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

[Andrew Trick]

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

> 
> 
> Thanks for your comments!
> 
> Mehdi
> 
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