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//===- FusionOnTensors.cpp - Implementation of linalg Fusion --------------===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// This file implements linalg fusion on tensors
#include "PassDetail.h"
#include "mlir/Analysis/SliceAnalysis.h"
#include "mlir/Dialect/Affine/IR/AffineOps.h"
#include "mlir/Dialect/Linalg/IR/LinalgOps.h"
#include "mlir/Dialect/Linalg/IR/LinalgTypes.h"
#include "mlir/Dialect/Linalg/Passes.h"
#include "mlir/Dialect/Linalg/Transforms/Transforms.h"
#include "mlir/Dialect/Linalg/Utils/Utils.h"
#include "mlir/Dialect/Tensor/IR/Tensor.h"
#include "mlir/IR/AffineExpr.h"
#include "mlir/IR/AffineMap.h"
#include "mlir/Support/LLVM.h"
using namespace mlir;
using namespace linalg;
// StructuredOp specific helpers.
/// Returns the tiled slice dimensions given the tiled consumer loop dimensions.
/// The slice defines a hyper rectangular iteration space and fusing the
/// producer is always possible. However, depending on the consumer indexing
/// map, not all slice elements may be consumed and the tiles may overlap. In
/// these cases, fusion introduces redundant computation.
static SmallVector<int64_t> getTiledSliceDims(OpOperand *consumerOperand,
ArrayRef<int64_t> tiledLoopDims) {
// Get the consumer operand indexing map.
LinalgOp consumerOp = consumerOperand->getOwner();
AffineMap indexingMap = consumerOp.getTiedIndexingMap(consumerOperand);
// Search the slice dimensions tiled by a tile loop dimension.
DenseSet<int64_t> tiledSliceDimIndices;
for (auto en : enumerate(indexingMap.getResults())) {
for (auto tiledLoopDim : tiledLoopDims) {
if (en.value().isFunctionOfDim(tiledLoopDim))
return {tiledSliceDimIndices.begin(), tiledSliceDimIndices.end()};
/// Given a vector of `tiledSliceDimIndices` that represent the tiled dimensions
/// of the producer result slice returns the tiled producer loop dimensions.
/// Example:
/// ```
/// %res = linalg.fill(%cst, %input)
/// scf.for %i
/// scf.for %j
/// %slice = tensor.extract_slice %res[%i, %j]
/// ```
/// getTiledProducerLoops(%res, [0, 1]) returns the loop indices [0, 1].
static SmallVector<int64_t>
getTiledProducerLoops(OpResult producerResult,
ArrayRef<int64_t> tiledSliceDimIndices) {
LinalgOp producerOp = producerResult.getOwner();
// Get the indexing map of the `producerOp` output operand that matches
// ┬┤producerResult┬┤.
AffineMap producerIndexingMap = producerOp.getTiedIndexingMap(
// Keep only the tiled result slice dimensions of `producerIndexingMap`.
AffineMap tiledProducerIndexingSubMap =
tiledSliceDimIndices.begin(), tiledSliceDimIndices.end()));
// Compute the producer loop indices mapped to the tiled result slice
// dimensions. As the output indexing map of structured operations are
// projected permutations, `tiledProducerIndexingSubMap` has to be a
// projected permutation as well. We can thus obtain the producer loop indices
// by getting the positions of the result dimensions.
// Example:
// (d0, d1, d2) -> (d0, d2) has the result positions [0, 2].
assert(tiledProducerIndexingSubMap.isProjectedPermutation() &&
"expect slice and producer loop dimensions map one-to-one");
SmallVector<int64_t> tiledProducerLoopIndices;
transform(llvm::seq<unsigned>(0, tiledProducerIndexingSubMap.getNumResults()),
std::back_inserter(tiledProducerLoopIndices), [&](unsigned idx) {
return tiledProducerIndexingSubMap.getDimPosition(idx);
return tiledProducerLoopIndices;
/// Returns the producer fused in place of `sliceOp`. Tile the producer operands
/// along the `tiledSliceDimIndices` and clone the producer. Consider the case
/// of fusion of an output tensor:
/// ```
/// %1 = producer ins(...) outs(%0)
/// %2 = consumer ins(...) outs(%1)
/// ```
/// When consumer is tiled, %1 appears in the loop iter_args:
/// ```
/// %1 = producer ins(...) outs(%0)
/// %2 = scf.for ... iter_args(%1) .. (%bbarg) {
/// %t1 = tensor.extract_slice %bbarg[..]
/// %t2 = consumer ins(...) outs(%t1)
/// %r = tensor.insert_slice %t2, %bbarg[...]
/// }
/// ```
/// Fusing %1 into the loop requires updating iter_args(%1) to iter_args(%0):
/// ```
/// %2 = scf.for ... iter_args(%0) .. (%bbarg) {
/// %t0 = tensor.extract_slice %bbarg[..]
/// %t1 = producer ins(...) outs(%t0)
/// %t2 = consumer ins(...) outs(%t1)
/// %r = tensor.insert_slice %t2, %bbarg[...]
/// }
/// ```
/// This transformation is only valid if %bbarg is exclusively used by the
/// output ExtractSliceOp / InsertSliceOp pair, which is checked by the
/// `fuseProducer` method.
/// TODO: instead of check and failure, insert new iter_args each time a
/// producer is fused into a consumer and fold away unused iter_args.
static LinalgOp getTiledProducer(OpBuilder &b, OpResult producerResult,
tensor::ExtractSliceOp sliceOp,
ArrayRef<int64_t> tiledSliceDimIndices,
ArrayRef<int64_t> tiledProducerLoopIndices,
OpOperand *iterArg) {
// Clone the producer after `sliceOp` since the slice may be reused to pass in
// the producer result.
OpBuilder::InsertionGuard guard(b);
// Get the producer.
LinalgOp producerOp = producerResult.getOwner();
Location loc = producerOp.getLoc();
// Obtain the `producerOp` loop bounds and the `sliceOp` ranges.
SmallVector<Value> producerLoopBounds;
transform(producerOp.createLoopRanges(b, loc),
[](Range range) { return range.size; });
SmallVector<Range> sliceOpRanges = sliceOp.getOrCreateRanges(b, loc);
// Tile the producer operands given the `sliceOp` ranges. Iterate the
// `tiledSliceDimIndices` and store the tile offset and size for the tiled
// slice dimension.
auto zero = b.create<arith::ConstantIndexOp>(loc, 0);
SmallVector<Value> tileIvs(producerOp.getNumLoops(), nullptr);
SmallVector<Value> tileSizes(producerOp.getNumLoops(), zero);
SmallVector<Value> allIvs(producerOp.getNumLoops(), nullptr);
for (auto it : zip(tiledSliceDimIndices, tiledProducerLoopIndices)) {
int64_t tiledSliceDim = std::get<0>(it);
int64_t tiledProducerLoop = std::get<1>(it);
tileIvs[tiledProducerLoop] = sliceOpRanges[tiledSliceDim].offset;
tileSizes[tiledProducerLoop] = sliceOpRanges[tiledSliceDim].size;
allIvs[tiledProducerLoop] = tileIvs[tiledProducerLoop];
erase_value(tileIvs, nullptr);
SmallVector<Value> tiledOperands = producerOp.getInputAndOutputOperands();
tiledOperands = makeTiledShapes(b, loc, producerOp, tiledOperands, tileIvs,
tileSizes, producerLoopBounds);
// Output fusion has to update the iteration arguments of the tile loop nest.
// In particular, the iteration argument of the outermost tile loop needs to
// be set to the producer output instead of the producer result and `clonedOp`
// shall use the existing `sliceOp` result instead of the tiled producer
// output operand.
if (iterArg) {
OpOperand *outputOperand =
tiledOperands[outputOperand->getOperandNumber()] = sliceOp.getResult();
// Clone the producer using the tiled producer operands.
TypeRange resultTypes = ValueRange(tiledOperands)
LinalgOp clonedOp = producerOp.clone(b, loc, resultTypes, tiledOperands);
// Shift all IndexOp results by the tile offset.
addTileLoopIvsToIndexOpResults(b, clonedOp, allIvs);
return clonedOp;
// TileLoopNest specific helpers.
bool TileLoopNest::isEmpty() { return tileLoopOps.empty(); }
bool TileLoopNest::isValid() {
// Check if `rootOp` has been tiled at least once.
if (isEmpty() || tiledRootAndFusedOpsLoops.count(rootOp) == 0)
return false;
// Check if the number of loop operations and dimensions match.
if (tileLoopOps.size() != tiledRootAndFusedOpsLoops[rootOp].size())
return false;
// Check if the innermost tile loop is the parent of `tiledOp`.
if (rootOp->getParentOp() != tileLoopOps.back())
return false;
// Check if the tile loops are directly nested.
return std::adjacent_find(tileLoopOps.begin(), tileLoopOps.end(),
[](Operation *op1, Operation *op2) {
return op1 != op2->getParentOp();
}) == tileLoopOps.end();
SmallVector<BlockArgument> TileLoopNest::getTiedBBArgs(BlockArgument bbArg) {
assert(bbArg && "expect the block argument to be non-zero");
SmallVector<BlockArgument> bbArgs;
// Search all tile loop block arguments from inner to outer.
for (auto tileLoop : reverse(tileLoopOps)) {
if (bbArg.getOwner()->getParentOp() != tileLoop)
return {};
OpOperand *iterArg = &tileLoop.getOpOperandForRegionIterArg(bbArg);
bbArg = iterArg->get().dyn_cast<BlockArgument>();
// Reverse the block arguments to order them from outer to inner.
return {bbArgs.rbegin(), bbArgs.rend()};
OpOperand *TileLoopNest::getTiedIterArg(BlockArgument bbArg) {
// Search all block arguments and return the matching iteration argument.
SmallVector<BlockArgument> bbArgs = getTiedBBArgs(bbArg);
if (bbArgs.size() != tileLoopOps.size())
return nullptr;
return &tileLoopOps.front().getOpOperandForRegionIterArg(bbArgs.front());
bool TileLoopNest::hasOtherUses(BlockArgument bbArg,
tensor::ExtractSliceOp sliceOp) {
// Check the innermost block argument is either used by the ExtractSliceOp
// `sliceOp`, the matching InsertSliceOp, or by a DimOp. Handle other uses
// conservatively.
for (Operation *op : bbArg.getUsers()) {
if (!isa<tensor::DimOp, tensor::InsertSliceOp, tensor::ExtractSliceOp>(op))
return false;
if (auto extractSliceOp = dyn_cast<tensor::ExtractSliceOp>(op)) {
if (extractSliceOp != sliceOp)
return false;
if (auto insertSliceOp = dyn_cast<tensor::InsertSliceOp>(op)) {
SetVector<Operation *> backwardSlice;
getBackwardSlice(insertSliceOp.source(), &backwardSlice,
[](Operation *op) {
return isa<LinalgOp, tensor::InsertSliceOp>(op);
if (backwardSlice.empty() || backwardSlice.front() != sliceOp)
return false;
// Check the block arguments, except for the innermost one, have one use.
SmallVector<BlockArgument> bbArgs = getTiedBBArgs(bbArg);
return !all_of(bbArgs, [&](BlockArgument bbArg) {
return bbArg.hasOneUse() || bbArg == bbArgs.back();
LogicalResult TileLoopNest::tileRootOp(OpBuilder &b,
ArrayRef<int64_t> tileSizes,
ArrayRef<int64_t> tileInterchange) {
// Exit if all tile sizes are zero.
if (tileSizes.size() == static_cast<size_t>(count(tileSizes, 0)))
return success();
// Tile the root operation.
LinalgTilingOptions tilingOptions;
tilingOptions = tilingOptions
tileInterchange.begin(), tileInterchange.end()))
Optional<TiledLinalgOp> tiledRootOp = tileLinalgOp(b, rootOp, tilingOptions);
// Exit if tiling the root operation fails.
if (!tiledRootOp.hasValue())
return failure();
// Replace all uses of the root operation if it has been tiled before. All
// uses of the original untiled root operation are updated by the calling pass
// or pattern.
if (!isEmpty())
// Transfer the stored `rootOp` loop dimensions if it has been tiled before.
if (tiledRootAndFusedOpsLoops.count(rootOp) != 0) {
tiledRootAndFusedOpsLoops[tiledRootOp->op] =
// Update the root operation and append the loops and tile loop dimensions.
rootOp = tiledRootOp->op;
tileLoopOps.append(tiledRootOp->loops.begin(), tiledRootOp->loops.end());
for (auto en : enumerate(tileSizes)) {
// Copy only the tiled loop dimensions with non-zero tile size.
if (en.value() == 0)
assert(isValid() && "expect tile loop nest to be valid after tiling");
return success();
FailureOr<LinalgOp> TileLoopNest::fuseProducer(OpBuilder &b,
OpOperand *consumerOpOperand) {
// Check if the consumer has been tiled before. For example, it may not have
// been tiled if the outermost tile loop is a reduction loop.
if (tiledRootAndFusedOpsLoops.count(consumerOpOperand->getOwner()) == 0)
return failure();
assert(this->isValid() &&
"expect the tile loop nest to satisfy all invariants");
// Check the tile loop nest is non-empty.
if (isEmpty())
return failure();
// Check `consumerOpOperand` is defined by an ExtractSliceOp.
auto sliceOp =
if (!sliceOp)
return failure();
// Check `sliceOp` and `consumerOp` are in the same block.
LinalgOp consumerOp = consumerOpOperand->getOwner();
if (sliceOp->getBlock() != rootOp->getBlock() ||
consumerOp->getBlock() != rootOp->getBlock())
return failure();
// Check if the producer is a LinalgOp possibly passed by iteration argument.
OpOperand *iterArg = nullptr;
auto producerResult = sliceOp.source().dyn_cast<OpResult>();
if (auto bbArg = sliceOp.source().dyn_cast<BlockArgument>()) {
iterArg = getTiedIterArg(bbArg);
// Check the iteration argument may be used to pass in the producer output.
if (!iterArg || hasOtherUses(bbArg, sliceOp))
return failure();
producerResult = iterArg->get().dyn_cast<OpResult>();
if (!producerResult || !isa<LinalgOp>(producerResult.getOwner()))
return failure();
// Compute the tiled producer slice dimensions given the tiled consumer loops.
SmallVector<int64_t> tiledSliceDimIndices = getTiledSliceDims(
consumerOpOperand, tiledRootAndFusedOpsLoops[consumerOp]);
if (tiledSliceDimIndices.empty())
return failure();
// Compute the tiled producer loop indices.
SmallVector<int64_t> tiledProducerLoopIndices =
getTiledProducerLoops(producerResult, tiledSliceDimIndices);
// Tile the producer operands and clone the producer in place of `sliceOp`.
LinalgOp clonedOp =
getTiledProducer(b, producerResult, sliceOp, tiledSliceDimIndices,
tiledProducerLoopIndices, iterArg);
tiledRootAndFusedOpsLoops[clonedOp] = tiledProducerLoopIndices;
// Cast the `clonedOp` result to gap type mismatches before canonicalization.
Type consumerOperandType = consumerOpOperand->get().getType();
Value newResult = clonedOp->getResult(producerResult.getResultNumber());
if (newResult.getType() != consumerOperandType) {
OpBuilder::InsertionGuard guard(b);
newResult = b.create<tensor::CastOp>(producerResult.getLoc(),
consumerOperandType, newResult);
// Replace the `sliceOp` uses except for the `clonedOp` output uses.
sliceOp.getResult().replaceAllUsesExcept(newResult, clonedOp);
return clonedOp;
ValueRange TileLoopNest::getRootOpReplacementResults() {
assert(!isEmpty() && "expect tile loop nest to be non-empty");
return tileLoopOps.front()->getOpResults();
SmallVector<LinalgOp> TileLoopNest::getAllTiledAndFusedOps() {
SmallVector<LinalgOp> result;
for (const auto &kvp : tiledRootAndFusedOpsLoops) {
auto linalgOp = dyn_cast<LinalgOp>(kvp.getFirst());
assert(linalgOp &&
"expect all tiled and fused operations are linalg operations");
return result;
// Tile and fuse entry-points.
mlir::linalg::tileConsumerAndFuseProducers(OpBuilder &b, LinalgOp consumerOp,
ArrayRef<int64_t> tileSizes,
ArrayRef<int64_t> tileInterchange) {
assert(tileSizes.size() == tileInterchange.size() &&
"expect the number of tile sizes and interchange dims to match");
assert(isPermutation(tileInterchange) &&
"expect tile interchange is a permutation");
// Create an empty tile loop nest.
TileLoopNest tileLoopNest(consumerOp);
// Search the number of outer parallel loops to separate them from possible
// inner reduction dimensions.
SmallVector<StringAttr> iterTypes =
applyPermutationToVector(iterTypes, tileInterchange);
auto *it = find_if(iterTypes, [&](StringAttr iterType) {
return !isParallelIterator(iterType);
int64_t split = std::distance(iterTypes.begin(), it);
// Helper to fuse the producers greedily using a queue of fusion candidates.
auto fuseProducersGreedily = [&](ArrayRef<OpOperand *> operands) {
SmallVector<OpOperand *> candidates(operands.begin(), operands.end());
while (!candidates.empty()) {
FailureOr<LinalgOp> fusedProducer =
tileLoopNest.fuseProducer(b, candidates.pop_back_val());
if (failed(fusedProducer))
// Tile the outer parallel loops and fuse the output operands.
SmallVector<int64_t> outerTileSizes;
outerTileSizes.append(tileSizes.begin(), tileSizes.begin() + split);
outerTileSizes.append(tileSizes.size() - split, 0);
if (failed(tileLoopNest.tileRootOp(b, outerTileSizes, tileInterchange)))
return failure();
// Tile the remaining loops and fuse the input operands.
SmallVector<int64_t> innerTileSizes;
innerTileSizes.append(split, 0);
innerTileSizes.append(tileSizes.begin() + split, tileSizes.end());
if (failed(tileLoopNest.tileRootOp(b, innerTileSizes, tileInterchange)))
return failure();
return tileLoopNest;