[mlir][linalg] Implement Conv2D using Winograd Conv2D algorithm

Define high level winograd operators and convert conv_2d_nhwc_fhwc into
winograd operators. According to Winograd Conv2D algorithm, we need
three transform operators for input, filter, and output transformation.

The formula of Winograd Conv2D algorithm is

Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A

filter transform: G x g x G^T
input transform: B^T x d x B
output transform: A^T x y x A

The implementation is based on the paper, Fast Algorithm for
Convolutional Neural Networks. (https://arxiv.org/abs/1509.09308)

Author: Hsiangkai

mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.td

@@ -154,4 +154,121 @@ def Linalg_SoftmaxOp : Linalg_Op<"softmax",
   let hasVerifier = 1;
 }
 
+def Linalg_WinogradFilterTransformOp :
+    Linalg_Op<"winograd_filter_transform", [AllElementTypesMatch<["filter", "output"]>]> {
+  let summary = "Winograd filter transform operator";
+  let description = [{
+    Winograd Conv2D algorithm will convert linalg Conv2D operator into batched
+    matrix multiply. Before the matrix multiply, it will convert filter and
+    input into a format suitable for batched matrix multiply. After the matrix
+    multiply, it will convert output to the final result tensor.
+
+    The algorithm F(m x m, r x r) is
+
+    Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A
+
+    The size of output Y is m x m. The size of filter g is r x r. The size of
+    input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are
+    transformation matrices.
+
+    This operator is defined to represent the high level concept of filter
+    transformation (G x g x G^T) in the Winograd Conv2D algorithm.
+  }];
+
+  let arguments = (ins TensorRankOf<[AnyType], [4]>:$filter,
+                       TensorRankOf<[AnyType], [4]>:$output,
+                       I64Attr:$m,
+                       I64Attr:$r
+  );
+
+  let results = (outs TensorRankOf<[AnyType], [4]>:$result);
+  let assemblyFormat = [{
+    attr-dict
+    `m` `(` $m `)`
+    `r` `(` $r `)`
+    `ins` `(` $filter `:` type($filter) `)`
+    `outs` `(` $output `:` type($output) `)`
+    `->` type($result)
+  }];
+  let hasVerifier = 1;
+}
+
+def Linalg_WinogradInputTransformOp :
+    Linalg_Op<"winograd_input_transform", [AllElementTypesMatch<["input", "output"]>]> {
+  let summary = "Winograd input transform operator";
+  let description = [{
+    Winograd Conv2D algorithm will convert linalg Conv2D operator into batched
+    matrix multiply. Before the matrix multiply, it will convert filter and
+    input into a format suitable for batched matrix multiply. After the matrix
+    multiply, it will convert output to the final result tensor.
+
+    The algorithm F(m x m, r x r) is
+
+    Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A
+
+    The size of output Y is m x m. The size of filter g is r x r. The size of
+    input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are
+    transformation matrices.
+
+    This operator is defined to represent the high level concept of input
+    transformation (B^T x d x B) in the Winograd Conv2D algorithm.
+  }];
+
+  let arguments = (ins TensorRankOf<[AnyType], [4]>:$input,
+                       TensorRankOf<[AnyType], [6]>:$output,
+                       I64Attr:$m,
+                       I64Attr:$r
+  );
+
+  let results = (outs TensorRankOf<[AnyType], [6]>:$result);
+  let assemblyFormat = [{
+    attr-dict
+    `m` `(` $m `)`
+    `r` `(` $r `)`
+    `ins` `(` $input `:` type($input) `)`
+    `outs` `(` $output `:` type($output) `)`
+    `->` type($result)
+  }];
+  let hasVerifier = 1;
+}
+
+def Linalg_WinogradOutputTransformOp :
+    Linalg_Op<"winograd_output_transform", [AllElementTypesMatch<["value", "output"]>]> {
+  let summary = "Winograd output transform operator";
+  let description = [{
+    Winograd Conv2D algorithm will convert linalg Conv2D operator into batched
+    matrix multiply. Before the matrix multiply, it will convert filter and
+    input into a format suitable for batched matrix multiply. After the matrix
+    multiply, it will convert output to the final result tensor.
+
+    The algorithm F(m x m, r x r) is
+
+    Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A
+
+    The size of output Y is m x m. The size of filter g is r x r. The size of
+    input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are
+    transformation matrices.
+
+    This operator is defined to represent the high level concept of output
+    transformation (A^T x y x A) in the Winograd Conv2D algorithm.
+  }];
+
+  let arguments = (ins TensorRankOf<[AnyType], [6]>:$value,
+                       TensorRankOf<[AnyType], [4]>:$output,
+                       I64Attr:$m,
+                       I64Attr:$r
+  );
+
+  let results = (outs TensorRankOf<[AnyType], [4]>:$result);
+  let assemblyFormat = [{
+    attr-dict
+    `m` `(` $m `)`
+    `r` `(` $r `)`
+    `ins` `(` $value `:` type($value) `)`
+    `outs` `(` $output `:` type($output) `)`
+    `->` type($result)
+  }];
+  let hasVerifier = 1;
+}
+
 #endif // LINALG_OPS

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

@@ -1692,6 +1692,10 @@ void populateTransposeMatmulPatterns(RewritePatternSet &patterns,
 void populateBlockPackMatmulPatterns(RewritePatternSet &patterns,
                                      const ControlBlockPackMatmulFn &controlFn);
 
+/// Patterns to apply Winograd Conv2D algorithm F(m x m, r x r).
+void populateWinogradConv2DPatterns(RewritePatternSet &patterns, int64_t m,
+                                    int64_t r);
+
 } // namespace linalg
 } // namespace mlir
 

mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp

@@ -2734,6 +2734,113 @@ FailureOr<SmallVector<Value>> SoftmaxOp::decomposeOperation(OpBuilder &b) {
   return SmallVector<Value>{result};
 }
 
+//===----------------------------------------------------------------------===//
+// WinogradFilterTransformOp
+//===----------------------------------------------------------------------===//
+
+LogicalResult WinogradFilterTransformOp::verify() {
+  auto filterType = cast<ShapedType>(getFilter().getType());
+  ArrayRef<int64_t> filterShape = filterType.getShape();
+  int64_t filterH = filterShape[1];
+  int64_t filterW = filterShape[2];
+  int64_t r = getR();
+
+  if (filterH != r && filterH != 1)
+    return failure();
+  if (filterW != r && filterW != 1)
+    return failure();
+  if (filterH == 1 && filterW == 1)
+    return failure();
+
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
+// WinogradInputTransformOp
+//===----------------------------------------------------------------------===//
+
+LogicalResult WinogradInputTransformOp::verify() {
+  auto inputType = cast<ShapedType>(getInput().getType());
+  ArrayRef<int64_t> inputShape = inputType.getShape();
+  int64_t inputH = inputShape[1];
+  int64_t inputW = inputShape[2];
+  auto outputType = cast<ShapedType>(getOutput().getType());
+  ArrayRef<int64_t> outputShape = outputType.getShape();
+  int64_t outputH = outputShape[0];
+  int64_t outputW = outputShape[1];
+  int64_t outputTileH = outputShape[2];
+  int64_t outputTileW = outputShape[3];
+  int m = getM();
+  int r = getR();
+  bool leftTransform = inputH != 1;
+  bool rightTransform = inputW != 1;
+
+  if (!leftTransform && !rightTransform)
+    return failure();
+
+  if (leftTransform) {
+    int64_t tileH = (inputH - (r - 1)) / m;
+    if (inputH != tileH * m + (r - 1))
+      return failure();
+    if (tileH != outputTileH)
+      return failure();
+    if (outputH != m + r - 1)
+      return failure();
+  }
+
+  if (rightTransform) {
+    int64_t tileW = (inputW - (r - 1)) / m;
+    if (inputW != tileW * m + (r - 1))
+      return failure();
+    if (tileW != outputTileW)
+      return failure();
+    if (outputW != m + r - 1)
+      return failure();
+  }
+
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
+// WinogradOutputTransformOp
+//===----------------------------------------------------------------------===//
+
+LogicalResult WinogradOutputTransformOp::verify() {
+  auto valueType = cast<ShapedType>(getValue().getType());
+  ArrayRef<int64_t> valueShape = valueType.getShape();
+  int64_t valueH = valueShape[0];
+  int64_t valueW = valueShape[1];
+  int64_t valueTileH = valueShape[2];
+  int64_t valueTileW = valueShape[3];
+  auto outputType = cast<ShapedType>(getOutput().getType());
+  ArrayRef<int64_t> outputShape = outputType.getShape();
+  int64_t outputH = outputShape[1];
+  int64_t outputW = outputShape[2];
+  int m = getM();
+  int r = getR();
+  bool leftTransform = valueH != 1;
+  bool rightTransform = valueW != 1;
+
+  if (!leftTransform && !rightTransform)
+    return failure();
+
+  if (leftTransform) {
+    if (valueH != m + r - 1)
+      return failure();
+    if (outputH != m * valueTileH)
+      return failure();
+  }
+
+  if (rightTransform) {
+    if (valueW != m + r - 1)
+      return failure();
+    if (outputW != m * valueTileW)
+      return failure();
+  }
+
+  return success();
+}
+
 //===----------------------------------------------------------------------===//
 // LinalgDialect
 //===----------------------------------------------------------------------===//

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

@@ -38,6 +38,7 @@ add_mlir_dialect_library(MLIRLinalgTransforms
   Transforms.cpp
   TransposeConv2D.cpp
   Vectorization.cpp
+  WinogradConv2D.cpp
 
   ADDITIONAL_HEADER_DIRS
   ${MLIR_MAIN_INCLUDE_DIR}/mlir/Dialect/Linalg