Mul and Div become two f64 adds/subs with no sqrt in the hot path.
mu() and sigma() are computed on demand from stored pi/tau.
Key implementation notes:
- exclude() returns N00 when var <= 0 to avoid inf/inf = NaN when
two Gaussians have the same precision (ULP-level round-trip error
from the pi→sigma accessor).
- Mul<f64> by 0.0 returns N00 (point mass at 0), matching old behavior.
- from_ms(0, 0) == N00 {pi:inf, tau:0}; from_ms(0, inf) == N_INF {pi:0, tau:0}.
Golden values in test_1vs1vs1_draw updated: nat-param arithmetic
rounds mu to 25.0 (was 24.999999) and shifts sigma by ~3e-7.
Both differences are bounded and validated against the original Python
reference values.
Part of T0 engine redesign.
- Promotes Gaussian::pi and Gaussian::tau to public so benches/gaussian.rs
compiles, then captures baseline numbers for the T0 acceptance gate.
- Fixes the divide bench: g1/g2 panicked (g1 has lower precision than g2;
cavity requires pi_num >= pi_den). Swapped to g2/g1 (well-defined).
Baseline on Apple M5 Pro:
Batch::iteration 29.840 µs
Gaussian::mul 1.568 ns (vs ~220 ps for add/sub — hot path)
Gaussian::div 1.572 ns
