PARALLEL TRACK 3: Comparative benchmark suite for PhD (12 formats × 4 benchmarks)

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📊 PARALLEL TRACK 3 — Comparative benchmark suite (PhD artifact)

Owner: any code agent · Repo: zig-golden-float + trios-trainer-igla · Time: ~60 min · NOT BLOCKED on bisect

This delivers reusable PhD-grade comparison data for the dissertation. Independent of training collapse — uses pure roundtrip + φ-distance metrics.

Benchmarks to add in benches/comparative.rs:

1. Roundtrip MSE on sacred constants:

   • Inputs: [1.0, φ, φ², 1/φ, 1/φ², √5, e, π, 0.0, 1e-10, 1e10]
   • For each format: f64 → fmtN → f64, log MSE
   • Output: CSV with columns format, exp_bits, mant_bits, phi_bias, mse, max_abs_err, sacred_const

2. φ-distance benchmark:

   • For each format: phi_distance = |exp_bits/mant_bits - 1/φ| per spec
   • Cross-check actual ratio matches PHI_BIAS_SSOT table
   • Output: leaderboard sorted by φ-distance ASC

3. ML-typical value distribution:

   • 10000 random Xavier-initialized weights N(0, 1/sqrt(h)) for h ∈ {384, 512, 1024}
   • Roundtrip through each format → measure cumulative distortion
   • Plot histogram of error per format

4. Gradient quantization stress test:

   • Synthetic gradients: g ~ N(0, sigma=1e-4) (typical Adam moments scale)
   • Measure update precision after f64 → format → f64
   • Output: CSV with format, sigma, mean_rel_err, max_rel_err

Output artifacts:

• benches/results/comparative_<date>.csv (publish-ready data)
• docs/PHD_BENCHMARK_REPORT.md with markdown tables + observations
• docs/figures/*.png (matplotlib via Python script tools/plot_bench.py)

Acceptance:

• 9 GF + 3 IEEE formats covered (12 cells × 4 benchmarks)
• All R5-honest, no fake numbers — CSV is publishable raw data
• Coq-style invariant φ² + φ⁻² = 3 preserved through quantization (sanity check)

Triplet R7 (per benchmark row):
MSE=<v> format=<f> sigma=<s> sha=<7c> jsonl_row=phd-bench gate_status=BENCH-EVIDENCE

This Track is the PhD's main deliverable. Sergeant prioritizes it independent of trainer status.