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For functions that converge via Newton-Raphson over a fixed factor-of-2 range, the initial seed determines how many iterations are needed. By choosing seeds that balance worst-case over/underestimate across the range, one iteration can be dropped while maintaining sufficient precision for the floor/ceil correction. 512Math._sqrt: replace 2^127 with √(2^255) ≈ √2·2^127 (geometric mean of [2^127, 2^128)). Balances ε to ±0.41/0.29, giving >128 bits after 6 Babylonian steps instead of 7. Move floor correction into _sqrt so sqrtUp never sees z=2^128 (prevents mul overflow). 512Math._cbrt: replace 2^84 with ⌊∛(3·2^251)⌋ (balancing point for [2^83.67, 2^84.67)). Balances ε to ±0.44/0.28, giving >85 bits after 6 Newton-Raphson steps. Replace conditional 7th iteration + floor with branchless floor correction. Cbrt._cbrt: multiply the clz-based seed by 233/256 ≈ ∛(3/4), balancing each octave triplet. Drop from 7 to 6 Newton-Raphson iterations. Sqrt._sqrt: the alternating-endpoint seed already equalizes ε₁=0.0607 via the AM-GM identity. Simply drop the 7th Babylonian step and move the floor correction into _sqrt. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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e1Ru1o
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