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Unverified Commit 0f3c9b54 authored by Roman Lebedev's avatar Roman Lebedev
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[SCEV] SCEVExpander::isHighCostExpansionHelper(): cost-model polynomial recurrence

Summary:
So, i wouldn't call this *obviously* correct,
but i think i got it right this time :)

Roughly, we have
```
Op0*x^0 + Op1*x^1 + Op2*x^2 ...
```
where `Op_{n} * x^{n}` is called term, and `n` the degree of term.

Due to the way they are stored internally in `SCEVAddRecExpr`,
i believe we can have `Op_{n}` to be `0`, so we should not charge for those.

I think it is most straight-forward to count the cost in 4 steps:
1. First, count it the same way we counted `scAddExpr`, but be sure to skip terms with zero constants.
   Much like with `add` expr we will have one less addition than number of terms.
2. Each non-constant term (term degree >= 1) requires a multiplication between the `Op_{n}` and `x^{n}`.
   But again, only charge for it if it is required - `Op_{n}` must not be 0 (no term) or 1 (no multiplication needed),
   and obviously don't charge constant terms (`x^0 == 1`).
3. We must charge for all the `x^0`..`x^{poly_degree}` themselves.
   Since `x^{poly_degree}` is `x * x * ...  * x`, i.e. `poly_degree` `x`'es multiplied,
   for final `poly_degree` term we again require `poly_degree-1` multiplications.
   Note that all the `x^{0}`..`x^{poly_degree-1}` will be computed for the free along the way there.
4. And finally, the operands themselves.

Here, much like with add/mul exprs, we really don't look for preexisting instructions..

Reviewers: reames, mkazantsev, wmi, sanjoy

Reviewed By: mkazantsev

Subscribers: hiraditya, javed.absar, llvm-commits

Tags: #llvm

Differential Revision: https://reviews.llvm.org/D73741
parent 756af2f8
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