SCF/Transforms/TileUsingInterface.cpp

//===- Tiling.cpp - Implementation of tiling using TilingInterface -------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file implements the tiling using TilingInterface.
//
//===----------------------------------------------------------------------===//

#include "mlir/Dialect/SCF/Transforms/TileUsingInterface.h"

#include "mlir/Dialect/Affine/IR/AffineOps.h"
#include "mlir/Dialect/Arith/IR/Arith.h"
#include "mlir/Dialect/Arith/Utils/Utils.h"
#include "mlir/Dialect/Func/IR/FuncOps.h"
#include "mlir/Dialect/SCF/Utils/Utils.h"
#include "mlir/Dialect/Tensor/IR/Tensor.h"
#include "mlir/Dialect/Utils/IndexingUtils.h"
#include "mlir/IR/Matchers.h"
#include "mlir/IR/PatternMatch.h"
#include "mlir/Interfaces/DestinationStyleOpInterface.h"
#include "mlir/Interfaces/TilingInterface.h"
#include "llvm/Support/Debug.h"
#include <optional>

#define DEBUG_TYPE "tile-using-interface"

using namespace mlir;

scf::SCFTilingOptions &
scf::SCFTilingOptions::setTileSizes(ArrayRef<int64_t> ts) {
  assert(!tileSizeComputationFunction && "tile sizes already set");
  SmallVector<int64_t> tileSizes(ts.begin(), ts.end());
  tileSizeComputationFunction = [tileSizes](OpBuilder &b, Operation *op) {
    OpBuilder::InsertionGuard guard(b);
    b.setInsertionPointToStart(
        &op->getParentWithTrait<OpTrait::IsIsolatedFromAbove>()
             ->getRegion(0)
             .front());
    return llvm::to_vector<4>(map_range(tileSizes, [&](int64_t s) {
      Value v = b.create<arith::ConstantIndexOp>(op->getLoc(), s);
      return v;
    }));
  };
  return *this;
}

/// Helper method to adjust the interchange vector to match the iteration
/// domain.
static SmallVector<int64_t>
fillInterchangeVector(ArrayRef<int64_t> interchangeVector,
                      size_t iterationDomainSize) {
  SmallVector<int64_t> filledVector = llvm::to_vector(interchangeVector);
  if (filledVector.size() < iterationDomainSize) {
    auto range = llvm::seq<int64_t>(filledVector.size(), iterationDomainSize);
    filledVector.append(range.begin(), range.end());
  }
  if (filledVector.size() > iterationDomainSize)
    filledVector.resize(iterationDomainSize);
  return filledVector;
}

//===----------------------------------------------------------------------===//
// tileUsingSCFForOp implementation.
//===----------------------------------------------------------------------===//

// Check if `stride` evenly divides the trip count `size - offset`.
static bool tileDividesIterationDomain(Range loopRange) {
  std::optional<int64_t> offsetAsInt = getConstantIntValue(loopRange.offset);
  if (!offsetAsInt)
    return false;
  std::optional<int64_t> sizeAsInt = getConstantIntValue(loopRange.size);
  if (!sizeAsInt)
    return false;
  std::optional<int64_t> strideAsInt = getConstantIntValue(loopRange.stride);
  if (!strideAsInt)
    return false;
  return ((sizeAsInt.value() - offsetAsInt.value()) % strideAsInt.value() == 0);
}

/// Returns the bounded tile size given the current `iv`, `loopRange` and
/// `tileSize`, i.e., `min(tileSize, range.end() - iv)`.
static OpFoldResult getBoundedTileSize(OpBuilder &b, Location loc,
                                       Range loopRange, Value iv,
                                       Value tileSize) {
  std::optional<int64_t> ts = getConstantIntValue(tileSize);
  if (ts && ts.value() == 1)
    return getAsOpFoldResult(tileSize);

  if (tileDividesIterationDomain(
          Range{loopRange.offset, loopRange.size, tileSize}))
    return tileSize;

  // The tile size to use (to avoid out of bounds access) is  minimum of
  // `tileSize` and `ub - iv`, where `iv` is the induction variable of the tiled
  // loop.
  AffineExpr s0, s1, d0;
  bindDims(b.getContext(), d0);
  bindSymbols(b.getContext(), s0, s1);
  AffineMap minMap = AffineMap::get(1, 2, {s0, s1 - d0}, b.getContext());
  Value size = getValueOrCreateConstantIndexOp(b, loc, loopRange.size);
  return affine::makeComposedFoldedAffineMin(
      b, loc, minMap, SmallVector<OpFoldResult>{iv, tileSize, size});
}

/// Generate an empty loop nest that represents the tiled loop nest shell.
/// - `loopRanges` specifies the lb, ub and step of the untiled iteration space.
/// - `tileSizeVals` is the tile sizes to use. Zero represent untiled loops.
/// - In `offsets` and `sizes` return the multi-dimensional offset and size of
/// the
///   tile processed within the inner most loop.
static SmallVector<scf::ForOp>
generateTileLoopNest(OpBuilder &builder, Location loc,
                     ArrayRef<Range> loopRanges, ArrayRef<Value> tileSizeVals,
                     SmallVector<OpFoldResult> &offsets,
                     SmallVector<OpFoldResult> &sizes) {
  assert(!loopRanges.empty() && "expected at least one loop range");
  assert(loopRanges.size() == tileSizeVals.size() &&
         "expected as many tile sizes as loop ranges");
  OpBuilder::InsertionGuard guard(builder);
  SmallVector<scf::ForOp> loops;
  offsets.resize(loopRanges.size());
  sizes.resize(loopRanges.size());

  for (auto loopRange : llvm::enumerate(loopRanges)) {
    Value offset =
        getValueOrCreateConstantIndexOp(builder, loc, loopRange.value().offset);
    Value size =
        getValueOrCreateConstantIndexOp(builder, loc, loopRange.value().size);
    Value tileSize = tileSizeVals[loopRange.index()];
    // No loops if tile size is zero. Set offset and size to the loop
    // offset and size.
    if (matchPattern(tileSize, m_Zero())) {
      offsets[loopRange.index()] = offset;
      sizes[loopRange.index()] = size;
      continue;
    }

    auto loop = builder.create<scf::ForOp>(
        loc, offset, size, tileSize, ValueRange{},
        [&](OpBuilder &bodyBuilder, Location bodyLoc, Value iv,
            ValueRange /*iterArgs*/) {
          sizes[loopRange.index()] = getBoundedTileSize(
              bodyBuilder, bodyLoc, loopRange.value(), iv, tileSize);
          builder.create<scf::YieldOp>(loc);
        });
    offsets[loopRange.index()] = loop.getInductionVar();
    loops.push_back(loop);
    builder.setInsertionPoint(loop.getBody()->getTerminator());
  }
  return loops;
}

/// For a value to be yielded (`yieldedValue`) from within a loop nest `loops`,
/// construct the destructive update pattern that inserts the yielded
/// value into a destination tensor provided by `initValue` at offset
/// `tileOffsets` and size `tileSizes`. For example,
///
/// ```mlir
/// scf.for %iv0 = ... {
///   %0 = tiled_op
/// }
/// ```
///
/// is transformed to
///
/// ```mlir
/// scf.for %iv0 = ... iter_args(%arg = %0) {
///   %1 = tensor.extract_slice %arg
///   %2 = tiled_op
///   %3 = tensor.insert_slice %2 into %arg
///   scf.yield %3
/// }
/// ```
/// TODO: This API can be cleaned up by using `SubsetExtractOpInterface`.
static SmallVector<Value>
yieldTiledValues(RewriterBase &rewriter, ValueRange initValues,
                 ValueRange yieldedValues,
                 ArrayRef<SmallVector<OpFoldResult>> tileOffsetsList,
                 ArrayRef<SmallVector<OpFoldResult>> tileSizesList,
                 MutableArrayRef<scf::ForOp> loops) {
  NewYieldValueFn yieldValueFn =
      [&](OpBuilder &b, Location loc,
          ArrayRef<BlockArgument> newBBArgs) -> SmallVector<Value> {
    SmallVector<Value> inserts;
    for (const auto &yieldedValue : llvm::enumerate(yieldedValues)) {
      ArrayRef<OpFoldResult> tileOffsets =
          tileOffsetsList[yieldedValue.index()];
      ArrayRef<OpFoldResult> tileSizes = tileSizesList[yieldedValue.index()];
      SmallVector<OpFoldResult> tileStrides(tileOffsets.size(),
                                            b.getIndexAttr(1));
      Value insert = b.create<tensor::InsertSliceOp>(
          loc, yieldedValue.value(), newBBArgs[yieldedValue.index()],
          tileOffsets, tileSizes, tileStrides);
      inserts.push_back(insert);
    }
    return inserts;
  };

  SmallVector<scf::ForOp> newLoops =
      replaceLoopNestWithNewYields(rewriter, loops, initValues, yieldValueFn,
                                   /*replaceIterOperandsUsesInLoop =*/false);
  for (const auto &loop : llvm::enumerate(loops)) {
    rewriter.eraseOp(loop.value());
    loops[loop.index()] = newLoops[loop.index()];
  }
  return llvm::to_vector(llvm::map_range(
      loops.front().getResults().take_back(yieldedValues.size()),
      [](OpResult r) -> Value { return r; }));
}

/// If the tiled operation is destination passing style, update the
/// slice of the destination used (which refers to the untiled destination)
/// to use the corresponding region argument of the innermost loop.
///
/// ```mlir
/// %0 =
/// scf.for %iv0 = ... iter_args(%arg = %0) {
///   %1 = tensor.extract_slice %0
///   %2 = tiled_op
///   %3 = tensor.insert_slice %2 into %arg
///   scf.yield %3
/// }
/// ```
///
/// is transformed to
///
/// ```mlir
/// scf.for %iv0 = ... iter_args(%arg = %0) {
///   %1 = tensor.extract_slice %arg
///   %2 = tiled_op
///   %3 = tensor.insert_slice %2 into %arg
///   scf.yield %3
/// }
/// ```
static void
updateDestinationOperandsForTiledOp(OpBuilder &builder,
                                    ValueRange tiledOpDestinationValues,
                                    ValueRange bbArgsList) {
  for (const auto &destValue : llvm::enumerate(tiledOpDestinationValues)) {
    auto sliceOp = destValue.value().getDefiningOp<tensor::ExtractSliceOp>();
    if (!sliceOp)
      continue;
    sliceOp.setOperand(0, bbArgsList[destValue.index()]);
  }
}

/// Helper method to yield the values of the tiled op, as well as
/// update the destination operands of the tiled op, if it is
/// a destination passing style op.
static SmallVector<Value>
yieldTiledValues(RewriterBase &rewriter, ArrayRef<Value> initValues,
                 TilingResult tilingResult,
                 ArrayRef<SmallVector<OpFoldResult>> tileOffsetsList,
                 ArrayRef<SmallVector<OpFoldResult>> tileSizesList,
                 MutableArrayRef<scf::ForOp> loops) {
  SmallVector<Value> replacements =
      yieldTiledValues(rewriter, initValues, tilingResult.tiledValues,
                       tileOffsetsList, tileSizesList, loops);
  for (auto tiledOp : tilingResult.tiledOps) {
    if (auto dstOp = dyn_cast<DestinationStyleOpInterface>(tiledOp)) {
      auto innerMostLoop = loops.back();
      SmallVector<Value> tiledOpDestinationTensors = dstOp.getDpsInitOperands();
      updateDestinationOperandsForTiledOp(rewriter, tiledOpDestinationTensors,
                                          innerMostLoop.getRegionIterArgs());
    }
  }
  return replacements;
}

/// Implementation of tiling transformation of `op` that implements the
/// `TilingInterface` using `scf.for` to iterate over the tiles.
FailureOr<scf::SCFTilingResult>
mlir::scf::tileUsingSCFForOp(RewriterBase &rewriter, TilingInterface op,
                             const scf::SCFTilingOptions &options) {
  OpBuilder::InsertionGuard guard(rewriter);
  rewriter.setInsertionPointAfter(op);

  if (!options.tileSizeComputationFunction) {
    return rewriter.notifyMatchFailure(
        op, "missing tile size computation function");
  }

  // 1. Get the range of the loops that are represented by the operation.
  SmallVector<Range> iterationDomain = op.getIterationDomain(rewriter);
  size_t numLoops = iterationDomain.size();
  if (numLoops == 0) {
    return rewriter.notifyMatchFailure(
        op, "unable to tile op with no iteration domain");
  }

  // 2. Materialize the tile sizes. Enforce the convention that "tiling by zero"
  // skips tiling a particular dimension. This convention is significantly
  // simpler to handle instead of adjusting affine maps to account for missing
  // dimensions.
  SmallVector<Value> tileSizeVector =
      options.tileSizeComputationFunction(rewriter, op);
  if (tileSizeVector.size() < iterationDomain.size()) {
    auto zero = rewriter.create<arith::ConstantIndexOp>(op.getLoc(), 0);
    tileSizeVector.append(numLoops - tileSizeVector.size(), zero);
  }

  scf::SCFTilingResult tilingResult;
  SmallVector<OpFoldResult> offsets, sizes;
  {
    // If there is an interchange specified, permute the iteration domain and
    // the tile sizes.
    SmallVector<int64_t> interchangeVector;
    if (!options.interchangeVector.empty()) {
      interchangeVector = fillInterchangeVector(options.interchangeVector,
                                                iterationDomain.size());
    }
    if (!interchangeVector.empty()) {
      if (!isPermutationVector(interchangeVector)) {
        return rewriter.notifyMatchFailure(
            op, "invalid intechange vector, not a permutation of the entire "
                "iteration space");
      }

      applyPermutationToVector(iterationDomain, interchangeVector);
      applyPermutationToVector(tileSizeVector, interchangeVector);
    }

    // 3. Materialize an empty loop nest that iterates over the tiles. These
    // loops for now do not return any values even if the original operation has
    // results.
    tilingResult.loops = generateTileLoopNest(
        rewriter, op.getLoc(), iterationDomain, tileSizeVector, offsets, sizes);

    if (!interchangeVector.empty()) {
      auto inversePermutation = invertPermutationVector(interchangeVector);
      applyPermutationToVector(offsets, inversePermutation);
      applyPermutationToVector(sizes, inversePermutation);
    }
  }

  LLVM_DEBUG({
    if (!tilingResult.loops.empty()) {
      llvm::dbgs() << "LoopNest shell :\n";
      tilingResult.loops.front().dump();
      llvm::dbgs() << "\n";
    }
  });

  // 4. Generate the tiled implementation within the inner most loop.
  if (!tilingResult.loops.empty())
    rewriter.setInsertionPoint(
        tilingResult.loops.back().getBody()->getTerminator());
  FailureOr<TilingResult> tiledImplementation =
      op.getTiledImplementation(rewriter, offsets, sizes);
  tilingResult.tiledOps.append(tiledImplementation->tiledOps);
  if (op->getNumResults() == 0) {
    // nothing more to do.
    return tilingResult;
  }

  // If loops are empty, the tiled op is used as the replacement for the untiled
  // op.
  if (tilingResult.loops.empty()) {
    tilingResult.replacements = tiledImplementation->tiledValues;
    return tilingResult;
  }

  // 5. Yield all the results of the tiled operation. The surrounding loop
  //    nest is modified to insert a destructive update pattern to yield
  //    from the loop nest values to replace the untiled op with.
  int64_t numResults = op->getNumResults();
  SmallVector<SmallVector<OpFoldResult>> resultOffsetsList(numResults),
      resultSizesList(numResults);
  for (const auto &result : llvm::enumerate(op->getResults())) {
    if (failed(op.getResultTilePosition(rewriter, result.index(), offsets,
                                        sizes,
                                        resultOffsetsList[result.index()],
                                        resultSizesList[result.index()]))) {
      return rewriter.notifyMatchFailure(
          op, "failed to get slice of result produced");
    }
  }

  SmallVector<Value> destinationTensors;
  if (failed(tensor::getOrCreateDestinations(rewriter, op.getLoc(), op,
                                             destinationTensors)))
    return rewriter.notifyMatchFailure(op, "failed to get destinations");

  tilingResult.replacements = yieldTiledValues(
      rewriter, destinationTensors, tiledImplementation.value(),
      resultOffsetsList, resultSizesList, tilingResult.loops);

  LLVM_DEBUG({
    if (!tilingResult.loops.empty()) {
      llvm::dbgs() << "After tiled implementation :\n";
      tilingResult.loops.front().dump();
      llvm::dbgs() << "\n";
    }
  });
  return tilingResult;
}

FailureOr<scf::SCFReductionTilingResult>
mlir::scf::tileReductionUsingScf(RewriterBase &b,
                                 PartialReductionOpInterface op,
                                 ArrayRef<OpFoldResult> tileSize) {
  Location loc = op.getLoc();
  // Ops implementing PartialReductionOpInterface are expected to implement
  // TilingInterface.
  auto tilingInterfaceOp = cast<TilingInterface>(op.getOperation());
  SmallVector<Range> iterationDomain = tilingInterfaceOp.getIterationDomain(b);
  SmallVector<Value> tileSizeVector =
      getValueOrCreateConstantIndexOp(b, loc, tileSize);
  if (tileSizeVector.size() < iterationDomain.size()) {
    auto zero = b.create<arith::ConstantIndexOp>(loc, 0);
    tileSizeVector.append(iterationDomain.size() - tileSizeVector.size(), zero);
  }
  if (op->getNumResults() != 1)
    return b.notifyMatchFailure(
        op, "don't support ops with multiple results for now");
  SmallVector<utils::IteratorType> iterators =
      tilingInterfaceOp.getLoopIteratorTypes();
  int64_t numReductionDims = llvm::count(
      tilingInterfaceOp.getLoopIteratorTypes(), utils::IteratorType::reduction);
  if (numReductionDims != 1)
    return b.notifyMatchFailure(
        op, "only support ops with one reduction dimension.");
  int reductionDim;
  for (auto [idx, iteratorType] :
       llvm::enumerate(tilingInterfaceOp.getLoopIteratorTypes())) {
    if (iteratorType == utils::IteratorType::reduction) {
      reductionDim = idx;
      break;
    }
  }
  if (static_cast<size_t>(reductionDim) >= tileSize.size())
    return b.notifyMatchFailure(op, "reduction dimension must be tiled");

  // 1. create the inital tensor value.
  FailureOr<Operation *> identityTensor =
      op.generateInitialTensorForPartialReduction(b, loc, tileSize,
                                                  reductionDim);
  if (failed(identityTensor))
    return b.notifyMatchFailure(op,
                                "cannot create a tensor of identity value.");
  // 2. Create the nested loops.
  SmallVector<OpFoldResult> offsets, sizes;
  SmallVector<scf::ForOp> loops = generateTileLoopNest(
      b, loc, iterationDomain, tileSizeVector, offsets, sizes);

  // 3. Generate the tiled implementation within the inner most loop.
  b.setInsertionPoint(loops.back().getBody()->getTerminator());
  Operation *parallelOp = op.tileToPartialReduction(
      b, loc, (*identityTensor)->getResults(), offsets, sizes, reductionDim);

  SmallVector<OpFoldResult> resultSizesList;
  for (size_t i = 0; i < offsets.size(); i++)
    resultSizesList.push_back(
        b.createOrFold<tensor::DimOp>(loc, parallelOp->getResult(0), i));
  SmallVector<OpFoldResult> outOffsets(offsets.size(), b.getIndexAttr(0));
  SmallVector<Value> replacements = yieldTiledValues(
      b, (*identityTensor)->getResults(), parallelOp->getResults(), outOffsets,
      resultSizesList, loops);

  auto dstOp = cast<DestinationStyleOpInterface>(parallelOp);
  auto innerMostLoop = loops.back();
  SmallVector<Value> destinationTensors = dstOp.getDpsInitOperands();
  assert(destinationTensors.size() ==
             innerMostLoop.getRegionIterArgs().size() &&
         "unexpected number of outputs");
  updateDestinationOperandsForTiledOp(b, destinationTensors,
                                      innerMostLoop.getRegionIterArgs());

  // 4. Apply the merge reduction to combine all the partial values.
  b.setInsertionPointAfter(*loops.begin());
  Operation *mergeOp = op.mergeReductions(b, loc, replacements, reductionDim);
  b.replaceOp(op, mergeOp->getResults());

  SCFReductionTilingResult results;
  results.initialOp = *identityTensor;
  results.loops = std::move(loops);
  results.parallelTiledOp = parallelOp;
  results.mergeOp = mergeOp;
  return results;
}
//===----------------------------------------------------------------------===//
// tileConsumerAndFuseProducerGreedilyUsingSCFForOp implementation.
//===----------------------------------------------------------------------===//

/// Return the untiled producer whose slice is used in a tiled consumer. The
/// method traverses the tile loop nest (`loops`) if needed, and returns the
/// `iter_args` of the outer most that is encountered. Traversing the iter_args
/// indicates that this is a destination operand of the consumer. If there was
/// no loop traversal needed, the second value of the returned tuple is empty.
static std::tuple<OpResult, std::optional<OpOperand *>>
getUntiledProducerFromSliceSource(OpOperand *source,
                                  ArrayRef<scf::ForOp> loops) {
  std::optional<OpOperand *> destinationIterArg;
  auto loopIt = loops.rbegin();
  while (auto iterArg = source->get().dyn_cast<BlockArgument>()) {
    scf::ForOp loop = *loopIt;
    if (iterArg.getOwner()->getParentOp() != loop)
      break;
    source = &loop.getOpOperandForRegionIterArg(iterArg);
    loopIt++;
  }
  if (loopIt == loops.rend())
    destinationIterArg = source;
  return {source->get().dyn_cast<OpResult>(), destinationIterArg};
}

/// Implementation of fusing producer of a single slice by computing the
/// slice of the producer in-place.
std::optional<scf::SCFFuseProducerOfSliceResult>
mlir::scf::tileAndFuseProducerOfSlice(RewriterBase &rewriter,
                                      tensor::ExtractSliceOp candidateSliceOp,
                                      MutableArrayRef<scf::ForOp> loops) {
  // 1. Get the producer of the source (potentially walking through
  // `iter_args` of nested `scf.for`)
  auto [fusableProducer, destinationIterArg] =
      getUntiledProducerFromSliceSource(&candidateSliceOp->getOpOperand(0),
                                        loops);
  if (!fusableProducer)
    return std::nullopt;

  // 2. Generate the tiled implementation of the producer of the source
  OpBuilder::InsertionGuard g(rewriter);
  rewriter.setInsertionPoint(candidateSliceOp);
  FailureOr<TilingResult> tileAndFuseResult =
      tensor::replaceExtractSliceWithTiledProducer(rewriter, candidateSliceOp,
                                                   fusableProducer);
  if (failed(tileAndFuseResult))
    return std::nullopt;
  rewriter.replaceAllUsesWith(candidateSliceOp,
                              tileAndFuseResult->tiledValues[0]);

  // 3. If the slice is for a destination operand, for example,
  //
  // ```mlir
  // %0 = linalg.init
  // %1 = linalg.fill .. outs(%0 : )
  // %2 = scf.for .. iter_args(%arg0 = %1) {
  //   %3 = scf.for .. iter_args(%arg1 = %arg0) {
  //     %4 = tensor.extract_slice %arg1 [..]
  //     .. = linalg.matmul .. outs(%4 : )
  //   }
  // }
  // ```
  //
  // the IR is currently
  //
  // ```
  // %0 = linalg.init
  // %1 = linalg.fill
  // %2 = scf.for .. iter_args(%arg0 = %1 /* incorrect value */ ) {
  //   %3 = scf.for .. iter_args(%arg1 = %arg0) {
  //     %4 = tensor.extract_slice %0 /*incorrect value */ [..]
  //     %5 = linalg.fill .. outs(%4 : )
  //     .. = linalg.matmul .. outs(%5 : )
  //   }
  // }
  // ```
  //
  // The untiled `linalg.fill` is still used as the `init_value` since it
  // was originally a destination operand of the untiled `linalg.matmul`.
  // When fusing an operand that is a destination operand.
  //   - Update the iter_arg of the outer most loop to use the destination
  //     of the untiled producer.
  //   - Update the destination of the slice of the tiled producer generated
  //     to use the same basic block argument as the slice that was used to
  //     generate inplace the tiled implementation of the producer.
  // With this the IR will be.
  //
  // ```
  // %0 = linalg.init
  // %1 = scf.for .. iter_args(%arg0 = %0 /* corrected value */ ) {
  //   %2 = scf.for .. iter_args(%arg1 = %arg0) {
  //     %3 = tensor.extract_slice %arg1 /* corrected value */ [..]
  //     %4 = linalg.fill .. outs(%3 : )
  //     .. = linalg.matmul .. outs(%4 : )
  //   }
  // }
  // ```
  // TODO: This can be modeled better if the `DestinationStyleOpInterface`.
  // Update to use that when it does become available.
  scf::ForOp outerMostLoop = loops.front();
  std::optional<unsigned> iterArgNumber;
  if (destinationIterArg) {
    iterArgNumber =
        outerMostLoop.getIterArgNumberForOpOperand(*destinationIterArg.value());
  }
  if (iterArgNumber) {
    int64_t resultNumber = fusableProducer.getResultNumber();
    if (auto dstOp =
            dyn_cast<DestinationStyleOpInterface>(fusableProducer.getOwner())) {
      outerMostLoop.setIterArg(iterArgNumber.value(),
                               dstOp.getTiedOpOperand(fusableProducer)->get());
    }
    for (auto tileAndFusedOp : tileAndFuseResult->tiledOps) {
      auto dstOp = dyn_cast<DestinationStyleOpInterface>(tileAndFusedOp);
      if (!dstOp)
        continue;
      scf::ForOp innerMostLoop = loops.back();
      updateDestinationOperandsForTiledOp(
          rewriter, dstOp.getDpsInitOperand(resultNumber)->get(),
          innerMostLoop.getRegionIterArgs()[iterArgNumber.value()]);
    }
  }
  return scf::SCFFuseProducerOfSliceResult{fusableProducer,
                                           tileAndFuseResult->tiledValues[0],
                                           tileAndFuseResult->tiledOps};
}

/// Reconstruct the fused producer from within the tiled-and-fused code.
void mlir::scf::yieldReplacementForFusedProducer(
    RewriterBase &rewriter, tensor::ExtractSliceOp sliceOp,
    scf::SCFFuseProducerOfSliceResult fusedProducerInfo,
    MutableArrayRef<scf::ForOp> loops) {
  auto [fusableProducer, fusedProducerValue, tileAndFusedOps] =
      fusedProducerInfo;
  SmallVector<Value> initValues;
  FailureOr<Value> initValue = tensor::getOrCreateDestination(
      rewriter, fusableProducer.getOwner()->getLoc(), fusableProducer);
  if (succeeded(initValue)) {
    SmallVector<OpFoldResult> resultOffsets = sliceOp.getMixedOffsets();
    SmallVector<OpFoldResult> resultSizes = sliceOp.getMixedSizes();
    SmallVector<Value> yieldedVals =
        yieldTiledValues(rewriter, initValue.value(), fusedProducerValue,
                         resultOffsets, resultSizes, loops);
  }
  for (auto tileAndFusedOp : tileAndFusedOps) {
    auto dstStyleProducer =
        dyn_cast<DestinationStyleOpInterface>(tileAndFusedOp);
    if (!dstStyleProducer)
      continue;
    Value dstValue =
        dstStyleProducer.getDpsInitOperand(fusableProducer.getResultNumber())
            ->get();
    updateDestinationOperandsForTiledOp(
        rewriter, dstValue, loops.back().getRegionIterArgs().back());
  }
}

/// Implementation of tile consumer and fuse producer greedily.
FailureOr<scf::SCFTileAndFuseResult>
mlir::scf::tileConsumerAndFuseProducerGreedilyUsingSCFForOp(
    RewriterBase &rewriter, TilingInterface consumer,
    const scf::SCFTileAndFuseOptions &options) {
  // This transformation is only valid for ops that return values (i.e. not
  // valid to use with operations that have memref operands).
  if (!consumer->getNumResults()) {
    return rewriter.notifyMatchFailure(
        consumer, "invalid pattern for op with no results");
  }

  // 1. First tile the consumer.
  scf::SCFTileAndFuseResult tileAndFuseResult;
  llvm::SmallDenseMap<Value, int64_t> yieldedValueToResultNumber;
  {
    FailureOr<scf::SCFTilingResult> tilingResult =
        tileUsingSCFForOp(rewriter, consumer, options.tilingOptions);
    if (failed(tilingResult))
      return rewriter.notifyMatchFailure(consumer, "failed to tile consumer");
    for (auto *tiledOp : tilingResult->tiledOps)
      tileAndFuseResult.tiledAndFusedOps.insert(tiledOp);
    tileAndFuseResult.loops = std::move(tilingResult->loops);
    for (const auto &result : llvm::enumerate(
             llvm::zip(consumer->getResults(), tilingResult->replacements))) {
      tileAndFuseResult.replacements[std::get<0>(result.value())] =
          std::get<1>(result.value());
      yieldedValueToResultNumber[tilingResult->tiledOps.back()->getResult(
          result.index())] = result.index();
    }
  }

  // If there are no loops generated, fusion is immaterial.
  if (tileAndFuseResult.loops.empty())
    return tileAndFuseResult;

  // 2. Typically, the operands of the tiled operation are slices of the
  //    operands of the untiled operation. These are expressed in IR using
  //    `tensor.extract_slice` operations with source being the operands of the
  //    untiled operation. Create a worklist of these `tensor.extract_slice`
  //    operations. If the producers of the source of the `tensor.extract_slice`
  //    can be tiled such that the tiled value is generated in-place, that
  //    effectively tiles + fuses the operations.
  auto addCandidateSlices = [](Operation *fusedOp,
                               std::deque<tensor::ExtractSliceOp> &candidates) {
    for (Value operand : fusedOp->getOperands())
      if (auto sliceOp = operand.getDefiningOp<tensor::ExtractSliceOp>())
        candidates.push_back(sliceOp);
  };

  std::deque<tensor::ExtractSliceOp> candidates;
  addCandidateSlices(tileAndFuseResult.tiledAndFusedOps.back(), candidates);
  OpBuilder::InsertionGuard g(rewriter);
  while (!candidates.empty()) {
    // Traverse the slices in BFS fashion.
    tensor::ExtractSliceOp candidateSliceOp = candidates.front();
    candidates.pop_front();

    // The operands of the fused producer might themselved be slices of
    // values produced by operations that implement the `TilingInterface`.
    // Add these operations to the worklist.
    std::optional<scf::SCFFuseProducerOfSliceResult> fusedProducer =
        tileAndFuseProducerOfSlice(rewriter, candidateSliceOp,
                                   tileAndFuseResult.loops);
    if (!fusedProducer)
      continue;

    if (Operation *tiledAndFusedOp =
            fusedProducer->tiledAndFusedProducer.getDefiningOp()) {
      tileAndFuseResult.tiledAndFusedOps.insert(tiledAndFusedOp);
      addCandidateSlices(tiledAndFusedOp, candidates);
    }
  }
  return tileAndFuseResult;
}

//===----------------------------------------------------------------------===//
// lowerToLoopsUsingSCFForOp implementation.
//===----------------------------------------------------------------------===//

FailureOr<SmallVector<scf::ForOp>>
mlir::scf::lowerToLoopsUsingSCFForOp(RewriterBase &rewriter,
                                     TilingInterface op) {
  // TODO: Handle cases where the op has results if needed.
  if (op->getNumResults() > 0) {
    return rewriter.notifyMatchFailure(
        op, "unable to lower to loops operations with return values");
  }

  SmallVector<Range> domain = op.getIterationDomain(rewriter);
  SmallVector<Value> ivs;
  SmallVector<scf::ForOp> loops;
  Location loc = op.getLoc();
  for (auto loopRange : domain) {
    Value offsetVal =
        getValueOrCreateConstantIndexOp(rewriter, loc, loopRange.offset);
    Value sizeVal =
        getValueOrCreateConstantIndexOp(rewriter, loc, loopRange.size);
    Value strideVal =
        getValueOrCreateConstantIndexOp(rewriter, loc, loopRange.stride);
    auto loop = rewriter.create<scf::ForOp>(op.getLoc(), offsetVal, sizeVal,
                                            strideVal, ValueRange{});
    loops.push_back(loop);
    ivs.push_back(loop.getInductionVar());
    rewriter.setInsertionPoint(loop.getBody()->getTerminator());
  }
  if (failed(op.generateScalarImplementation(rewriter, op.getLoc(), ivs))) {
    return failure();
  }
  return loops;
}