[PATCH] D150425: [ValueTracking] deduce `X * Y != 0` if `LowestKnownBit(X) * LowestKnownBit(Y) != 0`

[Nikita Popov via Phabricator via llvm-commits]

nikic added a comment.

In D150425#4340213 <https://reviews.llvm.org/D150425#4340213>, @goldstein.w.n wrote:

> In D150425#4340211 <https://reviews.llvm.org/D150425#4340211>, @nikic wrote:
>
>> In D150425#4340196 <https://reviews.llvm.org/D150425#4340196>, @goldstein.w.n wrote:
>>
>>> In D150425#4340195 <https://reviews.llvm.org/D150425#4340195>, @nikic wrote:
>>>
>>>> In D150425#4340187 <https://reviews.llvm.org/D150425#4340187>, @goldstein.w.n wrote:
>>>>
>>>>> In D150425#4340180 <https://reviews.llvm.org/D150425#4340180>, @nikic wrote:
>>>>>
>>>>>> I find the formulation here kind of confusing. Wouldn't something like this be more obvious? https://alive2.llvm.org/ce/z/p5wWid
>>>>>
>>>>> That works for the second proof, but not the first. We can't actually compute the LSB. Only the Lowest KnownBit.
>>>>> Truthfully the first formula is enough for everything (as the arbitrary `x_subset` and `y_subset` include the set
>>>>> of an known lowest bit).
>>>>
>>>> Maybe I'm missing something, but can't we implement this as `return XKnown.countMaxTrailingZeros() + YKnown.countMaxTrailingZeros() < BitWidth`?
>>>
>>> We can. Just through LowBit(X) * LowBit(Y) != 0 was clearer. Would you prefer trailing zeros version?
>>
>> Yes, as it is less code and requires less proofs.
>
> Okay.
>
>> I expect you can also drop the separate `KnownBits::mul(XKnown, YKnown).isNonZero()` call and just return this in all cases.
>
> I would prefer not to do that. I _think_ this should cover all cases, but I'm by no means certain there aren't other edge cases. I think its more future-proof to still fallback on `KnownBits::mul`. Since we already have the KnownBits for X/Y, I think the cost is pretty minimal. That okay?

The alive2 proof shows that this is as good as we can do (it's not an implication, it's an equivalence). I think it's valuable to retain that fact.


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