[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
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