style: cargo fmt

.gitignore

@@ -4,3 +4,6 @@
 /temp
 .justfile
 *.svg
+NOTEPAD.md
+
+/.claude

CLAUDE.md

@@ -0,0 +1,45 @@
+# CLAUDE.md
+
+This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
+
+## Commands
+
+```bash
+cargo build                          # Build the library
+cargo test --lib                     # Run all library tests
+cargo test --lib <test_name>         # Run a single test by name
+cargo test --lib -- --nocapture      # Run tests with stdout output
+cargo clippy                         # Lint
+cargo bench                          # Run benchmarks (criterion)
+```
+
+The `approx` feature enables `approx::AbsDiffEq` for `Gaussian`:
+```bash
+cargo test --features approx
+```
+
+## Architecture
+
+This is a Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py) — a Bayesian skill rating system that tracks skill evolution over time using Gaussian message passing.
+
+### Data flow
+
+```
+History  →  Batch[]  →  Game[]  →  teams/players
+```
+
+- **`History`** (`history.rs`) — top-level container. Organizes games by time into `Batch`es, runs forward/backward message passing across batches, and exposes `learning_curves()` and `log_evidence()`.
+- **`Batch`** (`batch.rs`) — all games at a single time step. Runs `iteration()` to update skill estimates via `Game::posteriors()`, collecting `Skill` distributions per player.
+- **`Game`** (`game.rs`) — a single match. Given teams (slices of `Gaussian`), computes posterior skill distributions using Gaussian factor graphs and `message.rs` helpers.
+- **`Agent`** (`agent.rs`) — wraps a `Player` with temporal state (`last_time`, `message`). `receive()` applies time-decay (`gamma`) when the player reappears after a gap.
+- **`Player`** (`player.rs`) — static configuration: prior `Gaussian`, `beta` (performance noise), `gamma` (skill drift per time unit).
+- **`Gaussian`** (`gaussian.rs`) — core probability type. Stored as natural parameters (`pi = 1/sigma²`, `tau = mu/sigma²`). Arithmetic ops implement message multiplication/division in the factor graph.
+- **`message.rs`** — `TeamMessage` and `DiffMessage`: intermediate factor graph messages used inside `Game`.
+- **`lib.rs`** — exports the public API (`Game`, `Gaussian`, `History`, `Player`) and standalone functions (`quality()`, `pdf()`, `cdf()`, `erfc()`). Also defines global defaults: `MU=0.0`, `SIGMA=6.0`, `BETA=1.0`, `GAMMA=0.03`, `P_DRAW=0.0`, `EPSILON=1e-6`, `ITERATIONS=30`.
+
+### Key design points
+
+- `History` uses `IndexMap<K>` (defined in `lib.rs`) to map arbitrary player keys to `Agent` state.
+- Convergence is measured by the maximum `delta()` across all skill distributions; iteration stops when below `EPSILON` or after `ITERATIONS` rounds.
+- The `approx` feature gates `AbsDiffEq` on `Gaussian` for use in tests — the feature is optional and only needed for approximate equality assertions.
+- `time` in `History`/`Batch` is currently an `f64`; the README notes it needs to become an enum to support richer temporal states.

Cargo.toml

@@ -1,7 +1,7 @@
 [package]
 name = "trueskill-tt"
 version = "0.1.0"
-edition = "2021"
+edition = "2024"
 
 [lib]
 bench = false
@@ -10,6 +10,10 @@ bench = false
 name = "batch"
 harness = false
 
+[[bench]]
+name = "gaussian"
+harness = false
+
 [dependencies]
 approx = { version = "0.5.1", optional = true }
 

NOTEPAD.md

@@ -1,8 +0,0 @@
-# History
-
-```rust
-let mut history = History::new();
-
-let agent_a = history.new_agent();
-let agent_b = history.new_agent_with_prior(Prior::new(Gaussian::default(), BETA, GAMMA));
-```

README.md

@@ -11,6 +11,66 @@ Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillTh
 - [TrueSkill Through Time: Revisiting the History of Chess](https://www.microsoft.com/en-us/research/wp-content/uploads/2008/01/NIPS2007_0931.pdf)
 - [TrueSkill Through Time. The full scientific documentation](https://glandfried.github.io/publication/landfried2021-learning/)
 
+## Drift
+
+Skill drift models how a player's true skill can change between appearances. Each time a player reappears after a gap, their skill uncertainty is widened by the drift model before the new evidence is incorporated.
+
+Drift is represented by the `Drift` trait:
+
+```rust
+pub trait Drift: Copy + Debug {
+    fn variance_delta(&self, elapsed: i64) -> f64;
+}
+```
+
+`variance_delta` returns the amount to add to `σ²` given the elapsed time since the player last played. Internally, `Gaussian::forget` uses this to compute the new sigma: `σ_new = sqrt(σ² + variance_delta)`.
+
+### ConstantDrift
+
+The built-in `ConstantDrift` implements a linear random walk — skill uncertainty grows proportionally to time:
+
+```
+variance_delta = elapsed * γ²
+```
+
+This is the standard TrueSkill Through Time model. Use it by passing a `ConstantDrift(gamma)` when constructing a `Player`:
+
+```rust
+use trueskill_tt::{Player, Gaussian, drift::ConstantDrift};
+
+// gamma = 0.1 means skill can shift ~0.1 per time unit
+let player = Player::new(Gaussian::from_ms(0.0, 6.0), 1.0, ConstantDrift(0.1));
+```
+
+### Custom drift
+
+Implement `Drift` to express any other model. For example, a drift that saturates after a long absence (uncertainty grows with the square root of elapsed time instead of linearly):
+
+```rust
+use trueskill_tt::drift::Drift;
+
+#[derive(Clone, Copy, Debug)]
+struct SqrtDrift {
+    gamma: f64,
+}
+
+impl Drift for SqrtDrift {
+    fn variance_delta(&self, elapsed: i64) -> f64 {
+        (elapsed as f64).sqrt() * self.gamma * self.gamma
+    }
+}
+
+let player = Player::new(Gaussian::from_ms(0.0, 6.0), 1.0, SqrtDrift { gamma: 0.5 });
+```
+
+To use a custom drift type with `History`, use the `.drift()` builder method instead of `.gamma()`:
+
+```rust
+let h = History::builder()
+    .drift(SqrtDrift { gamma: 0.5 })
+    .build();
+```
+
 ## Todo
 
 - [x] Implement approx for Gaussian

benches/batch.rs

@@ -1,9 +1,9 @@
 use std::collections::HashMap;
 
-use criterion::{criterion_group, criterion_main, Criterion};
+use criterion::{Criterion, criterion_group, criterion_main};
 use trueskill_tt::{
-    agent::Agent, batch::Batch, gaussian::Gaussian, player::Player, IndexMap, BETA, GAMMA, MU,
+    BETA, GAMMA, IndexMap, MU, P_DRAW, SIGMA, agent::Agent, batch::Batch, drift::ConstantDrift,
-    P_DRAW, SIGMA,
+    gaussian::Gaussian, player::Player,
 };
 
 fn criterion_benchmark(criterion: &mut Criterion) {
@@ -19,21 +19,21 @@ fn criterion_benchmark(criterion: &mut Criterion) {
         map.insert(
             a,
             Agent {
-                player: Player::new(Gaussian::from_ms(MU, SIGMA), BETA, GAMMA),
+                player: Player::new(Gaussian::from_ms(MU, SIGMA), BETA, ConstantDrift(GAMMA)),
                 ..Default::default()
             },
         );
         map.insert(
             b,
             Agent {
-                player: Player::new(Gaussian::from_ms(MU, SIGMA), BETA, GAMMA),
+                player: Player::new(Gaussian::from_ms(MU, SIGMA), BETA, ConstantDrift(GAMMA)),
                 ..Default::default()
             },
         );
         map.insert(
             c,
             Agent {
-                player: Player::new(Gaussian::from_ms(MU, SIGMA), BETA, GAMMA),
+                player: Player::new(Gaussian::from_ms(MU, SIGMA), BETA, ConstantDrift(GAMMA)),
                 ..Default::default()
             },
         );

benches/gaussian.rs

@@ -0,0 +1,50 @@
+use criterion::{Criterion, criterion_group, criterion_main};
+use trueskill_tt::gaussian::Gaussian;
+
+fn benchmark_gaussian_arithmetic(criterion: &mut Criterion) {
+    // Define test Gaussians
+    let g1 = Gaussian::from_ms(25.0, 25.0 / 3.0);
+    let g2 = Gaussian::from_ms(0.0, 1.0);
+    let g3 = Gaussian::from_ms(1.0, 1.0);
+
+    // Benchmark addition
+    criterion.bench_function("Gaussian::add", |bencher| {
+        bencher.iter(|| g1 + g2);
+    });
+
+    // Benchmark subtraction
+    criterion.bench_function("Gaussian::sub", |bencher| {
+        bencher.iter(|| g1 - g3);
+    });
+
+    // Benchmark multiplication
+    criterion.bench_function("Gaussian::mul", |bencher| {
+        bencher.iter(|| g1 * g2);
+    });
+
+    // Benchmark division
+    criterion.bench_function("Gaussian::div", |bencher| {
+        bencher.iter(|| g1 / g2);
+    });
+
+    // Benchmark natural parameter conversions
+    criterion.bench_function("Gaussian::pi", |bencher| {
+        bencher.iter(|| g1.pi());
+    });
+
+    criterion.bench_function("Gaussian::tau", |bencher| {
+        bencher.iter(|| g1.tau());
+    });
+
+    // Benchmark combined pi/tau operations (used in mul/div)
+    criterion.bench_function("Gaussian::pi_tau_combined", |bencher| {
+        bencher.iter(|| {
+            let pi = g1.pi();
+            let tau = g1.tau();
+            (pi, tau)
+        });
+    });
+}
+
+criterion_group!(benches, benchmark_gaussian_arithmetic);
+criterion_main!(benches);

cliff.toml

@@ -0,0 +1,65 @@
+# git-cliff ~ configuration file
+# https://git-cliff.org/docs/configuration
+
+[changelog]
+# A Tera template to be rendered as the changelog's header.
+# See https://keats.github.io/tera/docs/#introduction
+header = """
+# Changelog\n
+All notable changes to this project will be documented in this file.\n
+"""
+# A Tera template to be rendered for each release in the changelog.
+# See https://keats.github.io/tera/docs/#introduction
+body = """
+{% if version %}\
+    ## {{ version | trim_start_matches(pat="v") }} - {{ timestamp | date(format="%Y-%m-%d") }}
+{% else %}\
+    ## Unreleased
+{% endif %}\
+{% for group, commits in commits | group_by(attribute="group") %}
+    ### {{ group | upper_first }}
+    {% for commit in commits %}
+        - {{ commit.message | split(pat="\n") | first | trim_end }}\
+    {% endfor %}
+{% endfor %}\n
+"""
+# A Tera template to be rendered as the changelog's footer.
+# See https://keats.github.io/tera/docs/#introduction
+footer = """
+<!-- generated by git-cliff -->
+"""
+# Remove leading and trailing whitespaces from the changelog's body.
+trim = true
+
+
+[git]
+# Parse commits according to the conventional commits specification.
+# See https://www.conventionalcommits.org
+conventional_commits = false
+# Exclude commits that do not match the conventional commits specification.
+filter_unconventional = false
+# Split commits on newlines, treating each line as an individual commit.
+split_commits = false
+# An array of regex based parsers for extracting data from the commit message.
+# Assigns commits to groups.
+# Optionally sets the commit's scope and can decide to exclude commits from further processing.
+commit_parsers = [
+    { message = "^feat", group = "Features" },
+    { message = "^fix", group = "Bug Fixes" },
+    { message = "^doc", group = "Documentation" },
+    { message = "^perf", group = "Performance" },
+    { message = "^refactor", group = "Refactor" },
+    { message = "^style", group = "Styling" },
+    { message = "^test", group = "Testing" },
+    { message = "^chore\\(release\\): prepare for", skip = true },
+    { message = "^chore", group = "Miscellaneous Tasks" },
+    { body = ".*security", group = "Security" },
+    { body = ".*", group = "Other (unconventional)" },
+]
+# Exclude commits that are not matched by any commit parser.
+filter_commits = false
+# Order releases topologically instead of chronologically.
+topo_order = false
+# Order of commits in each group/release within the changelog.
+# Allowed values: newest, oldest
+sort_commits = "oldest"

examples/atp.rs

@@ -159,10 +159,12 @@ fn main() {
 }
 
 mod csv {
-    use std::fs::File;
+    use std::{
-    use std::io::{self, BufRead, BufReader, Lines};
+        fs::File,
-    use std::ops;
+        io::{self, BufRead, BufReader, Lines},
-    use std::path::Path;
+        ops,
+        path::Path,
+    };
 
     pub struct Reader {
         header_map: Vec<String>,

graph.d2

@@ -0,0 +1,64 @@
+vars: {
+  d2-config: {
+    layout-engine: elk
+    # Terminal theme code
+    theme-id: 300
+  }
+}
+
+History: {
+  shape: class
+
+  agents: "HashMap<Index, Agent>"
+  batches: "Vec<Batch>"
+}
+
+Batch: {
+  shape: class
+
+  skills: "HashMap<Index, Skill>"
+  events: "Vec<Event>"
+  time: "i64"
+  p_draw: "f64"
+}
+
+Event: {
+  shape: class
+
+  teams: "Vec<Team>"
+  weights: "Vec<Vec<f64>>"
+  evidence: "f64"
+}
+
+Team: {
+  shape: class
+
+  items: "Vec<Item>"
+  output: "f64"
+}
+
+Item: {
+  shape: class
+
+  agent: "Index"
+  likelihood: "Gaussian"
+}
+
+Skill: {
+  shape: class
+
+  forward: "Gaussian"
+  backward: "Gaussian"
+  likelihood: "Gaussian"
+  elapsed: "i64"
+  online: "Gaussian"
+}
+
+History -> Batch
+
+Batch -> Skill
+Batch -> Event
+
+Event -> Team
+
+Team -> Item

release.toml

@@ -0,0 +1 @@
+pre-release-hook = ["git", "cliff", "-o", "CHANGELOG.md", "--tag", "{{version}}"]

rustfmt.toml

@@ -0,0 +1,2 @@
+imports_granularity = "Crate"
+group_imports = "StdExternalCrate"

src/agent.rs

@@ -1,23 +1,29 @@
-use crate::{gaussian::Gaussian, player::Player, N_INF};
+use crate::{
+    N_INF,
+    drift::{ConstantDrift, Drift},
+    gaussian::Gaussian,
+    player::Player,
+};
 
 #[derive(Debug)]
-pub struct Agent {
+pub struct Agent<D: Drift = ConstantDrift> {
-    pub player: Player,
+    pub player: Player<D>,
     pub message: Gaussian,
     pub last_time: i64,
 }
 
-impl Agent {
+impl<D: Drift> Agent<D> {
     pub(crate) fn receive(&self, elapsed: i64) -> Gaussian {
         if self.message != N_INF {
-            self.message.forget(self.player.gamma, elapsed)
+            self.message
+                .forget(self.player.drift.variance_delta(elapsed))
         } else {
             self.player.prior
         }
     }
 }
 
-impl Default for Agent {
+impl Default for Agent<ConstantDrift> {
     fn default() -> Self {
         Self {
             player: Player::default(),
@@ -27,7 +33,10 @@ impl Default for Agent {
     }
 }
 
-pub(crate) fn clean<'a, A: Iterator<Item = &'a mut Agent>>(agents: A, last_time: bool) {
+pub(crate) fn clean<'a, D: Drift + 'a, A: Iterator<Item = &'a mut Agent<D>>>(
+    agents: A,
+    last_time: bool,
+) {
     for a in agents {
         a.message = N_INF;
 

src/batch.rs

@@ -1,7 +1,8 @@
 use std::collections::HashMap;
 
 use crate::{
-    agent::Agent, game::Game, gaussian::Gaussian, player::Player, tuple_gt, tuple_max, Index, N_INF,
+    Index, N_INF, agent::Agent, drift::Drift, game::Game, gaussian::Gaussian, player::Player,
+    tuple_gt, tuple_max,
 };
 
 #[derive(Debug)]
@@ -38,22 +39,22 @@ struct Item {
 }
 
 impl Item {
-    fn within_prior(
+    fn within_prior<D: Drift>(
         &self,
         online: bool,
         forward: bool,
         skills: &HashMap<Index, Skill>,
-        agents: &HashMap<Index, Agent>,
+        agents: &HashMap<Index, Agent<D>>,
-    ) -> Player {
+    ) -> Player<D> {
         let r = &agents[&self.agent].player;
         let skill = &skills[&self.agent];
 
         if online {
-            Player::new(skill.online, r.beta, r.gamma)
+            Player::new(skill.online, r.beta, r.drift)
         } else if forward {
-            Player::new(skill.forward, r.beta, r.gamma)
+            Player::new(skill.forward, r.beta, r.drift)
         } else {
-            Player::new(skill.posterior() / self.likelihood, r.beta, r.gamma)
+            Player::new(skill.posterior() / self.likelihood, r.beta, r.drift)
         }
     }
 }
@@ -79,13 +80,13 @@ impl Event {
             .collect::<Vec<_>>()
     }
 
-    pub(crate) fn within_priors(
+    pub(crate) fn within_priors<D: Drift>(
         &self,
         online: bool,
         forward: bool,
         skills: &HashMap<Index, Skill>,
-        agents: &HashMap<Index, Agent>,
+        agents: &HashMap<Index, Agent<D>>,
-    ) -> Vec<Vec<Player>> {
+    ) -> Vec<Vec<Player<D>>> {
         self.teams
             .iter()
             .map(|team| {
@@ -116,12 +117,12 @@ impl Batch {
         }
     }
 
-    pub fn add_events(
+    pub fn add_events<D: Drift>(
         &mut self,
         composition: Vec<Vec<Vec<Index>>>,
         results: Vec<Vec<f64>>,
         weights: Vec<Vec<Vec<f64>>>,
-        agents: &HashMap<Index, Agent>,
+        agents: &HashMap<Index, Agent<D>>,
     ) {
         let mut unique = Vec::with_capacity(10);
 
@@ -207,7 +208,7 @@ impl Batch {
             .collect::<HashMap<_, _>>()
     }
 
-    pub fn iteration(&mut self, from: usize, agents: &HashMap<Index, Agent>) {
+    pub fn iteration<D: Drift>(&mut self, from: usize, agents: &HashMap<Index, Agent<D>>) {
         for event in self.events.iter_mut().skip(from) {
             let teams = event.within_priors(false, false, &self.skills, agents);
             let result = event.outputs();
@@ -229,7 +230,7 @@ impl Batch {
     }
 
     #[allow(dead_code)]
-    pub(crate) fn convergence(&mut self, agents: &HashMap<Index, Agent>) -> usize {
+    pub(crate) fn convergence<D: Drift>(&mut self, agents: &HashMap<Index, Agent<D>>) -> usize {
         let epsilon = 1e-6;
         let iterations = 20;
 
@@ -259,18 +260,18 @@ impl Batch {
         skill.forward * skill.likelihood
     }
 
-    pub(crate) fn backward_prior_out(
+    pub(crate) fn backward_prior_out<D: Drift>(
         &self,
         agent: &Index,
-        agents: &HashMap<Index, Agent>,
+        agents: &HashMap<Index, Agent<D>>,
     ) -> Gaussian {
         let skill = &self.skills[agent];
         let n = skill.likelihood * skill.backward;
 
-        n.forget(agents[agent].player.gamma, skill.elapsed)
+        n.forget(agents[agent].player.drift.variance_delta(skill.elapsed))
     }
 
-    pub(crate) fn new_backward_info(&mut self, agents: &HashMap<Index, Agent>) {
+    pub(crate) fn new_backward_info<D: Drift>(&mut self, agents: &HashMap<Index, Agent<D>>) {
         for (agent, skill) in self.skills.iter_mut() {
             skill.backward = agents[agent].message;
         }
@@ -278,7 +279,7 @@ impl Batch {
         self.iteration(0, agents);
     }
 
-    pub(crate) fn new_forward_info(&mut self, agents: &HashMap<Index, Agent>) {
+    pub(crate) fn new_forward_info<D: Drift>(&mut self, agents: &HashMap<Index, Agent<D>>) {
         for (agent, skill) in self.skills.iter_mut() {
             skill.forward = agents[agent].receive(skill.elapsed);
         }
@@ -286,12 +287,12 @@ impl Batch {
         self.iteration(0, agents);
     }
 
-    pub(crate) fn log_evidence(
+    pub(crate) fn log_evidence<D: Drift>(
         &self,
         online: bool,
         targets: &[Index],
         forward: bool,
-        agents: &HashMap<Index, Agent>,
+        agents: &HashMap<Index, Agent<D>>,
     ) -> f64 {
         if targets.is_empty() {
             if online || forward {
@@ -390,9 +391,8 @@ pub(crate) fn compute_elapsed(last_time: i64, actual_time: i64) -> i64 {
 mod tests {
     use approx::assert_ulps_eq;
 
-    use crate::{agent::Agent, player::Player, IndexMap};
-
     use super::*;
+    use crate::{IndexMap, agent::Agent, drift::ConstantDrift, player::Player};
 
     #[test]
     fn test_one_event_each() {
@@ -414,7 +414,7 @@ mod tests {
                     player: Player::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        25.0 / 300.0,
+                        ConstantDrift(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },
@@ -490,7 +490,7 @@ mod tests {
                     player: Player::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        25.0 / 300.0,
+                        ConstantDrift(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },
@@ -569,7 +569,7 @@ mod tests {
                     player: Player::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        25.0 / 300.0,
+                        ConstantDrift(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },

src/drift.rs

@@ -0,0 +1,14 @@
+use std::fmt::Debug;
+
+pub trait Drift: Copy + Debug {
+    fn variance_delta(&self, elapsed: i64) -> f64;
+}
+
+#[derive(Clone, Copy, Debug)]
+pub struct ConstantDrift(pub f64);
+
+impl Drift for ConstantDrift {
+    fn variance_delta(&self, elapsed: i64) -> f64 {
+        elapsed as f64 * self.0 * self.0
+    }
+}

src/game.rs

@@ -1,14 +1,16 @@
 use crate::{
-    approx, compute_margin, evidence,
+    N_INF, N00, approx, compute_margin,
+    drift::Drift,
+    evidence,
     gaussian::Gaussian,
     message::{DiffMessage, TeamMessage},
     player::Player,
-    sort_perm, tuple_gt, tuple_max, N00, N_INF,
+    sort_perm, tuple_gt, tuple_max,
 };
 
 #[derive(Debug)]
-pub struct Game<'a> {
+pub struct Game<'a, D: Drift> {
-    teams: Vec<Vec<Player>>,
+    teams: Vec<Vec<Player<D>>>,
     result: &'a [f64],
     weights: &'a [Vec<f64>],
     p_draw: f64,
@@ -16,9 +18,9 @@ pub struct Game<'a> {
     pub(crate) evidence: f64,
 }
 
-impl<'a> Game<'a> {
+impl<'a, D: Drift> Game<'a, D> {
     pub fn new(
-        teams: Vec<Vec<Player>>,
+        teams: Vec<Vec<Player<D>>>,
         result: &'a [f64],
         weights: &'a [Vec<f64>],
         p_draw: f64,
@@ -176,7 +178,7 @@ impl<'a> Game<'a> {
                     .zip(w.iter())
                     .map(|(p, &w)| {
                         ((m - performance.exclude(p.performance() * w)) * (1.0 / w))
-                            .forget(p.beta, 1)
+                            .forget(p.beta.powi(2))
                     })
                     .collect::<Vec<_>>()
             })
@@ -201,21 +203,20 @@ impl<'a> Game<'a> {
 mod tests {
     use ::approx::assert_ulps_eq;
 
-    use crate::{Gaussian, Player, GAMMA, N_INF};
-
     use super::*;
+    use crate::{ConstantDrift, GAMMA, Gaussian, N_INF, Player};
 
     #[test]
     fn test_1vs1() {
         let t_a = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
         let t_b = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0]];
@@ -228,8 +229,16 @@ mod tests {
         assert_ulps_eq!(a, Gaussian::from_ms(20.794779, 7.194481), epsilon = 1e-6);
         assert_ulps_eq!(b, Gaussian::from_ms(29.205220, 7.194481), epsilon = 1e-6);
 
-        let t_a = Player::new(Gaussian::from_ms(29.0, 1.0), 25.0 / 6.0, GAMMA);
+        let t_a = Player::new(
-        let t_b = Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, GAMMA);
+            Gaussian::from_ms(29.0, 1.0),
+            25.0 / 6.0,
+            ConstantDrift(GAMMA),
+        );
+        let t_b = Player::new(
+            Gaussian::from_ms(25.0, 25.0 / 3.0),
+            25.0 / 6.0,
+            ConstantDrift(GAMMA),
+        );
 
         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);
@@ -241,8 +250,8 @@ mod tests {
         assert_ulps_eq!(a, Gaussian::from_ms(28.896475, 0.996604), epsilon = 1e-6);
         assert_ulps_eq!(b, Gaussian::from_ms(32.189211, 6.062063), epsilon = 1e-6);
 
-        let t_a = Player::new(Gaussian::from_ms(1.139, 0.531), 1.0, 0.2125);
+        let t_a = Player::new(Gaussian::from_ms(1.139, 0.531), 1.0, ConstantDrift(0.2125));
-        let t_b = Player::new(Gaussian::from_ms(15.568, 0.51), 1.0, 0.2125);
+        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);
@@ -257,17 +266,17 @@ mod tests {
             vec![Player::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                25.0 / 300.0,
+                ConstantDrift(25.0 / 300.0),
             )],
             vec![Player::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                25.0 / 300.0,
+                ConstantDrift(25.0 / 300.0),
             )],
             vec![Player::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                25.0 / 300.0,
+                ConstantDrift(25.0 / 300.0),
             )],
         ];
 
@@ -309,12 +318,12 @@ mod tests {
         let t_a = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
         let t_b = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0]];
@@ -327,8 +336,16 @@ mod tests {
         assert_ulps_eq!(a, Gaussian::from_ms(24.999999, 6.469480), epsilon = 1e-6);
         assert_ulps_eq!(b, Gaussian::from_ms(24.999999, 6.469480), epsilon = 1e-6);
 
-        let t_a = Player::new(Gaussian::from_ms(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0);
+        let t_a = Player::new(
-        let t_b = Player::new(Gaussian::from_ms(29.0, 2.0), 25.0 / 6.0, 25.0 / 300.0);
+            Gaussian::from_ms(25.0, 3.0),
+            25.0 / 6.0,
+            ConstantDrift(25.0 / 300.0),
+        );
+        let t_b = Player::new(
+            Gaussian::from_ms(29.0, 2.0),
+            25.0 / 6.0,
+            ConstantDrift(25.0 / 300.0),
+        );
 
         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);
@@ -346,17 +363,17 @@ mod tests {
         let t_a = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
         let t_b = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
         let t_c = Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
@@ -376,9 +393,21 @@ mod tests {
         assert_ulps_eq!(b, Gaussian::from_ms(25.000000, 5.707423), epsilon = 1e-6);
         assert_ulps_eq!(c, Gaussian::from_ms(24.999999, 5.729068), epsilon = 1e-6);
 
-        let t_a = Player::new(Gaussian::from_ms(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0);
+        let t_a = Player::new(
-        let t_b = Player::new(Gaussian::from_ms(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0);
+            Gaussian::from_ms(25.0, 3.0),
-        let t_c = Player::new(Gaussian::from_ms(29.0, 2.0), 25.0 / 6.0, 25.0 / 300.0);
+            25.0 / 6.0,
+            ConstantDrift(25.0 / 300.0),
+        );
+        let t_b = Player::new(
+            Gaussian::from_ms(25.0, 3.0),
+            25.0 / 6.0,
+            ConstantDrift(25.0 / 300.0),
+        );
+        let t_c = Player::new(
+            Gaussian::from_ms(29.0, 2.0),
+            25.0 / 6.0,
+            ConstantDrift(25.0 / 300.0),
+        );
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
         let g = Game::new(
@@ -401,17 +430,33 @@ mod tests {
     #[test]
     fn test_2vs1vs2_mixed() {
         let t_a = vec![
-            Player::new(Gaussian::from_ms(12.0, 3.0), 25.0 / 6.0, 25.0 / 300.0),
+            Player::new(
-            Player::new(Gaussian::from_ms(18.0, 3.0), 25.0 / 6.0, 25.0 / 300.0),
+                Gaussian::from_ms(12.0, 3.0),
+                25.0 / 6.0,
+                ConstantDrift(25.0 / 300.0),
+            ),
+            Player::new(
+                Gaussian::from_ms(18.0, 3.0),
+                25.0 / 6.0,
+                ConstantDrift(25.0 / 300.0),
+            ),
         ];
         let t_b = vec![Player::new(
             Gaussian::from_ms(30.0, 3.0),
             25.0 / 6.0,
-            25.0 / 300.0,
+            ConstantDrift(25.0 / 300.0),
         )];
         let t_c = vec![
-            Player::new(Gaussian::from_ms(14.0, 3.0), 25.0 / 6.0, 25.0 / 300.0),
+            Player::new(
-            Player::new(Gaussian::from_ms(16., 3.0), 25.0 / 6.0, 25.0 / 300.0),
+                Gaussian::from_ms(14.0, 3.0),
+                25.0 / 6.0,
+                ConstantDrift(25.0 / 300.0),
+            ),
+            Player::new(
+                Gaussian::from_ms(16., 3.0),
+                25.0 / 6.0,
+                ConstantDrift(25.0 / 300.0),
+            ),
         ];
 
         let w = [vec![1.0, 1.0], vec![1.0], vec![1.0, 1.0]];
@@ -433,12 +478,12 @@ mod tests {
         let t_a = vec![Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            0.0,
+            ConstantDrift(0.0),
         )];
         let t_b = vec![Player::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            0.0,
+            ConstantDrift(0.0),
         )];
 
         let w = [w_a, w_b];
@@ -495,8 +540,16 @@ mod tests {
         let w_a = vec![1.0];
         let w_b = vec![0.0];
 
-        let t_a = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
+        let t_a = vec![Player::new(
-        let t_b = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift(0.0),
+        )];
+        let t_b = vec![Player::new(
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift(0.0),
+        )];
 
         let w = [w_a, w_b];
         let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
@@ -516,8 +569,16 @@ mod tests {
         let w_a = vec![1.0];
         let w_b = vec![-1.0];
 
-        let t_a = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
+        let t_a = vec![Player::new(
-        let t_b = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift(0.0),
+        )];
+        let t_b = vec![Player::new(
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift(0.0),
+        )];
 
         let w = [w_a, w_b];
         let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
@@ -529,14 +590,30 @@ mod tests {
     #[test]
     fn test_2vs2_weighted() {
         let t_a = vec![
-            Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
+            Player::new(
-            Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
+                Gaussian::from_ms(25.0, 25.0 / 3.0),
+                25.0 / 6.0,
+                ConstantDrift(0.0),
+            ),
+            Player::new(
+                Gaussian::from_ms(25.0, 25.0 / 3.0),
+                25.0 / 6.0,
+                ConstantDrift(0.0),
+            ),
         ];
         let w_a = vec![0.4, 0.8];
 
         let t_b = vec![
-            Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
+            Player::new(
-            Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
+                Gaussian::from_ms(25.0, 25.0 / 3.0),
+                25.0 / 6.0,
+                ConstantDrift(0.0),
+            ),
+            Player::new(
+                Gaussian::from_ms(25.0, 25.0 / 3.0),
+                25.0 / 6.0,
+                ConstantDrift(0.0),
+            ),
         ];
         let w_b = vec![0.9, 0.6];
 
@@ -628,7 +705,7 @@ mod tests {
                 vec![Player::new(
                     Gaussian::from_ms(25.0, 25.0 / 3.0),
                     25.0 / 6.0,
-                    0.0,
+                    ConstantDrift(0.0),
                 )],
             ],
             &[1.0, 0.0],

src/gaussian.rs

@@ -40,10 +40,10 @@ impl Gaussian {
         }
     }
 
-    pub(crate) fn forget(&self, gamma: f64, t: i64) -> Self {
+    pub(crate) fn forget(&self, variance_delta: f64) -> Self {
         Self {
             mu: self.mu,
-            sigma: (self.sigma.powi(2) + t as f64 * gamma.powi(2)).sqrt(),
+            sigma: (self.sigma.powi(2) + variance_delta).sqrt(),
         }
     }
 }

src/history.rs

@@ -1,25 +1,27 @@
 use std::collections::HashMap;
 
 use crate::{
+    BETA, GAMMA, Index, MU, N_INF, P_DRAW, SIGMA,
     agent::{self, Agent},
     batch::{self, Batch},
+    drift::{ConstantDrift, Drift},
     gaussian::Gaussian,
     player::Player,
-    sort_time, tuple_gt, tuple_max, Index, BETA, GAMMA, MU, P_DRAW, SIGMA,
+    sort_time, tuple_gt, tuple_max,
 };
 
 #[derive(Clone)]
-pub struct HistoryBuilder {
+pub struct HistoryBuilder<D: Drift = ConstantDrift> {
     time: bool,
     mu: f64,
     sigma: f64,
     beta: f64,
-    gamma: f64,
+    drift: D,
     p_draw: f64,
     online: bool,
 }
 
-impl HistoryBuilder {
+impl<D: Drift> HistoryBuilder<D> {
     pub fn time(mut self, time: bool) -> Self {
         self.time = time;
         self
@@ -40,9 +42,16 @@ impl HistoryBuilder {
         self
     }
 
-    pub fn gamma(mut self, gamma: f64) -> Self {
+    pub fn drift<D2: Drift>(self, drift: D2) -> HistoryBuilder<D2> {
-        self.gamma = gamma;
+        HistoryBuilder {
-        self
+            drift,
+            time: self.time,
+            mu: self.mu,
+            sigma: self.sigma,
+            beta: self.beta,
+            p_draw: self.p_draw,
+            online: self.online,
+        }
     }
 
     pub fn p_draw(mut self, p_draw: f64) -> Self {
@@ -55,7 +64,7 @@ impl HistoryBuilder {
         self
     }
 
-    pub fn build(self) -> History {
+    pub fn build(self) -> History<D> {
         History {
             size: 0,
             batches: Vec::new(),
@@ -64,41 +73,48 @@ impl HistoryBuilder {
             mu: self.mu,
             sigma: self.sigma,
             beta: self.beta,
-            gamma: self.gamma,
+            drift: self.drift,
             p_draw: self.p_draw,
             online: self.online,
         }
     }
 }
 
-impl Default for HistoryBuilder {
+impl HistoryBuilder<ConstantDrift> {
+    pub fn gamma(mut self, gamma: f64) -> Self {
+        self.drift = ConstantDrift(gamma);
+        self
+    }
+}
+
+impl Default for HistoryBuilder<ConstantDrift> {
     fn default() -> Self {
         Self {
             time: true,
             mu: MU,
             sigma: SIGMA,
             beta: BETA,
-            gamma: GAMMA,
+            drift: ConstantDrift(GAMMA),
             p_draw: P_DRAW,
             online: false,
         }
     }
 }
 
-pub struct History {
+pub struct History<D: Drift = ConstantDrift> {
     size: usize,
     pub(crate) batches: Vec<Batch>,
-    agents: HashMap<Index, Agent>,
+    agents: HashMap<Index, Agent<D>>,
     time: bool,
     mu: f64,
     sigma: f64,
     beta: f64,
-    gamma: f64,
+    drift: D,
     p_draw: f64,
     online: bool,
 }
 
-impl Default for History {
+impl Default for History<ConstantDrift> {
     fn default() -> Self {
         Self {
             size: 0,
@@ -108,18 +124,20 @@ impl Default for History {
             mu: MU,
             sigma: SIGMA,
             beta: BETA,
-            gamma: GAMMA,
+            drift: ConstantDrift(GAMMA),
             p_draw: P_DRAW,
             online: false,
         }
     }
 }
 
-impl History {
+impl History<ConstantDrift> {
-    pub fn builder() -> HistoryBuilder {
+    pub fn builder() -> HistoryBuilder<ConstantDrift> {
         HistoryBuilder::default()
     }
+}
 
+impl<D: Drift> History<D> {
     fn iteration(&mut self) -> (f64, f64) {
         let mut step = (0.0, 0.0);
 
@@ -247,7 +265,7 @@ impl History {
         results: Vec<Vec<f64>>,
         times: Vec<i64>,
         weights: Vec<Vec<Vec<f64>>>,
-        mut priors: HashMap<Index, Player>,
+        mut priors: HashMap<Index, Player<D>>,
     ) {
         assert!(times.is_empty() || self.time, "length(times)>0 but !h.time");
         assert!(
@@ -286,10 +304,11 @@ impl History {
                             Player::new(
                                 Gaussian::from_ms(self.mu, self.sigma),
                                 self.beta,
-                                self.gamma,
+                                self.drift,
                             )
                         }),
-                        ..Default::default()
+                        message: N_INF,
+                        last_time: i64::MIN,
                     },
                 );
             }
@@ -414,9 +433,8 @@ impl History {
 mod tests {
     use approx::assert_ulps_eq;
 
-    use crate::{Game, Gaussian, IndexMap, Player, EPSILON, ITERATIONS, P_DRAW};
-
     use super::*;
+    use crate::{ConstantDrift, EPSILON, Game, Gaussian, ITERATIONS, IndexMap, P_DRAW, Player};
 
     #[test]
     fn test_init() {
@@ -441,7 +459,7 @@ mod tests {
                 Player::new(
                     Gaussian::from_ms(25.0, 25.0 / 3.0),
                     25.0 / 6.0,
-                    0.15 * 25.0 / 3.0,
+                    ConstantDrift(0.15 * 25.0 / 3.0),
                 ),
             );
         }
@@ -503,7 +521,7 @@ mod tests {
                 Player::new(
                     Gaussian::from_ms(25.0, 25.0 / 3.0),
                     25.0 / 6.0,
-                    0.15 * 25.0 / 3.0,
+                    ConstantDrift(0.15 * 25.0 / 3.0),
                 ),
             );
         }
@@ -552,7 +570,7 @@ mod tests {
                 Player::new(
                     Gaussian::from_ms(25.0, 25.0 / 3.0),
                     25.0 / 6.0,
-                    25.0 / 300.0,
+                    ConstantDrift(25.0 / 300.0),
                 ),
             );
         }
@@ -610,7 +628,7 @@ mod tests {
                 Player::new(
                     Gaussian::from_ms(25.0, 25.0 / 3.0),
                     25.0 / 6.0,
-                    25.0 / 300.0,
+                    ConstantDrift(25.0 / 300.0),
                 ),
             );
         }

src/lib.rs

@@ -1,13 +1,16 @@
-use std::borrow::{Borrow, ToOwned};
+use std::{
-use std::cmp::Reverse;
+    borrow::{Borrow, ToOwned},
-use std::collections::HashMap;
+    cmp::Reverse,
-use std::f64::consts::{FRAC_1_SQRT_2, FRAC_2_SQRT_PI, SQRT_2};
+    collections::HashMap,
-use std::hash::Hash;
+    f64::consts::{FRAC_1_SQRT_2, FRAC_2_SQRT_PI, SQRT_2},
+    hash::Hash,
+};
 
 pub mod agent;
 #[cfg(feature = "approx")]
 mod approx;
 pub mod batch;
+pub mod drift;
 mod game;
 pub mod gaussian;
 mod history;
@@ -15,6 +18,7 @@ mod matrix;
 mod message;
 pub mod player;
 
+pub use drift::{ConstantDrift, Drift};
 pub use game::Game;
 pub use gaussian::Gaussian;
 pub use history::History;
@@ -82,7 +86,7 @@ where
     pub fn key(&self, idx: Index) -> Option<&K> {
         self.0
             .iter()
-            .find(|(_, &value)| value == idx)
+            .find(|&(_, value)| *value == idx)
             .map(|(key, _)| key)
     }
 
@@ -115,11 +119,7 @@ fn erfc(x: f64) -> f64 {
 
     let r = t * (-z * z - 1.26551223 + t * h).exp();
 
-    if x >= 0.0 {
+    if x >= 0.0 { r } else { 2.0 - r }
-        r
-    } else {
-        2.0 - r
-    }
 }
 
 fn erfc_inv(mut y: f64) -> f64 {
@@ -147,11 +147,7 @@ fn erfc_inv(mut y: f64) -> f64 {
         x += err / (FRAC_2_SQRT_PI * (-(x.powi(2))).exp() - x * err)
     }
 
-    if y < 1.0 {
+    if y < 1.0 { x } else { -x }
-        x
-    } else {
-        -x
-    }
 }
 
 fn ppf(p: f64, mu: f64, sigma: f64) -> f64 {
@@ -239,9 +235,9 @@ pub(crate) fn sort_time(xs: &[i64], reverse: bool) -> Vec<usize> {
     let mut x = xs.iter().enumerate().collect::<Vec<_>>();
 
     if reverse {
-        x.sort_by_key(|(_, &x)| Reverse(x));
+        x.sort_by_key(|&(_, x)| Reverse(x));
     } else {
-        x.sort_by_key(|(_, &x)| x);
+        x.sort_by_key(|&(_, x)| x);
     }
 
     x.into_iter().map(|(i, _)| i).collect()

src/message.rs

@@ -1,5 +1,4 @@
-use crate::gaussian::Gaussian;
+use crate::{N_INF, gaussian::Gaussian};
-use crate::N_INF;
 
 pub(crate) struct TeamMessage {
     pub(crate) prior: Gaussian,

src/player.rs

@@ -1,35 +1,32 @@
-use crate::{gaussian::Gaussian, BETA, GAMMA};
+use crate::{
+    BETA, GAMMA,
+    drift::{ConstantDrift, Drift},
+    gaussian::Gaussian,
+};
 
 #[derive(Clone, Copy, Debug)]
-pub struct Player {
+pub struct Player<D: Drift = ConstantDrift> {
     pub(crate) prior: Gaussian,
     pub(crate) beta: f64,
-    pub(crate) gamma: f64,
+    pub(crate) drift: D,
-    // pub(crate) draw: Gaussian,
 }
 
-impl Player {
+impl<D: Drift> Player<D> {
-    pub fn new(prior: Gaussian, beta: f64, gamma: f64) -> Self {
+    pub fn new(prior: Gaussian, beta: f64, drift: D) -> Self {
-        Self {
+        Self { prior, beta, drift }
-            prior,
-            beta,
-            gamma,
-            // draw: N_INF,
-        }
     }
 
     pub(crate) fn performance(&self) -> Gaussian {
-        self.prior.forget(self.beta, 1)
+        self.prior.forget(self.beta.powi(2))
     }
 }
 
-impl Default for Player {
+impl Default for Player<ConstantDrift> {
     fn default() -> Self {
         Self {
             prior: Gaussian::default(),
             beta: BETA,
-            gamma: GAMMA,
+            drift: ConstantDrift(GAMMA),
-            // draw: N_INF,
         }
     }
 }