Make abs and lohi exact; bring coverage to 100%

[timholy]

Started as a coverage pass (66.1% → 100%), which turned up two correctness bugs along the way.

abs is now exact when the span crosses zero

Previously, abs always reflected: abs(0 ± 1) returned 0.0 ± 1.0. The center was wrong by O(σ) — the folded normal's mean is σ√(2/π) ≈ 0.8 — and the code compensated by charging σ to moment_error rather than by giving the right answer.

The folded normal's first three moments have a closed form, so abs now computes them. With α = c/σ, ϕ the standard normal density, and e = erf(α/√2) = E[sign(x)]:

E[|x|]  = σ(2ϕ + αe)
E[|x|²] = c² + σ²
E[|x|³] = σ³((α³ + 3α)e + 2(α² + 2)ϕ)

So abs(0 ± 1) is now 0.798 ± 0.603, exact, with moment_error == 0; distrust still flags it, but through the skew (the half-normal's skewness is ≈0.995), which is the honest defect. Beyond |α| = 8 the wrong-side mass is below roundoff and E[|x|²] - E[|x|]² starts to cancel badly, so the reflection branch is kept there. The two branches agree where they meet.

This needs erf, hence the new SpecialFunctions dependency.

lohi now produces a span that actually contains [lo, hi]

Two problems with G((lo + hi)/2, nextfloat((hi - lo)/2)):

1. The unconditional nextfloat inflated even exact spans — a degenerate span got a subnormal radius, which is how min(3 ± 1, 2.0) came out as 2.0 ± 5.0e-324.
2. Containment was broken anyway: 3020 random spans per million failed loval(g) <= lo && hival(g) >= hi. When the span is narrow but far from zero, an ulp of σ is far smaller than an ulp of the center, so no amount of widening (hi - lo)/2 can recover what rounding the center lost.

Measuring the radius from the rounded center, max(center - lo, hi - center), fixes both: it is exact in the narrow-span case (Sterbenz), needs at most a single ulp of widening in the rest (verified over 10⁶ adversarial spans — adjacent floats, extreme and mixed magnitudes), and leaves a degenerate span with σ == 0.

Coverage

66.1% → 100%. New tests cover sums/differences of GVars (which were entirely untested), abs, min/max, scalar arithmetic in both argument orders, the integer-backed methods (reachable only via GVar{Int}, since GVar(1, 2) float-promotes), show, hash, and the trait functions. The folded-normal moments are checked against both the half-normal closed form and Monte Carlo; regression tests pin the lohi containment property.

175 tests pass on both release and LTS.

🤖 Generated with Claude Code