MLIR — Writing Our First Pass

Table of Contents

This series is an introduction to MLIR and an onboarding tutorial for the HEIR project.

Last time we saw how to run and test a basic lowering. This time we will write some simple passes to illustrate the various parts of the MLIR API and the pass infrastructure.

As mentioned previously, the main work in MLIR is defining passes that either optimize part of a program, lower from parts of one dialect to others, or perform various normalization and canonicalization operations. In this article, we’ll start by defining a pass that operates entirely within a given dialect by fully unrolling loops. Then we’ll define a pass that does a simple replacement of one instruction with another. Neither pass will be particularly complex, but rather they will show how to set up a pass, how to navigate through a program via the MLIR API, and how to modify the IR by deleting and adding operations.

The code for this post is contained within this pull request.

tutorial-opt and project organization

Last time we used the mlir-opt binary as the main entry point to parse MLIR, run a pass, and emit the output IR. A compiler might run mlir-opt as a subroutine in between the front end (C++ to some MLIR dialects) and the backend (MLIR’s LLVM dialect to LLVM to machine code).

In an out-of-tree MLIR project, mlir-opt can’t be used because it isn’t compiled with the project’s custom dialects or passes. Instead, MLIR makes it easy to build a custom version of the mlir-opt tool for an out-of-tree project. It primarily provides a set of registration hooks that you can use to plug in your dialects and passes, and the framework handles reading/writing, CLI flags, and adds that all on top of the baseline MLIR passes and dialects. We’ll start this article by creating the shell for such a tool with an empty custom pass, which we’ll call tutorial-opt. If this repository were to become one step of an end-to-end compiler, then tutorial-opt would be the main interface to the MLIR part.

The structure of the codebase is a persnickety question here. A typical MLIR codebase seems to split the code into two directories with roughly equivalent hierarchies: an include/ directory for headers and tablegen files (more on tablegen in a future article), and a lib/ directory for implementation code. Then, within those two directories a project would have a Transform/ subdirectory that stores the files for passes that transform code within a dialect, Conversion/ for passes that convert between dialects, Analysis/ for analysis passes, etc. Each of these directories might have subdirectories for the specific dialects they operate on.

For this tutorial we will do it slightly differently by merging include/ and lib/ together (header files will live next to implementation files). I believe the reason that C++ codebases separate this is a combination of implicit public/private interface (client code should only depend on headers in include/, not headers in lib/ or src/). But bazel has many more facilities for enforcing private/public interface boundaries, I find it tedious to navigate parallel directory structures, and this is a tutorial so simpler is better.

So the project’s directory structure will add like this once we create the initial pass:

├── bazel
│   └──  . . .
├── lib
│   └── Transform
│       └── Affine
│           ├── AffineFullUnroll.cpp
│           ├── AffineFullUnroll.h
│           └── BUILD
├── tests
│   └── . . .
└── tools
    ├── BUILD
    └── tutorial-opt.cpp

Unrolling loops, a starter pass

Though MLIR provides multiple mechanisms for defining loops and control flow, the highest level one is in the affine dialect. Originally defined for polyhedral loop analysis (using lattices to study loop structure!), it also simply defines a nice for operation that you can use whenever you have simple loop bounds like iterating over a range with an optional step size. An example loop that sums some values in an array stored in memory might look like:

func.func @sum_buffer(%buffer: memref<4xi32>) -> (i32) {
  %sum_0 = arith.constant 0 : i32
  %sum = affine.for %i = 0 to 4 iter_args(%sum_iter = %sum_0) -> i32 {
    %t = affine.load %buffer[%i] : memref<4xi32>
    %sum_next = arith.addi %sum_iter, %t : i32
    affine.yield %sum_next : i32
  return %sum : i32

The iter_args is a custom bit of syntax that defines accumulation variables to operate across the loop body (to be in compliance with SSA form; for more on SSA, see this MLIR doc), along with an initial value.

Unrolling loops is a nontrivial operation, but thankfully MLIR provides a utility method for fully unrolling a loop, so our pass will be a thin wrapper around this function call, to showcase some of the rest of the infrastructure before we write a more meaningful pass. The code for this section is in this commit.

This implementation will be technically the most general implementation, by implementing directly from the C++ API, rather than using the more special case features like the pattern rewrite engine, the dialect conversion framework, or tablegen. Those will all come later.

The main idea is to implement the required methods for the OperationPass base class, which “anchors” the pass to work within the context of a specific instance of a specific type of operation, and is applied to every operation of that type. It looks like this:

// lib/Transform/Affine/AffineFullUnroll.h
class AffineFullUnrollPass
    : public PassWrapper<AffineFullUnrollPass,
                         OperationPass<mlir::func::FuncOp>> {
  void runOnOperation() override;  // implemented in AffineFullUnroll.cpp

  StringRef getArgument() const final { return "affine-full-unroll"; }

  StringRef getDescription() const final {
    return "Fully unroll all affine loops";

The PassWrapper helps implement some of the required methods for free (mainly adding a compliant copy method), and uses the Curiously Recurring Template Pattern (CRTP) to achieve that. But what matters for us is that OperationPass<FuncOp> anchors this pass to operation on function bodies, and provides the getOperation method in the class which returns the FuncOp being operated on.

Aside: The MLIR docs more formally describe what is required of an OperationPass, and in particular it limits the “anchoring” to specific operations like functions and modules, the insides of which are isolated from modifying the semantics of the program outside of the operation’s scope. That’s a fancy way of saying FuncOps in MLIR can’t screw with variables outside the lexical scope of their function body. More importantly for this example, it explains why we can’t anchor this pass on a for loop operation directly: a loop can modify stuff outside its body (like the contents of memory) via the operations within the loop (store, etc.). This matters because the MLIR pass infrastructure runs passes in parallel. If some other pass is tinkering with neighboring operations, race conditions ensue.

The three functions we need to implement are

  • runOnOperation: the function that performs the pass logic.
  • getArgument: the CLI argument for an mlir-opt-like tool.
  • getDescription: the CLI description when running --help on the mlir-opt-like tool.

The initial implementation of runOperation is empty in the commit for this section. Next, we create a tutorial-opt binary that registers the pass.

// tools/tutorial-opt.cpp
#include "lib/Transform/Affine/AffineFullUnroll.h"
#include "mlir/include/mlir/InitAllDialects.h"
#include "mlir/include/mlir/Pass/PassManager.h"
#include "mlir/include/mlir/Pass/PassRegistry.h"
#include "mlir/include/mlir/Tools/mlir-opt/MlirOptMain.h"

int main(int argc, char **argv) {
  mlir::DialectRegistry registry;


  return mlir::asMainReturnCode(
      mlir::MlirOptMain(argc, argv, "Tutorial Pass Driver", registry));

This registers all the built-in MLIR dialects, adds our AffineFullUnrollPass, and then calls the MlirOptMain function which handles the rest. At this point we can run bazel run tools:tutorial-opt --help and see a long list of options with our new pass in it.

OVERVIEW: Tutorial Pass Driver
Available Dialects: acc, affine, amdgpu, <...SNIP...>
USAGE: tutorial-opt [options] <input file>


General options:

  Compiler passes to run
      --affine-full-unroll                             -   Fully unroll all affine loops
  --allow-unregistered-dialect                         - Allow operation with no registered dialects
  --disable-i2p-p2i-opt                                - Disables inttoptr/ptrtoint roundtrip optimization

To allow us to run lit tests that use this tool, we add it to the test_utilities target in this commit, and then we add a first (failing) test in this commit. To avoid complexity, I’m just asserting that the output has no for loops in it.

// RUN: tutorial-opt %s --affine-full-unroll > %t
// RUN: FileCheck %s < %t

func.func @test_single_nested_loop(%buffer: memref<4xi32>) -> (i32) {
  %sum_0 = arith.constant 0 : i32
  // CHECK-NOT: affine.for
  %sum = affine.for %i = 0 to 4 iter_args(%sum_iter = %sum_0) -> i32 {
    %t = affine.load %buffer[%i] : memref<4xi32>
    %sum_next = arith.addi %sum_iter, %t : i32
    affine.yield %sum_next : i32
  return %sum : i32

Next, we can implement the pass itself in this commit:

#include "lib/Transform/Affine/AffineFullUnroll.h"
#include "mlir/Dialect/Affine/IR/AffineOps.h"
#include "mlir/Dialect/Affine/LoopUtils.h"
#include "mlir/include/mlir/Pass/Pass.h"

using mlir::affine::AffineForOp;
using mlir::affine::loopUnrollFull;

void AffineFullUnrollPass::runOnOperation() {
  getOperation().walk([&](AffineForOp op) {
    if (failed(loopUnrollFull(op))) {
      op.emitError("unrolling failed");

getOperation returns a FuncOp, though we don’t use any specific information about it being a function. We instead call the walk method (present on all Operation instances), which traverses the abstract syntax tree (AST) of the operation in post-order (i.e., the function body), and for each operation it encounters, if the type of that operation matches the input type of the callback, the callback is executed. In our case, we attempt to unroll the loop, and if it fails we quit with a diagnostic error.

Exercise: determine how the loop unrolling might fail, and create a test MLIR input that causes it to fail, and observe the error messages that result.

Running this on our test shows the operation is applied:

$ bazel run tools:tutorial-opt -- --affine-full-unroll < tests/affine_loop_unroll.mlir
#map = affine_map<(d0) -> (d0 + 1)>
#map1 = affine_map<(d0) -> (d0 + 2)>
#map2 = affine_map<(d0) -> (d0 + 3)>
module {
  func.func @test_single_nested_loop(%arg0: memref<4xi32>) -> i32 {
    %c0 = arith.constant 0 : index
    %c0_i32 = arith.constant 0 : i32
    %0 = affine.load %arg0[%c0] : memref<4xi32>
    %1 = arith.addi %c0_i32, %0 : i32
    %2 = affine.apply #map(%c0)
    %3 = affine.load %arg0[%2] : memref<4xi32>
    %4 = arith.addi %1, %3 : i32
    %5 = affine.apply #map1(%c0)
    %6 = affine.load %arg0[%5] : memref<4xi32>
    %7 = arith.addi %4, %6 : i32
    %8 = affine.apply #map2(%c0)
    %9 = affine.load %arg0[%8] : memref<4xi32>
    %10 = arith.addi %7, %9 : i32
    return %10 : i32

I won’t explain what this affine.apply thing is doing, but suffice it to say the loop is correctly unrolled. A subsequent commit does the same test for a doubly-nested loop.

A Rewrite Pattern Version

In this commit, we rewrote the loop unroll pass in the next level of abstraction provided by MLIR: the pattern rewrite engine. It is useful in the kind of situation where one wants to repeatedly apply the same subset of transformations to a given IR substructure until that substructure is completely removed. The next section will write a pass that uses that in a meaningful way, but for now we’ll just rewrite the loop unroll pass to show the extra boilerplate.

A rewrite pattern is a subclass of OpRewritePattern, and it has a method called matchAndRewrite which performs the transformation.

struct AffineFullUnrollPattern :
  public OpRewritePattern<AffineForOp> {
  AffineFullUnrollPattern(mlir::MLIRContext *context)
      : OpRewritePattern<AffineForOp>(context, /*benefit=*/1) {}

  LogicalResult matchAndRewrite(AffineForOp op,
                                PatternRewriter &rewriter) const override {
    return loopUnrollFull(op);

The return value of matchAndRewrite is a LogicalResult, which is a wrapper around a boolean to signal success or failure, along with named utility functions like failure() and success() to generate instances, and failed(...) to test for failure. LogicalResult also comes with a subclass FailureOr that is subclass of optional that inter-operates with LogicalResult via the presence or absence of a value.

Aside: In a proper OpRewritePattern, the mutations of the IR must go through the PatternRewriter argument, but because loopUnrollFull doesn’t have a variant that takes a PatternRewriter as input, we’re violating that part of the function contract. More generally, the PatternRewriter handles atomicity of the mutations that occur within the OpRewritePattern, ensuring that the operations are applied only if the method reaches the end and succeeds.

Then we instantiate the pattern inside the pass

// A pass that invokes the pattern rewrite engine.
void AffineFullUnrollPassAsPatternRewrite::runOnOperation() {
  mlir::RewritePatternSet patterns(&getContext());
  // One could use GreedyRewriteConfig here to slightly tweak the behavior of
  // the pattern application.
  (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));

The overall pass is still anchored on FuncOp, but an OpRewritePattern can match against any op. The rewrite engine invokes the walk that we did manually, and one can pass an optional configuration struct that chooses the walk order.

The PatternSet can accept any number of patterns, and the greedy rewrite engine will keep trying to apply them (in a certain order related to the benefit constructor argument) until there are no matching operations to apply, all applied patterns return failure, or some large iteration limit is reached to avoid infinite loops.

A proper greedy RewritePattern

In homomorphic encryption (FHE), multiplication ops are typically MUCH more expensive than addition ops. I’m not an expert in classical CPU hardware performance, but if I recall correctly, on a typical CPU multiplication is something like 2-4x slower than addition, and that advantage probably goes away when doing multiplications in bulk/pipelines.

In FHE, the operations introduce noise growth in the ciphertext, and in some schemes multiplication introduces something like 100x the noise of addition, and reducing that noise is very time consuming. So it makes sense that one would want to convert multiplication ops into addition ops. In this section we’ll write a very simple pass that greedily rewrites multiplication ops as repeated additions.

The idea is to rewrite an operation like y = 9*x as y = 8*x + x (the 8 is a power of 2) and then expand it further as a = x+x; b = a+a; c = b+b; y = c+x. It replaces a multiplication by a constant with a roughly log-number of additions (the base-2 logarithm of the constant), though it gets worse the further away the constant gets from a power of two.

This commit contains a similar “empty shell” of a pass, with two patterns defined. The first, PowerOfTwoExpand, will be a pattern that rewrites y=C*x as y = C/2*x + C/2*x, when C is a power of 2, otherwise fails. The second, PeelFromMul “peels” a single addition off a product that is not with a power of 2, rewriting y = 9x as y = 8*x + x. These are applied repeatedly via the greedy pattern rewrite engine. By setting the benefit argument of PowerOfTwoExpand to be larger than PeelFromMul, we tell the greedy rewrite engine to prefer PowerOfTwoExpand whenever possible. Together, that achieves the transformation mentioned above.

This commit adds a failing test that only exercises PowerOfTwoExpand, and then this commit implements it. Here’s the implementation:

  LogicalResult matchAndRewrite(
       MulIOp op, PatternRewriter &rewriter) const override {
    Value lhs = op.getOperand(0);

    // canonicalization patterns ensure the constant is on the right, if there is a constant
    // See
    Value rhs = op.getOperand(1);
    auto rhsDefiningOp = rhs.getDefiningOp<arith::ConstantIntOp>();
    if (!rhsDefiningOp) {
      return failure();

    int64_t value = rhsDefiningOp.value();
    bool is_power_of_two = (value & (value - 1)) == 0;

    if (!is_power_of_two) {
      return failure();

    ConstantOp newConstant = rewriter.create<ConstantOp>(
        rhsDefiningOp.getLoc(), rewriter.getIntegerAttr(rhs.getType(), value / 2));
    MulIOp newMul = rewriter.create<MulIOp>(op.getLoc(), lhs, newConstant);
    AddIOp newAdd = rewriter.create<AddIOp>(op.getLoc(), newMul, newMul);

    rewriter.replaceOp(op, {newAdd});

    return success();

Some notes:

  • Value is the type that represents an SSA value (i.e., an MLIR variable), and getDefiningOp fetches the unique operation that defines it in its scope.
  • There are a variety of “casting” operations like rhs.getDefiningOp<arith::ConstantIntOp>() that take the type you want as output as a template parameter, and return null if the type cannot be converted. You might also see dyn_cast<>
  • (value & (value - 1)) is a classic bit-twiddling trick to compute if an integer is a power of two. We check it and skip the pattern if it’s not.
  • The actual constant itself is represented as an MLIR attribute, which is essentially compile-time static data attached to the op. You can put strings or dictionaries as attributes, but for ConstantOp it’s just an int.

The rewriter.create part is where we actually do the real work. Create a new constant that is half the original constant, create new multiplication and addition ops, and then finally rewriter.replaceOp removes the original multiplication op and uses the output of newAdd for any other operations that used the original multiplication op’s output.

It’s worth noting that we’re relying on MLIR’s built-in canonicalization passes in a few ways here:

  • To ensure that the constant is always the second operand of a multiplication op.
  • To ensure that the base case (x*1) is “folded” into a plain x and the constant 1 is removed.
  • The fold part of applyPatternsAndFoldGreedily is what runs these cleanup steps for us.

PeelFromMul is similar, implemented and tested in this commit:

  LogicalResult matchAndRewrite(MulIOp op,
                                PatternRewriter &rewriter) const override {
    Value lhs = op.getOperand(0);
    Value rhs = op.getOperand(1);
    auto rhsDefiningOp = rhs.getDefiningOp<arith::ConstantIntOp>();
    if (!rhsDefiningOp) { return failure(); }
    int64_t value = rhsDefiningOp.value();

    // We are guaranteed `value` is not a power of two, because the greedy
    // rewrite engine ensures the PowerOfTwoExpand pattern is run first, since
    // it has higher benefit.

    ConstantOp newConstant = rewriter.create<ConstantOp>(
        rhsDefiningOp.getLoc(), rewriter.getIntegerAttr(rhs.getType(), value - 1));
    MulIOp newMul = rewriter.create<MulIOp>(op.getLoc(), lhs, newConstant);
    AddIOp newAdd = rewriter.create<AddIOp>(op.getLoc(), newMul, lhs);

    rewriter.replaceOp(op, {newAdd});

Running it! Input:

func.func @power_of_two_plus_one(%arg: i32) -> i32 {
  %0 = arith.constant 9 : i32
  %1 = arith.muli %arg, %0 : i32
  func.return %1 : i32


module { 
  func.func @power_of_two_plus_one(%arg0: i32) -> i32 {
    %0 = arith.addi %arg0, %arg0 : i32
    %1 = arith.addi %0, %0 : i32
    %2 = arith.addi %1, %1 : i32
    %3 = arith.addi %2, %arg0 : i32
    return %3 : i32

Exercise: Try swapping the benefit arguments to see how the output changes.

Though this pass is quite naive, you can imagine a more sophisticated technique that builds a cost model for multiplications and additions, and optimizes for the cheapest cost representation of an arithmetic operation in terms of repeated additions, multiplications, and other supported ops.

Should we walk?

With two options for how to define a pass—one to walk the entire syntax tree from the root operation, and one to match and rewrite patterns with the rewrite engine—the natural question is when should you use one versus the other.

The MLIR docs describe the motivation behind the pattern rewrite engine, and it comes from a long history of experience with the LLVM project. For one, the pattern rewrite engine expresses a convenient subset of what can be achieved with an MLIR pass. This is conceptually trivial, in the sense that anyone who can walk the entire AST can, with enough effort, do anything they want including reimplementing the pattern rewrite engine.

More practically, the pattern rewrite engine is convenient to represent local transformations. “Local” here means that the input and output can be detected via a subset of the AST as a directed acyclic graph. More pragmatically, think of it as any operation you can identify by looking around at neighboring operations in the same block and applying some filtering logic. E.g., “is this exp operation followed by a log operation with no other uses of the output of the exp?”

On the other hand, some analyses and optimizations need to construct the entire dataflow of a program to work. A good example is common subexpression elimination, which determines whether it is cost effective to extract a subexpression used in multiple places into a separate variable. Doing so may introduce additional cost of memory access, so it depends both on the operation’s cost and on the availability of registers at that point in the program. You can’t get this information by pattern matching the AST locally.

The wisdom seems to be: using the pattern rewrite engine is usually easier than writing a pass that. walks the AST. You don’t need large case/switch statements to handle everything that could show up in the IR. The engine handles re-applying patterns many times. And so you can write the patterns in isolation and trust the engine to combine them appropriately.

Bonus: IDEs and CI

Since we explored the C++ API, it helps to have an IDE integration. I use neovim with the clangd LSP, and to make it work with a Bazel C++ project, one needs to use something analogous to Hedron Vision’s compile_commands extractor, which I configured for this tutorial project in this commit. It’s optional, but if you want to use it you have to run bazel run @hedron_compile_commands//:refresh_all once to set it up, and then clangd and clang-tidy, etc., should find the generated json file and use it. Also, if you edit a BUILD file, you have to re-run refresh_all for the changes to show up in the LSP.

Though it’s not particularly relevant to this tutorial, I also added a commit that configures GitHub actions to build and test the project in CI in this commit. It is worth noting that the GitHub cache action reduces subsequent build times from 1-2 hours down to just a few minutes.

Thanks to Patrick Schmidt for feedback on a draft of this article.

MLIR — Running and Testing a Lowering

Table of Contents

Last time, we covered a Bazel build system setup for an MLIR project. This time we’ll give an overview of a simple lowering and show how end-to-end tests work in MLIR. All of the code for this article is contained in this pull request on GitHub, and the commits are nicely organized and quite readable.

Two of the central concepts in MLIR are dialects and lowerings. These are the scaffolding within which we can do the truly interesting parts of a compiler—that is, the optimizations and analyses. In traditional compilers, there is typically one “dialect” (called an intermediate representation, or IR) that is the textual or data-structural description of a program within the compiler’s code. For example, in GCC the IR is called GIMPLE, and in LLVM it’s called LLVM-IR. They convert the input program to the IR, do their optimizations, and then convert the optimized IR to machine code.

In MLIR one splits the job into much smaller steps. First, MLIR allows one to define many dialects, some considered “high level” and some “low level,” but each with a set of types, operations, metadata, and semantics that defines what the operations do. Then, one writes a set of lowering passes that incrementally converts different parts of the program from higher level dialects to lower and lower dialects until you get to machine code (or, in many cases, LLVM, which finishes the job). Along the way, optimizing passes are run to make the code more efficient. The main point here is that the high level dialects exist so that they make it easy to write these important optimizing passes. And there’s not a special distinction between lowering passes and optimizing passes, they’re both just called passes in MLIR and are generic IR-rewriting modules.

Aside: From what I can gather, a big part of the motivation for MLIR was to build the affine dialect, which is specifically designed to enable polyhedral optimizations for loop transformations, along with the linalg dialect, which does optimization passes like tiling for low-level ML operations on specialized hardware. Folks built polyhedral optimizations in LLVM and GCC (without affine), and it was a huge pain in the ass, mainly because they had to take a low-level mess of branches and GOTOs and try to reconstruct a simple (‘affine’) for loop structure from it. This was necessary even if the input program was a simple set of for loops, because by the time they got to the compiler, the rigid for loop structure had been discarded. MLIR instead says, keep the structure in the higher level dialect, optimize there, and then discard it when you lower to lower level dialects.

Two example programs

A general understanding properly begins with concrete examples. Here are two MLIR programs that define a function that counts the leading zeroes of a 32-bit integer (i32). The first uses the math dialect’s defined ctlz operation and just returns it.

func.func @main(%arg0: i32) -> i32 {
  %0 = math.ctlz %arg0 : i32
  func.return %0 : i32

This shows the basic structure of an MLIR operation (see here for a more complete spec). Variable names are prefixed with %, functions by @, and each variable/value in a program has a type, often expressed after a colon. In this case all the types are i32, except for the function type which is (i32) -> i32 (not specified explicitly above, but you’ll see it in the in the next code snippet).

Each statement is anchored around an expression like math.ctlz which specifies the dialect math and the operation ctlz. The rest of the syntax of the operation is determined by a parser defined by the dialect, and so many operations will have different syntaxes, though many are pulled from a fixed set of options we’ll see later in the series. In the simple case of math.ctlz, the sole argument is the integer whose leading zeros are to be counted, and the trailing : i32 denotes the output type.

It’s also important to note that func is itself a dialect, and func.func is considered an “operation,” where the braces and the function’s body is part of the syntax. In MLIR a set of operations within braces is called a region, and an operation can have zero or many regions.

There is a lot more to say about regions, and their cousins “basic blocks,” but in brief: operations may have attached regions, like the body of a for loop, and each region is a list of blocks (with an implicit block if non is explicitly listed). A block is a list of operations that is guaranteed to have only one entry and exit point. I think of the label in a block as the destination of a jump command in assembly languages. A block has exactly one “jumping in” point and one “jumping out” point. It has a more precise definition that aligns with the classical compiler concept of a basic block.

Also note, in MLIR multiple dialects often coexist in the same program as it is progressively lowered to some final backend target.

The second version of this program has a software implementation of the ctlz function and calls it.

func.func @main(%arg0: i32) -> i32 {
  %0 = @my_ctlz(%arg0) : (i32) -> i32
  func.return %0 : i32
func.func @my_ctlz(%arg0: i32) -> i32 {
  %c32_i32 = arith.constant 32 : i32
  %c0_i32 = arith.constant 0 : i32
  %0 = arith.cmpi eq, %arg0, %c0_i32 : i32
  %1 = scf.if %0 -> (i32) {
    scf.yield %c32_i32 : i32
  } else {
    %c1 = arith.constant 1 : index
    %c1_i32 = arith.constant 1 : i32
    %c32 = arith.constant 32 : index
    %c0_i32_0 = arith.constant 0 : i32
    %2:2 = scf.for %arg1 = %c1 to %c32 step %c1 iter_args(%arg2 = %arg0, %arg3 = %c0_i32_0) -> (i32, i32) {
      %3 = arith.cmpi slt, %arg2, %c0_i32 : i32
      %4:2 = scf.if %3 -> (i32, i32) {
        scf.yield %arg2, %arg3 : i32, i32
      } else {
        %5 = arith.addi %arg3, %c1_i32 : i32
        %6 = arith.shli %arg2, %c1_i32 : i32
        scf.yield %6, %5 : i32, i32
      scf.yield %4#0, %4#1 : i32, i32
    scf.yield %2#1 : i32
  func.return %1 : i32

The algorithm above is not relevant to this post, but either way it is quite simple: count the leading zeros by shifting the input left one bit at a time until it becomes negative (as a signed integer), because that occurs exactly when its leading bit is a 1. Then add a special case to handle zero, which would loop infinitely otherwise.

Here you can see two more MLIR dialects. arith is for low-level arithmetic and boolean conditions on integers and floats. You can define constants, compare integers with arith.cmpi, and do things like add and bit shift (arith.shli is a left shift). scf, short for “structured control flow,” defines for loops, while loops, and control flow branching. scf.yield defines the “output” value from each region of an if/else operation or loop body which is necessary here because, as you can see, an if operation has a result value.

Two other minor aspects of the syntax are on display. First is the syntax %4:2, which defines a variable %4 which is a tuple of two values. The corresponding %4#1 accesses the second entry in the tuple. Second, you’ll notice there’s a type called index that is different from i32. Though they both represent integers, index is intended to be a platform-dependent integer type which is suitable for indexing arrays, representing sizes and dimensions of things, and, in our case, being loop counters and iteration bounds. More details on index in the MLIR docs.

Lowerings and the math-to-funcs pass

We have two versions of the same program because one is a lowered version of the other. In most cases, the machine you’re going to run a program on has a “count leading zeros” function, so the lowering would simply map math.ctlz to the corresponding machine instruction. But if there is no ctlz instruction, a lowering can provide an implementation in terms of lower level dialects and ops. Specifically, this one lowers ctlz to {func, arith, scf}.

The second version of this code was actually generated by the mlir-opt command line tool, which is the main entry-point to running MLIR passes on specific MLIR code. For starters, one can take the mlir-opt tool and run it with no arguments on any MLIR code, and it will parse it, verify it is well formed, and print it back out with some slight normalizations. In this case, it will wrap the code in a module, which is a namespace isolation mechanism.

$ echo 'func.func @main(%arg0: i32) -> i32 {
  %0 = math.ctlz %arg0 : i32
  func.return %0 : i32
}' > ctlz.mlir
$ bazel run @llvm-project//mlir:mlir-opt -- $(pwd)/ctlz.mlir
<... snip ...>
module {
  func.func @main(%arg0: i32) -> i32 {
    %0 = math.ctlz %arg0 : i32
    return %0 : i32

Aside: The -- $(pwd)/ctlz.mlir is a quirk of bazel. When one program runs another program, the -- is the standard mechanism to separate CLI flags from the runner program (bazel) and the run program (mlir-opt). Everything after -- goes to mlir-opt. Also, the need for $(pwd) is because when bazel runs mlir-opt, it runs it with a working directory that is in some temporary, isolated location on the filesystem. So we need to give it an absolute path to the MLIR file to input. Or we could pipe from standard in. Or we could run the mlir-opt binary directly from bazel-bin/external/llvm-project/mlir/mlir-opt.

Next we can run our first lowering, which is already built-in to mlir-opt, and which generates the long program above.

$ bazel run @llvm-project//mlir:mlir-opt -- --convert-math-to-funcs=convert-ctlz $(pwd)/ctlz.mlir
<... snip ...>
module {
  func.func @main(%arg0: i32) {
    %0 = call @__mlir_math_ctlz_i32(%arg0) : (i32) -> i32
  func.func private @__mlir_math_ctlz_i32(%arg0: i32) -> i32 attributes {llvm.linkage = #llvm.linkage<linkonce_odr>} {
<... snip ...>

Each pass gets its own command line flag, some are grouped into pipelines, and the --pass-pipeline command line flag can be used to provide a (serialized version of) an ordered list of passes to run on the input MLIR.1

We won’t cover the internal workings of the math-to-funcs pass in this or a future article, but next time we will actually write our own, simpler pass that does something nontrivial. Until then, I’ll explain a bit about how testing works in MLIR, using these two ctlz programs as example test cases.

For those who are interested, the MLIR documentation contains a complete list of passes owned by the upstream MLIR project, which can be used by invoking the corresponding command line flag or nesting it inside of a larger --pass-pipeline.

Lit, FileCheck, and Bazel again

The LLVM and MLIR projects both use the same testing framework, which is split into two parts. The first is lit (LLVM Integrated Tester; though I don’t know why it’s called “integrated”), which handles test discovery and running. The second is FileCheck, which handles test assertions and reporting.

I don’t know why they’re two separate tools, but they are primarily end to end testing tools—as opposed to unit testing tools. Because end-to-end testing in a compiler toolchain implies the inputs and outputs are essentially big strings (programs) in unknown languages (user-defined MLIR dialects), these tools basically have you express the test setup and assertions in comments inside of the file representing the input program to be tested. An example might look like this:

// RUN: mlir-opt %s --convert-math-to-funcs=convert-ctlz | FileCheck %s

func.func @main(%arg0: i32) -> i32 {
  // CHECK-NOT: math.ctlz
  // CHECK: call
  %0 = math.ctlz %arg0 : i32
  func.return %0 : i32

I added this test in this commit. This trivial function calls math.ctlz on its input and promptly returns it. The interesting parts are the comments, which define the test command and assertions.

Warning: you may run into a python issue where python cannot find the lit module. See, wherein I realized too late that bazel uses the system Python by default. tl;dr: you can either run pip install lit on your system Python, or else cherry-pick a commit in that issue to use a bazel-managed Python.

A lit test file contains some number of lines with RUN: as the lead of a comment, and the text after that describes a shell script to run, with some magic strings instructing lit to make substitutions. In this case %s is the current file path, but there is a table of default substitutions and one can add their own custom substitutions in a config file (see later).

In typical unix fashion, all lit does is check for the exit status of the RUN command to determine if the test passes or fails. Hence, this test pipes the output of mlir-opt to the FileCheck program, again passing in the current file path, which contains the assertions to check for.

FileCheck is a bit more complicated than lit, but in brief it takes the input passed to stdin, scans for CHECK comments in the file passed as the CLI argument, and then for each CHECK comment, it does some logic to determine if the assertion passes. The simplest kind of assertion is a // CHECK: foo which searches for a line matching the foo regular expression. Similarly, a // CHECK-NOT: assertion asserts the regular expression is not matched in the file. Beyond that, the main thing that is enforced is that multiple CHECK assertions match the input file in the same order that the CHECK comments occur. So if you had

// RUN: mlir-opt %s --convert-math-to-funcs=convert-ctlz | FileCheck %s

func.func @main(%arg0: i32) -> i32 {
  // CHECK: call
  // CHECK: foo
  // CHECK: return
  %0 = math.ctlz %arg0 : i32
  func.return %0 : i32

Then it would expect that there are three lines (possibly with other lines between them) that match these regular expressions in order. A line matching call and a line matching return would fail unless there is a line between them matching foo.

FileCheck can do a lot more, like use regular expressions to capture variable names and then refer to them in later CHECK assertions. With this, one can give a much more precise test on the ctlz lowering, expecting a relatively rigid structure of the output function, as in this commit. I won’t give full details here, but you can read the FileCheck documentation here and intuitively tell that an expression like %[[ARGCMP:.*]] captures a variable name where ARCMP is how it is referred to in later assertions, while .* is the regular expression used to capture it (and % is an anchor that ensures it only applies to a variable name).

To run these tests, requires a bit of finnicky configuration. lit can be run like a normal python program, and if all the executables invoked in the RUN directives are in the PATH environment variable, then it will just work. However, in any build system the executables are in exotic places, which is especially true in Bazel.

Aside: In typical CMake-oriented MLIR projects, there are actually two config files, one called something like, which has variables that CMake substitutes in pointing to the build artifact paths, and one called which configures lit to use those paths. In my opinion the Bazel configuration is marginally simpler, but I am biased because I’m more familiar with it.

In bazel a single test would correspond to a build target in a BUILD file of the following form:

     name = "my_test_file.mlir.test",
     srcs = ["@llvm_project//llvm:lit"],
     args = ["-v", "tests/my_test_file.mlir"],
     data = ["@llvm-project//llvm:FileCheck", ..., ":my_test_file.mlir"],
     main = "",

This tells bazel to run lit with the right arguments, and crucially, the data argument allows us to pull in binary targets corresponding to the commands used in the RUN directives. Then two things happen. First, lit runs in a working directory determined arbitrarily by bazel (with the data stuff pulled in somehow). We need to understand the directory structure of this working directory in order to configure lit properly. Then, when lit runs, it looks for a file called in the directory containing the test (and recursively upward to the project root), loads it, and uses that to set the PATH and other configuration.

In our case, the looks like this

import os
from pathlib import Path
from lit.formats import ShTest = "mlir_tutorial"
config.test_format = ShTest()
config.suffixes = [".mlir"]

runfiles_dir = Path(os.environ["RUNFILES_DIR"])
tool_relpaths = [

config.environment["PATH"] = (
    ":".join(str(runfiles_dir.joinpath(Path(path))) for path in tool_relpaths)
    + ":"
    + os.environ["PATH"]

Two weird things are happening here. First, config is an undefined variable at first glance, but the lit documentation states that an instance is inserted into the module scope when lit runs. Second, we are using the RUNFILES_DIR environment variable as the base for the paths we will construct pointing to the binaries. RUNFILES_DIR is defined by bazel, and it is generally different from the working directory of the binary run by native.py_test. It contains a directory tree for the current project (mlir_tutorial) as well as all dependent projects defined in the WORKSPACE, so long as some targets from those projects were included in the data option of the test rule.

Once this is all worked out, one can define individual test targets for each lit test. However, since that is laborious, instead what I did in this commit was define all of the above configuration together with a bazel macro that will search for all .mlir files in a given directory and create test targets for them. So in this project, a new .mlir file added to tests/ will be automatically run when you run bazel test //.... Then, tests/BUILD contains the glob_lit_tests macro invocation, and a filegroup that describes all the tools and files that should be included in the data to run them.

# tests/BUILD
load("//bazel:lit.bzl", "glob_lit_tests")

# Bundle together all of the test utilities that are used by tests.
    name = "test_utilities",
    testonly = True,
    data = [


Bonus: functional testing

The previous lowering of math.ctlz to a software implementation has a very detailed test, but in MLIR the lowerings are primarily syntactic in nature. That is, the test does not assert that the lowering itself is functionally correct. The author may have created assertions that align with the generated code, but the generated code has a bug or otherwise does not compute what it is supposed to compute.

One way around this is to continue compiling the MLIR code down through LLVM to machine code, running it, and asserting something about the output (presumably printed to stdout). While this is possible in lit, since RUN can run anything, it does require pulling in quite a few more dependencies. A slightly more lightweight means to achieve this is to use mlir-cpu-runner, which is an interpreter for some of the lowest-level MLIR dialects (in particular, the llvm dialect, which is the “exit” dialect before going to LLVM).

Here’s what such a test might look like in lit for our ctlz lowering pass, which tests that 7, as a 32-bit integer, has 29 leading zeros. I added the test in this commit. Notably, I had to add the mlir-cpu-runner binary to that list of test_utilities mentioned in the previous section, or else the test will fail with the inability to find the mlir-cpu-runner binary.

// RUN: mlir-opt %s \
// RUN:   --pass-pipeline="builtin.module( \
// RUN:      convert-math-to-funcs{convert-ctlz}, \
// RUN:      func.func(convert-scf-to-cf,convert-arith-to-llvm), \
// RUN:      convert-func-to-llvm, \
// RUN:      convert-cf-to-llvm, \
// RUN:      reconcile-unrealized-casts)" \
// RUN: | mlir-cpu-runner -e test_7i32_to_29 -entry-point-result=i32 > %t
// RUN: FileCheck %s --check-prefix=CHECK_TEST_7i32_TO_29 < %t

func.func @test_7i32_to_29() -> i32 {
  %arg = arith.constant 7 : i32
  %0 = math.ctlz %arg : i32
  func.return %0 : i32
// CHECK_TEST_7i32_TO_29: 29

The RUN command is quite a bit more complicated. First, we need to run more passes than just convert-math-to-funcs in order to get the code down to the LLVM dialect, which is what mlir-cpu-runner supports. The --pass-pipeline flag allows you to build a more complex chain of passes on the command line. Then the result is piped to mlir-cpu-runner, which takes as command line flags the top level function to run and the type of the result. Finally, the output is piped to %t, which is a lit substitution magic that represents a per-test temporary file. In this case, it is used so that if this first command fails, the error message from that is displayed in the test failure, rather than the subsequent failure of FileCheck to parse an empty input from the pipe.

Then, a second RUN command runs FileCheck, again using the current file for the test assertion, piping the input to test as %t, and adding the special --check-prefix flag so that it only runs a subset of CHECK assertions in the file (allowing us to add a second test in the same file, as in the next commit that runs a similar test for an i64 input). Then, because mlir-cpu-runner prints the result of the function to stdout, the CHECK assertion just expects the output to be 29 for input 7.

It may also be interesting to the reader to see what MLIR outputs when I run the full pass (but not the mlir-cpu-runner on the input. Here it is:

module attributes {llvm.data_layout = ""} {
  llvm.func @test_7i32_to_29() -> i32 {
    %0 = llvm.mlir.constant(7 : i32) : i32
    %1 = llvm.mlir.constant(29 : i32) : i32
    llvm.return %1 : i32
  llvm.func linkonce_odr @__mlir_math_ctlz_i32(%arg0: i32) -> i32 attributes {sym_visibility = "private"} {
    %0 = llvm.mlir.constant(32 : i32) : i32
    %1 = llvm.mlir.constant(0 : i32) : i32
    %2 = llvm.icmp "eq" %arg0, %1 : i32
    llvm.cond_br %2, ^bb1, ^bb2
  ^bb1:  // pred: ^bb0 ^bb10(%0 : i32)
  ^bb2:  // pred: ^bb0
    %3 = llvm.mlir.constant(1 : index) : i64
    %4 = llvm.mlir.constant(1 : i32) : i32
    %5 = llvm.mlir.constant(32 : index) : i64
    %6 = llvm.mlir.constant(0 : i32) : i32 ^bb3(%3, %arg0, %6 : i64, i32, i32)
  ^bb3(%7: i64, %8: i32, %9: i32):  // 2 preds: ^bb2, ^bb8
    %10 = llvm.icmp "slt" %7, %5 : i64
    llvm.cond_br %10, ^bb4, ^bb9
  ^bb4:  // pred: ^bb3
    %11 = llvm.icmp "slt" %8, %1 : i32
    llvm.cond_br %11, ^bb5, ^bb6
  ^bb5:  // pred: ^bb4 ^bb7(%8, %9 : i32, i32)
  ^bb6:  // pred: ^bb4
    %12 = llvm.add %9, %4  : i32
    %13 = llvm.shl %8, %4  : i32 ^bb7(%13, %12 : i32, i32)
  ^bb7(%14: i32, %15: i32):  // 2 preds: ^bb5, ^bb6 ^bb8
  ^bb8:  // pred: ^bb7
    %16 = llvm.add %7, %3  : i64 ^bb3(%16, %14, %15 : i64, i32, i32)
  ^bb9:  // pred: ^bb3 ^bb10(%9 : i32)
  ^bb10(%17: i32):  // 2 preds: ^bb1, ^bb9 ^bb11
  ^bb11:  // pred: ^bb10
    llvm.return %17 : i32

The main new thing here, besides all of the llvm dialect operations, is the ^bb1 syntax, which is the label identifier for those basic block syntax structures mentioned earlier. With the basic syntax and testing down, next time we will define a custom lowering and explore the MLIR API from that perspective. Then we’ll dive into defining a new dialect.

Thanks to Patrick Schmidt for feedback on a draft of this article.

MLIR — Getting Started

Table of Contents

As we announced recently, my team at Google has started a new effort to build production-worthy engineering tools for Fully Homomorphic Encryption (FHE). One focal point of this, and one which I’ll be focusing on as long as Google is willing to pay me to do so, is building out a compiler toolchain for FHE in the MLIR framework (Multi-Level Intermediate Representation). The project is called Homomorphic Encryption Intermediate Representation, or HEIR.

The MLIR community is vibrant. But because it’s both a new and a fast-moving project, there isn’t a lot in the way of tutorials and documentation available for it. There is no authoritative MLIR book. Most of the reasoning around things is in folk lore and heavily technical RFCs. And because MLIR is built on top of LLVM (the acronym formerly meaning “Low Level Virtual Machine”), much of the documentation that exists explains concepts by analogy to LLVM, which is unhelpful for someone like me who isn’t familiar with the internals of how LLVM works. Finally, the “proper” tutorials that do exist are, in my opinion, too high level to allow one to really get a sense for how to write programs in the framework.

I want people interested in FHE to contribute to HEIR. To that end, I want to lower the barrier to entry to working with MLIR. And so this series of blog posts will be a detailed introduction to MLIR in general, with some bias toward the topics that show up in HEIR and that I have spent time studying and internalizing.

This first article describes a typical MLIR project’s structure, and the build system that we use in HEIR. But the series as a whole will be built up along with a GitHub repository that breaks down each step into clean, communicative commits, similar to my series about the Riemann Hypothesis. To avoid being broken by upstream changes to MLIR (our project will be “out of tree”, so to speak), we will pin the dependency on MLIR to a specific commit hash. While this implies that the content in these articles will eventually become stale, I will focus on parts of MLIR that are relatively stable.

A brief history of MLIR and LLVM

The first thing you’ll notice about MLIR is that it lives within the LLVM project’s monorepo under a folder called mlir/. LLVM is a sort of abstracted assembly language that compiler developers can target as a backend, and then LLVM itself comes packaged with a host of optimizations and “real” backend targets that can be compiled to. If you’re, say, the Rust programming language and you want to compile to x86, ARM, and WebAssembly without having to do all that work, you can just output LLVM code and then run LLVM’s compilation suite.

I don’t want to get too much into the history of LLVM (see this interview for more details), and I don’t have any first hand knowledge of it, but from what I can gather LLVM (formerly standing for “Low Level Virtual Machine”) was the PhD project of Chris Lattner in the early 2000’s, aiming to be a next-generation C compiler. Chris moved to Apple, where he worked on LLVM and languages like Swift which build on LLVM. In 2017 he moved to Google Brain as a director of the TensorFlow infrastructure team, and he and his team built MLIR to unify the siloed tooling in their ecosystem.

We’ll talk more about what exactly MLIR is and what it provides in a future article. For a high level overview, see the MLIR paper. In short, it’s a framework for building compilers, with the underlying philosophy that a big compiler should be broken up into lots of small compilers between sub-languages (which compiler folks call “intermediate representations” or “IR”s), where each sub-language is designed to make a particular kind of optimization more natural to express. Hence the MLIR acronym standing for Multi-Level Intermediate Representation.

MLIR is relevant for TensorFlow because training and inference can both be thought of as programs whose instructions are things like “2d convolution” and “softmax.” And the process for optimizing those instructions, while converting them to lower level hardware instructions (especially on TPU accelerators) is very much a compilers problem. MLIR breaks the process up into IRs at various levels of abstraction, like Tensor operations, linear algebra, and lower-level control flow.

But LLVM just couldn’t be directly reused as a TensorFlow compiler. It was too legacy and too specialized to CPU, operated at a much lower abstraction layer, and had incidental tech debt. But LLVM did have lots of reusable pieces, like data structures, error handling, and testing infrastructure. And combined with Lattner’s intimate familiarity with a project he’d worked on for almost 20 years, it was probably just easier to jumpstart MLIR by putting it in the monorepo.

Build systems

The rest of this article is going to focus on setting up the build system for our tutorial project. It will describe each commit in this pull request.

Now, the official build system of LLVM and MLIR is CMake. But I’ll be using Bazel for a few reasons. First, I want to induct interested readers into HEIR, and that’s what HEIR uses because it’s a Google-owned project. Second, though one might worry that the Bazel configuration is complicated or unsupported, because MLIR and LLVM have become critical to Google’s production infrastructure, Google helps to main a Bazel “overlay” in parallel with the CMake configuration, and Google has on call engineers responsible for ensuring that both Google’s internal copy of MLIR stays up to date with the LLVM monorepo, and that any build issues are promptly fixed. The rough edges that remain are simple enough for an impatient dummy like me to handle.

So here’s an overview of Bazel (with parts repeated from my prior article). Bazel is the open source analogue of Google’s internal build system, “Blaze”, and Starlark is its Python-inspired scripting language. There are lots of opinions about Bazel that I won’t repeat here. You can install it using the bazelisk program.

First some terminology. To work with Bazel you do the following.

  • Define a WORKSPACE file which defines all your project’s external dependencies, how to fetch their source code, and what bazel commands should be used to build them. This can be thought of as a top-level CMakeLists, except that it doesn’t contain any instructions for building the project beyond declaring the root of the project’s directory tree and the project’s name.
  • Define a set of BUILD files in each subdirectory, declaring the build targets that can be built from the source files in that directory (but not its subdirectories). This is analogous to CMakeLists files in subdirectories. Each build target can declare dependence on other build targets, and bazel build ensures the dependencies are built first, and caches the build results across a session. Many projects have a BUILD file in the project root to expose the project’s public libraries and APIs.
  • Use the built-in bazel rules like cc_library and cc_binary and cc_test to group files into libraries that can be built with bazel build, executable binaries that can also be run with bazel run, and tests that can also be run with bazel test. Most bazel rules boil down to calling some executable program like gcc or javac with specific arguments, while also keeping track of the accumulated dependency set of build artifacts in a “hermetic” location on the filesystem.
  • Define new bazel rules that execute custom programs, and which declare dependencies and outputs for the static dependency graph. MLIR’s custom rules revolve around the tblgen program, which is MLIR’s custom templating language that generates C++ code.
  • Write any additional bazel macros that chain together built-in bazel commands. Macros look like Python functions that call individual bazel rules and possibly pass data between them. They’re written in .bzl files (containing Starlark code) which are interpreted directly by bazel. We’ll see a good example of a bazel macro when we talk about MLIR’s testing framework lit, but this article contains a simple one for setting up the LLVM dependency in the WORKSPACE file (which is also Starlark).

Generally, bazel builds targets in two phases. First—the analysis phase—it loads all the BUILD files and imported .bzl files, and scans for all the rules that were called. In particular, it runs the macros, because it needs to know what rules are called by the macros (and rules can be guarded by control flow, or their arguments can be generated dynamically, etc.). But it doesn’t run the build rules themselves. In doing this, it can build a complete graph of dependencies, and report errors about typos, missing dependencies, cycles, etc. Once the analysis phase is complete, it runs the underlying rules in dependency order, and caches the results. Bazel will only run a rule again if something changes with the files it depends on or its underlying dependencies.

The WORKSPACE and llvm-project dependency

The commits in this section will come from

After adding a .gitignore to filter out Bazel’s build directories, this commit sets up an initial WORKSPACE file and two bazel files that perform an unusual two-step dance for configuring the LLVM codebase. The workspace file looks like this:

workspace(name = "mlir_tutorial")

load("@bazel_tools//tools/build_defs/repo:http.bzl", "http_archive")
load("@bazel_tools//tools/build_defs/repo:utils.bzl", "maybe")

load("//bazel:import_llvm.bzl", "import_llvm")


load("//bazel:setup_llvm.bzl", "setup_llvm")


This is not a normal sort of dependency. A normal dependency might look like this:

    name = "abc",
    build_file = "//bazel:abc.BUILD",
    sha256 = "7fa5a448a4309fb4d6cf856c3fe4cc4be46b09dd552a05d5cfacd75f8d9504ad",
    urls = [

The above tells bazel: go pull the zip file from the given URL, double check it’s hashsum, and then (because the dependent project is not build with bazel) I’ll tell you where in my repository to find the BUILD file that you should use to build it. If the project had a BUILD file, we could omit build_file and it would just work.

Now, LLVM has bazel build files, but they are hidden in the utils/bazel subdirectory of the project. Bazel requires its special files to be in the right places, plus the bazel configuration is designed to be in sync with the CMake configuration. So the utils/bazel directory has an llvm_configure bazel macro which executes a python script that symlinks everything properly. More info about the upstream system can be found here.

So to run this macro we have to download the LLVM code as a repository, which I put into the import_llvm.bzl file, as well as call the macro, which I put into setup_llvm.bzl. Why two files? An apparent quirk of bazel is that you can’t load() a macro from a dependency’s bazel file in the same WORKSPACE file in which you download the dependency.

It’s also worth mentioning that import_llvm.bzl is where I put the hard-coded commit hash that pins this project to a specific LLVM version.

Getting past some build errors

In an ideal world this would be enough, but trying to build MLIR now gives errors. In the following examples I will try to build the @llvm-project//mlir:IR build target (arbitrarily chosen).

Side note: some readers of early drafts have had trouble getting these steps to work exactly. Despite bazel aiming to be a perfectly hermetic build system, it has to store temporary files somewhere, and that can lead to inconsistencies and permission errors. If you’re not able to get these steps to work, check out these links:

For starters, the build fails with

$ bazel build @llvm-project//mlir:IR
ERROR: Skipping '@llvm-project//mlir:IR': error loading package '@llvm-project//mlir': 
Unable to find package for @bazel_skylib//rules:write_file.bzl: 
The repository '@bazel_skylib' could not be resolved: 
Repository '@bazel_skylib' is not defined.

Bazel complains that it can’t find @bazel_skylib, which is a sort of extended standard library for Bazel. The MLIR Bazel overlay uses it for macros like “run shell command.” And so we learn another small quirk about Bazel, that each project must declare all transitive workspace dependencies (for now).

So in this commit we add bazel_skylib as a dependency.

Now it fails because of two other dependencies, llvm_zlib and llvm_std. This commit adds them.

$ bazel build @llvm-project//mlir:IR
ERROR: /home/j2kun/.cache/bazel/_bazel_j2kun/fc8ffaa09c93321753c7c87483153cea/external/llvm-project/llvm/BUILD.bazel:184:11: 
no such package '@llvm_zlib//': 
The repository '@llvm_zlib' could not be resolved: 
Repository '@llvm_zlib' is not defined and referenced by '@llvm-project//llvm:Support'

Now when you try to build you get a bona-fide compiler error.

$ bazel build @llvm-project//mlir:IR
INFO: Analyzed target @llvm-project//mlir:IR (41 packages loaded, 1495 targets configured).
INFO: Found 1 target...
ERROR: <... snip ...>
In file included from external/llvm-project/llvm/lib/Demangle/Demangle.cpp:13:
external/llvm-project/llvm/include/llvm/Demangle/Demangle.h:35:28: error: 
'string_view' is not a member of 'std'
   35 | char *itaniumDemangle(std::string_view mangled_name);
      |                            ^~~~~~~~~~~
external/llvm-project/llvm/include/llvm/Demangle/Demangle.h:35:28: note: 'std::string_view' is only available from C++17 onwards

note: ‘std::string_view’ is only available from C++17 onwards” suggests something is still wrong with our setup, and indeed, we need to tell bazel to compile with C++17 support. This can be done in a variety of ways, but the way that has been the most reliable for me is to add a .bazelrc file that enables this by default in every bazel build command run while the working directory is underneath the project root. This is done in this commit. (also see this extra step that may be needed for MacOS users)

# in .bazelrc
build --action_env=BAZEL_CXXOPTS=-std=c++17

Then, finally, it builds.

At this point you could build ALL of the LLVM/MLIR project by running bazel build @llvm-project//mlir/…:all. However, while you will need to do something similar to this eventually, and doing it now (while you read) is a good way to eagerly populate the build cache, it will take 30 minutes to an hour, make your computer go brrr, and use a few gigabytes of disk space for the cached build artifacts. (After working one three projects that each depend on LLVM and/or MLIR, my bazel cache is currently sitting at 23 GiB).

But! If you try there’s still one more error:

$ bazel build @llvm-project//mlir/...:all
ERROR: /home/j2kun/.cache/bazel/_bazel_j2kun/fc8ffaa09c93321753c7c87483153cea/external/llvm-project/mlir/test/BUILD.bazel:591:11: 
no such target '@llvm-project//llvm:NVPTXCodeGen': 
target 'NVPTXCodeGen' not declared in package 'llvm' defined by
(Tip: use `query "@llvm-project//llvm:*"` to see all the targets in that package) and referenced by '@llvm-project//mlir/test:TestGPU'

This is another little bug in the Bazel overlays that I hope will go away soon. It took me a while to figure this one out when I first encountered it, but here’s what’s happening. In the bazel/setup_llvm.bzl file that chooses which backend targets to compile, we chose only X86. The bazel overlay files are supposed to treat all backends as optional, and only define targets when the chosen backend dependencies are present. This is how you can avoid compiling a bunch of code for doing GPU optimization when you don’t want to target GPUs.

But, in this case the NVPTX backend (a GPU backend) is defined whether or not you include it as a target. So the simple option is to just include it as a target and take the hit on the cold-start build time. This commit fixes it.

Now you can build all of LLVM, and in particular you can build the main MLIR binary mlir-opt.

$ bazel run @llvm-project//mlir:mlir-opt -- --help
OVERVIEW: MLIR modular optimizer driver

Available Dialects: acc, affine, amdgpu, amx, arith, arm_neon, arm_sve, async, bufferization, builtin, cf,
complex, dlti, emitc, func, gpu, index, irdl, linalg, llvm, math, memref, ml_program, nvgpu, nvvm, omp, pdl, 
pdl_interp, quant, rocdl, scf, shape, sparse_tensor, spirv, tensor, test, test_dyn, tosa, transform, vector, 
USAGE: mlir-opt [options] <input file>


mlir-opt is the main entry point for running optimization passes and lowering code from one MLIR dialect to another. Next time, we’ll explore what some of the simpler dialects look like, run some pre-defined lowerings, and learn about how the end-to-end testing framework works.

Thanks to Patrick Schmidt for feedback on a draft of this article.

Google’s Recent FHE work, and starting HEIR

Today my team at Google published an article on Google’s Developers Blog with some updates on what we’ve been doing with fully homomorphic encryption (FHE). There’s fun stuff in there, including work on video processing FHE, compiling ML models to FHE, an FHE implementation for TPUs, and improvements to the compiler I wrote about earlier this year.

A simple object movement tracking algorithm in FHE, tracking a runaway lawn mower from a Nest camera. The video is 720p.

But as we’ve inched closer to having production clients, the more gaps we’ve found in our existing tool set. Teams interested in using FHE have seasoned, complex C/C++ codebases, or serious ML models. The parts where the computation should be private are interspersed with all sorts of FHE-incompatible constructions (or at least, incompatible with the assumptions in our compiler). They have certain latency and bandwidth constraints, or a nuanced key management story, and it became clear to us that bringing FHE to production will require a stronger engineering foundation.

At the same time, my team and I had the pleasure of traveling to Seoul and Tokyo for this year’s flagship FHE workshops, the standards meeting and the conference. My talk at the former presented this engineering problem and proposed MLIR as a common foundation that everyone working on FHE compilers can share.

We found kindred spirits among the attendees from ETH Zurich, Zama, Yonsei Univeristy, and others who had each implemented some flavor of FHE compiler on top of MLIR. We also met many folks working on hardware accelerators for FHE, everything from FPGAs to optical accelerators, and we agreed that getting fair evaluations across hardware and across FHE schemes is hindered by the current tooling and research silos. After a rousing discussion session, we decided to start work on a project we’re calling Homomorphic Encryption Internal Representation (HEIR, see website and GitHub), which we aim to make a standardized and “batteries included” starting point for researchers and practitioners interested in FHE compilers, as well as the basis for Google’s future compiler work.

The project is still very much in its early stages. The GitHub repository is quite sparse so far and we have no end-to-end compilation paths yet. But I’m excited and energetic about it, and working on it will be the bulk of my full time job for now. We also had a warm reception from the MLIR community. They’re going out of their way to help me sort through my MLIR questions, and some have expressed interest in upstreaming some of our more general ideas, like a dialect for polynomial arithmetic that is the core number crunching component of most FHE schemes.

In the mean time, I also want to encourage cryptographers, compiler engineers, and newcomers alike to participate. While we don’t yet have any “good first issues” to point to, there are quite a few active discussions going on, in-progress PRs we’re drafting, an open (video call) meeting every two weeks (see calendar), and past meeting notes to peruse.

Some members of the FHE community have also expressed to me that they’ve found MLIR to have too steep of a learning curve, and docs that are not low-level enough for a beginner. To help with that, I’ll be writing a series of “complete beginner” MLIR tutorials on this blog, with one pull request per article on this tutorial repository, in the style of my Searching for Riemann Hypothesis Counterexamples series. They’ll be slightly biased toward the HEIR project—using our chosen build system, bazel, rather than CMake, and focusing on out-of-tree development—but some MLIR beginners not involved in HEIR who read early drafts have told me they found it very useful. I’ll be publishing the first four articles this week and more periodically.