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

[Michael Kruse 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.
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Meinersbur wrote:

How do you want to express the "transivity" part? That is, that after a series of swaps you get back to the original order, without directly undoing a previous swap?

There is no need to use math for this, unless you want to get into formal proofs.

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