feat(poly-fast): add certified multipoint evaluation - #9610
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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.
The cached point/remainder tree evaluates bounded inputs in O(M(n) log n); the explicit Horner comparator performs Θ(n²) coefficient operations.
# 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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Summary
EvalPlanwith the original points, balancedProductTree, and cached reciprocal division plansDependency
This is stacked on #9608. The PR targets upstream
main; merge #9608 first, then this branch can be rebased or merged normally.Specification correction
The merged SPEC claimed a fixed finite
EvalPlancould cache the reciprocal precision needed for arbitrarily large input polynomials. That is impossible: cached reciprocal precision is finite. The implementation uses the cachedO(M(n) log n)route whenf.size <= plan.sizeand an explicit direct total fallback otherwise; the SPEC was corrected in #9608.Verification
lake build(10,294 jobs)lake build HexPolyFast.Conformancelake build HexPolyFast.Bench.lake/build/bin/hexpolyfast_bench verify --tag multipointpython3 scripts/check_phase4.py --base b4618ab98python3 scripts/bench/check_factor_sweep_freshness.pygit diff --check