[llvm] [LoopInterchange] Stop performing unprofitable interchange (PR #127473)

[Michael Kruse via llvm-commits]

================
@@ -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:

Considering that `interchange(a, b)` is the same as `interchange(b, a)`, the relation whether the two should be exchanged is symmetric, not asymmetric. What you are looking for is "areLoopsInTheRightOrder", independent of what the current order is.

Also consider that `isProfitable(a, b)` and `isProfitable(a, b)` on the interchanged loops are not the same input. The first is a query on
```
for a:
  for b:
```
the second is a query on:
```
for b':
  for a':
```
`a` and `a'`, as well as `b`, `b'` are not the same loops. They look very different to `isProfitablePerLoopCacheAnalysis`, `isProfitablePerInstrOrderCost`, and `isProfitableForVectorization`.

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