[mlir][scf] Add getPartialResultTilePosition to PartialReductionOpInterface (#120465)

This PR adds a new interface method to PartialReductionOpInterface which
allows it to query the result tile position for the partial result.
Previously, tiling the reduction dimension with
SplitReductionOuterReduction when the result has transposed parallel
dimensions would produce wrong results.

Other fixes that were needed to make this PR work:

- Instead of ad-hoc logic to decide where to place the new reduction
dimensions in the partial result based on the iteration space, the
reduction dimensions are always appended to the partial result tensor.
- Remove usage of PartialReductionOpInterface in Mesh dialect. The
implementation was trying to just get a neutral element, but ended up
trying to use PartialReductionOpInterface for it, which is not right. It
was also passing the wrong sizes to it.

mlir/lib/Dialect/SCF/Transforms/TileUsingInterface.cpp

@@ -657,21 +657,29 @@ getResultTilePosition(RewriterBase &rewriter, int64_t index, Value tiledResult,
                                     resultOffset, resultSize);
   case scf::SCFTilingOptions::ReductionTilingStrategy::
       PartialReductionOuterReduction: {
-    // TODO: This does not work for non identity accesses to the result tile.
-    // The proper fix is to add a getPartialResultTilePosition method to
-    // PartialReductionOpInterface.
-    resultOffset =
-        SmallVector<OpFoldResult>(offsets.size(), rewriter.getIndexAttr(0));
-    for (size_t i = 0; i < offsets.size(); i++) {
-      resultSize.push_back(
-          tensor::getMixedSize(rewriter, op.getLoc(), tiledResult, i));
+    auto redOp = dyn_cast<PartialReductionOpInterface>(op.getOperation());
+    if (!redOp) {
+      return rewriter.notifyMatchFailure(
+          op, "PartialReductionOuterReduction tiling strategy is only supported"
+              "for operations implementing PartialReductionOpInterface");
     }
-    return success();
+    // Get reduction dimensions.
+    // TODO: PartialReductionOpInterface should really query TilingInterface
+    // itself and find reduction dimensions.
+    SmallVector<int> reductionDims;
+    for (auto [idx, iteratorType] :
+         llvm::enumerate(op.getLoopIteratorTypes())) {
+      if (iteratorType == utils::IteratorType::reduction)
+        reductionDims.push_back(idx);
+    }
+    return redOp.getPartialResultTilePosition(rewriter, index, offsets, sizes,
+                                              resultOffset, resultSize,
+                                              reductionDims);
+  }
   default:
     return rewriter.notifyMatchFailure(op,
                                        "unhandled reduction tiling strategy");
   }
-  }
 }
 
 static FailureOr<MergeResult>