Initial implementation had too weak requirements to positive/negative
range crossings. Not crossing zero with nuw is not enough for two reasons:
- If ArLHS has negative step, it may turn from positive to negative
without crossing 0 boundary from left to right (and crossing right to
left doesn't count for unsigned);
- If ArLHS crosses SINT_MAX boundary, it still turns from positive to
negative;
In fact we require that ArLHS always stays non-negative or negative,
which an be enforced by the following set of preconditions:
- both nuw and nsw;
- positive step (looks liftable);
Because of positive step, boundary crossing is only possible from left
part to the right part. And because of no-wrap flags, it is guaranteed
to never happen.
Contextual knowledge may be used to prove invariance of some conditions.
For example, in this case:
```
; %len >= 0
guard(%iv = {start,+,1}<nuw> <s %len)
guard(%iv = {start,+,1}<nuw> <u %len)
```
the 2nd check always fails if `start` is negative and always passes otherwise.
It looks like there are more opportunities of this kind that are still to be
implemented in the future.
Differential Revision: https://reviews.llvm.org/D129753
Reviewed By: apilipenko
This patch teaches SCEV two implication rules:
x <u y && y >=s 0 --> x <s y,
x <s y && y <s 0 --> x <u y.
And all equivalents with signs/parts swapped.
Differential Revision: https://reviews.llvm.org/D110517
Reviewed By: nikic
