perf(bigint): batch digits in to_string_radix for non-power-of-two radixes

[bobzhang]

Closes #3827.

The generic radix path (radixes 3, 5, 6, 7, ... — anything not 10 or a power of two) extracted one digit per full BigInt division (grade_school_div per output digit — O(n²) overall). This PR generalizes the limb-by-limb algorithm the radix-10 path already uses: convert into base chunk = radix^chunk_len slots using only Int64 arithmetic (with chunk the largest power keeping (slot << RADIX_BIT_LEN) | limb inside Int64), then emit chunk_len digits per slot into a pre-sized buffer. The -self magnitude copy for negative inputs is gone too — limbs are sign-magnitude and are read directly, as radix-10 already does.

Benchmarks (native release, ~4000-bit value; committed)

radix	before	after
7	1.28 ms	83 µs	~15×
36	762 µs	95 µs	~8×
10 (reference, unchanged)	~105 µs	~105 µs	now matched by all radixes

Tests

Known values for radixes 3/6/36 (incl. negatives), from_string round-trips for ten non-power-of-two radixes on a 700+ bit value (positive and negative), and radix-3 digit-length checks across the chunk boundaries (3^e for e ∈ {1, 18, 19, 20, 37, 38, 39} — 19 digits per chunk).

Review

Reviewed by Codex CLI (codex-cli 0.144.1): "Approved; no findings" — including an explicit overflow-bound derivation (y ≤ chunk·2³² − 2³² + 2³² − 1 < Int64.max), slot-count and pos-underflow verification, sign-magnitude equivalence for negatives, and an independent 7,650-case differential check across all 30 applicable radixes.

Signed-off-by: Codex CLI codex@openai.com

Validation

• moon check clean, moon fmt applied, no .mbti changes
• moon test: 6716 passed, 0 failed (bigint 157/157)

🤖 Generated with Claude Code

[coveralls]

Coverage Report for CI Build 5187

Coverage increased (+0.02%) to 91.288%

Details

• Coverage increased (+0.02%) from the base build.
• Patch coverage: 15 of 15 lines across 1 file are fully covered (100%).
• No coverage regressions found.

Uncovered Changes

No uncovered changes found.

Coverage Regressions

No coverage regressions found.

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Coverage Stats

Relevant Lines:	17217
Covered Lines:	15717
Line Coverage:	91.29%
Coverage Strength:	191028.46 hits per line

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💛 - Coveralls