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.
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”).
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 binary operators to the right side - e.g. “(addi 4, x)” to “(addi x, 4)”.
These transformations are applied to builtin ops:
constant ops are uniqued and hoisted into the entry block of the first parent region that is isolated from above, e.g. the entry block of a function.affine.apply operations that directly feed each other.alloc operations to turn dynamic dimensions into static ones.memref_cast operations into users where possible.