[llvm] [LoopInterchange] Prevent from undoing its own transformation (PR #127473)

[Ryotaro Kasuga via llvm-commits]

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@@ -1184,11 +1218,27 @@ std::optional<bool> LoopInterchangeProfitability::isProfitableForVectorization(
   return std::optional<bool>(!DepMatrix.empty());
 }
 
-bool LoopInterchangeProfitability::isProfitable(
-    const Loop *InnerLoop, const Loop *OuterLoop, unsigned InnerLoopId,
-    unsigned OuterLoopId, CharMatrix &DepMatrix,
-    const DenseMap<const Loop *, unsigned> &CostMap,
-    std::unique_ptr<CacheCost> &CC) {
+// The bubble-sort fashion algorithm is adopted to sort the loop nest, so the
+// comparison function should ideally induce a strict weak ordering required by
+// some standard C++ libraries. In particular, isProfitable should hold the
+// following properties.
+//
+// Asymmetry: If isProfitable(a, b) is true then isProfitable(b, a) is false.
+// Transitivity: If both isProfitable(a, b) and isProfitable(b, c) is true then
+// isProfitable(a, c) is true.
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kasuga-fj wrote:

I don't intend to require transitivity for LoopInterchange. I just wrote a property that the comparison function of a comparison sort holds, but that `LoopInterchangeProfitability::isProfitable` does not. But I still think that the transitivity should be satisfied if it is possible, under the assumption that the profitability decisions don't change depending on the current order of the nest. Your case looks to me the case where the profitability changes after interchanging, where in my understanding the profitability decision for b and c doesn't change before and after interchanging a and b.

https://github.com/llvm/llvm-project/pull/127473