[LLVMdev] SCEV implementation and limitations, do we need "pow"?

[Andrew Trick]

On Feb 7, 2014, at 9:51 PM, Mehdi Amini <mehdi.amini at silkan.com> wrote:

> On 2/7/14, 10:24 AM, Andrew Trick wrote:
>> 
>> On Feb 5, 2014, at 12:54 AM, Mehdi Amini <mehdi.amini at silkan.com> wrote:
>> 
>>> Hi,
>>> 
>>> I was looking at some bugs to play with, and I started with http://llvm.org/bugs/show_bug.cgi?id=18606
>>> 
>>> As I commented there, a loop is unrolled and exhibit this pattern:
>>> 
>>>   %mul.1 = mul i32 %mul, %mul
>>>   %mul.2 = mul i32 %mul.1, %mul.1
>>>   ....
>>> 
>>> With an unroll factor of 32, the last multiply has 2^32 terms in its SCEV expression. 
>>> (I mean I expect it would have those terms if I was patient enough to wait for opt to finish :) )
>>> 
>>> So I suppose SCEV is lacking some protection, for instance degrading to "unknow" when an expression is above a given threshold, or stop flattening and keeping only a reference to another SCEV as a term of the expression.
>>> Nick and Chandler also mentioned on IRC that SCEV should be extended with a "pow" operator to tackle such situation and being able to fold multiply-tree.
>>> 
>>> 
>>> While looking at SCEV, another thing is puzzling in the implementation. Focusing on multiply (ScalarEvolution:3730), the SCEV is computed by taking the SCEV of the second operand and then checking if the first one is a multiply, if it is it "recurse" (iteratively) and repeat on this multiply.
>>> Example :
>>> 
>>>    a = b * c;
>>>    d = e * f;
>>>    g = a * d;
>>> 
>>> when computing SCEV(g), (if I got it right)  it is actually computing:
>>> 
>>> SCEV(g) = getMulExpr(b , SCEV(c), SCEV(d))
>>> 
>>> There is a lack of symmetry for which I can't see the rational. I would expect one of these three possibilities:
>>> 
>>> 1) Just using the SCEV of the operands: SCEV(g) = getMulExpr(SCEV(a), SCEV(d));
>>> 
>>> 2) Being "smart" and flatten when operands are multiply, but symmetric : SCEV(g) = getMulExpr(SCEV(b), SCEV(c), SCEV(e), SCEV(f));
>>> 
>>> 3) Being "smart" and flatten when the *SCEV of the operands* are multiply. So instead of tackling recursively the operand it could use the (hopefully already computed) SCEV.
>>> 
>>> Number 3 is my favorite, but it is already implemented in getMulExpr() (line 1963), so I propose to got with Number 1 :)
>> 
>> I haven’t fully processed your suggestions. Hopefully someone else will comment. My initial thought is that we should never flatten an operand if its SCEV is identical to a previous operand.
>> -Andy
> 
> Do you mean that for this sequence:
> 
> a = b * c
> d = b * c
> e = a * d
> 
> you are expecting SCEV(e) to be "a * d" instead of "b * c * b * c" ?
> 
> I ask because I used the term "flatten" earlier to describe the transformation of "(b*c) * (b*c)"  to  "b*c*b*c”.

Yes, that's what I meant. The moment you flatten the same expression on multiple operands it’s exponential, unless we implement pow. I’m not sure if that fits what you suggested above.
-Andy

> 
> Thank,
> 
> -- 
> Mehdi
> 

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