Operation Canonicalization

Canonicalization is an important part of compiler IR design: it makes it easier to implement reliable compiler transformations and to reason about what is better or worse in the code, and it forces interesting discussions about the goals of a particular level of IR. Dan Gohman wrote an article exploring these issues; it is worth reading if you're not familiar with these concepts.

Most compilers have canonicalization passes, and sometimes they have many different ones (e.g. instcombine, dag combine, etc in LLVM). Because MLIR is a multi-level IR, we can provide a single canonicalization infrastructure and reuse it across many different IRs that it represents. This document describes the general approach, global canonicalizations performed, and provides sections to capture IR-specific rules for reference.

General Design

MLIR has a single canonicalization pass, which iteratively applies canonicalization transformations in a greedy way until the IR converges. These transformations are defined by the operations themselves, which allows each dialect to define its own set of operations and canonicalizations together.

Some important things to think about w.r.t. canonicalization patterns:

  • Repeated applications of patterns should converge. Unstable or cyclic rewrites will cause infinite loops in the canonicalizer.

  • It is generally better to canonicalize towards operations that have fewer uses of a value when the operands are duplicated, because some patterns only match when a value has a single user. For example, it is generally good to canonicalize “x + x” into “x * 2”, because this reduces the number of uses of x by one.

  • It is always good to eliminate operations entirely when possible, e.g. by folding known identities (like “x + 0 = x”).

Globally Applied Rules

These transformations are applied to all levels of IR:

  • Elimination of operations that have no side effects and have no uses.

  • Constant folding - e.g. “(addi 1, 2)” to “3”. Constant folding hooks are specified by operations.

  • Move constant operands to commutative operators to the right side - e.g. “(addi 4, x)” to “(addi x, 4)”.

  • constant-like operations are uniqued and hoisted into the entry block of the first parent barrier region. This is a region that is either isolated from above, e.g. the entry block of a function, or one marked as a barrier via the shouldMaterializeInto method on the DialectFoldInterface.

Defining Canonicalizations

Two mechanisms are available with which to define canonicalizations; getCanonicalizationPatterns and fold.

Canonicalizing with getCanonicalizationPatterns

This mechanism allows for providing canonicalizations as a set of RewritePatterns, either imperatively defined in C++ or declaratively as Declarative Rewrite Rules. The pattern rewrite infrastructure allows for expressing many different types of canonicalizations. These transformations may be as simple as replacing a multiplication with a shift, or even replacing a conditional branch with an unconditional one.

In ODS, an operation can set the hasCanonicalizer bit to generate a declaration for the getCanonicalizationPatterns method.

def MyOp : ... {
  let hasCanonicalizer = 1;

Canonicalization patterns can then be provided in the source file:

void MyOp::getCanonicalizationPatterns(OwningRewritePatternList &patterns,
                                       MLIRContext *context) {

See the quickstart guide for information on defining operation rewrites.

Canonicalizing with fold

The fold mechanism is an intentionally limited, but powerful mechanism that allows for applying canonicalizations in many places throughout the compiler. For example, outside of the canonicalizer pass, fold is used within the dialect conversion infrastructure as a legalization mechanism, and can be invoked directly anywhere with an OpBuilder via OpBuilder::createOrFold.

fold has the restriction that no new operations may be created, and only the root operation may be replaced. It allows for updating an operation in-place, or returning a set of pre-existing values (or attributes) to replace the operation with. This ensures that the fold method is a truly “local” transformation, and can be invoked without the need for a pattern rewriter.

In ODS, an operation can set the hasFolder bit to generate a declaration for the fold method. This method takes on a different form, depending on the structure of the operation.

def MyOp : ... {
  let hasFolder = 1;

If the operation has a single result the following will be generated:

/// Implementations of this hook can only perform the following changes to the
/// operation:
///  1. They can leave the operation alone and without changing the IR, and
///     return nullptr.
///  2. They can mutate the operation in place, without changing anything else
///     in the IR. In this case, return the operation itself.
///  3. They can return an existing value or attribute that can be used instead
///     of the operation. The caller will remove the operation and use that
///     result instead.
OpFoldResult MyOp::fold(ArrayRef<Attribute> operands) {

Otherwise, the following is generated:

/// Implementations of this hook can only perform the following changes to the
/// operation:
///  1. They can leave the operation alone and without changing the IR, and
///     return failure.
///  2. They can mutate the operation in place, without changing anything else
///     in the IR. In this case, return success.
///  3. They can return a list of existing values or attribute that can be used
///     instead of the operation. In this case, fill in the results list and
///     return success. The results list must correspond 1-1 with the results of
///     the operation, partial folding is not supported. The caller will remove
///     the operation and use those results instead.
LogicalResult MyOp::fold(ArrayRef<Attribute> operands,
                         SmallVectorImpl<OpFoldResult> &results) {

In the above, for each method an ArrayRef<Attribute> is provided that corresponds to the constant attribute value of each of the operands. These operands are those that implement the ConstantLike trait. If any of the operands are non-constant, a null Attribute value is provided instead. For example, if MyOp provides three operands [a, b, c], but only b is constant then operands will be of the form [Attribute(), b-value, Attribute()].

Also above, is the use of OpFoldResult. This class represents the possible result of folding an operation result: either an SSA Value, or an Attribute(for a constant result). If an SSA Value is provided, it must correspond to an existing value. The fold methods are not permitted to generate new Values. There are no specific restrictions on the form of the Attribute value returned, but it is important to ensure that the Attribute representation of a specific Type is consistent.

When the fold hook on an operation is not successful, the dialect can provide a fallback by implementing the DialectFoldInterface and overriding the fold hook.

Generating Constants from Attributes

When a fold method returns an Attribute as the result, it signifies that this result is “constant”. The Attribute is the constant representation of the value. Users of the fold method, such as the canonicalizer pass, will take these Attributes and materialize constant operations in the IR to represent them. To enable this materialization, the dialect of the operation must implement the materializeConstant hook. This hook takes in an Attribute value, generally returned by fold, and produces a “constant-like” operation that materializes that value.

In ODS, a dialect can set the hasConstantMaterializer bit to generate a declaration for the materializeConstant method.

def MyDialect_Dialect : ... {
  let hasConstantMaterializer = 1;

Constants can then be materialized in the source file:

/// Hook to materialize a single constant operation from a given attribute value
/// with the desired resultant type. This method should use the provided builder
/// to create the operation without changing the insertion position. The
/// generated operation is expected to be constant-like. On success, this hook
/// should return the value generated to represent the constant value.
/// Otherwise, it should return nullptr on failure.
Operation *MyDialect::materializeConstant(OpBuilder &builder, Attribute value,
                                          Type type, Location loc) {