[llvm-dev] RFC: (Co-)Convergent functions and uniform function parameters

[Nicolai Hähnle via llvm-dev]

On 25.10.2016 01:17, Mehdi Amini wrote:
>
>> On Oct 24, 2016, at 4:15 PM, Nicolai Hähnle <nhaehnle at gmail.com> wrote:
>>
>> On 25.10.2016 01:11, Nicolai Hähnle wrote:
>>> On 24.10.2016 21:54, Mehdi Amini wrote:
>>>>> On Oct 24, 2016, at 12:38 PM, Nicolai Hähnle via llvm-dev
>>>>> <llvm-dev at lists.llvm.org> wrote:
>>>>> Some brain-storming on an issue with SPMD/SIMT backend support where
>>>>> I think some additional IR attributes would be useful. Sorry for the
>>>>> somewhat long mail; the short version of my current thinking is that
>>>>> I would like to have the following:
>>>>>
>>>>> 1) convergent: a call to a function with this attribute cannot be
>>>>> moved to have additional control dependencies; i.e., moving it from A
>>>>> to B is only possible if B dominates or post-dominates A.
>>>>>
>>>>> 2) co-convergent (divergent? for lack of a better name...): a call to
>>>>> a function with this attribute cannot be moved to have _fewer_
>>>>> control dependencies; i.e., moving it from A to B is only possible if
>>>>> A dominates or post-dominates B.
>>>>>
>>>>> 3) uniform (for function arguments): transformations are not allowed
>>>>> to introduce additional non-uniformity in this argument.
>>>>
>>>> Can you describe it in terms that are non-SPMD/SIMT?
>>>> I.e. I’m not sure that “uniformity” refers to an existing LLVM IR
>>>> concept.
>>>
>>> Yeah, that's actually the key problem I've been struggling with.
>>>
>>> The first example I sent shows the gist of it. It also shows that the
>>> concept can't be expressed in terms of the CFG, which makes this tricky.
>>>
>>> In a way it's the data-flow analog of the convergent attribute: the
>>> argument cannot be changed to have additional dependencies in its
>>> computation. That captures the basic intention, but I'm not completely
>>> sure that it works.
>>
>> One big question is whether there are transformations in LLVM today that replace a value %a with a value %b, where %b "has additional dependencies in its computation". I can't think of anything obvious where that would be the case, but I'm not sure.
>
> What do you mean by “additional dependencies in its computation" here?

Minus phi-nodes, loads, and intrinsic calls, it could be: look at the 
directed graph where %a -> %b if %a is an operand of the instruction 
that defines %b. Take all nodes of that graph that do not have predecessors.

But I fear that this path leads to eternal fuzziness. Let me try a 
completely different approach to define what we need by augmenting the 
semantics of IR with "divergence tokens". In addition to its usual 
value, every IR value carries a "divergence set" of divergence tokens.

The basic rule is: the divergence set of a value is (at least) the union 
of the divergence sets of its operands.

Every function input carries a unique divergence token.

For phi-nodes, the divergence set also includes the branch conditions 
that can affect which predecessor value is taken. (A simpler, more 
conservative rule, would be to add a unique divergence token; this can 
be per-basic block.)

Loads add a unique divergence token. (This is a very conservative rule 
mostly required for per-thread-allocas. It could be relaxed quite a bit 
by treating per-thread-memory like SSA-values augmented with divergence 
sets.)

Atomic operations add a unique divergence token.

Additional target-specific intrinsics may also add a divergence token.

By transitivity, most function calls have to add a unique divergence token.

The first restriction on the transformation of a call to a function with 
'uniform' function argument is then:

1. The corresponding argument of the call can be changed only if the 
change preserves (or shrinks) the divergence set (on top of that, the 
new value obviously has to be equal to the old one in single threaded 
semantics).

With this definition,

def @fn(s0, s1, cond) {
   v0 = texelFetch(s0, ...)
   v1 = texelFetch(s1, ...)
   v = select i1 cond, v0, v1
}

cannot be transformed to

def @fn(s0, s1, cond) {
   s = select i1 cond, s0, s1
   v = texelFetch(s, ...)
}

because s has a larger divergence set.

On the other hand, at least the InstCombine transforms should all be 
safe because they locally transform a DAG of values in a way that can 
only shrink the set of predecessors of the locally transformed region of 
the DAG.

Transforms that modify the CFG could be problematic especially with the 
simpler phi-node-rule, e.g. when a new basic block is created, you end 
up introducing new divergence tokens for "downstream" values. That's 
probably not a problem with the first definition for phi-nodes, though 
I'm not sure.

.....
The above definition still allows the transformation of

   masked &= 1
   if (masked == 1) {
     v1 = texelFetch(array[masked], ...)
   } else {
     v0 = texelFetch(array[masked], ...)
   }
   v = phi(v1, v0)

to

   masked &= 1
   v = texelFetch(array[masked], ...);

which is incorrect. So for a set of divergence tokens D, let's say A 
D-dominates B if the following holds: there exists a way of fixing the 
branching directions of conditional branches whose condition's 
divergence set is disjoint from D, such that A dominates B in the 
resulting CFG. Similarly for D-post-domination.

If D \subset D', then D'-domination implies D-domination.

We can then formulate the second condition as:

2a. A function call with a uniform argument with divergence set D can be 
moved from location A to location B if A D-dominates or D-post-dominates B.

2b. Simpler but more conservatively, just treat the function call as 
co-convergent (i.e., it can only be moved to positions that are 
dominated or post-dominated by its current position in the usual sense.)

.....
The full definition of D-domination is probably too involved to be 
turned into practical algorithms. But with this model of divergence 
sets, it should be possible to think of DivergenceAnalysis as an 
analysis that proves divergence sets of values to be empty (using 
additional target specific information to be less conservative). 
Combined with DivergenceAnalysis, (1)+(2a) still leave room for some 
useful and practical optimizations of functions with uniform arguments 
even across basic blocks.

In practical terms for a first version, the effect of the attribute 
should just be to prevent the two transformations shown above.

Thanks,
Nicolai