Add cached Newton polynomial division - #9599
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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.
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# 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
Dependency
Stacked on #9598; merge that PR first. This PR targets upstream
mainas required.Verification
lake build HexPolyFast.Divisionlake build HexPolyFast HexPolyFast.Conformancelake build HexPolyFast.Bench