perf(bigint): cache decimal division reciprocal

[Yu-zh]

Summary

• cache the Möller–Granlund reciprocal for the decimal chunk divisor at module initialization
• reuse the already-normalized 10^19 divisor with shift zero in every decimal conversion
• preserve the 64-bit-limb formatter and its large-input scaling gains

Performance

Native release benchmark (moon bench bigint/to_string_bench_test.mbt --target native --release):

• 40 digits: 205.14 ns before, 190.58 ns after
• 400 digits: 1.38 µs after
• 4000 digits: 88.51 µs after

Validation

• moon check --deny-warn --target all
• moon info --target wasm,wasm-gc,js,native (no .mbti changes)
• moon fmt
• moon test --target all
• moon test --release --target all
• moon bundle --all

[chatgpt-codex-connector]

Codex Review Summary

This comment shows the latest Codex review activity on this pull request.

Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-09-02T06:30:25.402430Z	c4ca463	PR opened

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review" or "@codex security review".

Codex reacts with 👀 while any review is running, comments if it has suggestions, and reacts with 👍 once all reviews finish with no findings.

[coveralls]

Coverage Report for CI Build 6498

Coverage remained the same at 90.976%

Details

• Coverage remained the same as the base build.
• Patch coverage: 3 of 3 lines across 1 file are fully covered (100%).
• No coverage regressions found.

Uncovered Changes

No uncovered changes found.

Coverage Regressions

No coverage regressions found.

---

Coverage Stats

Relevant Lines:	18539
Covered Lines:	16866
Line Coverage:	90.98%
Coverage Strength:	283378.18 hits per line

---

💛 - Coveralls

[bobzhang]

Perf sign-off ✅

Reviewed the change and verified it on this machine (absolute numbers differ from the PR's box, but the trend is what matters).

Correctness

• Pure hoist, no behavior change: DECIMAL_CHUNK = 10^19 has its top bit set (10^19 > 2^63), so nlz(DECIMAL_CHUNK) == 0, dn == DECIMAL_CHUNK, and the cached reciprocal_word(DECIMAL_CHUNK) is exactly the value the old code recomputed once per to_string. The call div_w(..., DECIMAL_CHUNK, rec, 0) takes the identical s == 0 fast path.
• moon check --deny-warn --target all ✅
• moon test bigint --target all (debug and --release) ✅ — 158 wasm / 188 wasm-gc / 162 js / 158 native, all passing
• moon fmt --check bigint ✅

Perf — moon bench bigint/to_string_bench_test.mbt --target <t> --release, 3 interleaved A/B rounds of base 4099af7 vs head a6bc339 (mean of 3 rounds):

target	40 digits	400 digits	4000 digits
native	186.1 → 159.8 ns (−14%)	1.33 → 1.29 µs (−3.5%)	85.2 → 89.1 µs (noise)
wasm-gc	183.0 → 179.7 ns (−1.8%)	3.47 → 3.51 µs (noise)	228.3 → 231.0 µs (noise)
js	75.1 → 73.7 ns (−1.8%)	2.27 → 2.28 µs (noise)	49.1 → 49.5 µs (noise)

The native win is exactly what the change predicts — one software reciprocal_word (synthesized 128/64 division) saved per conversion, a larger fraction for few-limb inputs and amortized to nothing at 4000 digits. wasm-gc/js are neutral within run-to-run noise, and there is no regression anywhere; the large-input scaling gains are preserved.

LGTM, thanks for the clean hoist 👍