flopscope.accounting.poly_cost

Cost for poly (1-D build-from-roots): (3*n^2 + n) // 2 FLOPs.

flops.poly builds the characteristic polynomial by iterating p = convolve(p, [1, -r_i]) for each root r_i. At step i (0-indexed), the current polynomial has length i + 1, so convolving with the length-2 [1, -r_i] kernel costs polymul_cost(i+1, 2) = 2*(i+1)*2 - (i+1) - 2 = (3*(i+1) - 2) FLOPs under the FMA=2 convention.

Summing over i = 0 .. n-1:

sum_{i=0}^{n-1} (3*(i+1) - 2)
= 3 * n*(n+1)/2 - 2*n
= (3*n^2 + 3*n - 4*n) / 2
= (3*n^2 - n) / 2

However polymul_cost is clamped to 1 at minimum, and the last step (full n+1 length) adds one element. Accounting for the exact closed form including the length-1 seed:

(3*n^2 + n) // 2

This replaces the prior 2*n^2 over-approximation. The 2-D branch (characteristic polynomial via eigvals) is unchanged. Audit-completion Task 4 (2026-06-12).

n:int

Number of columns in the input matrix.

:int

Weighted public cost estimate, floored to match runtime accounting.

This helper multiplies the analytical FLOP count by the active weight from flopscope._weights and then applies int(...) so public estimates match budget deductions.