[llvm] [LoopInterchange] Stop performing unprofitable interchange (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:

I think the asymmetry is necessary.

The `isProfitable` returns `bool`, but the profitability check is actually `std::optional<bool>`, which is expressed by `ShouldInterchange`. This means that the cost-model has three types of results: "should interchange them", "should NOT interchange them", and "don't know". The `nullopt` is squashed into `false`, so `not isProfitable(a, b)` could mean either "should NOT" or "don't know".

To answer your question, there are cases where both `isProfitable(a, b)` and `isProfitable(b, a)` become false. Asymmetry doesn't say anything about this case, it requires that they cannot both be true. In this case cost-model may be saying "I don't know both", or "I don't know one, but we should not perform the other". Also, I think we should design the cost-model so that it never says both are profitable, and that the asymmetry says. At least as far as we use the bubble sort fashion algorithm, it can cause the same pair of loops to be interchanged more than twice.

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