[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.
----------------
Meinersbur wrote:

> If f(a, b) is true, then f(b, a) is false (or nullopt).

The mathematical terms do not match what you want to say.

1. `isProfitable` requires the inner loop to be the first argument, the second is the outer loop. If `a` is the outer loops, then `isProfitable(b,a)` is undefined. 

2. In order for $f$ to be a function, all inputs must be in its arguments, namly the LLVM-IR, for $f_R(a,b)$. After interchange having been applied, `R` has changed. You get a new function `f_{R'})(a,b)`. Even if the a (and b) are considered "equal" in some some sense, the underlying LLVM-IR has changed, and with it the function result. One could say make relationship claims between `f_R` and `f_{R'}`, but its not asymmetry or transitivity, sine those are about a single relation.



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