Game::likelihoods now uses VarStore (for diff vars) and TruncFactor
(for EP truncation + evidence caching) instead of TeamMessage and
DiffMessage. The EP loop structure is preserved exactly; VarId-keyed
diff vars live in the arena's VarStore (capacity reused per batch).
ScratchArena loses teams/diffs/ties/margins; gains VarStore and
sort_buf (sort_perm allocation eliminated). message.rs deleted.
Public API of Game (new, posteriors, likelihoods, evidence) unchanged.
Game::likelihoods previously allocated four Vecs (teams, diffs, ties,
margins) on every call. Batch now owns one ScratchArena reused across
all Game::new calls in the iteration loop; likelihoods() clears and
extends the arena buffers instead of allocating fresh.
For log_evidence (called infrequently), a local ScratchArena is created
per invocation so the method signature stays &self.
Also: add #[derive(Debug)] to TeamMessage and DiffMessage (required by
ScratchArena's own Debug derive).
Part of T0 engine redesign.
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.
