[LoopInterchange] Exit early in certain cases in legality check (NFC)

The legality check in LoopInterchange allows two loops to be exchanged
if all direction vectors are lexicographically positive (or zero) for
both before and after the swap. The current implementation performs this
routine naively.  However, if a direction vector is lexicographically
positive due to an element corresponding to a loop that is outside the
given two loops (i.e., if there is an element `<` before the loops we
are trying to interchange), then obviously it is also positive after
exchanging them. For example, for a direction vector `[< < >]`, swapping
the last two elements doesn't make it lexicographically negative because
the first element is `<`.
This patch adds an early exit logic for such cases. Note that this is
only a small improvement on its own, but it's necessary to relax the
legality check I'm working on.

Author: kasuga-fj

llvm/lib/Transforms/Scalar/LoopInterchange.cpp

@@ -231,18 +231,22 @@ static void interChangeDependencies(CharMatrix &DepMatrix, unsigned FromIndx,
     std::swap(DepMatrix[I][ToIndx], DepMatrix[I][FromIndx]);
 }
 
-// After interchanging, check if the direction vector is valid.
+// Check if a direction vector is lexicographically positive. Return true if it
+// is positive, nullopt if it is "zero", othrewise false.
 // [Theorem] A permutation of the loops in a perfect nest is legal if and only
 // if the direction matrix, after the same permutation is applied to its
 // columns, has no ">" direction as the leftmost non-"=" direction in any row.
-static bool isLexicographicallyPositive(std::vector<char> &DV) {
-  for (unsigned char Direction : DV) {
+static std::optional<bool> isLexicographicallyPositive(std::vector<char> &DV,
+                                                       unsigned Begin,
+                                                       unsigned End) {
+  ArrayRef<char> DVRef(DV);
+  for (unsigned char Direction : DVRef.slice(Begin, End - Begin)) {
     if (Direction == '<')
       return true;
     if (Direction == '>' || Direction == '*')
       return false;
   }
-  return true;
+  return std::nullopt;
 }
 
 // Checks if it is legal to interchange 2 loops.
@@ -256,10 +260,19 @@ static bool isLegalToInterChangeLoops(CharMatrix &DepMatrix,
     // Create temporary DepVector check its lexicographical order
     // before and after swapping OuterLoop vs InnerLoop
     Cur = DepMatrix[Row];
-    if (!isLexicographicallyPositive(Cur))
+
+    // If the direction vector is lexicographically positive due to an element
+    // to the left of OuterLoopId, it is still positive after exchanging the two
+    // loops. In such a case we can skip the subsequent check.
+    if (isLexicographicallyPositive(Cur, 0, OuterLoopId) == true)
+      continue;
+
+    // Check if the direction vector is lexicographically positive (or zero)
+    // for both before/after exchanged.
+    if (isLexicographicallyPositive(Cur, 0, Cur.size()) == false)
       return false;
     std::swap(Cur[InnerLoopId], Cur[OuterLoopId]);
-    if (!isLexicographicallyPositive(Cur))
+    if (isLexicographicallyPositive(Cur, 0, Cur.size()) == false)
       return false;
   }
   return true;