[llvm] [LoopInterchange] Motivating example for interchange. NFC. (PR #171631)

[Ryotaro Kasuga via llvm-commits]

kasuga-fj wrote:

> Please explain why it is not enough "emitting array size information from frontend" as metadata with "the semantics of the original language, e.g., out-of-bounds array access is UB in C/C++/Fortran".

Consider cases where the result of delinearization is not uniquely determined. For example, in the following case:

```c
int A[16][8];
e = ...; // Maybe negative
for (int i = 0; i < N; i++) {
  // We can infer `N < 8` as `16 <= 2*i` is UB
  use A[2*i][i + e]
}
```

The SCEV for the access `A[2*i][i + e]` will be something like `{(%e + %A),+,17}`. In this case, we cannot determine which of `%A[2 * %i][%i + %e]` or `%A[%i][11 * %i + %e]` is "correct" even though we know the size of the array `A`. So we cannot infer `%N < 8`.

Another example is:

```c
int A[16][4];
for (int i = 0; i < N; i++)
  if (i % 4 == 0)
    use A[i / 4][0];
```

This can be lowered to the following LLVM:

```llvm
loop.header:
  %i = ...
  %rem = and i32 %i, 3
  %cond = icmp eq i32 %rem, 0
  br i1 %cond, label %if.then, ...

if.then:
  %gep = getelementptr i32, ptr %A, i32 %i
  ...
```

In this case, the SCEV for `%gep` will be something like `{%A,+,1}`. So delinearization will yield `%A[0][%i]`, but `%i < 4` doesn't hold.

Even if we somehow know the size of the array, I don't think we can unconditionally justify the delinearization result.

https://github.com/llvm/llvm-project/pull/171631