[llvm] [LoopInterchange] Improve profitability check for vectorization (PR #133672)

[Michael Kruse via llvm-commits]

================
@@ -1197,27 +1209,57 @@ LoopInterchangeProfitability::isProfitablePerInstrOrderCost() {
   return std::nullopt;
 }
 
+static char flipDirection(char Dir) {
+  switch (Dir) {
+  case '<':
+    return '>';
+  case '>':
+    return '<';
+  case '=':
+  case 'I':
+  case '*':
+    return Dir;
+  default:
+    llvm_unreachable("Unknown direction");
+  }
+}
+
 /// Return true if we can vectorize the loop specified by \p LoopId.
-static bool canVectorize(const CharMatrix &DepMatrix, unsigned LoopId) {
+static bool canVectorize(const CharMatrix &DepMatrix,
+                         const BitVector &IsNegatedVec, unsigned LoopId) {
+  // The loop can be vectorized if there are no negative dependencies. Consider
+  // the dependency of `j` in the following example.
+  //
+  //   Positive: ... = A[i][j]       Negative: ... = A[i][j-1]
+  //             A[i][j-1] = ...               A[i][j] = ...
----------------
Meinersbur wrote:

> (This is probably off-topic, but seeing this made me realize that I was almost confusing the "lexicographical order" in the context of direction vectors with the "lexical forward/backward" in LAA.)

They are related: 
 * [lexical](https://en.wikipedia.org/wiki/Lexical_analysis) (in opposition to [semantics](https://en.wikipedia.org/wiki/Semantic_analysis_(computational))): Order within a text (not well established, confusingly also used as synonym of lexicographic)
 * [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order): Order within a [dictionary](https://en.wikipedia.org/wiki/Lexicon)

https://github.com/llvm/llvm-project/pull/133672