MeshToMPI.cpp

Go to the documentation of this file.

//===- MeshToMPI.cpp - Mesh to MPI  dialect conversion -----------------===//
//
// 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 a translation of Mesh communication ops tp MPI ops.
//
//===----------------------------------------------------------------------===//
 
#include "mlir/Conversion/MeshToMPI/MeshToMPI.h"
 
#include "mlir/Dialect/Arith/IR/Arith.h"
#include "mlir/Dialect/Bufferization/IR/Bufferization.h"
#include "mlir/Dialect/DLTI/DLTI.h"
#include "mlir/Dialect/Func/IR/FuncOps.h"
#include "mlir/Dialect/Func/Transforms/FuncConversions.h"
#include "mlir/Dialect/Linalg/IR/Linalg.h"
#include "mlir/Dialect/MPI/IR/MPI.h"
#include "mlir/Dialect/MemRef/IR/MemRef.h"
#include "mlir/Dialect/Mesh/IR/MeshDialect.h"
#include "mlir/Dialect/Mesh/IR/MeshOps.h"
#include "mlir/Dialect/SCF/IR/SCF.h"
#include "mlir/Dialect/Tensor/IR/Tensor.h"
#include "mlir/Dialect/Utils/StaticValueUtils.h"
#include "mlir/IR/Builders.h"
#include "mlir/IR/BuiltinAttributes.h"
#include "mlir/IR/BuiltinTypes.h"
#include "mlir/IR/PatternMatch.h"
#include "mlir/IR/SymbolTable.h"
#include "mlir/Transforms/DialectConversion.h"
#include "mlir/Transforms/GreedyPatternRewriteDriver.h"
 
#define DEBUG_TYPE "mesh-to-mpi"
#define DBGS() (llvm::dbgs() << "[" DEBUG_TYPE "]: ")
 
namespace mlir {
#define GEN_PASS_DEF_CONVERTMESHTOMPIPASS
#include "mlir/Conversion/Passes.h.inc"
} // namespace mlir
 
using namespace mlir;
using namespace mesh;
 
namespace {
/// Converts a vector of OpFoldResults (ints) into vector of Values of the
/// provided type.
static SmallVector<Value> getMixedAsValues(OpBuilder b, const Location &loc,
                                           llvm::ArrayRef<int64_t> statics,
                                           ValueRange dynamics,
                                           Type type = Type()) {
  SmallVector<Value> values;
  auto dyn = dynamics.begin();
  Type i64 = b.getI64Type();
  if (!type)
    type = i64;
  assert((i64 == type || b.getIndexType() == type) &&
         "expected an i64 or an intex type");
  for (auto s : statics) {
    if (s == ShapedType::kDynamic) {
      values.emplace_back(*(dyn++));
    } else {
      TypedAttr val = type == i64 ? b.getI64IntegerAttr(s) : b.getIndexAttr(s);
      values.emplace_back(b.create<arith::ConstantOp>(loc, type, val));
    }
  }
  return values;
}
 
/// Create operations converting a linear index to a multi-dimensional index.
static SmallVector<Value> linearToMultiIndex(Location loc, OpBuilder b,
                                             Value linearIndex,
                                             ValueRange dimensions) {
  int n = dimensions.size();
  SmallVector<Value> multiIndex(n);
 
  for (int i = n - 1; i >= 0; --i) {
    multiIndex[i] = b.create<arith::RemSIOp>(loc, linearIndex, dimensions[i]);
    if (i > 0)
      linearIndex = b.create<arith::DivSIOp>(loc, linearIndex, dimensions[i]);
  }
 
  return multiIndex;
}
 
/// Create operations converting a multi-dimensional index to a linear index.
Value multiToLinearIndex(Location loc, OpBuilder b, ValueRange multiIndex,
                         ValueRange dimensions) {
 
  Value linearIndex = b.create<arith::ConstantIndexOp>(loc, 0);
  Value stride = b.create<arith::ConstantIndexOp>(loc, 1);
 
  for (int i = multiIndex.size() - 1; i >= 0; --i) {
    Value off = b.create<arith::MulIOp>(loc, multiIndex[i], stride);
    linearIndex = b.create<arith::AddIOp>(loc, linearIndex, off);
    stride = b.create<arith::MulIOp>(loc, stride, dimensions[i]);
  }
 
  return linearIndex;
}
 
/// Replace GetShardingOp with related/dependent ShardingOp.
struct ConvertGetShardingOp : public OpConversionPattern<GetShardingOp> {
  using OpConversionPattern::OpConversionPattern;
 
  LogicalResult
  matchAndRewrite(GetShardingOp op, OpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
    auto shardOp = adaptor.getSource().getDefiningOp<ShardOp>();
    if (!shardOp)
      return failure();
    auto shardingOp = shardOp.getSharding().getDefiningOp<ShardingOp>();
    if (!shardingOp)
      return failure();
 
    rewriter.replaceOp(op, shardingOp.getResult());
    return success();
  }
};
 
/// Convert a sharding op to a tuple of tensors of its components
///   (SplitAxes, HaloSizes, ShardedDimsOffsets)
/// as defined by type converter.
struct ConvertShardingOp : public OpConversionPattern<ShardingOp> {
  using OpConversionPattern::OpConversionPattern;
 
  LogicalResult
  matchAndRewrite(ShardingOp op, OpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
    auto splitAxes = op.getSplitAxes().getAxes();
    int64_t maxNAxes = 0;
    for (auto axes : splitAxes)
      maxNAxes = std::max<int64_t>(maxNAxes, axes.size());
 
    // To hold the split axes, create empty 2d tensor with shape
    // {splitAxes.size(), max-size-of-split-groups}.
    // Set trailing elements for smaller split-groups to -1.
    Location loc = op.getLoc();
    auto i16 = rewriter.getI16Type();
    auto i64 = rewriter.getI64Type();
    std::array<int64_t, 2> shape = {static_cast<int64_t>(splitAxes.size()),
                                    maxNAxes};
    Value resSplitAxes = rewriter.create<tensor::EmptyOp>(loc, shape, i16);
    auto attr = IntegerAttr::get(i16, -1);
    Value fillValue = rewriter.create<arith::ConstantOp>(loc, i16, attr);
    resSplitAxes = rewriter.create<linalg::FillOp>(loc, fillValue, resSplitAxes)
                       .getResult(0);
 
    // explicitly write values into tensor row by row
    std::array<int64_t, 2> strides = {1, 1};
    int64_t nSplits = 0;
    ValueRange empty = {};
    for (auto [i, axes] : llvm::enumerate(splitAxes)) {
      int64_t size = axes.size();
      if (size > 0)
        ++nSplits;
      std::array<int64_t, 2> offs = {(int64_t)i, 0};
      std::array<int64_t, 2> sizes = {1, size};
      auto tensorType = RankedTensorType::get({size}, i16);
      auto attrs = DenseIntElementsAttr::get(tensorType, axes.asArrayRef());
      auto vals = rewriter.create<arith::ConstantOp>(loc, tensorType, attrs);
      resSplitAxes = rewriter.create<tensor::InsertSliceOp>(
          loc, vals, resSplitAxes, empty, empty, empty, offs, sizes, strides);
    }
 
    // To hold halos sizes, create 2d Tensor with shape {nSplits, 2}.
    // Store the halo sizes in the tensor.
    SmallVector<Value> haloSizes =
        getMixedAsValues(rewriter, loc, adaptor.getStaticHaloSizes(),
                         adaptor.getDynamicHaloSizes());
    auto type = RankedTensorType::get({nSplits, 2}, i64);
    Value resHaloSizes =
        haloSizes.empty()
            ? rewriter
                  .create<tensor::EmptyOp>(loc, std::array<int64_t, 2>{0, 0},
                                           i64)
                  .getResult()
            : rewriter.create<tensor::FromElementsOp>(loc, type, haloSizes)
                  .getResult();
 
    // To hold sharded dims offsets, create Tensor with shape {nSplits,
    // maxSplitSize+1}. Store the offsets in the tensor but set trailing
    // elements for smaller split-groups to -1. Computing the max size of the
    // split groups needs using collectiveProcessGroupSize (which needs the
    // MeshOp)
    Value resOffsets;
    if (adaptor.getStaticShardedDimsOffsets().empty()) {
      resOffsets = rewriter.create<tensor::EmptyOp>(
          loc, std::array<int64_t, 2>{0, 0}, i64);
    } else {
      SymbolTableCollection symbolTableCollection;
      auto meshOp = getMesh(op, symbolTableCollection);
      int64_t maxSplitSize = 0;
      for (auto axes : splitAxes) {
        int64_t splitSize =
            collectiveProcessGroupSize(axes.asArrayRef(), meshOp.getShape());
        assert(splitSize != ShapedType::kDynamic);
        maxSplitSize = std::max<int64_t>(maxSplitSize, splitSize);
      }
      assert(maxSplitSize);
      ++maxSplitSize; // add one for the total size
 
      resOffsets = rewriter.create<tensor::EmptyOp>(
          loc, std::array<int64_t, 2>{nSplits, maxSplitSize}, i64);
      Value zero = rewriter.create<arith::ConstantOp>(
          loc, i64, rewriter.getI64IntegerAttr(ShapedType::kDynamic));
      resOffsets =
          rewriter.create<linalg::FillOp>(loc, zero, resOffsets).getResult(0);
      SmallVector<Value> offsets =
          getMixedAsValues(rewriter, loc, adaptor.getStaticShardedDimsOffsets(),
                           adaptor.getDynamicShardedDimsOffsets());
      int64_t curr = 0;
      for (auto [i, axes] : llvm::enumerate(splitAxes)) {
        int64_t splitSize =
            collectiveProcessGroupSize(axes.asArrayRef(), meshOp.getShape());
        assert(splitSize != ShapedType::kDynamic && splitSize < maxSplitSize);
        ++splitSize; // add one for the total size
        ArrayRef<Value> values(&offsets[curr], splitSize);
        Value vals = rewriter.create<tensor::FromElementsOp>(loc, values);
        std::array<int64_t, 2> offs = {static_cast<int64_t>(i), 0};
        std::array<int64_t, 2> sizes = {1, splitSize};
        resOffsets = rewriter.create<tensor::InsertSliceOp>(
            loc, vals, resOffsets, empty, empty, empty, offs, sizes, strides);
        curr += splitSize;
      }
    }
 
    // return a tuple of tensors as defined by type converter
    SmallVector<Type> resTypes;
    if (failed(getTypeConverter()->convertType(op.getResult().getType(),
                                               resTypes)))
      return failure();
 
    resSplitAxes =
        rewriter.create<tensor::CastOp>(loc, resTypes[0], resSplitAxes);
    resHaloSizes =
        rewriter.create<tensor::CastOp>(loc, resTypes[1], resHaloSizes);
    resOffsets = rewriter.create<tensor::CastOp>(loc, resTypes[2], resOffsets);
 
    rewriter.replaceOpWithNewOp<UnrealizedConversionCastOp>(
        op, TupleType::get(op.getContext(), resTypes),
        ValueRange{resSplitAxes, resHaloSizes, resOffsets});
 
    return success();
  }
};
 
struct ConvertProcessMultiIndexOp
    : public OpConversionPattern<ProcessMultiIndexOp> {
  using OpConversionPattern::OpConversionPattern;
 
  LogicalResult
  matchAndRewrite(ProcessMultiIndexOp op, OpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
 
    // Currently converts its linear index to a multi-dimensional index.
 
    SymbolTableCollection symbolTableCollection;
    Location loc = op.getLoc();
    auto meshOp = getMesh(op, symbolTableCollection);
    // For now we only support static mesh shapes
    if (ShapedType::isDynamicShape(meshOp.getShape()))
      return failure();
 
    SmallVector<Value> dims;
    llvm::transform(
        meshOp.getShape(), std::back_inserter(dims), [&](int64_t i) {
          return rewriter.create<arith::ConstantIndexOp>(loc, i).getResult();
        });
    Value rank = rewriter.create<ProcessLinearIndexOp>(op.getLoc(), meshOp);
    auto mIdx = linearToMultiIndex(loc, rewriter, rank, dims);
 
    // optionally extract subset of mesh axes
    auto axes = adaptor.getAxes();
    if (!axes.empty()) {
      SmallVector<Value> subIndex;
      for (auto axis : axes) {
        subIndex.emplace_back(mIdx[axis]);
      }
      mIdx = std::move(subIndex);
    }
 
    rewriter.replaceOp(op, mIdx);
    return success();
  }
};
 
class ConvertProcessLinearIndexOp
    : public OpConversionPattern<ProcessLinearIndexOp> {
  int64_t worldRank; // rank in MPI_COMM_WORLD if available, else < 0
 
public:
  using OpConversionPattern::OpConversionPattern;
 
  // Constructor accepting worldRank
  ConvertProcessLinearIndexOp(const TypeConverter &typeConverter,
                              MLIRContext *context, int64_t worldRank = -1)
      : OpConversionPattern(typeConverter, context), worldRank(worldRank) {}
 
  LogicalResult
  matchAndRewrite(ProcessLinearIndexOp op, OpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
 
    Location loc = op.getLoc();
    if (worldRank >= 0) { // if rank in MPI_COMM_WORLD is known -> use it
      rewriter.replaceOpWithNewOp<arith::ConstantIndexOp>(op, worldRank);
      return success();
    }
 
    // Otherwise call create mpi::CommRankOp
    auto rank = rewriter
                    .create<mpi::CommRankOp>(
                        loc, TypeRange{mpi::RetvalType::get(op->getContext()),
                                       rewriter.getI32Type()})
                    .getRank();
    rewriter.replaceOpWithNewOp<arith::IndexCastOp>(op, rewriter.getIndexType(),
                                                    rank);
    return success();
  }
};
 
struct ConvertNeighborsLinearIndicesOp
    : public OpConversionPattern<NeighborsLinearIndicesOp> {
  using OpConversionPattern::OpConversionPattern;
 
  LogicalResult
  matchAndRewrite(NeighborsLinearIndicesOp op, OpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
 
    // Computes the neighbors indices along a split axis by simply
    // adding/subtracting 1 to the current index in that dimension.
    // Assigns -1 if neighbor is out of bounds.
 
    auto axes = adaptor.getSplitAxes();
    // For now only single axis sharding is supported
    if (axes.size() != 1)
      return failure();
 
    Location loc = op.getLoc();
    SymbolTableCollection symbolTableCollection;
    auto meshOp = getMesh(op, symbolTableCollection);
    auto mIdx = adaptor.getDevice();
    auto orgIdx = mIdx[axes[0]];
    SmallVector<Value> dims;
    llvm::transform(
        meshOp.getShape(), std::back_inserter(dims), [&](int64_t i) {
          return rewriter.create<arith::ConstantIndexOp>(loc, i).getResult();
        });
    Value dimSz = dims[axes[0]];
    Value one = rewriter.create<arith::ConstantIndexOp>(loc, 1);
    Value minus1 = rewriter.create<arith::ConstantIndexOp>(loc, -1);
    Value atBorder = rewriter.create<arith::CmpIOp>(
        loc, arith::CmpIPredicate::sle, orgIdx,
        rewriter.create<arith::ConstantIndexOp>(loc, 0));
    auto down = rewriter.create<scf::IfOp>(
        loc, atBorder,
        [&](OpBuilder &builder, Location loc) {
          builder.create<scf::YieldOp>(loc, minus1);
        },
        [&](OpBuilder &builder, Location loc) {
          SmallVector<Value> tmp = mIdx;
          tmp[axes[0]] =
              rewriter.create<arith::SubIOp>(op.getLoc(), orgIdx, one)
                  .getResult();
          builder.create<scf::YieldOp>(
              loc, multiToLinearIndex(loc, rewriter, tmp, dims));
        });
    atBorder = rewriter.create<arith::CmpIOp>(
        loc, arith::CmpIPredicate::sge, orgIdx,
        rewriter.create<arith::SubIOp>(loc, dimSz, one).getResult());
    auto up = rewriter.create<scf::IfOp>(
        loc, atBorder,
        [&](OpBuilder &builder, Location loc) {
          builder.create<scf::YieldOp>(loc, minus1);
        },
        [&](OpBuilder &builder, Location loc) {
          SmallVector<Value> tmp = mIdx;
          tmp[axes[0]] =
              rewriter.create<arith::AddIOp>(op.getLoc(), orgIdx, one);
          builder.create<scf::YieldOp>(
              loc, multiToLinearIndex(loc, rewriter, tmp, dims));
        });
    rewriter.replaceOp(op, ValueRange{down.getResult(0), up.getResult(0)});
    return success();
  }
};
 
struct ConvertShardShapeOp : public OpConversionPattern<ShardShapeOp> {
  using OpConversionPattern::OpConversionPattern;
 
  LogicalResult
  matchAndRewrite(ShardShapeOp op, OneToNOpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
    auto sharding = op.getSharding().getDefiningOp<ShardingOp>();
    if (!sharding) {
      return op->emitError()
             << "Expected SharingOp as defining op for sharding"
             << " but found " << adaptor.getSharding()[0].getDefiningOp();
    }
 
    // Compute the sharded shape by applying the sharding to the input shape.
    // If shardedDimsOffsets is not defined in the sharding, the shard shape is
    // computed by dividing the dimension size by the number of shards in that
    // dimension (which is given by the size of the mesh axes provided in
    // split-axes). Odd elements get distributed to trailing shards. If a
    // shardedDimsOffsets is provided, the shard shape is computed by
    // subtracting the offset of the current shard from the offset of the next
    // shard.
 
    Location loc = op.getLoc();
    Type index = rewriter.getIndexType();
 
    // This is a 1:N conversion because the sharding op is a 1:3 conversion.
    // The operands in the adaptor are a vector<ValeRange>. For dims and device
    // we have a 1:1 conversion.
    // For simpler access fill a vector with the dynamic dims.
    SmallVector<Value> dynDims, dynDevice;
    for (auto dim : adaptor.getDimsDynamic()) {
      // type conversion should be 1:1 for ints
      assert(dim.size() == 1);
      dynDims.emplace_back(dim[0]);
    }
    // same for device
    for (auto device : adaptor.getDeviceDynamic()) {
      assert(device.size() == 1);
      dynDevice.emplace_back(device[0]);
    }
 
    // To keep the code simple, convert dims/device to values when they are
    // attributes. Count on canonicalization to fold static values.
    SmallVector<Value> shape =
        getMixedAsValues(rewriter, loc, op.getDims(), dynDims, index);
    SmallVector<Value> multiIdx =
        getMixedAsValues(rewriter, loc, adaptor.getDevice(), dynDevice, index);
 
    // Get the MeshOp, the mesh shape is needed to compute the sharded shape.
    SymbolTableCollection symbolTableCollection;
    auto meshOp = getMesh(sharding, symbolTableCollection);
    // For now we only support static mesh shapes
    if (ShapedType::isDynamicShape(meshOp.getShape()))
      return failure();
 
    auto splitAxes = sharding.getSplitAxes().getAxes();
    // shardedDimsOffsets are optional and might be Values (not attributes).
    // Also, the shardId might be dynamic which means the position in the
    // shardedDimsOffsets is not statically known. Create a tensor of the
    // shardedDimsOffsets and later extract the offsets for computing the
    // local shard-size.
    Value shardedDimsOffs;
    {
      SmallVector<Value> tmp = getMixedAsValues(
          rewriter, loc, sharding.getStaticShardedDimsOffsets(),
          sharding.getDynamicShardedDimsOffsets(), index);
      if (!tmp.empty())
        shardedDimsOffs = rewriter.create<tensor::FromElementsOp>(
            loc, RankedTensorType::get({(int64_t)tmp.size()}, index), tmp);
    }
 
    // With static mesh shape the sizes of the split axes are known.
    // Hence the start/pos for each split axes in shardDimsOffsets can be
    // computed statically.
    int64_t pos = 0;
    SmallVector<Value> shardShape;
    Value zero =
        rewriter.create<arith::ConstantOp>(loc, rewriter.getZeroAttr(index));
    Value one =
        rewriter.create<arith::ConstantOp>(loc, rewriter.getOneAttr(index));
 
    // Iterate over the dimensions of the tensor shape, get their split Axes,
    // and compute the sharded shape.
    for (auto [i, dim] : llvm::enumerate(shape)) {
      // Trailing dimensions might not be annotated.
      if (i < splitAxes.size() && !splitAxes[i].empty()) {
        auto axes = splitAxes[i];
        // The current dimension might not be sharded.
        // Create a value from the static position in shardDimsOffsets.
        Value posVal =
            rewriter.create<arith::ConstantOp>(loc, rewriter.getIndexAttr(pos));
        // Get the index of the local shard in the mesh axis.
        Value idx = multiIdx[axes[0]];
        auto numShards =
            collectiveProcessGroupSize(axes.asArrayRef(), meshOp.getShape());
        if (shardedDimsOffs) {
          // If sharded dims offsets are provided, use them to compute the
          // sharded shape.
          if (axes.size() > 1) {
            return op->emitError() << "Only single axis sharding is "
                                   << "supported for each dimension.";
          }
          idx = rewriter.create<arith::AddIOp>(loc, posVal, idx);
          // Compute size = shardedDimsOffs[idx+1] - shardedDimsOffs[idx].
          Value off =
              rewriter.create<tensor::ExtractOp>(loc, shardedDimsOffs, idx);
          idx = rewriter.create<arith::AddIOp>(loc, idx, one);
          Value nextOff =
              rewriter.create<tensor::ExtractOp>(loc, shardedDimsOffs, idx);
          Value sz = rewriter.create<arith::SubIOp>(loc, nextOff, off);
          shardShape.emplace_back(sz);
        } else {
          Value numShardsVal = rewriter.create<arith::ConstantOp>(
              loc, rewriter.getIndexAttr(numShards));
          // Compute shard dim size by distributing odd elements to trailing
          // shards:
          // sz = dim / numShards
          //      + (idx >= (numShards - (dim % numShards)) ? 1 : 0)
          Value sz = rewriter.create<arith::DivSIOp>(loc, dim, numShardsVal);
          Value sz1 = rewriter.create<arith::RemSIOp>(loc, dim, numShardsVal);
          sz1 = rewriter.create<arith::SubIOp>(loc, numShardsVal, sz1);
          auto cond = rewriter.create<arith::CmpIOp>(
              loc, arith::CmpIPredicate::sge, idx, sz1);
          Value odd = rewriter.create<arith::SelectOp>(loc, cond, one, zero);
          sz = rewriter.create<arith::AddIOp>(loc, sz, odd);
          shardShape.emplace_back(sz);
        }
        pos += numShards + 1; // add one for the total size.
      } // else no sharding if split axis is empty or no split axis
      // If no size was added -> no sharding in this dimension.
      if (shardShape.size() <= i)
        shardShape.emplace_back(dim);
    }
    assert(shardShape.size() == shape.size());
    rewriter.replaceOp(op, shardShape);
    return success();
  }
};
 
struct ConvertUpdateHaloOp : public OpConversionPattern<UpdateHaloOp> {
  using OpConversionPattern::OpConversionPattern;
 
  LogicalResult
  matchAndRewrite(UpdateHaloOp op, OpAdaptor adaptor,
                  ConversionPatternRewriter &rewriter) const override {
 
    // The input/output memref is assumed to be in C memory order.
    // Halos are exchanged as 2 blocks per dimension (one for each side: down
    // and up). For each haloed dimension `d`, the exchanged blocks are
    // expressed as multi-dimensional subviews. The subviews include potential
    // halos of higher dimensions `dh > d`, no halos for the lower dimensions
    // `dl < d` and for dimension `d` the currently exchanged halo only.
    // By iterating form higher to lower dimensions this also updates the halos
    // in the 'corners'.
    // memref.subview is used to read and write the halo data from and to the
    // local data. Because subviews and halos can have mixed dynamic and static
    // shapes, OpFoldResults are used whenever possible.
 
    auto haloSizes = getMixedValues(adaptor.getStaticHaloSizes(),
                                    adaptor.getHaloSizes(), rewriter);
    if (haloSizes.empty()) {
      // no halos -> nothing to do
      rewriter.replaceOp(op, adaptor.getDestination());
      return success();
    }
 
    SymbolTableCollection symbolTableCollection;
    Location loc = op.getLoc();
 
    // convert a OpFoldResult into a Value
    auto toValue = [&rewriter, &loc](OpFoldResult &v) -> Value {
      if (auto value = dyn_cast<Value>(v))
        return value;
      return rewriter.create<arith::ConstantOp>(
          loc, rewriter.getIndexAttr(
                   cast<IntegerAttr>(cast<Attribute>(v)).getInt()));
    };
 
    auto dest = adaptor.getDestination();
    auto dstShape = cast<ShapedType>(dest.getType()).getShape();
    Value array = dest;
    if (isa<RankedTensorType>(array.getType())) {
      // If the destination is a memref, we need to cast it to a tensor
      auto tensorType = MemRefType::get(
          dstShape, cast<ShapedType>(array.getType()).getElementType());
      array =
          rewriter.create<bufferization::ToMemrefOp>(loc, tensorType, array);
    }
    auto rank = cast<ShapedType>(array.getType()).getRank();
    auto opSplitAxes = adaptor.getSplitAxes().getAxes();
    auto mesh = adaptor.getMesh();
    auto meshOp = getMesh(op, symbolTableCollection);
    // subviews need Index values
    for (auto &sz : haloSizes) {
      if (auto value = dyn_cast<Value>(sz))
        sz =
            rewriter
                .create<arith::IndexCastOp>(loc, rewriter.getIndexType(), value)
                .getResult();
    }
 
    // most of the offset/size/stride data is the same for all dims
    SmallVector<OpFoldResult> offsets(rank, rewriter.getIndexAttr(0));
    SmallVector<OpFoldResult> strides(rank, rewriter.getIndexAttr(1));
    SmallVector<OpFoldResult> shape(rank), dimSizes(rank);
    auto currHaloDim = -1; // halo sizes are provided for split dimensions only
    // we need the actual shape to compute offsets and sizes
    for (auto i = 0; i < rank; ++i) {
      auto s = dstShape[i];
      if (ShapedType::isDynamic(s))
        shape[i] = rewriter.create<memref::DimOp>(loc, array, s).getResult();
      else
        shape[i] = rewriter.getIndexAttr(s);
 
      if ((size_t)i < opSplitAxes.size() && !opSplitAxes[i].empty()) {
        ++currHaloDim;
        // the offsets for lower dim sstarts after their down halo
        offsets[i] = haloSizes[currHaloDim * 2];
 
        // prepare shape and offsets of highest dim's halo exchange
        Value _haloSz = rewriter.create<arith::AddIOp>(
            loc, toValue(haloSizes[currHaloDim * 2]),
            toValue(haloSizes[currHaloDim * 2 + 1]));
        // the halo shape of lower dims exlude the halos
        dimSizes[i] =
            rewriter.create<arith::SubIOp>(loc, toValue(shape[i]), _haloSz)
                .getResult();
      } else {
        dimSizes[i] = shape[i];
      }
    }
 
    auto tagAttr = rewriter.getI32IntegerAttr(91); // we just pick something
    auto tag = rewriter.create<arith::ConstantOp>(loc, tagAttr);
    auto zeroAttr = rewriter.getI32IntegerAttr(0); // for detecting v<0
    auto zero = rewriter.create<arith::ConstantOp>(loc, zeroAttr);
 
    SmallVector<Type> indexResultTypes(meshOp.getShape().size(),
                                       rewriter.getIndexType());
    auto myMultiIndex =
        rewriter.create<ProcessMultiIndexOp>(loc, indexResultTypes, mesh)
            .getResult();
    // traverse all split axes from high to low dim
    for (ssize_t dim = opSplitAxes.size() - 1; dim >= 0; --dim) {
      auto splitAxes = opSplitAxes[dim];
      if (splitAxes.empty())
        continue;
      assert(currHaloDim >= 0 && (size_t)currHaloDim < haloSizes.size() / 2);
      // Get the linearized ids of the neighbors (down and up) for the
      // given split
      auto tmp = rewriter
                     .create<NeighborsLinearIndicesOp>(loc, mesh, myMultiIndex,
                                                       splitAxes)
                     .getResults();
      // MPI operates on i32...
      Value neighbourIDs[2] = {rewriter.create<arith::IndexCastOp>(
                                   loc, rewriter.getI32Type(), tmp[0]),
                               rewriter.create<arith::IndexCastOp>(
                                   loc, rewriter.getI32Type(), tmp[1])};
 
      auto lowerRecvOffset = rewriter.getIndexAttr(0);
      auto lowerSendOffset = toValue(haloSizes[currHaloDim * 2]);
      auto upperRecvOffset = rewriter.create<arith::SubIOp>(
          loc, toValue(shape[dim]), toValue(haloSizes[currHaloDim * 2 + 1]));
      auto upperSendOffset = rewriter.create<arith::SubIOp>(
          loc, upperRecvOffset, toValue(haloSizes[currHaloDim * 2]));
 
      // Make sure we send/recv in a way that does not lead to a dead-lock.
      // The current approach is by far not optimal, this should be at least
      // be a red-black pattern or using MPI_sendrecv.
      // Also, buffers should be re-used.
      // Still using temporary contiguous buffers for MPI communication...
      // Still yielding a "serialized" communication pattern...
      auto genSendRecv = [&](bool upperHalo) {
        auto orgOffset = offsets[dim];
        dimSizes[dim] = upperHalo ? haloSizes[currHaloDim * 2 + 1]
                                  : haloSizes[currHaloDim * 2];
        // Check if we need to send and/or receive
        // Processes on the mesh borders have only one neighbor
        auto to = upperHalo ? neighbourIDs[0] : neighbourIDs[1];
        auto from = upperHalo ? neighbourIDs[1] : neighbourIDs[0];
        auto hasFrom = rewriter.create<arith::CmpIOp>(
            loc, arith::CmpIPredicate::sge, from, zero);
        auto hasTo = rewriter.create<arith::CmpIOp>(
            loc, arith::CmpIPredicate::sge, to, zero);
        auto buffer = rewriter.create<memref::AllocOp>(
            loc, dimSizes, cast<ShapedType>(array.getType()).getElementType());
        // if has neighbor: copy halo data from array to buffer and send
        rewriter.create<scf::IfOp>(
            loc, hasTo, [&](OpBuilder &builder, Location loc) {
              offsets[dim] = upperHalo ? OpFoldResult(lowerSendOffset)
                                       : OpFoldResult(upperSendOffset);
              auto subview = builder.create<memref::SubViewOp>(
                  loc, array, offsets, dimSizes, strides);
              builder.create<memref::CopyOp>(loc, subview, buffer);
              builder.create<mpi::SendOp>(loc, TypeRange{}, buffer, tag, to);
              builder.create<scf::YieldOp>(loc);
            });
        // if has neighbor: receive halo data into buffer and copy to array
        rewriter.create<scf::IfOp>(
            loc, hasFrom, [&](OpBuilder &builder, Location loc) {
              offsets[dim] = upperHalo ? OpFoldResult(upperRecvOffset)
                                       : OpFoldResult(lowerRecvOffset);
              builder.create<mpi::RecvOp>(loc, TypeRange{}, buffer, tag, from);
              auto subview = builder.create<memref::SubViewOp>(
                  loc, array, offsets, dimSizes, strides);
              builder.create<memref::CopyOp>(loc, buffer, subview);
              builder.create<scf::YieldOp>(loc);
            });
        rewriter.create<memref::DeallocOp>(loc, buffer);
        offsets[dim] = orgOffset;
      };
 
      auto doSendRecv = [&](int upOrDown) {
        OpFoldResult &v = haloSizes[currHaloDim * 2 + upOrDown];
        Value haloSz = dyn_cast<Value>(v);
        if (!haloSz)
          haloSz = rewriter.create<arith::ConstantOp>(
              loc, rewriter.getI32IntegerAttr(
                       cast<IntegerAttr>(cast<Attribute>(v)).getInt()));
        auto hasSize = rewriter.create<arith::CmpIOp>(
            loc, arith::CmpIPredicate::sgt, haloSz, zero);
        rewriter.create<scf::IfOp>(loc, hasSize,
                                   [&](OpBuilder &builder, Location loc) {
                                     genSendRecv(upOrDown > 0);
                                     builder.create<scf::YieldOp>(loc);
                                   });
      };
 
      doSendRecv(0);
      doSendRecv(1);
 
      // the shape for lower dims include higher dims' halos
      dimSizes[dim] = shape[dim];
      // -> the offset for higher dims is always 0
      offsets[dim] = rewriter.getIndexAttr(0);
      // on to next halo
      --currHaloDim;
    }
 
    if (isa<MemRefType>(op.getResult().getType())) {
      rewriter.replaceOp(op, array);
    } else {
      assert(isa<RankedTensorType>(op.getResult().getType()));
      rewriter.replaceOp(op, rewriter.create<bufferization::ToTensorOp>(
                                 loc, op.getResult().getType(), array,
                                 /*restrict=*/true, /*writable=*/true));
    }
    return success();
  }
};
 
struct ConvertMeshToMPIPass
    : public impl::ConvertMeshToMPIPassBase<ConvertMeshToMPIPass> {
  using Base::Base;
 
  /// Run the dialect converter on the module.
  void runOnOperation() override {
    uint64_t worldRank = -1;
    // Try to get DLTI attribute for MPI:comm_world_rank
    // If found, set worldRank to the value of the attribute.
    {
      auto dltiAttr =
          dlti::query(getOperation(), {"MPI:comm_world_rank"}, false);
      if (succeeded(dltiAttr)) {
        if (!isa<IntegerAttr>(dltiAttr.value())) {
          getOperation()->emitError()
              << "Expected an integer attribute for MPI:comm_world_rank";
          return signalPassFailure();
        }
        worldRank = cast<IntegerAttr>(dltiAttr.value()).getInt();
      }
    }
 
    auto *ctxt = &getContext();
    RewritePatternSet patterns(ctxt);
    ConversionTarget target(getContext());
 
    // Define a type converter to convert mesh::ShardingType,
    // mostly for use in return operations.
    TypeConverter typeConverter;
    typeConverter.addConversion([](Type type) { return type; });
 
    // convert mesh::ShardingType to a tuple of RankedTensorTypes
    typeConverter.addConversion(
        [](ShardingType type,
           SmallVectorImpl<Type> &results) -> std::optional<LogicalResult> {
          auto i16 = IntegerType::get(type.getContext(), 16);
          auto i64 = IntegerType::get(type.getContext(), 64);
          std::array<int64_t, 2> shp = {ShapedType::kDynamic,
                                        ShapedType::kDynamic};
          results.emplace_back(RankedTensorType::get(shp, i16));
          results.emplace_back(RankedTensorType::get(shp, i64)); // actually ?x2
          results.emplace_back(RankedTensorType::get(shp, i64));
          return success();
        });
 
    // To 'extract' components, a UnrealizedConversionCastOp is expected
    // to define the input
    typeConverter.addTargetMaterialization(
        [&](OpBuilder &builder, TypeRange resultTypes, ValueRange inputs,
            Location loc) {
          // Expecting a single input.
          if (inputs.size() != 1 || !isa<TupleType>(inputs[0].getType()))
            return SmallVector<Value>();
          auto castOp = inputs[0].getDefiningOp<UnrealizedConversionCastOp>();
          // Expecting an UnrealizedConversionCastOp.
          if (!castOp)
            return SmallVector<Value>();
          // Fill a vector with elements of the tuple/castOp.
          SmallVector<Value> results;
          for (auto oprnd : castOp.getInputs()) {
            if (!isa<RankedTensorType>(oprnd.getType()))
              return SmallVector<Value>();
            results.emplace_back(oprnd);
          }
          return results;
        });
 
    // No mesh dialect should left after conversion...
    target.addIllegalDialect<mesh::MeshDialect>();
    // ...except the global MeshOp
    target.addLegalOp<mesh::MeshOp>();
    // Allow all the stuff that our patterns will convert to
    target.addLegalDialect<BuiltinDialect, mpi::MPIDialect, scf::SCFDialect,
                           arith::ArithDialect, tensor::TensorDialect,
                           bufferization::BufferizationDialect,
                           linalg::LinalgDialect, memref::MemRefDialect>();
    // Make sure the function signature, calls etc. are legal
    target.addDynamicallyLegalOp<func::FuncOp>([&](func::FuncOp op) {
      return typeConverter.isSignatureLegal(op.getFunctionType());
    });
    target.addDynamicallyLegalOp<func::CallOp, func::ReturnOp>(
        [&](Operation *op) { return typeConverter.isLegal(op); });
 
    patterns.add<ConvertUpdateHaloOp, ConvertNeighborsLinearIndicesOp,
                 ConvertProcessMultiIndexOp, ConvertGetShardingOp,
                 ConvertShardingOp, ConvertShardShapeOp>(typeConverter, ctxt);
    // ConvertProcessLinearIndexOp accepts an optional worldRank
    patterns.add<ConvertProcessLinearIndexOp>(typeConverter, ctxt, worldRank);
 
    populateFunctionOpInterfaceTypeConversionPattern<func::FuncOp>(
        patterns, typeConverter);
    populateCallOpTypeConversionPattern(patterns, typeConverter);
    populateReturnOpTypeConversionPattern(patterns, typeConverter);
 
    (void)applyPartialConversion(getOperation(), target, std::move(patterns));
  }
};
 
} // namespace