[llvm] [DA] Check monotonicity for subscripts (PR #154527)

[Michael Kruse via llvm-commits]

================
@@ -3308,6 +3308,322 @@ void DependenceInfo::updateDirection(Dependence::DVEntry &Level,
     llvm_unreachable("constraint has unexpected kind");
 }
 
+namespace {
+
+enum class MonotonicityType {
+  MaySignedWrap, ///< The expression contains arithmetic operations that may
+                 ///< cause signed wrap.
+  Constant,      ///< The expression is constant. If a SCEV is classified as
+                 ///< Constant, it also implies that it doesn't contain any
+                 ///< arithmetic operations that may cause signed wrap.
+  Monotonic, ///< The expression is monotonically increasing or decreasing. This
+             ///< is exclusive of Constant. That is, we say an SCEV is Monotonic
+             ///< iff it contains at least one AddRec where its step reccurence
+             ///< value is non-zero.
----------------
Meinersbur wrote:

I think the description should mention it is relative to a specific loop. If it does not contain an SCEVAddRec, it could still contain a SCEVUnkown that is non-invariant in that loop.

It becomes interesting if you have a SCEVAddRec of a nested loop in there. How do you think those should be handled? E.g. the specific loop is counting up but the nested loop is counting down. 
```
for (int i = n; i >= 0; --i) {
  int j = 0;
  for (; j < m; ++j)
    A[i + j] = ...;
  B[i + j] = ...;
}
```
Is the SCEV for `A[i + j]` monotonic? I think it for `B[i + j]` because at that point `j==m` is invariant, so the min is `0 + m` and the max is `n + m`.

https://github.com/llvm/llvm-project/pull/154527