Performance Bit Lookup Tables

Integer bit lookup tables

BitOps.Log2(uint) and Log2(ulong) use bit smearing and de Bruijn indexing. Zero still returns zero, and signed overloads still interpret the unsigned bit pattern. Lookup data lives in constant read-only spans. Mono reads fixed array caches initialized once from those spans: span construction was slower in the native editor even after getter inlining. The caches hold 160 table bytes plus array overhead. Warm lookups create no arrays. The C# compiler lowers the constant new byte[] span expressions to static data addresses and a value-type span constructor; the emitted getters contain no newarr. A stack allocation would copy those constant bytes on every call. The captured IL covers all three getters.

Three alternating fresh process pairs on Windows x64 Unity 6000.6.7f1 Editor Mono compare main af80061e with this implementation. Inputs contain 4,096 values in a seeded shuffled order, with varied bit widths or values 1–40. Each capture uses 64 warm calls, batches calibrated to at least 20 ms and 21 raw rounds. Independent reference loops calculate the expected checksum. Every measured batch checks its result.

Operation	Input	Before median	After median	Paired after/before range
Log2(uint)	Varied widths	2.496 ns	1.276 ns	0.502–0.571
Log2(uint)	1–40	2.175 ns	1.275 ns	0.569–0.607
Log2(ulong)	Varied widths	9.062 ns	1.427 ns	0.156–0.619
Log2(ulong)	1–40	2.223 ns	1.436 ns	0.625–0.648
TrailingZeroCount(ulong)	Varied widths	0.926 ns	0.926 ns	0.983–1.022
TrailingZeroCount(ulong)	1–40	0.854 ns	0.846 ns	0.988–1.025

The table uses the median of three process medians. The varied 64-bit baseline is unstable: its three medians are 2.306, 9.062 and 9.335 ns. All three pairs improve, but the largest ratio is not a general speed guarantee. These loops include traversal and checksum costs. They do not establish isolated instruction latency, IL2CPP performance, another runtime's behavior, or a game workload speedup.

All six processes pass 619 cases with no skips or failures, including the existing cases and four exhaustive 16-bit-window oracle cases. Those functional cases use scalar checks without a per-value assertion allocation and remain in the normal suite. The timing fixture is in the Performance category and stays out of normal iteration.

Each process exits zero, reaches both output stream ends without a drain stop and retains unchanged input hashes. Loaded module identities are stable within each variant and differ between variants. Offline inspection of the captured DLL confirms the Mono cache fields, one array load per lookup and constant-data span getters without array creation. Initialization creates the caches once; the IL check describes warm lookup paths.

The replay archive contains source variants, fixtures, all six NUnit results, raw rounds, process receipts, source and assembly identities, IL records and replay steps.