eisenstein-bench

CLI benchmark suite for Eisenstein hexagonal arithmetic.

Compares E12 exact integer arithmetic vs IEEE 754 float drift for hexagonal lattice operations.

Install

cargo install --git https://github.com/SuperInstance/eisenstein-bench

Commands

eisenstein-bench drift [--rotations N]    — Rotate N times, compare E12 vs float drift
eisenstein-bench disk [--radius N]        — Benchmark HexDisk iteration at radius N
eisenstein-bench snap [--iterations N]    — Benchmark angle snapping throughput
eisenstein-bench norm [--iterations N]    — Benchmark norm vs float hypot
eisenstein-bench full [--json]            — Run all, print summary table

Defaults

Parameter	Default
--rotations	10,000
--radius	1,000
--iterations	100,000

Example Output

$ eisenstein-bench full
┌────────────────┬──────────────┬──────────────────────────────────────────┐
│ Benchmark      │ Time         │ Detail                                   │
├────────────────┼──────────────┼──────────────────────────────────────────┤
│ drift (rotate) │          0µs │ 10,000 rotations of (5,0)                │
│ drift (float)  │         19µs │ drift: 0.000000000000002                 │
│ disk           │        5.5ms │ radius=1,000, 3,003,001 pts              │
│ snap           │       32.6ms │ 100,000 calls                            │
│ norm           │        110µs │ 100,000 calls, sum=1,092,277,422         │
└────────────────┴──────────────┴──────────────────────────────────────────┘
  drift (rotate) — ✅ ZERO DRIFT
  drift (float) — drift: 0.000000000000002
  disk — 3,003,001 pts in 5.5ms
  snap — 326 ns/call
  norm — 1 ns/call

Why E12?

Eisenstein integers (a + bω where ω = e^(2πi/3)) provide exact arithmetic on the hexagonal lattice. No floating-point drift, ever. The norm a²-ab+b² is always an integer, and all D6 symmetry operations are exact.

Float rotation accumulates error with each operation. E12 does not.

License

MIT