[llvm] [DependenceAnalysis] Extending SIV to handle fusable loops (PR #128782)

[Ryotaro Kasuga via llvm-commits]

kasuga-fj wrote:

> The IR provided in the link appears to be incorrect. Specifically, k.0 should be replaced with k.1 in line 31. With this change, the current DA can already determine that there is no dependency by using the RDIV test. Therefore, my patch does not change the result in this case.

You are completely correct. I was stupid, sorry about that...
I now understand that the RDIV test already handles loops whose nesting levels are greater than CommonLevels. So, while I still suspect it might be incorrect in some situations, that's not relevant to your patch.
On the other hand, it turns out there are indeed cases where your patch changes the result. Consider the following case:

```c
for (int i = 0; i < 10; i++) {
  for (int j = 1; j < 11; j++)
    A[i][j+1][j-1] = 42;
  for (int j = 0; j < 10; j++)
    A[i][j][j] = 43;
}
```

The current DA produces the following result (godbolt: https://godbolt.org/z/5d6xej3bv):

```
Printing analysis 'Dependence Analysis' for function 'f':
Src:  store i32 42, ptr %idx.0, align 4 --> Dst:  store i32 42, ptr %idx.0, align 4
  da analyze - none!
Src:  store i32 42, ptr %idx.0, align 4 --> Dst:  store i32 43, ptr %idx.1, align 4
  da analyze - output [0|<]!
Src:  store i32 43, ptr %idx.1, align 4 --> Dst:  store i32 43, ptr %idx.1, align 4
  da analyze - none!
```

I also ran this locally with your patch, which produced:

```
Printing analysis 'Dependence Analysis' for function 'f':
Src:  store i32 42, ptr %idx.0, align 4 --> Dst:  store i32 42, ptr %idx.0, align 4
  da analyze - none!
Src:  store i32 42, ptr %idx.0, align 4 --> Dst:  store i32 43, ptr %idx.1, align 4
  da analyze - none!
Src:  store i32 43, ptr %idx.1, align 4 --> Dst:  store i32 43, ptr %idx.1, align 4
  da analyze - none!
```

This time it should be correct, and I'm still not sure whether using this result is sound for callers other than LoopFuse.

https://github.com/llvm/llvm-project/pull/128782