perf: lower Newton balanced band ratio from 2/1 to 4/3#88
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The wraparound-Newton PRs (#85-#87) cut Newton's constant ~35-45%, which moved the generic BZ/Newton crossover in the near-balanced band from ratio ~2 down to ~1.3 (measured at nb 100k-200k limbs: Newton wins from 1.3-1.35 up; at ratio 1.5 BZ is 1.7-1.9x slower, at 1.95 up to 3.4x; 2^k+1-family divisor sizes are 68x worse on BZ at ratio 1.5). Lower NEWTON_BALANCED from 2/1 to 4/3. Exact-power-of-two divisors (BZ's best case) regress <= ~25% in the narrow (4/3, ~1.4) sliver - same accepted tradeoff as PR #79. Measured after the change (M1 Max, min of 3): - nb=160000 limbs ratio 1.5: 244 -> 165 ms - nb=100000 limbs ratio 1.4: 201 -> 126 ms - nb=131073 (2^17+1) ratio 1.5: 10.7 s -> 157 ms Known residual ratio in (1, 4/3) still routes to BZ: generic sizes are genuinely faster there, but 2^k+1-family sizes still blow up (1.1-5.4 s at nb=131073, ratios 1.05-1.25). The follow-up fix is quotient-sized division, which scales with the quotient instead of the divisor. 246 unit tests + div_correctness pass. Docs updated (DIVISION.md, CLAUDE.md). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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What
Re-measure of the near-balanced division band after #85–#87 cut Newton's constant: the generic BZ/Newton crossover moved from ratio ~2 down to ~1.3. Lower
NEWTON_BALANCEDfrom 2/1 → 4/3 (sameb ≥ 98304limbs floor).Measurements (M1 Max, min of 3, paired)
Power-of-two divisors (BZ's best case) regress ≤ ~25% in the narrow (4/3, ~1.4) sliver — same accepted tradeoff as PR #79.
Known residual (documented)
ratio ∈ (1, 4/3) still routes to BZ: generic sizes are genuinely faster there (BZ wins below the crossover), but
2^k+1-family divisor sizes still hit the transform-doubling blowup (1.1–5.4 s at nb=131073, ratios 1.05–1.25). Follow-up: quotient-sized division (next PR).Testing
246/246 unit tests,
div_correctness(cross-checks +q·b + r == a,r < b).🤖 Generated with Claude Code