Test samplerz()'s output distribution in CI

[tprest]

The gap

sampler.c gets its output chi²-tested against the folded PDT (test_sampler_c.py) — but that covers only the base sampler: half-Gaussian plus sign bit, no BerExp.

samplerz() — the full sampler proposed in [HPRR20], with the BerExp rejection step, and the artifact's headline deliverable — was covered only by test_sampler_determinism.py, which checks reproducibility and never the output distribution.

So the paper's own sampler had no distribution test at all, while its C base-sampler cousin did.

The test

Five (mu, sigma) points chosen for the boundaries that matter:

(μ, σ)	why
(0, 1.55)	typical
(0.5, 1.55)	worst-case fractional center for the sign/BerExp recombination
(0, 1.2778)	σ_min — discreteness strongest here
(0, 1.80)	near σ₀ = 1.8205
(3.7, 1.55)	nonzero center

Plus a negative control: the battery must reject samples drawn at the wrong σ, so test_samplerz_passes_battery cannot be vacuous.

Seeded, hence deterministic. Verified bit-identical samples and p-values on Python 3.10 and 3.12 (the CI matrix):

py3.10  first 12 = [-3, 0, -3, 0, 0, 0, 3, 1, -1, -1, 1, -2]  chi2 p=0.876550  Fisher p=0.656100
py3.12  first 12 = [-3, 0, -3, 0, 0, 0, 3, 1, -1, -1, 1, -2]  chi2 p=0.876550  Fisher p=0.656100

Observed Fisher p-values run 0.11 … 0.82 against α = 0.001 — two orders of magnitude of headroom. Cost: ~3.3 s. No workflow change needed; pytest code/tests/ already discovers it.

Scope, stated honestly

This guards the class "the output distribution is wrong" — the same class test_sampler_c.py guards for the C sampler. Measured against deliberately broken variants:

Injected bug	Caught?
corrupted table entry (+2%)	✅ p = 0.0000
broken sign recombination	✅ p = 0.0000
ccs scaling (sf = σ/σ₀)	❌ no — a constant factor in z, so the output distribution is unchanged; only the rejection rate moves
berexp p = -1 edge case	❌ no — mass ~2⁻⁷², unobservable at any feasible N

Note that means it would not have caught either of the two samplerz bugs fixed earlier. It is a regression guard on the distribution, not a catch-all. (What would catch the ccs bug is a check that the mean iteration count is constant in σ — deliberately out of scope, as isochrony testing was descoped.)

Suite: 153 passed, 1 skipped.

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