[llvm-branch-commits] [mlir] [mlir][linalg] Decompose winograd operators (PR #96183)

[Hsiangkai Wang via llvm-branch-commits]

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@@ -23,6 +26,156 @@ namespace linalg {
 
 namespace {
 
+// clang-format off
+// Winograd Conv2D uses a minimal 2D filtering algorithm to calculate its
+// result. The formula of minimal 2D filtering algorithm F(m x m, r x r),
+// m is the output dimension and r is the filter dimension, is
+//
+// Y = A^T x [ (G x g x G^T) x (B^T x d x B) ] x A
+//
+// g is filter and d is input data. We need to prepare 6 constant
+// transformation matrices, G, G^T, B^T, B, A^T, and A for this formula.
+//
+// The following tables define these constant transformation matrices for
+// F(2 x 2, 3 x 3), F(4 x 4, 3 x 3), and F(2 x 2, 5 x 5)
+constexpr float G_2x2_3x3[] = {
+   -1,     0,   0,
+ 1./2, -1./2, 1./2,
+ 1./2,  1./2, 1./2,
+    0,     0,    1
+};
+
+constexpr float GT_2x2_3x3[] = {
+   -1,  1./2, 1./2, 0,
+    0, -1./2, 1./2, 0,
+    0,  1./2, 1./2, 1
+};
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Hsiangkai wrote:

Can you elaborate it a bit more? I am not sure what the idea is here. Thank you.

https://github.com/llvm/llvm-project/pull/96183