[Mlir-commits] [mlir] 000a05f - [mlir] Normalize dynamic memrefs with a map of tiled-layout.

Uday Bondhugula llvmlistbot at llvm.org
Sun May 23 20:12:47 PDT 2021


Author: Haruki Imai
Date: 2021-05-24T08:39:36+05:30
New Revision: 000a05fd1ab33329f7ef2dd85a3f027a7d0c3a4b

URL: https://github.com/llvm/llvm-project/commit/000a05fd1ab33329f7ef2dd85a3f027a7d0c3a4b
DIFF: https://github.com/llvm/llvm-project/commit/000a05fd1ab33329f7ef2dd85a3f027a7d0c3a4b.diff

LOG: [mlir] Normalize dynamic memrefs with a map of tiled-layout.

Steps for normalizing dynamic memrefs for tiled layout map
1. Check if original map is tiled layout. Only tiled layout is supported.
2. Create normalized memrefType. Dimensions that include dynamic dimensions
   in the map output will be dynamic dimensions.
3. Create new maps to calculate each dimension size of new memref.
   In tiled layout, the dimension size can be calculated by replacing
    "floordiv <tile size>" with "ceildiv <tile size>" and
    "mod <tile size>" with "<tile size>".
4. Create AffineApplyOp to apply the new maps. The output of AffineApplyOp is
   dynamicSizes for new AllocOp.
5. Add the new dynamic sizes in new AllocOp.

This patch also set MemRefsNormalizable trant in CastOp and DimOp since
they used with dynamic memrefs.

Reviewed By: bondhugula

Differential Revision: https://reviews.llvm.org/D97655

Added: 
    mlir/test/Transforms/normalize-memrefs-ops-dynamic.mlir

Modified: 
    mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
    mlir/include/mlir/Transforms/Passes.td
    mlir/lib/Transforms/PassDetail.h
    mlir/lib/Transforms/Utils/Utils.cpp

Removed: 
    


################################################################################
diff  --git a/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td b/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
index 4756a8223f7ad..a1878b90674f5 100644
--- a/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
+++ b/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
@@ -242,7 +242,8 @@ def MemRef_BufferCastOp : MemRef_Op<"buffer_cast",
 def MemRef_CastOp : MemRef_Op<"cast", [
       NoSideEffect, SameOperandsAndResultShape,
       DeclareOpInterfaceMethods<CastOpInterface>,
-      ViewLikeOpInterface
+      ViewLikeOpInterface,
+      MemRefsNormalizable
     ]> {
   let summary = "memref cast operation";
   let description = [{
@@ -392,7 +393,7 @@ def MemRef_DeallocOp : MemRef_Op<"dealloc", [MemRefsNormalizable]> {
 // DimOp
 //===----------------------------------------------------------------------===//
 
-def DimOp : MemRef_Op<"dim", [NoSideEffect]> {
+def DimOp : MemRef_Op<"dim", [NoSideEffect, MemRefsNormalizable]> {
   let summary = "dimension index operation";
   let description = [{
     The `dim` operation takes a memref and a dimension operand of type `index`.

diff  --git a/mlir/include/mlir/Transforms/Passes.td b/mlir/include/mlir/Transforms/Passes.td
index 34b1c950b674a..bfb6f242682ed 100644
--- a/mlir/include/mlir/Transforms/Passes.td
+++ b/mlir/include/mlir/Transforms/Passes.td
@@ -631,6 +631,7 @@ def NormalizeMemRefs : Pass<"normalize-memrefs", "ModuleOp"> {
   ```
   }];
   let constructor = "mlir::createNormalizeMemRefsPass()";
+  let dependentDialects = ["AffineDialect"];
 }
 
 def ParallelLoopCollapsing : Pass<"parallel-loop-collapsing"> {

diff  --git a/mlir/lib/Transforms/PassDetail.h b/mlir/lib/Transforms/PassDetail.h
index 81b9530c48353..0f998a7147ce8 100644
--- a/mlir/lib/Transforms/PassDetail.h
+++ b/mlir/lib/Transforms/PassDetail.h
@@ -12,6 +12,8 @@
 #include "mlir/Pass/Pass.h"
 
 namespace mlir {
+class AffineDialect;
+
 // Forward declaration from Dialect.h
 template <typename ConcreteDialect>
 void registerDialect(DialectRegistry &registry);

diff  --git a/mlir/lib/Transforms/Utils/Utils.cpp b/mlir/lib/Transforms/Utils/Utils.cpp
index 58e8d8cd5006b..ce514a887dfb9 100644
--- a/mlir/lib/Transforms/Utils/Utils.cpp
+++ b/mlir/lib/Transforms/Utils/Utils.cpp
@@ -12,7 +12,6 @@
 //===----------------------------------------------------------------------===//
 
 #include "mlir/Transforms/Utils.h"
-
 #include "mlir/Analysis/AffineAnalysis.h"
 #include "mlir/Analysis/AffineStructures.h"
 #include "mlir/Analysis/Utils.h"
@@ -380,6 +379,246 @@ void mlir::createAffineComputationSlice(
   }
 }
 
+/// Enum to set patterns of affine expr in tiled-layout map.
+/// TileFloorDiv: <dim expr> div <tile size>
+/// TileMod: <dim expr> mod <tile size>
+/// TileNone: None of the above
+/// Example:
+/// #tiled_2d_128x256 = affine_map<(d0, d1)
+///            -> (d0 div 128, d1 div 256, d0 mod 128, d1 mod 256)>
+/// "d0 div 128" and "d1 div 256" ==> TileFloorDiv
+/// "d0 mod 128" and "d1 mod 256" ==> TileMod
+enum TileExprPattern { TileFloorDiv, TileMod, TileNone };
+
+/// Check if `map` is a tiled layout. In the tiled layout, specific k dimensions
+/// being floordiv'ed by respective tile sizes appeare in a mod with the same
+/// tile sizes, and no other expression involves those k dimensions. This
+/// function stores a vector of tuples (`tileSizePos`) including AffineExpr for
+/// tile size, positions of corresponding `floordiv` and `mod`. If it is not a
+/// tiled layout, an empty vector is returned.
+static LogicalResult getTileSizePos(
+    AffineMap map,
+    SmallVectorImpl<std::tuple<AffineExpr, unsigned, unsigned>> &tileSizePos) {
+  // Create `floordivExprs` which is a vector of tuples including LHS and RHS of
+  // `floordiv` and its position in `map` output.
+  // Example: #tiled_2d_128x256 = affine_map<(d0, d1)
+  //                -> (d0 div 128, d1 div 256, d0 mod 128, d1 mod 256)>
+  // In this example, `floordivExprs` includes {d0, 128, 0} and {d1, 256, 1}.
+  SmallVector<std::tuple<AffineExpr, AffineExpr, unsigned>, 4> floordivExprs;
+  unsigned pos = 0;
+  for (AffineExpr expr : map.getResults()) {
+    if (expr.getKind() == AffineExprKind::FloorDiv) {
+      AffineBinaryOpExpr binaryExpr = expr.cast<AffineBinaryOpExpr>();
+      if (binaryExpr.getRHS().isa<AffineConstantExpr>())
+        floordivExprs.emplace_back(
+            std::make_tuple(binaryExpr.getLHS(), binaryExpr.getRHS(), pos));
+    }
+    pos++;
+  }
+  // Not tiled layout if `floordivExprs` is empty.
+  if (floordivExprs.empty()) {
+    tileSizePos = SmallVector<std::tuple<AffineExpr, unsigned, unsigned>>{};
+    return success();
+  }
+
+  // Check if LHS of `floordiv` is used in LHS of `mod`. If not used, `map` is
+  // not tiled layout.
+  for (std::tuple<AffineExpr, AffineExpr, unsigned> fexpr : floordivExprs) {
+    AffineExpr floordivExprLHS = std::get<0>(fexpr);
+    AffineExpr floordivExprRHS = std::get<1>(fexpr);
+    unsigned floordivPos = std::get<2>(fexpr);
+
+    // Walk affinexpr of `map` output except `fexpr`, and check if LHS and RHS
+    // of `fexpr` are used in LHS and RHS of `mod`. If LHS of `fexpr` is used
+    // other expr, the map is not tiled layout. Example of non tiled layout:
+    //   affine_map<(d0, d1, d2) -> (d0, d1, d2 floordiv 256, d2 floordiv 256)>
+    //   affine_map<(d0, d1, d2) -> (d0, d1, d2 floordiv 256, d2 mod 128)>
+    //   affine_map<(d0, d1, d2) -> (d0, d1, d2 floordiv 256, d2 mod 256, d2 mod
+    //   256)>
+    bool found = false;
+    pos = 0;
+    for (AffineExpr expr : map.getResults()) {
+      bool notTiled = false;
+      if (pos != floordivPos) {
+        expr.walk([&](AffineExpr e) {
+          if (e == floordivExprLHS) {
+            if (expr.getKind() == AffineExprKind::Mod) {
+              AffineBinaryOpExpr binaryExpr = expr.cast<AffineBinaryOpExpr>();
+              // If LHS and RHS of `mod` are the same with those of floordiv.
+              if (floordivExprLHS == binaryExpr.getLHS() &&
+                  floordivExprRHS == binaryExpr.getRHS()) {
+                // Save tile size (RHS of `mod`), and position of `floordiv` and
+                // `mod` if same expr with `mod` is not found yet.
+                if (!found) {
+                  tileSizePos.emplace_back(
+                      std::make_tuple(binaryExpr.getRHS(), floordivPos, pos));
+                  found = true;
+                } else {
+                  // Non tiled layout: Have multilpe `mod` with the same LHS.
+                  // eg. affine_map<(d0, d1, d2) -> (d0, d1, d2 floordiv 256, d2
+                  // mod 256, d2 mod 256)>
+                  notTiled = true;
+                }
+              } else {
+                // Non tiled layout: RHS of `mod` is 
diff erent from `floordiv`.
+                // eg. affine_map<(d0, d1, d2) -> (d0, d1, d2 floordiv 256, d2
+                // mod 128)>
+                notTiled = true;
+              }
+            } else {
+              // Non tiled layout: LHS is the same, but not `mod`.
+              // eg. affine_map<(d0, d1, d2) -> (d0, d1, d2 floordiv 256, d2
+              // floordiv 256)>
+              notTiled = true;
+            }
+          }
+        });
+      }
+      if (notTiled) {
+        tileSizePos = SmallVector<std::tuple<AffineExpr, unsigned, unsigned>>{};
+        return success();
+      }
+      pos++;
+    }
+  }
+  return success();
+}
+
+/// Check if `dim` dimension of memrefType with `layoutMap` becomes dynamic
+/// after normalization. Dimensions that include dynamic dimensions in the map
+/// output will become dynamic dimensions. Return true if `dim` is dynamic
+/// dimension.
+///
+/// Example:
+/// #map0 = affine_map<(d0, d1) -> (d0, d1 floordiv 32, d1 mod 32)>
+///
+/// If d1 is dynamic dimension, 2nd and 3rd dimension of map output are dynamic.
+/// memref<4x?xf32, #map0>  ==>  memref<4x?x?xf32>
+static bool
+isNormalizedMemRefDynamicDim(unsigned dim, AffineMap layoutMap,
+                             SmallVectorImpl<unsigned> &inMemrefTypeDynDims,
+                             MLIRContext *context) {
+  bool isDynamicDim = false;
+  AffineExpr expr = layoutMap.getResults()[dim];
+  // Check if affine expr of the dimension includes dynamic dimension of input
+  // memrefType.
+  expr.walk([&inMemrefTypeDynDims, &isDynamicDim, &context](AffineExpr e) {
+    if (e.isa<AffineDimExpr>()) {
+      for (unsigned dm : inMemrefTypeDynDims) {
+        if (e == getAffineDimExpr(dm, context)) {
+          isDynamicDim = true;
+        }
+      }
+    }
+  });
+  return isDynamicDim;
+}
+
+/// Create affine expr to calculate dimension size for a tiled-layout map.
+static AffineExpr createDimSizeExprForTiledLayout(AffineExpr oldMapOutput,
+                                                  TileExprPattern pat) {
+  // Create map output for the patterns.
+  // "floordiv <tile size>" ==> "ceildiv <tile size>"
+  // "mod <tile size>" ==> "<tile size>"
+  AffineExpr newMapOutput;
+  AffineBinaryOpExpr binaryExpr = nullptr;
+  switch (pat) {
+  case TileExprPattern::TileMod:
+    binaryExpr = oldMapOutput.cast<AffineBinaryOpExpr>();
+    newMapOutput = binaryExpr.getRHS();
+    break;
+  case TileExprPattern::TileFloorDiv:
+    binaryExpr = oldMapOutput.cast<AffineBinaryOpExpr>();
+    newMapOutput = getAffineBinaryOpExpr(
+        AffineExprKind::CeilDiv, binaryExpr.getLHS(), binaryExpr.getRHS());
+    break;
+  default:
+    newMapOutput = oldMapOutput;
+  }
+  return newMapOutput;
+}
+
+/// Create new maps to calculate each dimension size of `newMemRefType`, and
+/// create `newDynamicSizes` from them by using AffineApplyOp.
+///
+/// Steps for normalizing dynamic memrefs for a tiled layout map
+/// Example:
+///    #map0 = affine_map<(d0, d1) -> (d0, d1 floordiv 32, d1 mod 32)>
+///    %0 = dim %arg0, %c1 :memref<4x?xf32>
+///    %1 = alloc(%0) : memref<4x?xf32, #map0>
+///
+/// (Before this function)
+/// 1. Check if `map`(#map0) is a tiled layout using `getTileSizePos()`. Only
+/// single layout map is supported.
+///
+/// 2. Create normalized memrefType using `isNormalizedMemRefDynamicDim()`. It
+/// is memref<4x?x?xf32> in the above example.
+///
+/// (In this function)
+/// 3. Create new maps to calculate each dimension of the normalized memrefType
+/// using `createDimSizeExprForTiledLayout()`. In the tiled layout, the
+/// dimension size can be calculated by replacing "floordiv <tile size>" with
+/// "ceildiv <tile size>" and "mod <tile size>" with "<tile size>".
+/// - New map in the above example
+///   #map0 = affine_map<(d0, d1) -> (d0)>
+///   #map1 = affine_map<(d0, d1) -> (d1 ceildiv 32)>
+///   #map2 = affine_map<(d0, d1) -> (32)>
+///
+/// 4. Create AffineApplyOp to apply the new maps. The output of AffineApplyOp
+/// is used in dynamicSizes of new AllocOp.
+///   %0 = dim %arg0, %c1 : memref<4x?xf32>
+///   %c4 = constant 4 : index
+///   %1 = affine.apply #map1(%c4, %0)
+///   %2 = affine.apply #map2(%c4, %0)
+static void createNewDynamicSizes(MemRefType oldMemRefType,
+                                  MemRefType newMemRefType, AffineMap map,
+                                  memref::AllocOp *allocOp, OpBuilder b,
+                                  SmallVectorImpl<Value> &newDynamicSizes) {
+  // Create new input for AffineApplyOp.
+  SmallVector<Value, 4> inAffineApply;
+  ArrayRef<int64_t> oldMemRefShape = oldMemRefType.getShape();
+  unsigned dynIdx = 0;
+  for (unsigned d = 0; d < oldMemRefType.getRank(); ++d) {
+    if (oldMemRefShape[d] < 0) {
+      // Use dynamicSizes of allocOp for dynamic dimension.
+      inAffineApply.emplace_back(allocOp->dynamicSizes()[dynIdx]);
+      dynIdx++;
+    } else {
+      // Create ConstantOp for static dimension.
+      Attribute constantAttr =
+          b.getIntegerAttr(b.getIndexType(), oldMemRefShape[d]);
+      inAffineApply.emplace_back(
+          b.create<ConstantOp>(allocOp->getLoc(), constantAttr));
+    }
+  }
+
+  // Create new map to calculate each dimension size of new memref for each
+  // original map output. Only for dynamic dimesion of `newMemRefType`.
+  unsigned newDimIdx = 0;
+  ArrayRef<int64_t> newMemRefShape = newMemRefType.getShape();
+  SmallVector<std::tuple<AffineExpr, unsigned, unsigned>> tileSizePos;
+  (void)getTileSizePos(map, tileSizePos);
+  for (AffineExpr expr : map.getResults()) {
+    if (newMemRefShape[newDimIdx] < 0) {
+      // Create new maps to calculate each dimension size of new memref.
+      enum TileExprPattern pat = TileExprPattern::TileNone;
+      for (auto pos : tileSizePos) {
+        if (newDimIdx == std::get<1>(pos))
+          pat = TileExprPattern::TileFloorDiv;
+        else if (newDimIdx == std::get<2>(pos))
+          pat = TileExprPattern::TileMod;
+      }
+      AffineExpr newMapOutput = createDimSizeExprForTiledLayout(expr, pat);
+      AffineMap newMap =
+          AffineMap::get(map.getNumInputs(), map.getNumSymbols(), newMapOutput);
+      Value affineApp =
+          b.create<AffineApplyOp>(allocOp->getLoc(), newMap, inAffineApply);
+      newDynamicSizes.emplace_back(affineApp);
+    }
+    newDimIdx++;
+  }
+}
+
 // TODO: Currently works for static memrefs with a single layout map.
 LogicalResult mlir::normalizeMemRef(memref::AllocOp *allocOp) {
   MemRefType memrefType = allocOp->getType();
@@ -397,9 +636,25 @@ LogicalResult mlir::normalizeMemRef(memref::AllocOp *allocOp) {
   Value oldMemRef = allocOp->getResult();
 
   SmallVector<Value, 4> symbolOperands(allocOp->symbolOperands());
-  memref::AllocOp newAlloc = b.create<memref::AllocOp>(
-      allocOp->getLoc(), newMemRefType, allocOp->alignmentAttr());
   AffineMap layoutMap = memrefType.getAffineMaps().front();
+  memref::AllocOp newAlloc;
+  // Check if `layoutMap` is a tiled layout. Only single layout map is
+  // supported for normalizing dynamic memrefs.
+  SmallVector<std::tuple<AffineExpr, unsigned, unsigned>> tileSizePos;
+  (void)getTileSizePos(layoutMap, tileSizePos);
+  if (newMemRefType.getNumDynamicDims() > 0 && !tileSizePos.empty()) {
+    MemRefType oldMemRefType = oldMemRef.getType().cast<MemRefType>();
+    SmallVector<Value, 4> newDynamicSizes;
+    createNewDynamicSizes(oldMemRefType, newMemRefType, layoutMap, allocOp, b,
+                          newDynamicSizes);
+    // Add the new dynamic sizes in new AllocOp.
+    newAlloc =
+        b.create<memref::AllocOp>(allocOp->getLoc(), newMemRefType,
+                                  newDynamicSizes, allocOp->alignmentAttr());
+  } else {
+    newAlloc = b.create<memref::AllocOp>(allocOp->getLoc(), newMemRefType,
+                                         allocOp->alignmentAttr());
+  }
   // Replace all uses of the old memref.
   if (failed(replaceAllMemRefUsesWith(oldMemRef, /*newMemRef=*/newAlloc,
                                       /*extraIndices=*/{},
@@ -440,8 +695,12 @@ MemRefType mlir::normalizeMemRefType(MemRefType memrefType, OpBuilder b,
   // We don't do any checks for one-to-one'ness; we assume that it is
   // one-to-one.
 
-  // TODO: Only for static memref's for now.
-  if (memrefType.getNumDynamicDims() > 0)
+  // Normalize only static memrefs and dynamic memrefs with a tiled-layout map
+  // for now.
+  // TODO: Normalize the other types of dynamic memrefs.
+  SmallVector<std::tuple<AffineExpr, unsigned, unsigned>> tileSizePos;
+  (void)getTileSizePos(layoutMaps.front(), tileSizePos);
+  if (memrefType.getNumDynamicDims() > 0 && tileSizePos.empty())
     return memrefType;
 
   // We have a single map that is not an identity map. Create a new memref
@@ -449,9 +708,15 @@ MemRefType mlir::normalizeMemRefType(MemRefType memrefType, OpBuilder b,
   ArrayRef<int64_t> shape = memrefType.getShape();
   // FlatAffineConstraint may later on use symbolicOperands.
   FlatAffineConstraints fac(rank, numSymbolicOperands);
+  SmallVector<unsigned, 4> memrefTypeDynDims;
   for (unsigned d = 0; d < rank; ++d) {
-    fac.addConstantLowerBound(d, 0);
-    fac.addConstantUpperBound(d, shape[d] - 1);
+    // Use constraint system only in static dimensions.
+    if (shape[d] > 0) {
+      fac.addConstantLowerBound(d, 0);
+      fac.addConstantUpperBound(d, shape[d] - 1);
+    } else {
+      memrefTypeDynDims.emplace_back(d);
+    }
   }
   // We compose this map with the original index (logical) space to derive
   // the upper bounds for the new index space.
@@ -464,15 +729,23 @@ MemRefType mlir::normalizeMemRefType(MemRefType memrefType, OpBuilder b,
   fac.projectOut(newRank, fac.getNumIds() - newRank - fac.getNumLocalIds());
   SmallVector<int64_t, 4> newShape(newRank);
   for (unsigned d = 0; d < newRank; ++d) {
-    // The lower bound for the shape is always zero.
-    auto ubConst = fac.getConstantUpperBound(d);
-    // For a static memref and an affine map with no symbols, this is
-    // always bounded.
-    assert(ubConst.hasValue() && "should always have an upper bound");
-    if (ubConst.getValue() < 0)
-      // This is due to an invalid map that maps to a negative space.
-      return memrefType;
-    newShape[d] = ubConst.getValue() + 1;
+    // Check if each dimension of normalized memrefType is dynamic.
+    bool isDynDim = isNormalizedMemRefDynamicDim(
+        d, layoutMap, memrefTypeDynDims, b.getContext());
+    if (isDynDim) {
+      newShape[d] = -1;
+    } else {
+      // The lower bound for the shape is always zero.
+      auto ubConst = fac.getConstantUpperBound(d);
+      // For a static memref and an affine map with no symbols, this is
+      // always bounded.
+      assert(ubConst.hasValue() && "should always have an upper bound");
+      if (ubConst.getValue() < 0)
+        // This is due to an invalid map that maps to a negative space.
+        return memrefType;
+      // If dimension of new memrefType is dynamic, the value is -1.
+      newShape[d] = ubConst.getValue() + 1;
+    }
   }
 
   // Create the new memref type after trivializing the old layout map.

diff  --git a/mlir/test/Transforms/normalize-memrefs-ops-dynamic.mlir b/mlir/test/Transforms/normalize-memrefs-ops-dynamic.mlir
new file mode 100644
index 0000000000000..c26ed81fb3c5c
--- /dev/null
+++ b/mlir/test/Transforms/normalize-memrefs-ops-dynamic.mlir
@@ -0,0 +1,251 @@
+// RUN: mlir-opt -normalize-memrefs %s -split-input-file| FileCheck %s
+
+// For all these cases, we test if MemRefs Normalization works with the test
+// operations. These are test cases for MemRefs with dynamic dimension
+// and tiled-layout map.
+// * test.op_norm: this operation has the MemRefsNormalizable attribute. The tests
+//   that include this operation are constructed so that the normalization should
+//   happen.
+
+#map_tiled = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 floordiv 32, d3 floordiv 64, d2 mod 32, d3 mod 64)>
+
+// CHECK-DAG: #[[$MAP0:.+]] = affine_map<(d0, d1, d2, d3) -> (d1)>
+// CHECK-DAG: #[[$MAP1:.+]] = affine_map<(d0, d1, d2, d3) -> (d2 ceildiv 32)>
+// CHECK-DAG: #[[$MAP2:.+]] = affine_map<(d0, d1, d2, d3) -> (32)>
+
+// Test with op_norm and maps in arguments and in the operations in the function.
+// Memref has two dynamic dimensions.
+
+// CHECK-LABEL:  test_norm_dynamic12
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<1x?x?x1x?x64xf32>) {
+func @test_norm_dynamic12(%arg0 : memref<1x?x?x14xf32, #map_tiled>) -> () {
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %0 = memref.dim %arg0, %c1 :memref<1x?x?x14xf32, #map_tiled>
+    %1 = memref.dim %arg0, %c2 :memref<1x?x?x14xf32, #map_tiled>
+    %2 = memref.alloc(%0, %1) : memref<1x?x?x14xf32, #map_tiled>
+    "test.op_norm"(%arg0, %2) : (memref<1x?x?x14xf32, #map_tiled>, memref<1x?x?x14xf32, #map_tiled>) -> ()
+    memref.dealloc %2 :  memref<1x?x?x14xf32, #map_tiled>
+    return
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<1x?x?x1x?x64xf32>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<1x?x?x1x?x64xf32>
+    // CHECK-DAG:       [[CST_1_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_14_:%.+]] = constant 14 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[VAR_2_:%.+]] = affine.apply #[[$MAP0]]([[CST_1_1_]], [[DIM_0_]], [[DIM_1_]], [[CST_14_]])
+    // CHECK-DAG:       [[VAR_3_:%.+]] = affine.apply #[[$MAP1]]([[CST_1_1_]], [[DIM_0_]], [[DIM_1_]], [[CST_14_]])
+    // CHECK-DAG:       [[VAR_4_:%.+]] = affine.apply #[[$MAP2]]([[CST_1_1_]], [[DIM_0_]], [[DIM_1_]], [[CST_14_]])
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[VAR_2_]], [[VAR_3_]], [[VAR_4_]]) : memref<1x?x?x1x?x64xf32>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<1x?x?x1x?x64xf32>, memref<1x?x?x1x?x64xf32>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<1x?x?x1x?x64xf32>
+    // CHECK:           return
+}
+
+// -----
+
+// Test with op_norm and maps in arguments and in the operations in the function.
+// All of dimensions are dynamic.
+
+#map_tiled1 = affine_map<(d0, d1, d2, d3) -> (d0, d1, (d2 floordiv 4) floordiv 32, (d3 mod 8) floordiv 64, (d2 floordiv 4) mod 32, (d3 mod 8) mod 64)>
+
+// CHECK-DAG: #[[$MAP0:.+]] = affine_map<(d0, d1, d2, d3) -> (d1)>
+// CHECK-DAG: #[[$MAP1:.+]] = affine_map<(d0, d1, d2, d3) -> ((d2 floordiv 4) ceildiv 32)>
+// CHECK-DAG: #[[$MAP2:.+]] = affine_map<(d0, d1, d2, d3) -> (32)>
+// CHECK-DAG: #[[$MAP3:.+]] = affine_map<(d0, d1, d2, d3) -> (d0)>
+// CHECK-DAG: #[[$MAP4:.+]] = affine_map<(d0, d1, d2, d3) -> ((d3 mod 8) ceildiv 64)>
+// CHECK-DAG: #[[$MAP5:.+]] = affine_map<(d0, d1, d2, d3) -> (64)>
+
+// CHECK-LABEL:  test_norm_dynamic1234
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<?x?x?x?x?x?xf32>) {
+func @test_norm_dynamic1234(%arg0 : memref<?x?x?x?xf32, #map_tiled1>) -> () {
+    %c0 = constant 0 : index
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %c3 = constant 3 : index
+    %0 = memref.dim %arg0, %c0 :memref<?x?x?x?xf32, #map_tiled1>
+    %1 = memref.dim %arg0, %c1 :memref<?x?x?x?xf32, #map_tiled1>
+    %2 = memref.dim %arg0, %c2 :memref<?x?x?x?xf32, #map_tiled1>
+    %3 = memref.dim %arg0, %c3 :memref<?x?x?x?xf32, #map_tiled1>
+    %4 = memref.alloc(%0, %1, %2, %3) : memref<?x?x?x?xf32, #map_tiled1>
+    "test.op_norm"(%arg0, %4) : (memref<?x?x?x?xf32, #map_tiled1>, memref<?x?x?x?xf32, #map_tiled1>) -> ()
+    memref.dealloc %4 :  memref<?x?x?x?xf32, #map_tiled1>
+    return
+    // CHECK-DAG:       [[CST_0_:%.+]] = constant 0 : index
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-DAG:       [[CST_3_:%.+]] = constant 3 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_0_]] : memref<?x?x?x?x?x?xf32>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<?x?x?x?x?x?xf32>
+    // CHECK-DAG:       [[DIM_2_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<?x?x?x?x?x?xf32>
+    // CHECK-DAG:       [[DIM_3_:%.+]] = memref.dim [[ARG_0_]], [[CST_3_]] : memref<?x?x?x?x?x?xf32>
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[VAR_4_:%.+]] = affine.apply #[[$MAP3]]([[DIM_0_]], [[DIM_1_]], [[DIM_2_]], [[DIM_3_]])
+    // CHECK-DAG:       [[VAR_5_:%.+]] = affine.apply #[[$MAP0]]([[DIM_0_]], [[DIM_1_]], [[DIM_2_]], [[DIM_3_]])
+    // CHECK-DAG:       [[VAR_6_:%.+]] = affine.apply #[[$MAP1]]([[DIM_0_]], [[DIM_1_]], [[DIM_2_]], [[DIM_3_]])
+    // CHECK-DAG:       [[VAR_7_:%.+]] = affine.apply #[[$MAP4]]([[DIM_0_]], [[DIM_1_]], [[DIM_2_]], [[DIM_3_]])
+    // CHECK-DAG:       [[VAR_8_:%.+]] = affine.apply #[[$MAP2]]([[DIM_0_]], [[DIM_1_]], [[DIM_2_]], [[DIM_3_]])
+    // CHECK-DAG:       [[VAR_9_:%.+]] = affine.apply #[[$MAP5]]([[DIM_0_]], [[DIM_1_]], [[DIM_2_]], [[DIM_3_]])
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[VAR_4_]], [[VAR_5_]], [[VAR_6_]], [[VAR_7_]], [[VAR_8_]], [[VAR_9_]]) : memref<?x?x?x?x?x?xf32>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<?x?x?x?x?x?xf32>, memref<?x?x?x?x?x?xf32>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<?x?x?x?x?x?xf32>
+    // CHECK:           return
+}
+
+// -----
+
+// Same test with maps that are not tiled layout maps in the arguments and the operations in the function.
+// This is not normalized since this is not tiled-layout map. No mod and floordiv.
+
+#map_not_tiled0 = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 - d1, d3 - d2)>
+
+// CHECK-DAG: #[[$MAP6:.+]] = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 - d1, d3 - d2)>
+
+// CHECK-LABEL:  func @test_norm_dynamic_not_tiled0
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<1x?x?x14xf32, #[[$MAP6]]>) {
+func @test_norm_dynamic_not_tiled0(%arg0 : memref<1x?x?x14xf32, #map_not_tiled0>) -> () {
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %0 = memref.dim %arg0, %c1 :memref<1x?x?x14xf32, #map_not_tiled0>
+    %1 = memref.dim %arg0, %c2 :memref<1x?x?x14xf32, #map_not_tiled0>
+    %2 = memref.alloc(%0, %1) : memref<1x?x?x14xf32, #map_not_tiled0>
+    "test.op_norm"(%arg0, %2) : (memref<1x?x?x14xf32, #map_not_tiled0>, memref<1x?x?x14xf32, #map_not_tiled0>) -> ()
+    memref.dealloc %2 :  memref<1x?x?x14xf32, #map_not_tiled0>
+    return
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[DIM_0_]], [[DIM_1_]]) : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<1x?x?x14xf32, #[[$MAP6]]>, memref<1x?x?x14xf32, #[[$MAP6]]>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK:           return
+}
+
+// -----
+
+// Same test with maps that are not tiled layout maps in the arguments and the operations in the function.
+// This is not normalized since this is not tiled-layout map. No floordiv.
+
+#map_not_tiled1 = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 - d1, d3 - d2, d2 mod 32, d3 mod 64)>
+
+// CHECK-DAG: #[[$MAP6:.+]] = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 - d1, d3 - d2, d2 mod 32, d3 mod 64)>
+
+// CHECK-LABEL:  func @test_norm_dynamic_not_tiled1
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<1x?x?x14xf32, #[[$MAP6]]>) {
+func @test_norm_dynamic_not_tiled1(%arg0 : memref<1x?x?x14xf32, #map_not_tiled1>) -> () {
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %0 = memref.dim %arg0, %c1 :memref<1x?x?x14xf32, #map_not_tiled1>
+    %1 = memref.dim %arg0, %c2 :memref<1x?x?x14xf32, #map_not_tiled1>
+    %2 = memref.alloc(%0, %1) : memref<1x?x?x14xf32, #map_not_tiled1>
+    "test.op_norm"(%arg0, %2) : (memref<1x?x?x14xf32, #map_not_tiled1>, memref<1x?x?x14xf32, #map_not_tiled1>) -> ()
+    memref.dealloc %2 :  memref<1x?x?x14xf32, #map_not_tiled1>
+    return
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[DIM_0_]], [[DIM_1_]]) : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<1x?x?x14xf32, #[[$MAP6]]>, memref<1x?x?x14xf32, #[[$MAP6]]>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<1x?x?x14xf32, #[[$MAP6]]>
+    // CHECK:           return
+}
+
+// -----
+
+// Same test with maps that are not tiled layout maps in the arguments and the operations in the function.
+// This is not normalized since this is not tiled-layout map. RHS of floordiv is 
diff erent from that of mod.
+
+#map_not_tiled2 = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 - d1, d3 floordiv 64, d2 mod 32, d3 mod 32)>
+
+// CHECK-DAG: #[[$MAP7:.+]] = affine_map<(d0, d1, d2, d3) -> (d0, d1, d2 - d1, d3 floordiv 64, d2 mod 32, d3 mod 32)>
+
+// CHECK-LABEL:  func @test_norm_dynamic_not_tiled2
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<1x?x?x14xf32, #[[$MAP7]]>) {
+func @test_norm_dynamic_not_tiled2(%arg0 : memref<1x?x?x14xf32, #map_not_tiled2>) -> () {
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %0 = memref.dim %arg0, %c1 :memref<1x?x?x14xf32, #map_not_tiled2>
+    %1 = memref.dim %arg0, %c2 :memref<1x?x?x14xf32, #map_not_tiled2>
+    %2 = memref.alloc(%0, %1) : memref<1x?x?x14xf32, #map_not_tiled2>
+    "test.op_norm"(%arg0, %2) : (memref<1x?x?x14xf32, #map_not_tiled2>, memref<1x?x?x14xf32, #map_not_tiled2>) -> ()
+    memref.dealloc %2 :  memref<1x?x?x14xf32, #map_not_tiled2>
+    return
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<1x?x?x14xf32, #[[$MAP7]]>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<1x?x?x14xf32, #[[$MAP7]]>
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[DIM_0_]], [[DIM_1_]]) : memref<1x?x?x14xf32, #[[$MAP7]]>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<1x?x?x14xf32, #[[$MAP7]]>, memref<1x?x?x14xf32, #[[$MAP7]]>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<1x?x?x14xf32, #[[$MAP7]]>
+    // CHECK:           return
+}
+
+// -----
+
+// Same test with maps that are not tiled layout maps in the arguments and the operations in the function.
+// This is not normalized since this is not tiled-layout map. Multiple mod with the same LHS and RHS.
+
+#map_not_tiled3 = affine_map<(d0, d1, d2, d3) -> (d0, d1 floordiv 32, d2, d3, d1 mod 32, d1 mod 32)>
+
+// CHECK-DAG: #[[$MAP8:.+]] = affine_map<(d0, d1, d2, d3) -> (d0, d1 floordiv 32, d2, d3, d1 mod 32, d1 mod 32)>
+
+// CHECK-LABEL:  func @test_norm_dynamic_not_tiled3
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<1x?x?x14xf32, #[[$MAP8]]>) {
+func @test_norm_dynamic_not_tiled3(%arg0 : memref<1x?x?x14xf32, #map_not_tiled3>) -> () {
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %0 = memref.dim %arg0, %c1 :memref<1x?x?x14xf32, #map_not_tiled3>
+    %1 = memref.dim %arg0, %c2 :memref<1x?x?x14xf32, #map_not_tiled3>
+    %2 = memref.alloc(%0, %1) : memref<1x?x?x14xf32, #map_not_tiled3>
+    "test.op_norm"(%arg0, %2) : (memref<1x?x?x14xf32, #map_not_tiled3>, memref<1x?x?x14xf32, #map_not_tiled3>) -> ()
+    memref.dealloc %2 :  memref<1x?x?x14xf32, #map_not_tiled3>
+    return
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<1x?x?x14xf32, #[[$MAP8]]>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<1x?x?x14xf32, #[[$MAP8]]>
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[DIM_0_]], [[DIM_1_]]) : memref<1x?x?x14xf32, #[[$MAP8]]>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<1x?x?x14xf32, #[[$MAP8]]>, memref<1x?x?x14xf32, #[[$MAP8]]>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<1x?x?x14xf32, #[[$MAP8]]>
+    // CHECK:           return
+}
+
+// -----
+
+// Same test with maps that are not tiled layout maps in the arguments and the operations in the function.
+// This is not normalized since this is not tiled-layout map. floordiv and mod with the same LHS and RHS(d0 floordiv 32 and d0 mod 32), but, unrelaed d0 exists in other position.
+
+#map_not_tiled4 = affine_map<(d0, d1, d2, d3) -> (d0 floordiv 32, d1 floordiv 32, d0, d3, d0 mod 32, d1 mod 32)>
+
+// CHECK-DAG: #[[$MAP9:.+]] = affine_map<(d0, d1, d2, d3) -> (d0 floordiv 32, d1 floordiv 32, d0, d3, d0 mod 32, d1 mod 32)>
+
+// CHECK-LABEL:  func @test_norm_dynamic_not_tiled4
+// CHECK-SAME:   ([[ARG_0_:%.+]]: memref<1x?x?x14xf32, #[[$MAP9]]>) {
+func @test_norm_dynamic_not_tiled4(%arg0 : memref<1x?x?x14xf32, #map_not_tiled4>) -> () {
+    %c1 = constant 1 : index
+    %c2 = constant 2 : index
+    %0 = memref.dim %arg0, %c1 :memref<1x?x?x14xf32, #map_not_tiled4>
+    %1 = memref.dim %arg0, %c2 :memref<1x?x?x14xf32, #map_not_tiled4>
+    %2 = memref.alloc(%0, %1) : memref<1x?x?x14xf32, #map_not_tiled4>
+    "test.op_norm"(%arg0, %2) : (memref<1x?x?x14xf32, #map_not_tiled4>, memref<1x?x?x14xf32, #map_not_tiled4>) -> ()
+    memref.dealloc %2 :  memref<1x?x?x14xf32, #map_not_tiled4>
+    return
+    // CHECK-DAG:       [[CST_1_:%.+]] = constant 1 : index
+    // CHECK-DAG:       [[CST_2_:%.+]] = constant 2 : index
+    // CHECK-NOT: separator of consecutive DAGs
+    // CHECK-DAG:       [[DIM_0_:%.+]] = memref.dim [[ARG_0_]], [[CST_1_]] : memref<1x?x?x14xf32, #[[$MAP9]]>
+    // CHECK-DAG:       [[DIM_1_:%.+]] = memref.dim [[ARG_0_]], [[CST_2_]] : memref<1x?x?x14xf32, #[[$MAP9]]>
+    // CHECK:           [[RES_:%.+]] = memref.alloc([[DIM_0_]], [[DIM_1_]]) : memref<1x?x?x14xf32, #[[$MAP9]]>
+    // CHECK:           "test.op_norm"([[ARG_0_]], [[RES_]]) : (memref<1x?x?x14xf32, #[[$MAP9]]>, memref<1x?x?x14xf32, #[[$MAP9]]>) -> ()
+    // CHECK:           memref.dealloc [[RES_]] : memref<1x?x?x14xf32, #[[$MAP9]]>
+    // CHECK:           return
+}


        


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