Add balanced polynomial product trees - #9608
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August 25, 2026 04:05
The schoolbook path has quadratic coefficient work. Balanced multiplication and specialized squaring satisfy the three-recursion Karatsuba recurrence; the fixed 64-block skew dispatcher preserves that asymptotic bound.
Cost model: long division is quadratic because each leading-coefficient elimination updates a linear suffix. Cold Newton division costs O(M(n)): reciprocal doubling is a geometric series and the quotient/remainder use a constant number of clipped products.
# Conflicts: # .github/workflows/ci.yml # scripts/bench/proof_only_runtime_exemptions.json
# Conflicts: # .github/workflows/ci.yml # scripts/bench/proof_only_runtime_exemptions.json
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Adds the first product-tree layer for
hex-poly-fast:MulPlanO(M(n) log n)product-tree benchmark registrationThis also fixes a real inconsistency in the merged EvalPlan SPEC: the published signature accepts arbitrarily large polynomials but a finite point-only plan cannot cache unbounded root reciprocal precision. The corrected contract uses the cached remainder tree for
f.size <= plan.sizeand a total direct-evaluation fallback above that bound.Depends on #9599. This targets upstream
mainper repository convention and includes the stacked multiplication/division base until that PR merges.