Scalar Evolution Expressions Involving Sibling Loops

Forwarding to the dev list, in case others ran into similar issues and/or have input on this topic.

Bardia Mahjour

----- Forwarded by Bardia Mahjour/Toronto/IBM on 2020/03/30 02:25 PM -----

Forwarding to the dev list, in case others ran into similar issues and/or have input on this topic.

Bardia Mahjour

----- Forwarded by Bardia Mahjour/Toronto/IBMon 2020/03/30 02:25 PM-----

From: Bardia Mahjour/Toronto/IBM
To: listmail@philipreames.com
Cc: "Michael Kruse" <llvm@meinersbur.de>
Date: 2020/03/26 11:47 AM
Subject: Scalar Evolution Expressions Involving Sibling Loops

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Hi Philip,

I hope you are doing well.

We've recently run into an issue with SCEV in the context of dependence analysis, and would like your opinion on it. Background discussion can be found here https://reviews.llvm.org/D75628#inline-689527.

Basically in this case, the dependence equation requires us to symbolically create an expression involving two or more recurrences that recur with non-dominating loops (sibling loops).

I'm not following your example. If you have two sibling loops with the same parent, one will frequently, but not always dominate the other. Can you give a specific example of when forming a recurrence between two siblings (without one dominating the other), is useful?

Currently creating such a SCEV expression trips asserts in `CompareSCEVComplexity()` and `isKnownViaInduction()` saying that a given SCEV expression cannot be composed of recurrences that have no dominance relationship between them.

Michael tried explaining to me why there is this restriction about dominance, and I'm beginning to understand why such restriction may be necessary when evaluating or expanding SCEV expressions in outer scopes (eg. `getSCEVAtScope(nullptr)`) but I still don't understand why this restriction is imposed at construction. Shouldn't this restriction be asserted on when calling getSCEVAtScope instead of when creating AddRecs, given that simplification steps may remove identical terms involving non-dominating loops?

Well, SCEV construction is generally done to parallel IR. SSA requires dominance, so having the SCEV operands require dominance would seem like a reasonable thing. If you want to change this, you'll need to motivate the change. (i.e. see above question)

> I’m not following your example. If you have two sibling loops with the same parent, one will frequently, but not always dominate the other. Can you give a specific example of when forming a recurrence between two siblings (without one dominating the other), is useful?

The situation can happen with guarded loops or with a user guard like below:

if (c) {
for (i = 0; i < n; i++)

}
for (j = 0; j < n; j++)

The specific example that we ran into is described in https://reviews.llvm.org/D75628. Basically we have two triangular loops that are siblings and we’d like to run Banerjee MIV tests on the memory accesses in those loops. The loop looks like:

void foo(int *restrict A, int n1, int n2, int n3) {
for (int i1 = 0; i1 < n1; i1++) {
for (int i2 = 2; i2 < n2; i2++) {
for (int i3 = i2 + 1; i3 < n3; i3++) {
A[i2 + i3*n2] = 11;
}
}
for (int i4 = 2; i4 < n3; i4++) {
for (int i5 = 1; i5 < i4 - 1; i5++) {
A[i5] = 22;
}
}
}
}

To check the bounds of the dependence function we need to create a symbolic expression that involves AddRecs for i2 and i4.

Bardia Mahjour

Inactive hide details for Philip Reames ---2020/03/30 02:50:45 PM---On 3/30/20 11:27 AM, Bardia Mahjour via llvm-dev wrote: >Philip Reames —2020/03/30 02:50:45 PM—On 3/30/20 11:27 AM, Bardia Mahjour via llvm-dev wrote: >

Hi Bardia,

I am encountering a similar problem and totally agree that getAddExpr shouldn’t generate any assertion error or at least provide condition check. Even if this is something to avoid, would it be better to return nullptr instead of assertion error?

Thanks,

Jimmy

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Hi Jimmy,

It’s good to know that the problem is not specific to the case I ran into. May be you can provide your example as well, since Philip seems to be interested in some specific examples. If the assertion in getAddrExpr is deemed necessary, then I think a condition check would be the next best solution as it helps client code guard against such cases and make alternative arrangements to avoid an assertion or miscompile.

Bardia Mahjour
Compiler Optimizations
IBM Toronto Software Lab

graycol.gifJimmy Zhongduo Lin —2020/04/16 04:34:24 PM—Hi Bardia, I am encountering a similar problem and totally agree that getAddExpr shouldn’t generate

Hi Bardia,

This is actually a long known problem: http://lists.llvm.org/pipermail/llvm-bugs/2017-July/056757.html

As shown above, the problem gets triggered easily with scev-aa since it will compare two SCEVs from anywhere in the code, including your case of course. I believe the real problem is how to solve it properly. In the long run, checking satisfiesTotalOrder is too costly as it is duplicating part of the work in getAddExpr, but I agree it is way better than assertion error. Maybe SCEV_Unknown or nullptr can be used too.

Thanks,

Jimmy

graycol.gif

Thanks for sharing the known problem.

I think to solve the problem properly, we need to fully understand why that assumption about dominance is there and the implications of removing it.

It would be good if you could be more specific about your idea of nullptr or SCEV_unknown (eg which function would return those values and when), but returning nullptr from getAddExpr or getSCEVAtScope may be problematic since they currently return valid pointers all the time and changing that would be error prone and would increase code complexity. Returning SCEV_Unknown from getAddExpr would seem plausible except that it would not allow for expression simplifications where recurrences over non-dominating loops can get canceled out. Having said that it may still be a reasonable middle-ground solution.

Philip, do you have any thoughts on that?

Bardia Mahjour

graycol.gifJimmy Zhongduo Lin —2020/04/16 08:39:34 PM—Hi Bardia, This is actually a long known problem: INVALID URI REMOVED

Hi Bardia,

I agree that we need to understand the consequence of that. I thought SCEV is just folding operations to a tree-like structure, so I am surprised it couldn’t handle two AddRec of didfferent loops. To support that, it might break a lot of codes with that assumption. So we will likely need to review all the public interfaces to make sure it is safe.

So I am just talking about middle-ground solution. If we have GroupByComplexity returning bool to signal if the condition is satisfied, which will require the compare function to return certain flag too, we will avoid introducing a condition check and have the callers return SCEV_unknown etc.

Thanks,

Jimmy

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My interpretation of ScalarEvolution is that an AddRecExpr is only
intended in a context within a loop, since it references the loop
induction variable of which there is none outside the loop.
Outside the loop, one has to use the exit value obtainable by
getSCEVAtScope that removes the AddRecExpr not nested inside the
parameter.
With this interpretation, two AddRecExpr with two sibling loop would
always be invalid since one can never be in both loop at the same
time.

Michael