strasbg.fr/~bastoul/research/papers/GVBCPST06-IJPP.pdf).
+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](http://icps.u-strasbg.fr/~bastoul/research/papers/GVBCPST06-IJPP.pdf).
-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.
+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.
```mlir
// File name: example1.mlir
@@ -117,39 +122,38 @@ func @example(%arg0: memref<?xf32>, %arg1: memref<?xvector<4xf32>, #map0>) {
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).
+(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 *not yet
-materialized*. This is a necessary property if we want an abstraction that
+Before lowering to loop form, loop induction variables and iterators are *not
+yet materialized*. This is a necessary property if we want an abstraction that
works on both tensor values and buffers because ***values don’t escape
loops/nesting***.
-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.
+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
diff erent 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.
+about mixing
diff erent 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](https://www.lift-project.org/publications/2016/harries16sparse.pdf)
-and [position-dependent
-arrays](https://www.lift-project.org/publications/2019/pizzuti19positiondependentarrays.pdf),
+[sparse](https://www.lift-project.org/publications/2016/harries16sparse.pdf) and
+[position-dependent arrays](https://www.lift-project.org/publications/2019/pizzuti19positiondependentarrays.pdf),
as well as [TACO](http://tensor-compiler.org/), has shown.
#### Property 2: Reversible Mappings Between Control and Data Structures<a name="prop2"></a>
+
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.
+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
@@ -177,6 +181,7 @@ func @example(%A: memref<8x?xf32, offset: 0, strides: [2, 2]>,
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)>
@@ -198,78 +203,83 @@ func @example(%arg0: memref<8x?xf32, #map0>, %arg1: memref<?xvector<4xf32>>) {
}
```
-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?
+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](https://mlir.llvm.org/docs/LangRef/#affinemap-attribute) (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.
+In the current implementation, `linalg.generic` uses a list of
+[AffineMaps](https://mlir.llvm.org/docs/LangRef/#affinemap-attribute) (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 name="prop3"></a>
+
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](
-https://www.elsevier.com/books/optimizing-compilers-for-modern-architectures/allen/978-0-08-051324-9).
-The key idea of legality of loop transformations expressed by Kennedy is
-that ***the lexicographic order of all dependence vectors must be
-preserved***.
+the properties from Ken Kennedy's
+[Optimizing Compilers for Modern Architectures](https://www.elsevier.com/books/optimizing-compilers-for-modern-architectures/allen/978-0-08-051324-9).
+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*, ...
+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
+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](https://en.wikipedia.org/wiki/Integer_set_library) 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.
+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.
+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 name="prop4"></a>
-A `linalg.generic` op has a compute payload that is fully generic thanks to
-the use of
+
+A `linalg.generic` op has a compute payload that is fully generic thanks to the
+use of
[Regions](https://github.com/llvm/llvm-project/blob/58265ad42a90ae8905be6a447cb42e53529a54a0/mlir/docs/LangRef.md#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.
+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.
-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`:
-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
#indexing_maps = [
@@ -293,10 +303,12 @@ func @example(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
}
```
-This function basically element-wise adds up two matrices (`%A` and `%B`) and stores the result into another one (`%C`).
+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:
-The property "*The Compute Payload is Specified With a Region*" is
-materialized by a lowering into a form that will resemble:
```
// Run: mlir-opt example3.mlir -convert-linalg-to-loops
#indexing_maps = [
@@ -321,24 +333,27 @@ func @example(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
```
In the process of lowering to loops and lower-level constructs, similar
-requirements are encountered, as are discussed in the [inlined call op
-proposal](https://llvm.discourse.group/t/introduce-std-inlined-call-op-proposal/282/2).
-We expect to be able to reuse the common lower-level infrastructure provided
-it evolves to support both region arguments and captures.
+requirements are encountered, as are discussed in the
+[inlined call op proposal](https://llvm.discourse.group/t/introduce-std-inlined-call-op-proposal/282/2).
+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 name="prop5"></a>
+
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
diff erent transformations have been applied***.
+`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
diff erent 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.
-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:
-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 = [
@@ -363,8 +378,8 @@ func @example(%A: memref<?x?xf32>, %B: memref<?x?xf32>, %C: memref<?x?xf32>) {
}
```
-The property "*Map To an External Library Call*" is
-materialized by a lowering into a form that will resemble:
+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
@@ -384,6 +399,7 @@ func @pointwise_add(memref<?x?xf32, #map0>, memref<?x?xf32, #map0>, memref<?x?xf
```
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.
@@ -403,61 +419,64 @@ llvm.func @_mlir_ciface_pointwise_add(!llvm<"{ float*, float*, i64, [2 x i64], [
```
##### 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).
+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.
+Generally, `linalg` passes non-owning pointers to View data structures to
+pre-compiled library calls linked externally.
-There is an [ongoing
-discussion](https://llvm.discourse.group/t/lowering-optional-attributes-in-linalg-structuredops-to-standard-dialect/333/3)
+There is an
+[ongoing discussion](https://llvm.discourse.group/t/lowering-optional-attributes-in-linalg-structuredops-to-standard-dialect/333/3)
on the topic of extending interoperability in the presence of key attributes.
#### Property 6: Perfectly Nested Writes To The Whole Output Operands<a name="prop6"></a>
+
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.
+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.
+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.
+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.
+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).
+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<a name="summary"></a>
+
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](#guiding_principles).
+automatically while still maintaining the
+[core guiding principles](#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
@@ -535,52 +554,58 @@ linalg.matmul ins(%a, %b : memref<?x?xf32>, tensor<?x?xf32>)
```
### Data Representation: Views<a name="views"></a>
-The current implementation uses the [Strided MemRef (a.k.a View)](
-https://groups.google.com/a/tensorflow.org/forum/#!topic/mlir/MaL8m2nXuio)
+
+The current implementation uses the
+[Strided MemRef (a.k.a View)](https://groups.google.com/a/tensorflow.org/forum/#!topic/mlir/MaL8m2nXuio)
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
+*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](https://www.lift-project.org/publications/2016/harries16sparse.pdf)
-and [position-dependent
-arrays](https://www.lift-project.org/publications/2019/pizzuti19positiondependentarrays.pdf).
+[sparse](https://www.lift-project.org/publications/2016/harries16sparse.pdf) and
+[position-dependent arrays](https://www.lift-project.org/publications/2019/pizzuti19positiondependentarrays.pdf).
### Metadata Ops<a name="metadata_ops"></a>
+
A set of ops that manipulate metadata but do not move memory. These ops take
-`view` operands + extra attributes and return new `view`s. The returned
-`view`s generally alias the operand `view`. At the moment the existing ops
-are:
+`view` operands + extra attributes and return new `view`s. The returned `view`s
+generally alias the operand `view`. At the moment the existing ops are:
- * `std.view`,
- * `std.subview`,
- * `std.transpose`.
- * `linalg.range`,
- * `linalg.slice`,
- * `linalg.reshape`,
+```
+* `std.view`,
+* `std.subview`,
+* `std.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.
diff erence` (would need to work on a list of views).
+```
+* `linalg.tile`,
+* `linalg.intersection`,
+* `linalg.convex_union`,
+* `linalg.
diff erence` (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](https://legion.stanford.edu/overview/) seem generally
-appealing.
+In a longer-term future, the abstractions from
+[Legion data-centric programming model](https://legion.stanford.edu/overview/)
+seem generally appealing.
### Named Payload-Carrying Ops<a name="named_ops"></a>
+
Additionally, `linalg` provides a small subset of commonly named operations:
- * `linalg.copy`,
- * `linalg.fill`,
- * `linalg.dot`,
- * `linalg.matmul`,
- * `linalg.conv`.
+```
+* `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
@@ -608,7 +633,7 @@ better adapt to Linalg:
1. 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.
-1. Reduction dimensions are specified with angle bracket notation on the
+1. 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, a reduction is specified with `op=` operator and the
reduction dimensions are inferred.
@@ -677,23 +702,24 @@ void batchmatmul::regionBuilder(ArrayRef<BlockArgument> args) {
```
## Open Issues and Design Alternatives<a name="open_issues"></a>
-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?
-1. Should `linalg.generic` regions take views or only scalars?
-1. Should we try to solve automatic
diff erentiation at this level of
-abstraction?
-1. Are all the six properties really necessary?
-1. Is this relying too much on declarative specification and would we be
-better off relying more on analyses?
-1. Is this general enough for the community's needs? If not how should this be
-extended, if at all?
-...
+
+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?
+1. Should `linalg.generic` regions take views or only scalars?
+1. Should we try to solve automatic
diff erentiation at this level of
+ abstraction?
+1. Are all the six properties really necessary?
+1. Is this relying too much on declarative specification and would we be better
+ off relying more on analyses?
+1. 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
diff erent levels of IR interoperate seamlessly. In
-practice, it is not necessary (or beneficial) to try and solve all problems in the
-same IR.
+practice, it is not necessary (or beneficial) to try and solve all problems in
+the same IR.
## Operations
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