[llvm-dev] Improving SCEV's behavior around IR level no-wrap flags

[Hal Finkel via llvm-dev]

----- Original Message -----
> From: "Sanjoy Das" <sanjoy at playingwithpointers.com>
> To: "llvm-dev" <llvm-dev at lists.llvm.org>, "Andrew Trick" <atrick at apple.com>, "Dan Gohman" <dan433584 at gmail.com>, "Hal
> Finkel" <hfinkel at anl.gov>, "Chandler Carruth" <chandlerc at gmail.com>, "David Majnemer" <david.majnemer at gmail.com>,
> "Sebastian Pop" <sebpop at gmail.com>
> Sent: Friday, September 23, 2016 4:09:19 AM
> Subject: Improving SCEV's behavior around IR level no-wrap flags
> 
> Hi all,
> 
> This is about a project I've been prototyping on-and-off for a while
> that has finally reached a point where I can claim it to be
> "potentially viable".  I'd like to gather some input from the
> community before moving too far ahead.
> 
> 
> # The problem
> 
> There is a representation issue within SCEV that prevents it from
> fully using information from nsw/nuw flags present in the IR.  This
> isn't just a theoretical issue, e.g. today LLVM won't unroll this
> loop:
> 
> void f(int x, long* arr) {
>   for (int i = x + 1; i < x + 3; i++)
>     arr[i] = 40;
> }
> 
> since SCEV is unable to exploit the no-overflow on x+1 and x+3 to
> prove that the loop only runs twice.
> 
> The fundamental problem here is that SCEV expressions are unique'd
> but
> the nsw/nuw flags on SCEV expressions are not part of the key they're
> unique'd by.  Instead, nsw/nuw flags on SCEV expressions are
> expressed
> by mutating the SCEV expressions in place.

My understanding is that there were two problems; this is one of them. The second problem is that the SCEV expressions were meant to be context insensitive so that the expressions could be compared, and expanded, without worrying about potential control dependencies on the wrapping flags.

An attempt at an example...

for (int i = 0; i < n; ++i)
for (int j = 0; j < m + q; ++j) {
  array[j][i] = i + j;
}

The fact that (m+q) does not wrap may have a control dependency on n > 0. If we want, for example, to perform loop interchange, we need to drop the nsw on the (m+q) when we materialize the trip-count expression outside of the input's outer loop. Maybe we can just handle this issue in the expander, but I suspect we need to be careful in other contexts as well, for example, if we have:

for (int i = 0; i < n + q; ++i)
for (int j = 0; j < m + q; ++j) {
  array[j][i] = i + j;
}

and I want to construct a comparison between (n+q) < (m+q); I need to be careful about just using the nsw on (n+q) and (m+q) to simplify this to be n < m because the nsw on (m+q) is really only dependable if n + q > 0.

 -Hal

> 
> This means "add %x, 1" and "add nsw %x, 1" both map to the _same_
> SCEV
> expression (that is, literally the same SCEV* object), and we can't
> mutate the common SCEV expression to flag it as nsw since that will
> incorrectly denote "add %x, 1" as nsw too.
> 
> In general, this means SCEV has to be very conservative about marking
> SCEV expressions as no-wrap.  In some cases (e.g. the loop above),
> this ends up being excessively conservative.
> 
> One path forward is to have SCEV try to prove that if a certain
> operation produces poison, the program definitely has undefined
> behavior.  This can let us mutate the corresponding SCEV objects to
> pull the "nsw"-ness into SCEV.  For instance, if we have
> 
>   %x = load ...
>   %t = add i32 nsw %x, 1
>   %addr = gep(%array, %t)
>   store i32 0, %addr
>   %t2 = add i32 %x, 1
> 
> then transferring NSW to getSCEV(%t) is okay, since even though %t2
> (which will be mapped to the same SCEV expression as %t) does not
> have
> "nsw" on the instruction, we know adding 1 to %x cannot overflow
> since
> the program would have UB otherwise.
> 
> Bjarke Roune has implemented some of this. However, this is difficult
> to do for cases like the x+1 .. x+3 loop above without running a
> control flow analysis over the entire function.  And this approach
> does not work in the presence of function calls or general control
> flow, like
> 
>   %x = load ...
>   %t = add i32 nsw %x, 1
>   call void @f()
>   %addr = gep(%array, %t)
>   store i32 0, %addr
> 
> or
> 
>   %x = load ...
>   %t = add i32 nsw %x, 1
>   if (<condition>)
>     return;
>   %addr = gep(%array, %t)
>   store i32 0, %addr
> 
> since unless the side-effecting use of %t (the store) "strongly"[1]
> post dominates the def of %x, there is no guaranteed undefined
> behavior on a poisonous %t.  Things are even more complex if %x is
> not
> a load, but an expression SCEV an look through, like an add or a
> shift
> by a constant.
> 
> *I think the current representation of nsw/nuw in SCEV expressions is
> not congruent with LLVM's specification of poison values, and that is
> blocking us from exploiting poison values as intended by LLVM's
> design.*
> 
> 
> 
> # The proposed solution
> 
> Since poison values are, well, _values_, I propose we model them as
> data within SCEV.  We treat nsw/nuw flags as "operands" since they
> contribute to the result of an SCEV expression just like normal
> inputs
> to the expression.
> 
> This means we'd treat "add %x, %y" as a different SCEV expression
> than
> "add nsw %x, %y", since the latter sometimes produces poison while
> the
> former doesn't.  The latter would be known to not overflow, and SCEV
> would use that fact in the usual ways.
> 
> With this change SCEV expressions will be pointer equal less often,
> and while relying on pointer equality for value equality will be
> correct, it will be somewhat pessimistic; and we'll have to implement
> and use some form of structural equality.
> 
> In other words, some places that do
> 
>   SCEV *X = ...
>   SCEV *Y = ...
>   if (X == Y)
>     ...
> 
> will have to be changed to do
> 
>   SCEV *X = ...
>   SCEV *Y = ...
>   if (X->equals(Y))
>     ...
> 
> This has potential for compile-time regressions.  Hopefully they'll
> all be addressable.
> 
> There are cases in which SCEV (via trip count analysis, say) can
> _prove_ that a certain expression does not overflow.  In those cases
> we will mutate the SCEV expression to indicate no-wrap; since the
> no-wrap flag is just a "cache" of a proof based on the structure of
> the SCEV expression, and _does_ apply to all SCEV expressions with
> the
> same shapes.
> 
> Concretely, we'll endow relevant SCEV expression types with two sets
> distinct of flags:
> 
>  - AxiomaticFlags: These flags follow from nsw/nuw annotations in the
>    IR.  These will be part of the key the SCEV expression is unique'd
>    on.
>  - ComputedFlags: These flags are derived from the structure of the
>    SCEV expression, and they're *not* a part of the key the SCEV
>    expression is unique'd on.
> 
> For the purposes of consumption, there will be no difference between
> AxiomaticFlags and ComputedFlags.  Consumers will get a union of the
> two when they ask for the set of flags that apply to a specific SCEV
> expression.
> 
> ComputedFlags will, in general, depend on AxiomaticFlags.  For
> instance if AxiomaticFlags is "nsw" for, say, {1,+,1}, we can add
> "nuw" to its ComputedFlags.  There is no need to further distinguish
> "{1,+,1}-axiomatic<nsw>" on the computed<nuw> dimension since
> "{1,+,1}-axiomatic<nsw>" will always be computed<nuw>.
> 
> 
> 
> 
> What do you think?  Does the overall picture here make sense?
> 
> Alternate solutions are also more than welcome (especially if they're
> easier to implement!).
> 
> Thanks,
> -- Sanjoy
> 
> [1]: That is, it the store is guaranteed to execute once the load has
>   been issued.
> 

-- 
Hal Finkel
Lead, Compiler Technology and Programming Languages
Leadership Computing Facility
Argonne National Laboratory