perf(game): eliminate per-event allocations via ScratchArena

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.

src/arena.rs

@@ -0,0 +1,44 @@
+use crate::message::{DiffMessage, TeamMessage};
+
+/// Reusable scratch buffers for `Game::likelihoods`.
+///
+/// The four Vecs previously allocated fresh on every `Game::new` call —
+/// `teams`, `diffs`, `ties`, `margins` — are now borrowed from this arena,
+/// reset between uses.  A `Batch` owns one arena; all events in the slice
+/// share it across the convergence iterations.
+#[derive(Debug, Default)]
+pub struct ScratchArena {
+    pub(crate) teams: Vec<TeamMessage>,
+    pub(crate) diffs: Vec<DiffMessage>,
+    pub(crate) ties: Vec<bool>,
+    pub(crate) margins: Vec<f64>,
+}
+
+impl ScratchArena {
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    #[inline]
+    pub(crate) fn reset(&mut self) {
+        self.teams.clear();
+        self.diffs.clear();
+        self.ties.clear();
+        self.margins.clear();
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn reset_keeps_capacity() {
+        let mut arena = ScratchArena::new();
+        arena.teams.push(TeamMessage::default());
+        let cap = arena.teams.capacity();
+        arena.reset();
+        assert_eq!(arena.teams.len(), 0);
+        assert_eq!(arena.teams.capacity(), cap);
+    }
+}

src/batch.rs

@@ -3,6 +3,7 @@ use std::collections::HashMap;
 use crate::{
     Index, N_INF,
     agent::Agent,
+    arena::ScratchArena,
     drift::Drift,
     game::Game,
     gaussian::Gaussian,
@@ -111,6 +112,7 @@ pub struct Batch {
     pub(crate) skills: SkillStore,
     pub(crate) time: i64,
     p_draw: f64,
+    arena: ScratchArena,
 }
 
 impl Batch {
@@ -120,6 +122,7 @@ impl Batch {
             skills: SkillStore::new(),
             time,
             p_draw,
+            arena: ScratchArena::new(),
         }
     }
 
@@ -219,7 +222,7 @@ impl Batch {
             let teams = event.within_priors(false, false, &self.skills, agents);
             let result = event.outputs();
 
-            let g = Game::new(teams, &result, &event.weights, self.p_draw);
+            let g = Game::new(teams, &result, &event.weights, self.p_draw, &mut self.arena);
 
             for (t, team) in event.teams.iter_mut().enumerate() {
                 for (i, item) in team.items.iter_mut().enumerate() {
@@ -295,6 +298,9 @@ impl Batch {
         forward: bool,
         agents: &AgentStore<D>,
     ) -> f64 {
+        // log_evidence is infrequent; a local arena avoids needing &mut self.
+        let mut arena = ScratchArena::new();
+
         if targets.is_empty() {
             if online || forward {
                 self.events
@@ -306,6 +312,7 @@ impl Batch {
                             &event.outputs(),
                             &event.weights,
                             self.p_draw,
+                            &mut arena,
                         )
                         .evidence
                         .ln()
@@ -331,6 +338,7 @@ impl Batch {
                         &event.outputs(),
                         &event.weights,
                         self.p_draw,
+                        &mut arena,
                     )
                     .evidence
                     .ln()

src/game.rs

@@ -1,5 +1,7 @@
 use crate::{
-    N_INF, N00, approx, compute_margin,
+    N_INF, N00, approx,
+    arena::ScratchArena,
+    compute_margin,
     drift::Drift,
     evidence,
     gaussian::Gaussian,
@@ -24,6 +26,7 @@ impl<'a, D: Drift> Game<'a, D> {
         result: &'a [f64],
         weights: &'a [Vec<f64>],
         p_draw: f64,
+        arena: &mut ScratchArena,
     ) -> Self {
         debug_assert!(
             (result.len() == teams.len()),
@@ -61,56 +64,62 @@ impl<'a, D: Drift> Game<'a, D> {
             evidence: 0.0,
         };
 
-        this.likelihoods();
+        this.likelihoods(arena);
 
         this
     }
 
-    fn likelihoods(&mut self) {
+    fn likelihoods(&mut self, arena: &mut ScratchArena) {
+        arena.reset();
         let o = sort_perm(self.result, true);
+        let n_teams = o.len();
 
-        let mut team = o
+        // Phase 1: team messages into arena (avoids per-call allocation)
-            .iter()
+        arena.teams.extend(o.iter().map(|&e| {
-            .map(|&e| {
             let performance = self.teams[e]
                 .iter()
                 .zip(self.weights[e].iter())
                 .fold(N00, |p, (player, &weight)| {
                     p + (player.performance() * weight)
                 });
-
             TeamMessage {
                 prior: performance,
                 ..Default::default()
             }
-            })
+        }));
-            .collect::<Vec<_>>();
 
-        let mut diff = team
+        // Phase 2: diff messages (split-borrow: teams immut, diffs mut)
-            .windows(2)
+        {
-            .map(|w| DiffMessage {
+            let (teams, diffs) = (&arena.teams, &mut arena.diffs);
-                prior: w[0].prior - w[1].prior,
+            for i in 0..n_teams.saturating_sub(1) {
+                diffs.push(DiffMessage {
+                    prior: teams[i].prior - teams[i + 1].prior,
                     likelihood: N_INF,
-            })
+                });
-            .collect::<Vec<_>>();
+            }
+        }
 
-        let tie = o
+        // Phase 3: tie and margin
-            .windows(2)
+        arena
-            .map(|e| self.result[e[0]] == self.result[e[1]])
+            .ties
-            .collect::<Vec<_>>();
+            .extend(o.windows(2).map(|e| self.result[e[0]] == self.result[e[1]]));
 
-        let margin = if self.p_draw == 0.0 {
+        if self.p_draw == 0.0 {
-            vec![0.0; o.len() - 1]
+            arena.margins.resize(n_teams.saturating_sub(1), 0.0);
         } else {
-            o.windows(2)
+            arena.margins.extend(o.windows(2).map(|w| {
-                .map(|w| {
+                let a: f64 = self.teams[w[0]].iter().map(|p| p.beta.powi(2)).sum();
-                    let a: f64 = self.teams[w[0]].iter().map(|a| a.beta.powi(2)).sum();
+                let b: f64 = self.teams[w[1]].iter().map(|p| p.beta.powi(2)).sum();
-                    let b: f64 = self.teams[w[1]].iter().map(|a| a.beta.powi(2)).sum();
-
                 compute_margin(self.p_draw, (a + b).sqrt())
-                })
+            }));
-                .collect::<Vec<_>>()
+        }
-        };
+
+        // Use local aliases for the arena slices for readability in the EP loop.
+        // These are references into the arena, not copies.
+        let team = &mut arena.teams;
+        let diff = &mut arena.diffs;
+        let tie = &arena.ties;
+        let margin = &arena.margins;
 
         self.evidence = 1.0;
 
@@ -204,7 +213,7 @@ mod tests {
     use ::approx::assert_ulps_eq;
 
     use super::*;
-    use crate::{ConstantDrift, GAMMA, Gaussian, N_INF, Player};
+    use crate::{ConstantDrift, GAMMA, Gaussian, N_INF, Player, arena::ScratchArena};
 
     #[test]
     fn test_1vs1() {
@@ -220,7 +229,13 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 1.0], &w, 0.0);
+        let g = Game::new(
+            vec![vec![t_a], vec![t_b]],
+            &[0.0, 1.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -241,7 +256,13 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 1.0], &w, 0.0);
+        let g = Game::new(
+            vec![vec![t_a], vec![t_b]],
+            &[0.0, 1.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -254,7 +275,13 @@ mod tests {
         let t_b = Player::new(Gaussian::from_ms(15.568, 0.51), 1.0, ConstantDrift(0.2125));
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 1.0], &w, 0.0);
+        let g = Game::new(
+            vec![vec![t_a], vec![t_b]],
+            &[0.0, 1.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
 
         assert_eq!(g.likelihoods[0][0], N_INF);
         assert_eq!(g.likelihoods[1][0], N_INF);
@@ -281,7 +308,13 @@ mod tests {
         ];
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::new(teams.clone(), &[1.0, 2.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            teams.clone(),
+            &[1.0, 2.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -291,7 +324,13 @@ mod tests {
         assert_ulps_eq!(b, Gaussian::from_ms(31.311358, 6.698818), epsilon = 1e-6);
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::new(teams.clone(), &[2.0, 1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            teams.clone(),
+            &[2.0, 1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -301,7 +340,7 @@ mod tests {
         assert_ulps_eq!(b, Gaussian::from_ms(25.000000, 6.238469), epsilon = 1e-6);
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::new(teams, &[1.0, 2.0, 0.0], &w, 0.5);
+        let g = Game::new(teams, &[1.0, 2.0, 0.0], &w, 0.5, &mut ScratchArena::new());
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -327,7 +366,13 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 0.0], &w, 0.25);
+        let g = Game::new(
+            vec![vec![t_a], vec![t_b]],
+            &[0.0, 0.0],
+            &w,
+            0.25,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -348,7 +393,13 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 0.0], &w, 0.25);
+        let g = Game::new(
+            vec![vec![t_a], vec![t_b]],
+            &[0.0, 0.0],
+            &w,
+            0.25,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         let a = p[0][0];
@@ -382,6 +433,7 @@ mod tests {
             &[0.0, 0.0, 0.0],
             &w,
             0.25,
+            &mut ScratchArena::new(),
         );
         let p = g.posteriors();
 
@@ -417,6 +469,7 @@ mod tests {
             &[0.0, 0.0, 0.0],
             &w,
             0.25,
+            &mut ScratchArena::new(),
         );
         let p = g.posteriors();
 
@@ -462,7 +515,13 @@ mod tests {
         ];
 
         let w = [vec![1.0, 1.0], vec![1.0], vec![1.0, 1.0]];
-        let g = Game::new(vec![t_a, t_b, t_c], &[1.0, 0.0, 0.0], &w, 0.25);
+        let g = Game::new(
+            vec![t_a, t_b, t_c],
+            &[1.0, 0.0, 0.0],
+            &w,
+            0.25,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(p[0][0], Gaussian::from_ms(13.051, 2.864), epsilon = 1e-3);
@@ -489,7 +548,13 @@ mod tests {
         )];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a.clone(), t_b.clone()],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -507,7 +572,13 @@ mod tests {
         let w_b = vec![0.7];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a.clone(), t_b.clone()],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -525,7 +596,13 @@ mod tests {
         let w_b = vec![0.7];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a, t_b],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -554,7 +631,13 @@ mod tests {
         )];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a, t_b],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -583,7 +666,13 @@ mod tests {
         )];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a, t_b],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(p[0][0], p[1][0], epsilon = 1e-6);
@@ -620,7 +709,13 @@ mod tests {
         let w_b = vec![0.9, 0.6];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a.clone(), t_b.clone()],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -648,7 +743,13 @@ mod tests {
         let w_b = vec![0.7, 0.4];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a.clone(), t_b.clone()],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -676,7 +777,13 @@ mod tests {
         let w_b = vec![0.7, 2.4];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a.clone(), t_b.clone()],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(
@@ -713,6 +820,7 @@ mod tests {
             &[1.0, 0.0],
             &w,
             0.0,
+            &mut ScratchArena::new(),
         );
         let post_2vs1 = g.posteriors();
 
@@ -720,7 +828,13 @@ mod tests {
         let w_b = vec![1.0, 0.0];
 
         let w = [w_a, w_b];
-        let g = Game::new(vec![t_a, t_b.clone()], &[1.0, 0.0], &w, 0.0);
+        let g = Game::new(
+            vec![t_a, t_b.clone()],
+            &[1.0, 0.0],
+            &w,
+            0.0,
+            &mut ScratchArena::new(),
+        );
         let p = g.posteriors();
 
         assert_ulps_eq!(p[0][0], post_2vs1[0][0], epsilon = 1e-6);

src/history.rs

@@ -436,7 +436,10 @@ mod tests {
     use approx::assert_ulps_eq;
 
     use super::*;
-    use crate::{ConstantDrift, EPSILON, Game, Gaussian, ITERATIONS, IndexMap, P_DRAW, Player};
+    use crate::{
+        ConstantDrift, EPSILON, Game, Gaussian, ITERATIONS, IndexMap, P_DRAW, Player,
+        arena::ScratchArena,
+    };
 
     #[test]
     fn test_init() {
@@ -500,6 +503,7 @@ mod tests {
             &[0.0, 1.0],
             &w,
             P_DRAW,
+            &mut ScratchArena::new(),
         )
         .posteriors();
         let expected = p[0][0];

src/lib.rs

@@ -9,6 +9,7 @@ use std::{
 pub mod agent;
 #[cfg(feature = "approx")]
 mod approx;
+pub(crate) mod arena;
 pub mod batch;
 pub mod drift;
 mod error;

src/message.rs

@@ -1,5 +1,6 @@
 use crate::{N_INF, gaussian::Gaussian};
 
+#[derive(Debug)]
 pub(crate) struct TeamMessage {
     pub(crate) prior: Gaussian,
     pub(crate) likelihood_lose: Gaussian,
@@ -67,6 +68,7 @@ impl DrawMessage {
     }
 }
 */
+#[derive(Debug)]
 pub(crate) struct DiffMessage {
     pub(crate) prior: Gaussian,
     pub(crate) likelihood: Gaussian,