Lunderberg commented on code in PR #77: URL: https://github.com/apache/tvm-rfcs/pull/77#discussion_r892802660
########## rfcs/0077-layout-transform-padding.md: ########## @@ -0,0 +1,2522 @@ +- Feature Name: Layout Transformation Padding Roadmap +- Authors: [Eric Lunderberg](https://github.com/Lunderberg/), + [Chris Sullivan](https://github.com/csullivan), + [Wuwei Lin](https://github.com/vinx13/), + [Junru Shao](https://github.com/junrushao1994) +- Start Date: 2022-06-06 +- RFC PR: [apache/tvm-rfcs#0077](https://github.com/apache/tvm-rfcs/pull/0077) +- GitHub Issue: TBD + +# Table of contents +- [Table of contents](#table-of-contents) +- [Summary](#summary) +- [Motivation](#motivation) +- [Guide-level explanation](#guide-level-explanation) + - [Padded Transformations](#padded-transformations) + - [Defining Padded Values](#defining-padded-values) + - [Overcompute vs Branching](#overcompute-vs-branching) +- [Reference-level explanation](#reference-level-explanation) + - [TIR Changes](#tir-changes) + - [Buffer Annotation of Padding Predicate/Constraint Pairs](#buffer-annotation-of-padding-predicateconstraint-pairs) + - [New TIR Op, `tir::builtin::arbitrary`](#new-tir-op-tirbuiltinarbitrary) + - [Buffer Annotation of Layout Transforms](#buffer-annotation-of-layout-transforms) + - [Transformations/Metaschedule Primitives](#transformationsmetaschedule-primitives) + - [Enhancement - transform_layout](#enhancement---transform_layout) + - [New Primitive - Add buffer constraint](#new-primitive---add-buffer-constraint) + - [New Primitive - Reorder Loops According to Buffer](#new-primitive---reorder-loops-according-to-buffer) + - [Enhancement - Predicate for DomainTouched](#enhancement---predicate-for-domaintouched) + - [Enhancement - Remove No Op](#enhancement---remove-no-op) + - [Enhancement - Simplify](#enhancement---simplify) + - [New Transform - Hoist Expression](#new-transform---hoist-expression) + - [New Transform - Reduce Loop Extents](#new-transform---reduce-loop-extents) + - [Utility - Merge Adjacent Loops](#utility---merge-adjacent-loops) + - [New Primitive - Remove Branching Through Overcompute](#new-primitive---remove-branching-through-overcompute) + - [New Primitive - Remove Overcompute Through Branching](#new-primitive---remove-overcompute-through-branching) + - [New Lowering Transform - Remove T.Arbitrary](#new-lowering-transform---remove-tarbitrary) + - [Implementation options](#implementation-options) + - [Never write to transformation padding](#never-write-to-transformation-padding) + - [Never read from transformation padding](#never-read-from-transformation-padding) + - [Allocate internal buffer containing transformation padding](#allocate-internal-buffer-containing-transformation-padding) + - [Explicitly write next operator's desired default at end of function](#explicitly-write-next-operators-desired-default-at-end-of-function) + - [Implicitly write default value of next operator](#implicitly-write-default-value-of-next-operator) + - [Apply operator element-wise over the transformation padding](#apply-operator-element-wise-over-the-transformation-padding) + - [Multiple Buffer Semantics](#multiple-buffer-semantics) + - [Points of Communication](#points-of-communication) +- [Drawbacks](#drawbacks) +- [Rationale and alternatives](#rationale-and-alternatives) +- [Prior art](#prior-art) +- [Unresolved questions](#unresolved-questions) +- [Future possibilities](#future-possibilities) + +# Summary +[summary]: #summary + +Buffer layout transformations can require padding in the transformed +buffer. The efficiency of an operator depends on the semantics used +for loads and stores to values in the required padding. The choice of +buffer semantics can reduce branch divergence and avoid repeated +setting of default values, but also imposes constraints between the +producer and consumer of a buffer. + +This RFC discusses a general plan for specifying buffer semantics to +be used, and the constraints imposed. Subsequent RFCs will follow +describing the design for support of each of the semantics proposed in +this roadmap. + +# Motivation +[motivation]: #motivation + +Suppose a buffer of shape `[14]` is transformed such that each index +`i` is mapped to `[i//4, i%4]`. The first index can range from 0 +(`0//4`) to 3 (`14//4`), and the second index can range from 0 (`0%4`) +to 3 (`3%4`). Therefore, the transformed shape is `[4,4]`. However, +this has 16 elements, because the transformed coordinates `(3,2)` and `(3,3)` do +not have a corresponding index on the workload range `0 <= i < 14`. The final +result in these locations is not determined by the compute definition, +so we have flexibility in what to store in the padding that is +introduced by the transformation, and what assumptions can be made +when reading from those locations. + +For example, an element-wise function may be most efficiently written +using vectorized instructions over all values, regardless of whether +they exist in the compute definition. Or a maxpool may be most +efficiently written if input tensors have `-INF` stored in the +transformation padding. Satisfying both of these at the same time may +not be possible. While the compute definition doesn't impose +constraints on the values in the transformation padding, there are +still constraints imposed by the usage of those values by different +operators. + + +``` + ┌─Logical-index-space───────────────────┐ + │ │ +┌▼─┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬─▼┌──┬──┐ +│00│01│02│03│04│05│06│07│08│09│10│11│12│13│14│15│ +└▲─┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴─▲┘ + │ │ + └─Physical-index-space────────────────────────┘ + + ┌─Transformed-index-space─┐ + │ │ + │ ┌────┬────┬────┬───▼┐ + │ │ 00 │ 01 │ 02 │ 03 │ + │ ├────┼────┼────┼────┤ + │ │ 04 │ 05 │ 06 │ 07 │ + │ ├────┼────┼────┼────┤ + │ │ 08 │ 09 │ 10 │ 11 │ + │ ├────┼────┼────┼────┤ + └──────► 12 │ 13 │ 14 │ 15 │ + └────┴────┴────┴────┘ +``` + +# Guide-level explanation +[guide-level-explanation]: #guide-level-explanation + +## Padded Transformations + +In general, a transformation will introduce the minimum amount of +padding such that all values in the original buffer can be stored in +the layout specified. As a result, whether a transformation +introduces padding depends on the transformation being applied and the +buffer shape on which it is being applied. For example, consider a +schedule that contains tensor `A` with shape `[16]` and tensor `B` with shape +`[14]`. + +```python +# This transformation does not introduce padding. The original shape +# of [16] produces the transformed shape [2,8], which contains the +# original 16 values no additional padding. +sched[A].transform_layout(lambda i: [i//8, i%8]) + +# This transform introduces padding. The original shape of [14] also +# produces the transformed shape [2,8], which contains the original 14 +# values and an additional 2 values of padding. These are located at +# transformed indices [1,6] and [1,7]. +sched[B].transform_layout(lambda i: [i//8, i%8]) +``` + +The above example introduces padding at the end of a buffer. By +including an offset in the layout transformation, we can instead place +the padding at the beginning of a buffer. + +```python +# This transform introduces padding. For 0 <= i < 14, the transformed +# index (i+2)//8 can have values of 0 or 1, so the transformed shape +# is [2,8]. There are no valid values of i that would produce [0,0] +# or [0,1], so these transformed indices contain padding. +sched[B].transform_layout(lambda i: [(i+2)//8, (i+2)%8]) +``` + +In addition to moving the location of the padded indices, use of an +offset in a layout transformation can introduce additional padding. + +```python +# This transformation introduces padding. For 0 <= i < 16, the +# transformed index (i+2)//8 can have values of 0, 1, or 2, so the +# transformed shape is [3,8]. Padding is introduced from [0,0] to +# [0,1], and from [2,2] to [2,7]. +sched[A].transform_layout(lambda i: [(i+2)//8, (i+2)%8]) +``` + + +## Defining Padded Values + +When a buffer is transformed, the majority of values in the +transformed buffer are constrained to have the corresponding value in +the original buffer. However, when a buffer is padded to meet some +alignment criteria, these additional padded values have no such +constraint. + +To specify the values stored in the padding, the `transform_layout` +function takes an optional argument `pad_value` that +specifies the value that should be present in the padding. This +should be a function that maps from transformed indices to an +`Optional[PrimExpr]`. + +```python +# B.shape is [14] +transform = lambda i: [i//4, i%4] + +# Three equivalent calls to perform the same layout transformation. +# Padding is introduced, but access of the padding is forbidden. +sched[B].transform_layout(transform) +sched[B].transform_layout(transform, pad_value=None) +sched[B].transform_layout(transform, pad_value=lambda io,ii: None) + +# Padding is introduced, and contains zeros. +sched[B].transform_layout(transform, pad_value=0.0) +sched[B].transform_layout(transform, pad_value=lambda io,ii: 0.0) + +# Padding is introduced, and contains arbitrary values. +sched[B].transform_layout(transform, pad_value=tir.arbitrary(dtype="float32")) +sched[B].transform_layout(transform, pad_value=lambda io,ii: tir.arbitrary(dtype="float32")) + +# Padding is introduced, and wraps to the beginning of the array. +sched[B].transform_layout(transform, pad_value=lambda io,ii: B[0, (io-14)%4]) +``` + +The `Buffer` object stores a predicate to identify which indices +contain padding, along with the expression given in `pad_value`. This +expression may only contain constants and the transformed buffer +itself, and may not introduce dependencies on another buffer. + +For a producer of the transformed buffer, if `pad_value` is defined, +the padding value must be written to the padding prior to the +completion of the operator. Effectively, the producer must have a +postlude as follows: + +```python +for transformed_indices in T.grid(*transformed_shape): + if padding_predicate(*transformed_indices): + B[transformed_indices] = pad_value(*transformed_indices) +``` + +For a consumer of the transformed buffer, these padding values are +initially unused, but may be used in later simplifications. + +## Overcompute vs Branching + +Depending on the computation being performed and the value stored in +the padding, there can be trade-offs between branching and +overcompute. For example, consider the following `PrimFunc`, which +computes the sum over each row of the input data. + +```python +@T.prim_func +def row_summation(a: T.handle, b: T.handle): + A = T.match_buffer(shape=(16, 14), dtype="float32") + B = T.match_buffer(shape=(16,), dtype="float32") + for i in T.serial(16): + B[i] = 0.0 + for j in T.serial(14): + B[i] = B[i] + A[i, j] +``` + +We'd like to transform the layout of buffer `A` from `[i, j]` to `[i, +j//4, j%4]`, along with the loop iteration. By default, after using +the `transform_layout` and `split` metaschedule primitives, we have +the following function. + +```python +@T.prim_func +def row_summation(a: T.handle, b: T.handle): + A = T.match_buffer(shape=(16, 4, 4), dtype="float32") + B = T.match_buffer(shape=(16,), dtype="float32") + for i in T.serial(16): + B[i] = 0.0 + for j_outer, j_inner in T.grid(4, 4): + if 4*j_outer + j_inner < 14: + B[i] = B[i] + A[i, j_outer, j_inner] +``` + +If the conditional can be removed, this function would be much more +amenable for later vectorization, or to reduce branch divergence when +bound to a thread index. If the padding in `A` is pre-filled with +zero, then `B[i] = B[i] + 0.0` is a no-op, and can be performed +without changing the final computation. + +```python +@T.prim_func +def row_summation(a: T.handle, b: T.handle): + A = T.match_buffer(shape=(16, 4, 4), dtype="float32") + B = T.match_buffer(shape=(16,), dtype="float32") + for i in T.serial(16): + B[i] = 0.0 + for j_outer, j_inner in T.grid(4, 4): + B[i] = B[i] + A[i, j_outer, j_inner] +``` + +By annotating the layout transformation with the value stored in the +padding, this condition can be proven, allowing this conditional to +automatically be removed. Since the tradeoff between branching and +overcompute may or may not be beneficial dependent on the schedule, +these options are exposed as two additional transformations, +`tir.transform.RemoveBranchingThroughOvercompute` and +`tir.transform.RemoveOvercomputeThroughBranching`. + + +# Reference-level explanation +[reference-level-explanation]: #reference-level-explanation + +## TIR Changes + +### Buffer Annotation of Padding Predicate/Constraint Pairs Review Comment: Some notes from a conversation with @vinx13 @csullivan @tqchen @junrushao1994. Wording is mine, attempting to summarize statements made. * Hoist transformations into graph-level vs apply transformations in TIR. From @vinx13: The RFC proposal models layout transformations in TIR primarily focused on the TIR side. However, this isn't strictly necessary, as padding could instead be introduced and reasoned about at the relay/relax level. Example: A single operator that performs a conv1d could be replaced by a sequence of three operators, to transform the layout, perform a conv1d, then apply the inverse transform. If two adjacent conv1d use the same transform, then the transforms could be canceled out. From @Lunderberg: Uncertain how generic this could be for padding, as it would require a pre-existing implementation of the operator applied to a padded buffer, and would require graph-level knowledge of what padding can be applied to different buffers without effect. Buffer padding can also be trickier to reason about. A layout transform of NCHW to NHWC followed by a layout transformation of NHWC to NCHW cancel each other out. If a buffer is first cropped, then padded with zeros, these only cancel each other out if the contents of the cropped locations can be proven to have held zero. * Optimization of PrimFuncs From @Lunderberg: Had been visualizing the layout transformations not solely as transformations that would be made in isolation, but as transformations that would need to be done in conjunction with the calling scope. When optimizing a PrimFunc in isolation, `transform_layout` would only be allowed to be applied on internal buffers, not buffers passed in as arguments. * Graph-level optimization of buffer layouts. From @Lunderberg: Combining the previous two, this sounds like something that will be useful and doable in Relax, where a transformation could change both the input shape, and also the calling convention of all TIR functions that use the buffer. In relay, this would be trickier, but still possible. Would need some way to query what layouts/assumptions an operator would find useful, either through manual tagging or some automatic search. Relay would first query the operators, then decide the layouts, then pass these down to the operators to use. * Method to write compute definitions, especially for new hardware. From @csullivan: Modeling the layout transformation within TIR would have huge benefits when supporting new hardware targets. When writing a new operator, there isn't a specific "graph-level" that it is being designed for. The current state is quite difficult for hardware vendors, who must write a new compute definition and schedule for each shape of an operator. This is a benefit that wouldn't be present in the graph-level layout transformations, which would still require each supported layout to have a different implementation. From @Lunderberg: Writing a function that outputs a PrimFunc that follows a specific layout as a reasonable starting point for optimization would be a goal, and that writing in terms of a series of changes made to an initial PrimFunc would be the reasonable way to go about it. Whether that is best described as a schedule primitive, a function that applies a schedule primitive, or a function that returns a series of schedule primitives to be applied is less important than the functionality itself. -- This is an automated message from the Apache Git Service. To respond to the message, please log on to GitHub and use the URL above to go to the specific comment. To unsubscribe, e-mail: commits-unsubscr...@tvm.apache.org For queries about this service, please contact Infrastructure at: us...@infra.apache.org
