[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.
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kasuga-fj wrote:

You are right, my use of mathematical terms is incorrect. What I want is like

- $f_R(a, b)$ is true then $f_{R'}(b, a)$ is false, where 
    - a is the inner loop and b is the outer one in $R$.
    - $R'$ is what some interchanges are applied to $R$ so that the order of a and b is exchanged. 

I will fix the comment. So, do you think the changes of this patch is correct to accomplish that?

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