Bufferization

Overview ¶

Bufferization in MLIR is the process of converting ops with tensor semantics to ops with memref semantics. There are multiple MLIR passes that are related to bufferization. These passes typically run as one of the last steps in a pass pipeline, right before lowering to memref ops to LLVM. That is because many transformations are easier or only supported in tensor land; e.g., tile/fuse/… on tensors first, then bufferize the remaining IR.

The most important bufferization pass is One-Shot Bufferize: This pass rewrites tensor IR to memref IR. There are additional helper passes that preprocess IR (e.g., so that IR can be bufferized more efficiently), perform buffer-level optimizations such as allocation hoisting, and insert buffer deallocation ops so that the resulting memref IR has no memory leaks.

Deprecated Passes ¶

The buffer deallocation pass has been deprecated in favor of the ownership-based buffer deallocation pipeline. The deprecated pass has some limitations that may cause memory leaks in the resulting IR.

What is One-Shot Bufferize? ¶

One-Shot Bufferize is a tensor bufferization pass designed for IR in destination-passing style, and with aggressive in-place bufferization.

One-Shot Bufferize is:

• Monolithic: A single MLIR pass does the entire work.

• Extensible via an op interface: All ops that implement BufferizableOpInterface can be bufferized.

• A whole-function at a time analysis. In-place bufferization decisions are made by analyzing SSA use-def chains on tensors. Op interface implementations not only provide the rewrite logic from tensor ops to memref ops, but also helper methods for One-Shot Bufferize’s analysis to query information about an op’s bufferization/memory semantics.

• 2-Phase: Bufferization is internally broken down into 2 steps: First, analyze the entire IR and make bufferization decisions. Then, bufferize (rewrite) the IR. The analysis has access to exact SSA use-def information. It incrementally builds alias and equivalence sets and does not rely on a posteriori-alias analysis from preallocated memory.

• Greedy: Operations are analyzed one-by-one and it is decided on the spot whether a tensor OpOperand must be copied or not. Heuristics determine the order of analysis.

• Modular: The current One-Shot Analysis can be replaced with a different analysis. The result of the analysis are queried by the bufferization via AnalysisState, in particular AnalysisState::isInPlace. Any derived class of AnalysisState that implements a small number virtual functions can serve as a custom analysis. It is even possible to run One-Shot Bufferize without any analysis (AlwaysCopyAnalysisState), in which case One-Shot Bufferize copies every buffer before writing to it.

Note that One-Shot Bufferize does not deallocate buffers. That is done by the Ownership-based Buffer Deallocation passes.

Goals of Bufferization ¶

The high-level goal of every bufferization technique is to:

1. Use as little memory as possible.
2. Copy as little memory as possible.

This implies reusing already allocated buffers when possible, turning bufferization into an algorithmically complex problem with similarities to register allocation.

Depending on the concrete use case, there may be additional bufferization requirements. If the contents of a buffer are expensive to compute, there could be a tradeoff between recomputation and compute once and copy. On the contrary, it may not even be possible to allocate new buffers at runtime on some architectures.

Destination-Passing Style ¶

Bufferization is an algorithmically complex problem. Given an op with a tensor result, bufferization has to choose a memref buffer in which the result can be stored. It is always safe to allocate a brand new buffer, but such a bufferization strategy would be unacceptable for high-performance codegen. When choosing an already existing buffer, we must be careful not to accidentally overwrite data that is still needed later in the program.

To simplify this problem, One-Shot Bufferize was designed to take advantage of destination-passing style (DPS). In MLIR, DPS op should implement the DestinationStyleOpInterface. DPS exists in itself independently of bufferization and is tied to SSA semantics: many ops are “updating” a part of their input SSA variables. For example the LLVM instruction insertelement is inserting an element inside a vector. Since SSA values are immutable, the operation returns a copy of the input vector with the element inserted. Another example in MLIR is linalg.generic on tensors, which always has an extra outs operand for each result, which provides the initial values to update (for example when the operation is doing a reduction).

outs operands are referred to as “destinations” in the following (quotes are important as this operand isn’t modified in place but copied) and comes into place in the context of bufferization as a possible “anchor” for the bufferization algorithm. This allows the user to shape the input in a form that guarantees close to optimal bufferization result when carefully choosing the SSA value used as “destination”.

For every tensor result, a DPS op has a corresponding tensor operand. If there aren’t any other conflicting uses of this tensor, the bufferization can alias it with the op result and perform the operation “in-place” by reusing the buffer allocated for this “destination” input.

As an example, consider the following op: %r = tensor.insert %f into %t[%idx] : tensor<5xf32>

%t is the “destination” in this example. When choosing a buffer for the result %r, denoted as buffer(%r), One-Shot Bufferize considers only two options:

1. buffer(%r) = buffer(%t): store the result in the existing buffer(%t). Note that this is not always possible. E.g., if the old contents of buffer(%t) are still needed. One-Shot Bufferize’s main task is to detect such cases and fall back to the second option when necessary.
2. buffer(%r) is a newly allocated buffer.

There may be other buffers in the same function that could potentially be used for buffer(%r), but those are not considered by One-Shot Bufferize to keep the bufferization simple. One-Shot Bufferize could be extended to consider such buffers in the future to achieve a better quality of bufferization.

Tensor ops that are not in destination-passing style always bufferized to a memory allocation. E.g.:

%0 = tensor.generate %sz {
^bb0(%i : index):
  %cst = arith.constant 0.0 : f32
  tensor.yield %cst : f32
} : tensor<?xf32>

The result of tensor.generate does not have a “destination” operand, so bufferization allocates a new buffer. This could be avoided by instead using an op such as linalg.generic, which can express the same computation with a “destination” operand, as specified behind outputs (outs):

#map = affine_map<(i) -> (i)>
%0 = linalg.generic {indexing_maps = [#map], iterator_types = ["parallel"]}
                    outs(%t : tensor<?xf32>) {
  ^bb0(%arg0 : f32):
    %cst = arith.constant 0.0 : f32
    linalg.yield %cst : f32
} -> tensor<?xf32>

At first glance, the above linalg.generic op may not seem very useful because the output tensor %t is entirely overwritten. Why pass the tensor %t as an operand in the first place? As an example, this can be useful for overwriting a slice of a tensor:

%t = tensor.extract_slice %s [%idx] [%sz] [1] : tensor<?xf32> to tensor<?xf32>
%0 = linalg.generic ... outs(%t) { ... } -> tensor<?xf32>
%1 = tensor.insert_slice %0 into %s [%idx] [%sz] [1]
    : tensor<?xf32> into tensor<?xf32>

The above example bufferizes to a memref.subview, followed by a “linalg.generic on memrefs” that overwrites the memory of the subview, assuming that the slice %t has no other user. The tensor.insert_slice then bufferizes to a no-op (in the absence of RaW conflicts such as a subsequent read of %s).

RaW conflicts are detected with an analysis of SSA use-def chains (details later). One-Shot Bufferize works best if there is a single SSA use-def chain, where the result of a tensor op is the operand of the next tensor ops, e.g.:

%0 = "my_dialect.some_op"(%t) : (tensor<?xf32>) -> (tensor<?xf32>)
%1 = "my_dialect.another_op"(%0) : (tensor<?xf32>) -> (tensor<?xf32>)
%2 = "my_dialect.yet_another_op"(%1) : (tensor<?xf32>) -> (tensor<?xf32>)

Buffer copies are likely inserted if the SSA use-def chain splits at some point, e.g.:

%0 = "my_dialect.some_op"(%t) : (tensor<?xf32>) -> (tensor<?xf32>)
%1 = "my_dialect.another_op"(%0) : (tensor<?xf32>) -> (tensor<?xf32>)

// "yet_another_op" likely needs to read the data of %0, so "another_op" cannot
// in-place write to buffer(%0).
%2 = "my_dialect.yet_another_op"(%0) : (tensor<?xf32>) -> (tensor<?xf32>)

Tensor / MemRef Boundary ¶

The bufferization dialect provides a few helper ops to connect tensor IR (that should be bufferized) with existing buffers (that may be allocated/provided by a different runtime/library/etc.).

bufferization.to_memref %t returns the future buffer of a tensor SSA value. bufferization.to_tensor %m returns a tensor SSA value for a given MemRef buffer. bufferization.materialize_in_destination indicates that a tensor value should materialize in a certain buffer.

Consider the following example, where a TOSA matmul result should materialize in an existing buffer %C:

// Batched TOSA matrix multiplication. %A and %B are the
// inputs, %C is the output.
func.func @test_matmul(%A: memref<1x17x19xf32>,
                       %B: memref<1x19x29xf32>,
                       %C: memref<1x17x29xf32>) {

  %A_tensor = bufferization.to_tensor %A restrict : memref<1x17x19xf32> to tensor<1x17x19xf32>
  %B_tensor = bufferization.to_tensor %B restrict : memref<1x19x29xf32> to tensor<1x19x29xf32>

  %0 = tosa.matmul %A_tensor, %B_tensor
      : (tensor<1x17x19xf32>, tensor<1x19x29xf32>) ->
         tensor<1x17x29xf32>

  bufferization.materialize_in_destination
    %0 in restrict writable %C
      : (tensor<1x17x29xf32>, memref<1x17x29xf32>) -> ()

  return
}

Note that all bufferization ops in this example have the restrict unit attribute set. This attribute is similar to the C restrict keyword and indicates that there is no other to_tensor or materialize_in_destination op with the same or an aliasing MemRef operand. Only such to_tensor/materialize_in_destination ops are supported. The restrict attribute gives strong aliasing guarantees to the bufferization analysis and allows us to look only at the tensor IR in a program. (Ops that do not operate on tensors are ignored by the One-Shot Bufferize.)

Also note that tosa.matmul cannot be bufferized as is: there is no BufferizableOpInterface implementation for that op. However, the op can be lowered to a combination of tensor.empty and linalg.matmul, which can be bufferized.

Using One-Shot Bufferize ¶

MLIR provides a pass -one-shot-bufferize that performs an analysis and bufferizes all ops with tensor semantics that implement BufferizableOpInterface. For modularity reasons, these op interface implementations are typically external models that live in a dialect’s “Transforms” build unit. (External models are a mechanism for implementing an op interface in a different build unit.) It is the user’s responsibility to ensure that all needed external models are registered before running One-Shot Bufferize.

By default, One-Shot Bufferize fails when it encounters an op with tensor semantics (i.e., tensor result or tensor operand) that is not bufferizable (i.e., does not implement BufferizableOpInterface). This can be avoided with allow-unknown-ops. In that case, One-Shot Bufferize inserts to_memref/to_tensor ops around the bufferization boundary.

One-Shot Bufferize can be configured to bufferize only ops from a set of dialects with dialect-filter.

One-Shot Bufferize can also be called programmatically with bufferization::runOneShotBufferize. Alternatively, bufferization::bufferizeOp skips the analysis and inserts a copy on every buffer write.

By default, function boundaries are not bufferized. This is because there are currently limitations around function graph bufferization: recursive calls are not supported. As long as there are no recursive calls, function boundary bufferization can be enabled with bufferize-function-boundaries. Each tensor function argument and tensor function result is then turned into a memref. The layout map of the memref type can be controlled with function-boundary-type-conversion.

Memory Layouts ¶

One-Shot Bufferize bufferizes ops from top to bottom. This works well when all ops are bufferizable. However, when encountering a non-bufferizable tensor with allow-unknown-ops, One-Shot Bufferize must insert to_memref ops at the bufferization boundary and decide on a memref type. By default, One-Shot Bufferize choose the most dynamic memref type wrt. layout maps. E.g.:

%0 = "my_dialect.unbufferizable_op(%t) : (tensor<?x?xf32>) -> (tensor<?x?xf32>)
%1 = tensor.extract %0[%idx1, %idx2] : tensor<?xf32>

When bufferizing the above IR, One-Shot Bufferize inserts a to_memref ops with dynamic offset and strides:

%0 = "my_dialect.unbufferizable_op(%t) : (tensor<?x?xf32>) -> (tensor<?x?xf32>)
%0_m = bufferization.to_memref %0 : memref<?x?xf32, strided<[?, ?], offset: ?>>
%1 = memref.load %0_m[%idx1, %idx2] : memref<?x?xf32, strided<[?, ?], offset: ?>>

All users of %0 have fully dynamic layout maps. This ensures that the bufferized IR composes well with future bufferizations of unbufferizable_op (maybe bufferized by another pass), regardless of the exact memref type of the future bufferization. If the op turns out to be bufferized to an op with a simpler memref type (e.g., identity layout map), we expect that canonicalization patterns would clean up unnecessarily dynamic layout maps. (Some of these canonicalization patterns may not be implemented yet.)

One-Shot Bufferize tries to infer the most precise memref type when bufferizing an op. If the entire IR is bufferizable, we do not have to resort to conservatively use fully dynamic layout maps. In that case, we also do not have to rely on canonicalization patterns to clean up the bufferized IR.

Note: There are some bufferizable ops for which a percise layout map cannot be inferred. E.g., a tensor.cast from a tensor<*xf32> to a tensor<?x?xf32> must be bufferized to a memref.cast with a memref type that has a fully dynamic layout map.

One-Shot Bufferize has an option unknown-type-conversion to control the generation of layout maps when no precise layout can be inferred:

• fully-dynamic-layout-map uses fully dynamic layout maps and is the default behavior. This composes well when IR is partially bufferized.
• identity-layout-map uses static identity layout maps. This option can be useful for legacy code that cannot handle memref types with layout maps. Note that this setting can lead to additional buffer copies when folding a to_tensor/to_memref pair with memref types that are not cast-compatible.

Note: The unknown-type-conversion option does not affect layout maps of function signatures. There is a separate function-signature-type-conversion option that controls layout maps of function parameters and function results.

Extending One-Shot Bufferize ¶

Custom ops can be bufferized if they implement BufferizableOpInterface. Users must at least implement the following interface methods.

• bufferizesToMemoryRead: Return true if the buffer of the given tensor OpOperand is read.
• bufferizesToMemoryWrite: Return true if the buffer of the given tensor OpOperand is written (if bufferizing in-place).
• getAliasingOpResult: Return the OpResults that may share the same buffer as the given OpOperand. This interface method describes to OpOperand-to-OpResult mapping wrt. destination-passing style.
• bufferRelation: Return BufferRelation::Equivalent if the given OpResult is the exact same memref as the aliasing OpOperand after bufferization (in case of in-place bufferization). Otherwise, (e.g., they overlap but are not necessarily the exact same memrefs), BufferRelation::Unknown should be returned. Additional buffer relations will be added in the future, but BufferRelation::Unknown is always safe.
• bufferize: Rewrite the op with the given rewriter. Ops should be replaced with bufferization::replaceOpWithBufferizedValues.

To get a better intuition of the interface methods, we invite users to take a look at existing implementations in MLIR, e.g., the implementation of tensor.insert or tensor.extract.

Interface implementations of DPS ops (that implement DestinationStyleOpInterface) can derive from DstBufferizableOpInterfaceExternalModel, which provides all necessary method implementations except for bufferize.

Debugging Buffer Copies ¶

To get a better understanding of why One-Shot Bufferize introduced a buffer copy, users can run the pass with test-analysis-only print-conflicts. Every tensor op is then annotated with an attribute that has a boolean value for each tensor OpOperand. true means that the OpOperand bufferizes in-place. false means that the OpOperand bufferizes out-of-place and a buffer copy will be inserted.

There are two reasons why a buffer copy may be inserted.

1. Due to a RaW conflict, it is not safe to bufferize in-place. I.e., the overwritten data is still needed.
2. The buffer is not writable. E.g., memref.global buffers that are the result of arith.constant ops are never modified.

In the first case, print-conflicts illustrates the conflict in the form of a (“read”, “conflicting write”, “last write”) tuple.

A RaW conflict consists of three parts, in the following order according to op dominance:

1. Definition: A tensor %t is defined.
2. Conflicting Write: An operation writes to buffer(%t).
3. Read: An operation reads %t.

When such a RaW conflict is detected during the analysis phase, One-Shot Bufferize will insert a buffer copy for the conflicting write.

Example

// RUN: mlir-opt %s -one-shot-bufferize="bufferize-function-boundaries test-analysis-only print-conflicts"
func.func @test(%arg0: f32, %arg1: f32, %arg2: index, %arg3: index) -> (f32, tensor<3xf32>) {
  // Create a new tensor with [%arg0, %arg0, %arg0].
  %0 = tensor.from_elements %arg0, %arg0, %arg0 : tensor<3xf32>

  // Insert something into the new tensor.
  %1 = tensor.insert %arg1 into %0[%arg2] : tensor<3xf32>

  // Read from the old tensor.
  %r = tensor.extract %0[%arg3] : tensor<3xf32>

  // Return the extracted value and the result of the insertion.
  func.return %r, %1 : f32, tensor<3xf32>
}

The output IR is as follows:

func.func @test(%arg0: f32, %arg1: f32, %arg2: index, %arg3: index) -> (f32, tensor<3xf32>) {
  %from_elements = tensor.from_elements %arg0, %arg0, %arg0 {"C_0[DEF: result 0]"} : tensor<3xf32>
  %inserted = tensor.insert %arg1 into %from_elements[%arg2] {"C_0[CONFL-WRITE: 1]", __inplace_operands_attr__ = ["none", "false", "none"]} : tensor<3xf32>
  %extracted = tensor.extract %from_elements[%arg3] {"C_0[READ: 0]", __inplace_operands_attr__ = ["true", "none"]} : tensor<3xf32>
  return {__inplace_operands_attr__ = ["none", "true"]} %extracted, %inserted : f32, tensor<3xf32>
}

Note that the IR was not bufferized. It was merely annotated with the results of the bufferization analysis. Every operation with tensor semantics has a __inplace_operands_attr__ attribute with one value per operand. If an operand is not a tensor, the respective value is none. Otherwise, if the operand was decided to be bufferized in-place, the value is true. A value of false indicates a buffer copy. In the above example, a buffer copy would be inserted for tensor.insert, so that it does not overwrite buffer(%from_elements), which is still needed for tensor.extract.

For each RaW (there is only one in the example), three C_i attributes were added:

• C_0[DEF: result 0]: A tensor is defined: 0-th result of tensor.from_elements.
• C_0[CONFL-WRITE: 1]: An operation (if bufferized in-place) would write into the future buffer of the defined tensor: 1-st operand of tensor.insert.
• C_0[READ: 0]: An operation reads the tensor definition: 0-th operand of tensor.extract.

The fully bufferized IR (with the inserted buffer copy) is as follows:

func.func @test(%arg0: f32, %arg1: f32, %arg2: index, %arg3: index) -> (f32, memref<3xf32>) {
  %c2 = arith.constant 2 : index
  %c1 = arith.constant 1 : index
  %c0 = arith.constant 0 : index
  %alloc = memref.alloc() {alignment = 64 : i64} : memref<3xf32>
  memref.store %arg0, %alloc[%c0] : memref<3xf32>
  memref.store %arg0, %alloc[%c1] : memref<3xf32>
  memref.store %arg0, %alloc[%c2] : memref<3xf32>
  %alloc_0 = memref.alloc() {alignment = 64 : i64} : memref<3xf32>
  memref.copy %alloc, %alloc_0 : memref<3xf32> to memref<3xf32>
  memref.store %arg1, %alloc_0[%arg2] : memref<3xf32>
  %0 = memref.load %alloc[%arg3] : memref<3xf32>
  return %0, %alloc_0 : f32, memref<3xf32>
}

To get a better understanding of the SSA Use-Def Chain Analysis and the RaW conflict detection algorithm, interested users may want to refer to:

• Original design document
• ODM talk, ( slides).
• LLVM Dev Meeting 2023 tutorial slides