[LLVMdev] Inferring dependencies in phi instructions

[Evgeny Astigeevich]

Hi Anirudh,

I agree with Daniel. You can use the post-dominator tree.
In LLVM you can get it as follows:

getAnalysis<PostDominatorTree>()

Of course you must specify it in dependencies of your pass:

  void getAnalysisUsage(AnalysisUsage &AU) const override {
    ... // some code
    AU.addRequired<PostDominatorTree>();
   ... // some other code
  }

INITIALIZE_PASS_DEPENDENCY(PostDominatorTree)

To find all control dependencies the following simple algorithm can be used:

1. Consider all edges <X, Y> such that Y does not post-dominate X (X has more than one successor).
2. Traverse the post-dominator tree bottom-up:

B = Y
while (B != parent of X in PDT)
      B is control dependent on X
      B = parent of B in PDT

You can use the following algorithm to find all conditions a phi-function depends on:
1. For each incoming basic block, get all blocks it is control dependent on. Add the incoming block to the set if the parent of the phi-function is control dependent on it.
2. For each found block, get its terminator and find a condition the terminator uses. 

Let's consider your example:

CFG:

          ---- Entry----
         |                      |
         v                      v
         2                      3
         |                      |
          --->  4  <----

PDT:

            ----4-----
          |       |     |
          v       v     v
          2       3    Entry

Edges of interest in CFG: <Entry, 2>, <Entry, 3> (<2, 4> and <3, 4> are not because 4 post-dominates 2 and 3.)
The parent of Entry in PDT is 4.
We have:
  - 2 is control dependent on Entry
  - 3 is control dependent on Entry
  - 4 is not control dependent on any basic block

The phi-function in 4 has incoming blocks: 2 and 3. 
2 and 3 are control dependent on Entry. The terminator of entry uses %1. So the phi-function depends on %1. No other conditions are added as 2 and 3 have unconditional jumps.

Hope this gives you more understanding of the topic.

Kind regards,
Evgeny Astigeevich

 -----Original Message-----
From: Anirudh Sivaraman [mailto:sk.anirudh at gmail.com] 
Sent: 29 June 2015 18:58
To: Daniel Berlin
Cc: Evgeny Astigeevich; LLVM Developers Mailing List
Subject: Re: [LLVMdev] Inferring dependencies in phi instructions

On Mon, Jun 29, 2015 at 10:22 AM, Daniel Berlin <dberlin at dberlin.org> wrote:
> On Mon, Jun 29, 2015 at 10:16 AM, Evgeny Astigeevich 
> <Evgeny.Astigeevich at arm.com> wrote:
>> Hi Anirudh,
>>
>>
>>
>> I hope these lecture slides about SSA and the dominance frontier will 
>> help you with SSA and control flow analysis:
>>
>>
>>
>> http://www.seas.harvard.edu/courses/cs252/2011sp/slides/Lec04-SSA.pdf
>>
>>
>>
>> Unfortunately  a use of DominanceFrontierBase is deprecated in LLVM.
>>
>>
>>
>>>Thank you for your response. Going by your definition, x is control  
>>>dependent on y.
>>
>>> To extract this control dependency, do I need to maintain path 
>>> conditions for each basic block or can I do something simpler?
>>
>>>Also, I feel like this should be a recurring problem. Could you point 
>>>me to  any code example that identifies all dependencies (control and 
>>>data) for phi  instructions?
>>
>> You won’t have any of this problems if you build dominance frontiers 
>> in the reverse CFG (ReverseDominanceFrontiers).
>>
>
> You actually don't even need reverse dominance frontiers, you can do 
> it with a post-dominator tree.

Thanks for all these responses; they clarify quite a bit. I am still confused though. I don't see how a ReverseDominanceFrontier (or any other method to compute the CDG) helps me solve my problem. Here's a minimal working example:

define i32 @foo(i32 %a, i32 %b) #0 {
  %1 = icmp sgt i32 %a, %b
  br i1 %1, label %2, label %3

; <label>:2                                       ; preds = %0
  br label %4

; <label>:3                                       ; preds = %0
  br label %4

; <label>:4                                       ; preds = %3, %2
  %r.0 = phi i32 [ %a, %2 ], [ %b, %3 ]
  ret i32 %r.0
}

Here the basic block with label 4 isn't control dependent on basic blocks 0, 2, or 3 by the definition of control dependence (from Appel's book: "We say that a node y is control-dependent on x if from x we can branch to u or v; from u there is a path to exit that avoids y, and from v every path to exit hits y").

Because control _always_ flows from any of basic blocks 0, 2, or 3 to 4, 4 isn't control dependent on either of 0, 2, or 3. This in turn, means that the phi node within basic block 4 isn't control dependent on basic blocks 0, 2, or 3.

In this particular case, I know that using the simplifycfg pass solves my problem by converting phi nodes into selects. I would like to know how to handle the general case.

Thanks in advance for any advice you may have.
Anirudh