MLIR

Multi-Level IR Compiler Framework

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 the canonicalization patterns of all loaded dialects in a greedy way. Canonicalization is best-effort and not guaranteed to bring the entire IR in a canonical form. It applies patterns until either fixpoint is reached or the maximum number of iterations/rewrites (as specified via pass options) is exhausted. This is for efficiency reasons and to ensure that faulty patterns cannot cause infinite looping.

Canonicalization patterns are registered with 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:

  • The goal of canonicalization is to make subsequent analyses and optimizations more effective. Therefore, performance improvements are not necessary for canonicalization.

  • Pass pipelines should not rely on the canonicalizer pass for correctness. They should work correctly with all instances of the canonicalization pass removed.

  • Repeated applications of patterns should converge. Unstable or cyclic rewrites are considered a bug: they can make the canonicalizer pass less predictable and less effective (i.e., some patterns may not be applied) and prevent it from converging.

  • 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”).

  • Pattens with expensive running time (i.e. have O(n) complexity) or complicated cost models don’t belong to canonicalization: since the algorithm is executed iteratively until fixed-point we want patterns that execute quickly (in particular their matching phase).

  • Canonicalize shouldn’t lose the semantic of original operation: the original information should always be recoverable from the transformed IR.

For example, a pattern that transform

  %transpose = linalg.transpose
      ins(%input : tensor<1x2x3xf32>)
      outs(%init1 : tensor<2x1x3xf32>)
      dimensions = [1, 0, 2]
  %out = linalg.transpose
      ins(%tranpose: tensor<2x1x3xf32>)
      outs(%init2 : tensor<3x1x2xf32>)
      permutation = [2, 1, 0]

to

  %out= linalg.transpose
      ins(%input : tensor<1x2x3xf32>)
      outs(%init2: tensor<3x1x2xf32>)
      permutation = [2, 0, 1]

is a good canonicalization pattern because it removes a redundant operation, making other analysis optimizations and more efficient.

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; general RewritePatterns and the fold method.

Canonicalizing with RewritePatterns 

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 or the hasCanonicalizeMethod bit to generate a declaration for the getCanonicalizationPatterns method:

def MyOp : ... {
  // I want to define a fully general set of patterns for this op.
  let hasCanonicalizer = 1;
}

def OtherOp : ... {
  // A single "matchAndRewrite" style RewritePattern implemented as a method
  // is good enough for me.
  let hasCanonicalizeMethod = 1;
}

Canonicalization patterns can then be provided in the source file:

void MyOp::getCanonicalizationPatterns(RewritePatternSet &patterns,
                                       MLIRContext *context) {
  patterns.add<...>(...);
}

LogicalResult OtherOp::canonicalize(OtherOp op, PatternRewriter &rewriter) {
  // patterns and rewrites go here.
  return failure();
}

See the quickstart guide for information on defining operation rewrites.

Canonicalizing with the fold method 

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 (but not erased). 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(FoldAdaptor adaptor) {
  ...
}

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.
///
/// Note that this mechanism cannot be used to remove 0-result operations.
LogicalResult MyOp::fold(FoldAdaptor adaptor,
                         SmallVectorImpl<OpFoldResult> &results) {
  ...
}

In the above, for each method a FoldAdaptor is provided with getters for each of the operands, returning the corresponding constant attribute. 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 adaptor will return Attribute() for getA() and getC(), and b-value for getB().

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 : ... {
  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) {
  ...
}