[llvm-dev] more reassociation in IR

[Daniel Berlin via llvm-dev]

On Wed, May 9, 2018 at 10:39 AM, Hiroshi Yamauchi <yamauchi at google.com>
wrote:

>
>
> On Tue, May 8, 2018 at 11:15 AM Daniel Berlin <dberlin at dberlin.org> wrote:
>
>>
>>
>> On Tue, May 8, 2018 at 10:38 AM, Hiroshi Yamauchi via llvm-dev <
>> llvm-dev at lists.llvm.org> wrote:
>>
>>> (
>>> ​I came across this issue in the context of
>>>  D46336 <https://reviews.llvm.org/D46336>.
>>> ​ ​
>>> Thanks, Sanjay, for starting this discussion.)
>>>
>>> If
>>> ​we will
>>>  move
>>> ​reassociation,
>>> or keep additional ones
>>> ​,​
>>> out of instcombine,
>>> ​open questions for me would be
>>> ​​:
>>>
>>>
>>> 1. Since -reassociate isn't a fixed point pass,
>>>
>>
>> This is fixable, fwiw, without fixpointing it.
>>
>
> How?
>

Depends on specifically which part you would like to know about ;)


>
>
>>
>>> we might need to repeat "-instcombine -reassociate" multiple times to
>>> ​fold
>>>  down to what we want (relating to my comment here
>>> <https://reviews.llvm.org/D46336#1087082>). I assumed this isn't not
>>> what we want to do
>>> ​? My impression is we don't do a fixed-point with passes?
>>>
>>
>> Well, i mean there is no practical difference between passes that we
>> fixpoint externally and fixpoint internally.
>>
> ​​
> I had the following in mind: Does the pass manager support fixpointing
> externally? Is there any performance difference? Are people okay with that
> in general?
>
> But if there is no practical difference, I don't see any problem with
> that :)
>
>
>>
>>>
>>>
>> 2.
>>> ​Since -reassociate needs to come up with one operand order (at least
>>> currently as the only reassociate pass), would there exist a single,
>>> unique operand order that would enable all reassociative/commutative
>>> foldings that we want?
>>>
>>
>> In what way?
>> Are you asking whether there is a single reassociation order that makes
>> all foldings occur in the same operation or something?
>> I don't feel like i understand what you are asking.
>>
>
> Does this rephrase help: with the motivating examples (like and-of-shifts
> or bit check patterns) from the above differentials in mind, can we come up
> with a single reassociation order that solves all those and all the
> others that may come up in the future? Would we need different reassociation
> orders to fold different patterns?
>

It doesn't quite help.
When stated that generally, there can be no such ordering at all, that's
easy to prove.  It is a statically undecidable problem.

There is however, a different question and answer to a few related problems
that maybe you are really asking?
1. Is there a way to determine and apply the a maximal or nearly-maximal
set of folds/graph transforms that could be applied to a given set of code
in a sane and principled way -> yes

(see, e.g., http://www.cs.cornell.edu/~ross/publications/eqsat/)

2. Is there a way to determine all expressions in the program as it exists
that are equivalent or equivalent under constant time constant
folding/reassociation, in a reasonable time bound -> yes

(not a single easy link, happy to talk about it)

Your original question is basically equivalent to
Is there a way to determine all expressions in the program as it exists
that are equivalent or could be made equivalent through any type of folding
that one can think up?
The answer to that is "no", it's provable that this is not statically
decidable, so the time bound doesn't matter :)

You have to limit the possible folding/evaluation you apply in various ways
to make this decidable, and then further limit it to make the time bound
reasonable.

This all quickly devolves into herbrand equivalence and it's variations.
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