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IREE / MLIR / Linalg tutoriallink

Introductionlink

This tutorial is simultaneously about IREE, MLIR, and specifically the MLIR Linalg dialect.

What is MLIR?link

MLIR is a programming language, but MLIR in itself is almost just an empty shell. What it really provides is a framework allowing to define MLIR dialects which are where the features come from.

The "IR" part of the MLIR name stands for "intermediate representation". It means that MLIR is meant to be primarily for compiler-internal representations of code. But MLIR is actually fairly nice for humans to work with, and it's not hard to hand-author some MLIR programs from scratch. That is exactly the topic of this tutorial.

The "ML" part of the MLIR name stands for "multi-level" (not machine learning!). It means that MLIR allows for multiple dialects to be freely mixed in the same MLIR programs. Each dialect can define operations, types and attributes, and each single MLIR statement can mix ops, types and attributes coming from different dialects.

What is the Linalg dialect?link

Linalg is a MLIR dialect that essentially consists of a single op, linalg.generic, with most other ops in this dialect being just convenience aliases for special cases of linalg.generic. So, to describe Linalg dialect is essentially to describe linalg.generic.

The point of this is that this single op, linalg.generic, is:

  • General enough to express the entirety of usual machine learning workloads in any quantization scheme at all.
  • High-level enough to be lowered to efficient code for any target (CPU, GPU, ...)
  • Designed to be a good fit for compiler IR-to-IR transformations.

These traits make the Linalg dialect an ideal "middle-end" IR for a machine learning compiler.

What is IREE?link

IREE is a MLIR compiler and runtime that can lower MLIR programs through successive, ever lower-level dialects, ultimately producing machine code for various CPU, GPU and other hardware targets. Check out the Developer overview docs and the ML frameworks docs.

Front-ends can ingest source programs from various machine-learning frameworks into MLIR Linalg dialect. Boundaries are in flux, but it is a good enough mental model to think of anything up to Linalg as "front-end". One example is, for ingesting PyTorch programs, the front-end is torch-mlir and end-users are encouraged to use iree-turbine, which integrates IREE, torch-mlir and PyTorch.

This tutorial is only concerned about the Linalg dialect, and we are going to learn to hand-author some Linalg programs. The point of the above tangent about front-ends is to make it clear that no matter which way you feed a program into IREE, it will internally be rewritten into a Linalg program, because that really is the intermediate representation in this compiler.

Getting IREE binarieslink

IREE builds can be downloaded or installed as Python packages or built from sources.

First linalg programslink

Before we start: there is also an official Linalg tutorial. It takes a different approach compared to the present tutorial, so the two are complementary.

Static-shape, element-wise addition of two 1D arrayslink

Here is our first Linalg function. The scalar type used in this program, f32, is 32-bit floating-point.

Notice some elements of MLIR syntax:

  • The % prefix on an identifier indicates a SSA value, like here %result.
  • The @ prefix on an identifier indicates a function, like here @foo.
  • The ^ prefix on an identifier indicates a block, like here ^bb0.
  • The # prefix on an identifier indicates an attribute alias, like here #map_1d_identity.
  • The x letter is used as delimiter in shapes, and between the shape and the element type, like here 10xf32 meaning a 1D shape of size 10 with element type f32.
  • Operations have the form dialect.name. For example, tensor.empty is the empty operation within the tensor dialect, and func.func is the func operation within the func dialect.
// The 1D identity map, used below.
#map_1d_identity = affine_map<(m) -> (m)>

// Define a function @foo taking two tensor arguments `%lhs` and `%rhs` and returning a tensor.
func.func @foo(
      %lhs : tensor<10xf32>,
      %rhs : tensor<10xf32>
    ) -> tensor<10xf32> {
  // A constant used below.
  %c0f32 = arith.constant 0.0 : f32
  // Create a result "init value". Think of it as an abstract "allocation",
  // creating a tensor but not giving its elements any particular value. It would be
  // undefined behavior to read any element from this tensor.
  %result_empty =  tensor.empty() : tensor<10xf32>

  // Perform the computation. The following is all a single linalg.generic op.

  %result = linalg.generic {
    // This {...} section is the "attributes" - some compile-time settings for this op.
    indexing_maps=[
      // Indexing maps for the parameters listed in `ins(...)`
      #map_1d_identity,
      #map_1d_identity,
      // Indexing maps for the parameters listed in `outs(...)`
      #map_1d_identity
    ],
    // There is one tensor dimension, and it's a parallel-iteration dimension,
    // meaning that it occurs also as a result tensor dimension. The alternative
    // would be "reduction", for dimensions that do not occur in the result tensor.
    iterator_types=["parallel"]
  } // End of the attributes for this linalg.generic. Next come the parameters:
    // `ins` is where we pass regular input-parameters
    ins(%lhs, %rhs : tensor<10xf32>, tensor<10xf32>)
    // `outs` is where we pass the "outputs", but that term has a subtle meaning
    // in linalg. Here we are passing a tensor.empty, meaning just a placeholder
    // for the output with no preexisting element values. In other examples with
    // an accumulator, this is where the accumulator would be passed.
    outs(%result_empty : tensor<10xf32>)
    // End of parameters. The next {...} part is the "code block".
  {
    // bb0 is a code block taking one scalar from each input tensor as argument, and
    // computing and "yielding" (ie returning) the corresponding output tensor element.
    ^bb0(%lhs_entry : f32, %rhs_entry : f32, %unused_result_entry : f32):
      %add = arith.addf %lhs_entry, %rhs_entry : f32
      linalg.yield %add : f32
  } // End of the basic block. Finally, we describe the return type.
  -> tensor<10xf32>

  // End of the linalg.generic op.

  // Return the function's return value.
  return %result : tensor<10xf32>
}

Compile it like this:

iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb

Note

These are just minimalist iree-compile flags for running on CPU without trying to maximize performance.

  • To run on GPU or other non-CPU targets, explore other values for --iree-hal-target-backends=. You will then need to pass a matching --device= to iree-run-module below.
  • To cross-compile, explore --iree-llvmcpu-target-triple=.
  • To enable higher CPU performance by enabling CPU features:
    • On x86, explore --iree-llvmcpu-target-cpu= (e.g. --iree-llvmcpu-target-cpu=znver4 to target AMD Zen4).
    • On other architectures, explore --iree-llvmcpu-target-cpu-features=.
    • To optimize for running on the same machine that the compilation ran on, pass --iree-llvmcpu-target-cpu=host. That works regardless of CPU architecture.
  • Check out these docs for more useful iree-compile flags.

Run it like this:

$ iree-run-module --module=/tmp/prog.vmfb \
  --input=10xf32=[0,1,2,3,4,5,6,7,8,9] \
  --input=10xf32=[90,80,70,60,50,40,30,20,10,0]

EXEC @foo
result[0]: hal.buffer_view
10xf32=90 81 72 63 54 45 36 27 18 9

Here, each --input parameter specifies one input. First its shape and element type, 10xf32, then the example array elements in [...] brackets. The output of iree-run-module above shows the contents of the result.

Dynamic-shape, element-wise addition of two 1D arrayslink

While we are going to mostly focus on static shapes for simplicity in the rest of this tutorial, let us give one dynamic-shape example to at least show that that's not a problem. Here is the dynamic-shape equivalent of the previous example.

#map_1d_identity = affine_map<(m) -> (m)>

func.func @foo(
      %lhs : tensor<?xf32>,
      %rhs : tensor<?xf32>
    ) -> tensor<?xf32> {
  %c0f32 = arith.constant 0.0 : f32
  %c0 = arith.constant 0 : index
  %size = tensor.dim %lhs, %c0 : tensor<?xf32>
  %result_empty =  tensor.empty(%size) : tensor<?xf32>

  %result = linalg.generic {
    indexing_maps=[
      // Indexing maps for the parameters listed in `ins(...)`
      #map_1d_identity,
      #map_1d_identity,
      // Indexing maps for the parameters listed in `outs(...)`
      #map_1d_identity
    ],
    iterator_types=["parallel"]
  } ins(%lhs, %rhs : tensor<?xf32>, tensor<?xf32>)
    outs(%result_empty : tensor<?xf32>)
  {
    ^bb0(%lhs_entry : f32, %rhs_entry : f32, %unused_result_entry : f32):
      %add = arith.addf %lhs_entry, %rhs_entry : f32
      linalg.yield %add : f32
  }
  -> tensor<?xf32>

  return %result : tensor<?xf32>
}

This program can be compiled and run exactly like the previous one, except that now the iree-run-module command may specify inputs of arbitrary length. The only requirement is that both inputs have the same length, otherwise the linalg.generic will have undefined behavior.

$ iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb
$ iree-run-module --module=/tmp/prog.vmfb \
  --input=10xf32=[0,1,2,3,4,5,6,7,8,9] \
  --input=10xf32=[90,80,70,60,50,40,30,20,10,0]

EXEC @foo
result[0]: hal.buffer_view
10xf32=90 81 72 63 54 45 36 27 18 9

Passing one of the inputs in outslink

Here is a more concise variant achieving the same result in fewer lines of code, and giving us a first taste of that that outs(...) parameters list can do. We didn't want to show it first, because it's less idiomatic. outs will only become really necessary (and idiomatic) when we will look at reduction iterators. In the previous examples, we had only passed a tensor.empty placeholder for outs. This new example shows that we can actually pass there any of the inputs that are shaped like the result.

#map_1d_identity = affine_map<(m) -> (m)>

func.func @foo(
      %lhs : tensor<10xf32>,
      %rhs : tensor<10xf32>
    ) -> tensor<10xf32> {

  %result = linalg.generic {
    indexing_maps=[
      // Indexing maps for the parameters listed in `ins(...)`
      #map_1d_identity,
      // Indexing maps for the parameters listed in `outs(...)`
      #map_1d_identity
    ],
    iterator_types=["parallel"]
  } ins(%lhs : tensor<10xf32>)
    outs(%rhs : tensor<10xf32>)
  {
    ^bb0(%lhs_entry : f32, %rhs_entry : f32):
      %add = arith.addf %lhs_entry, %rhs_entry : f32
      linalg.yield %add : f32
  }
  -> tensor<10xf32>

  return %result : tensor<10xf32>
}

$ iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb
$ iree-run-module --module=/tmp/prog.vmfb \
  --input=10xf32=[0,1,2,3,4,5,6,7,8,9] \
  --input=10xf32=[90,80,70,60,50,40,30,20,10,0]

EXEC @foo
result[0]: hal.buffer_view
10xf32=90 81 72 63 54 45 36 27 18 9

A first reduction example: summing a 1D arraylink

This function takes a 1D array of floats and returns their sum. tensor<f32> is a 0-dimensional tensor type. We could as well extract the single f32 element and return that, but we wanted to make this example as simple as possible.

What's subtle here is how the bb0 block in the linalg.generic now actively uses the %result_entry as an operand to arith.addf, yielding the result of this addition on every iteration. Implicitly, this stores the result of that addition to the destination, from where it is re-loaded on the next iteration again as %result_entry. So the SSA value %result_entry has a different value on each iteration.

Because the values from the outs parameter are now actually used, we can't directly pass there the tensor.empty, whose elements are uninitialized. We have to initialize the result entries as zeroes, which is achieved by the linalg.fill.

#map_1d_identity = affine_map<(m) -> (m)>
#map_1d_proj_0d = affine_map<(m) -> ()>

func.func @foo(
      %input : tensor<10xf32>) -> tensor<f32> {
  %result_empty = tensor.empty() : tensor<f32>
  %cst_0 = arith.constant 0.0 : f32
  %result_init = linalg.fill ins(%cst_0 : f32) outs(%result_empty : tensor<f32>) -> tensor<f32>
  %result = linalg.generic {
    indexing_maps=[
      // Indexing maps for the parameters listed in `ins(...)`
      #map_1d_identity,
      // Indexing maps for the parameters listed in `outs(...)`
      #map_1d_proj_0d
    ],
    iterator_types=["reduction"]
  } ins(%input : tensor<10xf32>)
    outs(%result_init : tensor<f32>)
  {
    ^bb0(%input_entry : f32, %result_entry : f32):
      %add = arith.addf %input_entry, %result_entry : f32
      linalg.yield %add : f32
  }
  -> tensor<f32>

  return %result : tensor<f32>
}

$ iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb
$ iree-run-module --module=/tmp/prog.vmfb --input=10xf32=[0,1,2,3,4,5,6,7,8,9]

EXEC @foo
result[0]: hal.buffer_view
f32=45

Combining parallel and reduction iterators: summing each row of a 2D array.link

This is our first 2D example so for the first time we have to start explaining how the iterator_types are enumerated and we start seeing some more interesting examples of affine_map.

#map_2d_identity = affine_map<(m, n) -> (m, n)>
#map_2d_proj_first = affine_map<(m, n) -> (m)>

func.func @foo(
      %input : tensor<3x5xf32>) -> tensor<3xf32> {
  %result_empty = tensor.empty() : tensor<3xf32>
  %cst_0 = arith.constant 0.0 : f32
  %result_init = linalg.fill ins(%cst_0 : f32) outs(%result_empty : tensor<3xf32>) -> tensor<3xf32>
  %result = linalg.generic {
    indexing_maps=[
      // Indexing maps for the parameters listed in `ins(...)`
      #map_2d_identity,
      // Indexing maps for the parameters listed in `outs(...)`
      #map_2d_proj_first
    ],
    iterator_types=[
      // Rule: the i-th iterator_type corresponds to the i-th coordinate in the
      // source space of the affine_maps defined above, (m, n). So:
      "parallel",  // This refers to the `m` coordinate in the affine-maps.
                   // This is the coordinate that is preserved in the result,
                   // see the map_2d_proj_first map given above.
      "reduction" // This refers to the `n` coordinate in the affine-maps.
                  // This is the coordinate that is dropped by the map_2d_proj_first
                  // given above and thus not present in the 1D result.
    ]
  } ins(%input : tensor<3x5xf32>)
    outs(%result_init : tensor<3xf32>)
  {
    ^bb0(%input_entry : f32, %result_entry : f32):
      %add = arith.addf %input_entry, %result_entry : f32
      linalg.yield %add : f32
  }
  -> tensor<3xf32>

  return %result : tensor<3xf32>
}

$ iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb
$ iree-run-module --module=/tmp/prog.vmfb \
  --input=3x5xf32=[[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]

EXEC @foo
result[0]: hal.buffer_view
3xf32=10 35 60

Matrix multiplication as a linalg.matmul and as a linalg.genericlink

We are now ready to see how to express matrix multiplication as a linalg.generic. But actually, rather than just writing that by hand, we are going to let Linalg do it for us. Indeed, in addition to linalg.generic, Linalg contains a number of "named ops", which are essentially just short-hand notation for special cases of linalg.generic. One of them is linalg.matmul, doing matrix multiplication accumulating into an existing accumulator. Here is a simple function performing a matrix-multiplication-with-accumulation using linalg.matmul. Also in this example, we use dynamic shapes (the ? in the shapes, see the above section where we encountered that), but we could just as well use static shapes.

func.func @foo(%lhs: tensor<?x?xf32>, %rhs: tensor<?x?xf32>, %acc: tensor<?x?xf32>) -> tensor<?x?xf32> {
  %result = linalg.matmul
    ins(%lhs, %rhs: tensor<?x?xf32>, tensor<?x?xf32>)
    outs(%acc: tensor<?x?xf32>)
  -> tensor<?x?xf32>
  return %result: tensor<?x?xf32>
}

$ iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb
$ iree-run-module --module=/tmp/prog.vmfb \
  --input=2x2xf32=[[1,2][3,4]] \
  --input=2x2xf32=[[1,4][3,2]] \
  --input=2x2xf32=[[0,0][0,0]]

EXEC @matmul_dynamic
result[0]: hal.buffer_view
2x2xf32=[7 8][15 20]

Now we encounter another IREE tool: iree-opt. Unlike iree-compile which compiles a MLIR program all the way down to a .vmfb that's ready to run on the target device, iree-opt only applies selected transformations.

We run:

iree-opt --linalg-generalize-named-ops prog.mlir

And that prints:

#map = affine_map<(d0, d1, d2) -> (d0, d2)>
#map1 = affine_map<(d0, d1, d2) -> (d2, d1)>
#map2 = affine_map<(d0, d1, d2) -> (d0, d1)>
module {
  func.func @foo(%arg0: tensor<?x?xf32>, %arg1: tensor<?x?xf32>, %arg2: tensor<?x?xf32>) -> tensor<?x?xf32> {
    %0 = linalg.generic {indexing_maps = [#map, #map1, #map2], iterator_types = ["parallel", "parallel", "reduction"]} ins(%arg0, %arg1 : tensor<?x?xf32>, tensor<?x?xf32>) outs(%arg2 : tensor<?x?xf32>) {
    ^bb0(%in: f32, %in_0: f32, %out: f32):
      %1 = arith.mulf %in, %in_0 : f32
      %2 = arith.addf %out, %1 : f32
      linalg.yield %2 : f32
    } -> tensor<?x?xf32>
    return %0 : tensor<?x?xf32>
  }
}

So that's the linalg.generic implementing matrix multiplication equivalently to the above linalg.matmul form. We can compile and run that like the above program and it will have exactly the same result.

Here the 3 listed iterator_types, ["parallel", "parallel", "reduction"], correspond to the 3 listed coordinates in the affine_map's, (d0, d1, d2). So, d0 and d1 are parallel dimensions and d2 is the reduction dimension. That's why the first two affine_map's results involve d2 (they are respectively for the LHS %arg0 and RHS %arg1) and the last affine_map's result only involves the parallel d0 and d1, as it refers to the result matrix.

Note

Some current IREE compiler optimizations are only triggering on named ops like linalg.matmul, not on the equivalent linalg.generic form. Think of that as a non-essential current limitation, and the intent is over time to overcome these, but in the near term do use linalg.matmul when performance matters.

Integer element typeslink

MLIR defines integer types for absolutely any bit-width, including non-power-of-two bit-widths, and in three signedness flavors:

  • Signed integers, indicated by the letters si.
  • Unsigned integers, indicated by the letters ui.
  • Sign-less integers indicated by the letter i. "Sign-less" means that the integer type does not convey signedness; the integer value may be used as either a signed or an unsigned value but that's a property of the operation using that value as an operand, that's not encoded in the type.

So for instance, si16 is the 16-bit signed integer type, ui24 is the 24-bit unsigned integer type, and i8 is the sign-less 8-bit integer type.

Now here is a very important principle of how the MLIR dialects that are relevant to us in IREE operate:

Note

Only use sign-less types. Always encode signedness in operations, not in types.

For example, here is how we perform a matrix multiplication where the LHS is signed 8-bit integers, the RHS is unsigned 8-bit integers, and the accumulator is signed 32-bit integers. Notice how the fact that LHS is signed and the RHS is unsigned is encoded only in the implementation of the linalg.generic basic block, where the LHS and RHS entries are extended, respectively as signed (arith.extsi) and unsigned (arith.extui):

#map = affine_map<(d0, d1, d2) -> (d0, d2)>
#map1 = affine_map<(d0, d1, d2) -> (d2, d1)>
#map2 = affine_map<(d0, d1, d2) -> (d0, d1)>
module {
  func.func @foo(%lhs: tensor<?x?xi8>, %rhs: tensor<?x?xi8>, %acc: tensor<?x?xi32>) -> tensor<?x?xi32> {
    %result = linalg.generic
      {indexing_maps = [#map, #map1, #map2],
       iterator_types = ["parallel", "parallel", "reduction"]}
      ins(%lhs, %rhs : tensor<?x?xi8>, tensor<?x?xi8>)
      outs(%acc : tensor<?x?xi32>) {
    ^bb0(%lhs_entry: i8, %rhs_entry: i8, %acc_entry: i32):
      %lhs_extended = arith.extsi %lhs_entry : i8 to i32
      %rhs_extended = arith.extui %rhs_entry : i8 to i32
      %mul = arith.muli %lhs_extended, %rhs_extended : i32
      %add = arith.addi %acc_entry, %mul : i32
      linalg.yield %add : i32
    } -> tensor<?x?xi32>
    return %result : tensor<?x?xi32>
  }
}

$ iree-compile --iree-hal-target-backends=llvm-cpu prog.mlir -o /tmp/prog.vmfb
$ iree-run-module --module=/tmp/prog.vmfb \
  --input=2x2xi8=[[-1,-2][-3,-4]] \
  --input=2x2xi8=[[1,4][3,2]] \
  --input=2x2xi32=[[0,0][0,0]]

EXEC @foo
result[0]: hal.buffer_view
2x2xi32=[-7 -8][-15 -20]

Note

A current runtime limitation, https://github.com/iree-org/iree/issues/16241, prevents passing sub-byte-bit-width integers on the iree-run-module command line.