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

[Mehdi Amini]

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 
> <mailto: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".

Thank,

-- 
Mehdi

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20140207/4bcb513e/attachment.html>