[mlir][Affine] Expand affine.[de]linearize_index without affine maps

mlir/include/mlir/Dialect/Affine/LoopUtils.h

@@ -301,6 +301,11 @@ separateFullTiles(MutableArrayRef<AffineForOp> nest,
 /// Walk an affine.for to find a band to coalesce.
 LogicalResult coalescePerfectlyNestedAffineLoops(AffineForOp op);
 
+/// Count the number of loops surrounding `operand` such that operand could be
+/// hoisted above.
+/// Stop counting at the first loop over which the operand cannot be hoisted.
+/// This counts any LoopLikeOpInterface, not just affine.for.
+int64_t numEnclosingInvariantLoops(OpOperand &operand);
 } // namespace affine
 } // namespace mlir
 

mlir/include/mlir/Dialect/Affine/Passes.h

@@ -116,6 +116,10 @@ std::unique_ptr<OperationPass<func::FuncOp>> createPipelineDataTransferPass();
 /// operations (not necessarily restricted to Affine dialect).
 std::unique_ptr<Pass> createAffineExpandIndexOpsPass();
 
+/// Creates a pass to expand affine index operations into affine.apply
+/// operations.
+std::unique_ptr<Pass> createAffineExpandIndexOpsAsAffinePass();
+
 //===----------------------------------------------------------------------===//
 // Registration
 //===----------------------------------------------------------------------===//

mlir/include/mlir/Dialect/Affine/Passes.td

@@ -408,4 +408,9 @@ def AffineExpandIndexOps : Pass<"affine-expand-index-ops"> {
   let constructor = "mlir::affine::createAffineExpandIndexOpsPass()";
 }
 
+def AffineExpandIndexOpsAsAffine : Pass<"affine-expand-index-ops-as-affine"> {
+  let summary = "Lower affine operations operating on indices into affine.apply operations";
+  let constructor = "mlir::affine::createAffineExpandIndexOpsAsAffinePass()";
+}
+
 #endif // MLIR_DIALECT_AFFINE_PASSES

mlir/include/mlir/Dialect/Affine/Transforms/Transforms.h

@@ -37,6 +37,10 @@ class AffineApplyOp;
 /// operations (not necessarily restricted to Affine dialect).
 void populateAffineExpandIndexOpsPatterns(RewritePatternSet &patterns);
 
+/// Populate patterns that expand affine index operations into their equivalent
+/// `affine.apply` representations.
+void populateAffineExpandIndexOpsAsAffinePatterns(RewritePatternSet &patterns);
+
 /// Helper function to rewrite `op`'s affine map and reorder its operands such
 /// that they are in increasing order of hoistability (i.e. the least hoistable)
 /// operands come first in the operand list.

mlir/lib/Dialect/Affine/Transforms/AffineExpandIndexOps.cpp

@@ -10,6 +10,7 @@
 // fundamental operations.
 //===----------------------------------------------------------------------===//
 
+#include "mlir/Dialect/Affine/LoopUtils.h"
 #include "mlir/Dialect/Affine/Passes.h"
 
 #include "mlir/Dialect/Affine/IR/AffineOps.h"
@@ -28,6 +29,50 @@ namespace affine {
 using namespace mlir;
 using namespace mlir::affine;
 
+/// Given a basis (in static and dynamic components), return the sequence of
+/// suffix products of the basis, including the product of the entire basis,
+/// which must **not** contain an outer bound.
+///
+/// If excess dynamic values are provided, the values at the beginning
+/// will be ignored. This allows for dropping the outer bound without
+/// needing to manipulate the dynamic value array.
+static SmallVector<Value> computeStrides(Location loc, RewriterBase &rewriter,
+                                         ValueRange dynamicBasis,
+                                         ArrayRef<int64_t> staticBasis) {
+  if (staticBasis.empty())
+    return {};
+
+  SmallVector<Value> result;
+  result.reserve(staticBasis.size());
+  size_t dynamicIndex = dynamicBasis.size();
+  Value dynamicPart = nullptr;
+  int64_t staticPart = 1;
+  for (int64_t elem : llvm::reverse(staticBasis)) {
+    if (ShapedType::isDynamic(elem)) {
+      if (dynamicPart)
+        dynamicPart = rewriter.create<arith::MulIOp>(
+            loc, dynamicPart, dynamicBasis[dynamicIndex - 1]);
+      else
+        dynamicPart = dynamicBasis[dynamicIndex - 1];
+      --dynamicIndex;
+    } else {
+      staticPart *= elem;
+    }
+
+    if (dynamicPart && staticPart == 1) {
+      result.push_back(dynamicPart);
+    } else {
+      Value stride =
+          rewriter.createOrFold<arith::ConstantIndexOp>(loc, staticPart);
+      if (dynamicPart)
+        stride = rewriter.create<arith::MulIOp>(loc, dynamicPart, stride);
+      result.push_back(stride);
+    }
+  }
+  std::reverse(result.begin(), result.end());
+  return result;
+}
+
 namespace {
 /// Lowers `affine.delinearize_index` into a sequence of division and remainder
 /// operations.
@@ -36,18 +81,62 @@ struct LowerDelinearizeIndexOps
   using OpRewritePattern<AffineDelinearizeIndexOp>::OpRewritePattern;
   LogicalResult matchAndRewrite(AffineDelinearizeIndexOp op,
                                 PatternRewriter &rewriter) const override {
-    FailureOr<SmallVector<Value>> multiIndex =
-        delinearizeIndex(rewriter, op->getLoc(), op.getLinearIndex(),
-                         op.getEffectiveBasis(), /*hasOuterBound=*/false);
-    if (failed(multiIndex))
-      return failure();
-    rewriter.replaceOp(op, *multiIndex);
+    Location loc = op.getLoc();
+    Value linearIdx = op.getLinearIndex();
+    unsigned numResults = op.getNumResults();
+    ArrayRef<int64_t> staticBasis = op.getStaticBasis();
+    if (numResults == staticBasis.size())
+      staticBasis = staticBasis.drop_front();
+
+    if (numResults == 1) {
+      rewriter.replaceOp(op, linearIdx);
+      return success();
+    }
+
+    SmallVector<Value> results;
+    results.reserve(numResults);
+    SmallVector<Value> strides =
+        computeStrides(loc, rewriter, op.getDynamicBasis(), staticBasis);
+
+    Value zero = rewriter.createOrFold<arith::ConstantIndexOp>(loc, 0);
+
+    Value initialPart =
+        rewriter.create<arith::FloorDivSIOp>(loc, linearIdx, strides.front());
+    results.push_back(initialPart);
+
+    auto emitModTerm = [&](Value stride) -> Value {
+      Value remainder = rewriter.create<arith::RemSIOp>(loc, linearIdx, stride);
+      Value remainderNegative = rewriter.create<arith::CmpIOp>(
+          loc, arith::CmpIPredicate::slt, remainder, zero);
+      Value corrected = rewriter.create<arith::AddIOp>(loc, remainder, stride);
+      Value mod = rewriter.create<arith::SelectOp>(loc, remainderNegative,
+                                                   corrected, remainder);
+      return mod;
+    };
+
+    // Generate all the intermediate parts
+    for (size_t i = 0, e = strides.size() - 1; i < e; ++i) {
+      Value thisStride = strides[i];
+      Value nextStride = strides[i + 1];
+      Value modulus = emitModTerm(thisStride);
+      // We know both inputs are positive, so floorDiv == div.
+      // This could potentially be a divui, but it's not clear if that would
+      // cause issues.
+      Value divided = rewriter.create<arith::DivSIOp>(loc, modulus, nextStride);
+      results.push_back(divided);
+    }
+
+    results.push_back(emitModTerm(strides.back()));
+
+    rewriter.replaceOp(op, results);
     return success();
   }
 };
 
 /// Lowers `affine.linearize_index` into a sequence of multiplications and
-/// additions.
+/// additions. Make a best effort to sort the input indices so that
+/// the most loop-invariant terms are at the left of the additions
+/// to enable loop-invariant code motion.
 struct LowerLinearizeIndexOps final : OpRewritePattern<AffineLinearizeIndexOp> {
   using OpRewritePattern::OpRewritePattern;
   LogicalResult matchAndRewrite(AffineLinearizeIndexOp op,
@@ -58,13 +147,44 @@ struct LowerLinearizeIndexOps final : OpRewritePattern<AffineLinearizeIndexOp> {
       return success();
     }
 
-    SmallVector<OpFoldResult> multiIndex =
-        getAsOpFoldResult(op.getMultiIndex());
-    OpFoldResult linearIndex =
-        linearizeIndex(rewriter, op.getLoc(), multiIndex, op.getMixedBasis());
-    Value linearIndexValue =
-        getValueOrCreateConstantIntOp(rewriter, op.getLoc(), linearIndex);
-    rewriter.replaceOp(op, linearIndexValue);
+    Location loc = op.getLoc();
+    ValueRange multiIndex = op.getMultiIndex();
+    size_t numIndexes = multiIndex.size();
+    ArrayRef<int64_t> staticBasis = op.getStaticBasis();
+    if (numIndexes == staticBasis.size())
+      staticBasis = staticBasis.drop_front();
+
+    SmallVector<Value> strides =
+        computeStrides(loc, rewriter, op.getDynamicBasis(), staticBasis);
+    SmallVector<std::pair<Value, int64_t>> scaledValues;
+    scaledValues.reserve(numIndexes);
+
+    // Note: strides doesn't contain a value for the final element (stride 1)
+    // and everything else lines up. We use the "mutable" accessor so we can get
+    // our hands on an `OpOperand&` for the loop invariant counting function.
+    for (auto [stride, idxOp] :
+         llvm::zip_equal(strides, llvm::drop_end(op.getMultiIndexMutable()))) {
+      Value scaledIdx =
+          rewriter.create<arith::MulIOp>(loc, idxOp.get(), stride);
+      int64_t numHoistableLoops = numEnclosingInvariantLoops(idxOp);
+      scaledValues.emplace_back(scaledIdx, numHoistableLoops);
+    }
+    scaledValues.emplace_back(
+        multiIndex.back(),
+        numEnclosingInvariantLoops(op.getMultiIndexMutable()[numIndexes - 1]));
+
+    // Sort by how many enclosing loops there are, ties implicitly broken by
+    // size of the stride.
+    llvm::stable_sort(scaledValues,
+                      [&](auto l, auto r) { return l.second > r.second; });
+
+    Value result = scaledValues.front().first;
+    for (auto [scaledValue, numHoistableLoops] :
+         llvm::drop_begin(scaledValues)) {
+      std::ignore = numHoistableLoops;
+      result = rewriter.create<arith::AddIOp>(loc, result, scaledValue);
+    }
+    rewriter.replaceOp(op, result);
     return success();
   }
 };

mlir/lib/Dialect/Affine/Transforms/AffineExpandIndexOpsAsAffine.cpp

@@ -0,0 +1,98 @@
+//===- AffineExpandIndexOpsAsAffine.cpp - Expand index ops to apply pass --===//
+//
+// 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 pass to expand affine index ops into one or more more
+// fundamental operations.
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Dialect/Affine/Passes.h"
+
+#include "mlir/Dialect/Affine/IR/AffineOps.h"
+#include "mlir/Dialect/Affine/Transforms/Transforms.h"
+#include "mlir/Dialect/Affine/Utils.h"
+#include "mlir/Dialect/Arith/Utils/Utils.h"
+#include "mlir/Transforms/GreedyPatternRewriteDriver.h"
+
+namespace mlir {
+namespace affine {
+#define GEN_PASS_DEF_AFFINEEXPANDINDEXOPSASAFFINE
+#include "mlir/Dialect/Affine/Passes.h.inc"
+} // namespace affine
+} // namespace mlir
+
+using namespace mlir;
+using namespace mlir::affine;
+
+namespace {
+/// Lowers `affine.delinearize_index` into a sequence of division and remainder
+/// operations.
+struct LowerDelinearizeIndexOps
+    : public OpRewritePattern<AffineDelinearizeIndexOp> {
+  using OpRewritePattern<AffineDelinearizeIndexOp>::OpRewritePattern;
+  LogicalResult matchAndRewrite(AffineDelinearizeIndexOp op,
+                                PatternRewriter &rewriter) const override {
+    FailureOr<SmallVector<Value>> multiIndex =
+        delinearizeIndex(rewriter, op->getLoc(), op.getLinearIndex(),
+                         op.getEffectiveBasis(), /*hasOuterBound=*/false);
+    if (failed(multiIndex))
+      return failure();
+    rewriter.replaceOp(op, *multiIndex);
+    return success();
+  }
+};
+
+/// Lowers `affine.linearize_index` into a sequence of multiplications and
+/// additions.
+struct LowerLinearizeIndexOps final : OpRewritePattern<AffineLinearizeIndexOp> {
+  using OpRewritePattern::OpRewritePattern;
+  LogicalResult matchAndRewrite(AffineLinearizeIndexOp op,
+                                PatternRewriter &rewriter) const override {
+    // Should be folded away, included here for safety.
+    if (op.getMultiIndex().empty()) {
+      rewriter.replaceOpWithNewOp<arith::ConstantIndexOp>(op, 0);
+      return success();
+    }
+
+    SmallVector<OpFoldResult> multiIndex =
+        getAsOpFoldResult(op.getMultiIndex());
+    OpFoldResult linearIndex =
+        linearizeIndex(rewriter, op.getLoc(), multiIndex, op.getMixedBasis());
+    Value linearIndexValue =
+        getValueOrCreateConstantIntOp(rewriter, op.getLoc(), linearIndex);
+    rewriter.replaceOp(op, linearIndexValue);
+    return success();
+  }
+};
+
+class ExpandAffineIndexOpsAsAffinePass
+    : public affine::impl::AffineExpandIndexOpsAsAffineBase<
+          ExpandAffineIndexOpsAsAffinePass> {
+public:
+  ExpandAffineIndexOpsAsAffinePass() = default;
+
+  void runOnOperation() override {
+    MLIRContext *context = &getContext();
+    RewritePatternSet patterns(context);
+    populateAffineExpandIndexOpsAsAffinePatterns(patterns);
+    if (failed(
+            applyPatternsAndFoldGreedily(getOperation(), std::move(patterns))))
+      return signalPassFailure();
+  }
+};
+
+} // namespace
+
+void mlir::affine::populateAffineExpandIndexOpsAsAffinePatterns(
+    RewritePatternSet &patterns) {
+  patterns.insert<LowerDelinearizeIndexOps, LowerLinearizeIndexOps>(
+      patterns.getContext());
+}
+
+std::unique_ptr<Pass> mlir::affine::createAffineExpandIndexOpsAsAffinePass() {
+  return std::make_unique<ExpandAffineIndexOpsAsAffinePass>();
+}

mlir/lib/Dialect/Affine/Transforms/CMakeLists.txt

@@ -1,6 +1,7 @@
 add_mlir_dialect_library(MLIRAffineTransforms
   AffineDataCopyGeneration.cpp
   AffineExpandIndexOps.cpp
+  AffineExpandIndexOpsAsAffine.cpp
   AffineLoopInvariantCodeMotion.cpp
   AffineLoopNormalize.cpp
   AffineParallelize.cpp

mlir/lib/Dialect/Affine/Utils/LoopUtils.cpp

@@ -2772,3 +2772,15 @@ LogicalResult affine::coalescePerfectlyNestedAffineLoops(AffineForOp op) {
   }
   return result;
 }
+
+int64_t mlir::affine::numEnclosingInvariantLoops(OpOperand &operand) {
+  int64_t count = 0;
+  Operation *currentOp = operand.getOwner();
+  while (auto loopOp = currentOp->getParentOfType<LoopLikeOpInterface>()) {
+    if (!loopOp.isDefinedOutsideOfLoop(operand.get()))
+      break;
+    currentOp = loopOp;
+    count++;
+  }
+  return count;
+}