use std::{borrow::Borrow, collections::HashMap, hash::Hash, marker::PhantomData};

use crate::{
    BETA, GAMMA, Index, MU, P_DRAW, SIGMA,
    competitor::{self, Competitor},
    convergence::{ConvergenceOptions, ConvergenceReport},
    drift::{ConstantDrift, Drift},
    error::InferenceError,
    gaussian::Gaussian,
    key_table::KeyTable,
    observer::{NullObserver, Observer},
    predict::Prediction,
    rating::Rating,
    sort_time,
    storage::CompetitorStore,
    time::Time,
    time_slice::{self, EventKind, FilteredStep, TimeSlice},
    tuple_gt, tuple_max,
};

#[derive(Clone)]
pub struct HistoryBuilder<
    T: Time = i64,
    D: Drift<T> = ConstantDrift,
    O: Observer<T> = NullObserver,
    K: Eq + Hash + Clone = &'static str,
> {
    mu: f64,
    sigma: f64,
    beta: f64,
    drift: D,
    p_draw: f64,
    score_sigma: f64,
    convergence: ConvergenceOptions,
    observer: O,
    _time: PhantomData<T>,
    _key: PhantomData<K>,
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<T, D, O, K> {
    pub fn mu(mut self, mu: f64) -> Self {
        self.mu = mu;
        self
    }

    pub fn sigma(mut self, sigma: f64) -> Self {
        self.sigma = sigma;
        self
    }

    pub fn beta(mut self, beta: f64) -> Self {
        self.beta = beta;
        self
    }

    pub fn drift<D2: Drift<T>>(self, drift: D2) -> HistoryBuilder<T, D2, O, K> {
        HistoryBuilder {
            drift,
            mu: self.mu,
            sigma: self.sigma,
            beta: self.beta,
            p_draw: self.p_draw,
            score_sigma: self.score_sigma,
            convergence: self.convergence,
            observer: self.observer,
            _time: self._time,
            _key: self._key,
        }
    }

    /// Probability that two evenly-matched sides draw.
    ///
    /// Must be in `[0.0, 1.0)`. A zero draw probability asserts that draws
    /// cannot occur, so ingesting a tied outcome then fails with
    /// `InferenceError::TieWithoutDrawProbability`.
    ///
    /// # Panics
    ///
    /// Panics if `p_draw` is outside `[0.0, 1.0)` or is NaN.
    pub fn p_draw(mut self, p_draw: f64) -> Self {
        assert!(
            (0.0..1.0).contains(&p_draw),
            "p_draw must be in [0.0, 1.0) (got {p_draw})"
        );
        self.p_draw = p_draw;
        self
    }

    /// Default observation noise for scored outcomes.
    ///
    /// # Panics
    ///
    /// Panics if `score_sigma` is not strictly positive.
    pub fn score_sigma(mut self, score_sigma: f64) -> Self {
        assert!(
            score_sigma > 0.0,
            "score_sigma must be positive (got {score_sigma})"
        );
        self.score_sigma = score_sigma;
        self
    }

    /// Convergence tolerance, iteration cap, and EP damping.
    ///
    /// # Panics
    ///
    /// Panics if `alpha` is outside `(0.0, 1.0]`, or if `epsilon` is negative
    /// or NaN. An `alpha` of zero would leave every EP update unapplied, so
    /// inference would silently return the priors.
    pub fn convergence(mut self, opts: ConvergenceOptions) -> Self {
        assert!(
            opts.alpha > 0.0 && opts.alpha <= 1.0,
            "convergence alpha must be in (0.0, 1.0] (got {})",
            opts.alpha
        );
        assert!(
            opts.epsilon >= 0.0,
            "convergence epsilon must be non-negative (got {})",
            opts.epsilon
        );
        self.convergence = opts;
        self
    }

    pub fn observer<O2: Observer<T>>(self, observer: O2) -> HistoryBuilder<T, D, O2, K> {
        HistoryBuilder {
            mu: self.mu,
            sigma: self.sigma,
            beta: self.beta,
            drift: self.drift,
            p_draw: self.p_draw,
            score_sigma: self.score_sigma,
            convergence: self.convergence,
            observer,
            _time: self._time,
            _key: self._key,
        }
    }

    pub fn build(self) -> History<T, D, O, K> {
        History {
            size: 0,
            time_slices: Vec::new(),
            agents: CompetitorStore::new(),
            keys: KeyTable::new(),
            mu: self.mu,
            sigma: self.sigma,
            beta: self.beta,
            drift: self.drift,
            p_draw: self.p_draw,
            score_sigma: self.score_sigma,
            convergence: self.convergence,
            observer: self.observer,
        }
    }
}

impl Default for HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str> {
    fn default() -> Self {
        Self {
            mu: MU,
            sigma: SIGMA,
            beta: BETA,
            drift: ConstantDrift(GAMMA),
            p_draw: P_DRAW,
            score_sigma: 1.0,
            convergence: ConvergenceOptions::default(),
            observer: NullObserver,
            _time: PhantomData,
            _key: PhantomData,
        }
    }
}

/// Configuration a caller attached to a competitor via `Member`.
///
/// Carries *what was explicitly set* rather than a merged `Rating`, so a member
/// that sets only `drift_scale` does not also assert the default prior — which
/// would spuriously conflict with a prior seeded on an earlier event.
#[derive(Clone, Copy, Default)]
pub(crate) struct CompetitorConfig {
    prior: Option<Gaussian>,
    drift_scale: Option<f64>,
}

impl CompetitorConfig {
    fn is_empty(self) -> bool {
        self.prior.is_none() && self.drift_scale.is_none()
    }
}

pub struct History<
    T: Time = i64,
    D: Drift<T> = ConstantDrift,
    O: Observer<T> = NullObserver,
    K: Eq + Hash + Clone = &'static str,
> {
    size: usize,
    pub(crate) time_slices: Vec<TimeSlice<T>>,
    pub(crate) agents: CompetitorStore<T, D>,
    keys: KeyTable<K>,
    mu: f64,
    sigma: f64,
    beta: f64,
    drift: D,
    p_draw: f64,
    score_sigma: f64,
    convergence: ConvergenceOptions,
    observer: O,
}

impl Default for History<i64, ConstantDrift, NullObserver, &'static str> {
    fn default() -> Self {
        HistoryBuilder::default().build()
    }
}

impl History<i64, ConstantDrift, NullObserver, &'static str> {
    #[must_use]
    pub fn builder() -> HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str> {
        HistoryBuilder::default()
    }
}

impl<K: Eq + Hash + Clone> History<i64, ConstantDrift, NullObserver, K> {
    /// Like `builder()` but uses a custom key type `K` instead of the default `&'static str`.
    #[must_use]
    pub fn builder_with_key() -> HistoryBuilder<i64, ConstantDrift, NullObserver, K> {
        HistoryBuilder {
            mu: MU,
            sigma: SIGMA,
            beta: BETA,
            drift: ConstantDrift(GAMMA),
            p_draw: P_DRAW,
            score_sigma: 1.0,
            convergence: ConvergenceOptions::default(),
            observer: NullObserver,
            _time: PhantomData,
            _key: PhantomData,
        }
    }
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
    pub fn intern<Q>(&mut self, key: &Q) -> Index
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        self.keys.get_or_create(key)
    }

    pub fn lookup<Q>(&self, key: &Q) -> Option<Index>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        self.keys.get(key)
    }
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
    fn iteration(&mut self) -> (f64, f64) {
        let mut step = (0.0, 0.0);

        if self.time_slices.is_empty() {
            return step;
        }

        competitor::clean(self.agents.values_mut(), false);

        for j in (0..self.time_slices.len() - 1).rev() {
            for agent in self.time_slices[j + 1].skills.keys() {
                self.agents.get_mut(agent).unwrap().message =
                    Some(self.time_slices[j + 1].backward_prior_out(&agent, &self.agents));
            }

            let old = self.time_slices[j].posteriors();

            self.time_slices[j].new_backward_info(&self.agents);
            self.observer.on_slice_processed(
                &self.time_slices[j].time,
                j,
                self.time_slices[j].events.len(),
            );

            let new = self.time_slices[j].posteriors();

            step = old
                .iter()
                .fold(step, |step, (a, old)| tuple_max(step, old.delta(new[a])));
        }

        competitor::clean(self.agents.values_mut(), false);

        for j in 1..self.time_slices.len() {
            for agent in self.time_slices[j - 1].skills.keys() {
                self.agents.get_mut(agent).unwrap().message =
                    Some(self.time_slices[j - 1].forward_prior_out(&agent));
            }

            let old = self.time_slices[j].posteriors();

            self.time_slices[j].new_forward_info(&self.agents);
            self.observer.on_slice_processed(
                &self.time_slices[j].time,
                j,
                self.time_slices[j].events.len(),
            );

            let new = self.time_slices[j].posteriors();

            step = old
                .iter()
                .fold(step, |step, (a, old)| tuple_max(step, old.delta(new[a])));
        }

        if self.time_slices.len() == 1 {
            let old = self.time_slices[0].posteriors();

            self.time_slices[0].iteration(0, &self.agents);
            self.observer.on_slice_processed(
                &self.time_slices[0].time,
                0,
                self.time_slices[0].events.len(),
            );

            let new = self.time_slices[0].posteriors();

            step = old
                .iter()
                .fold(step, |step, (a, old)| tuple_max(step, old.delta(new[a])));
        }

        step
    }

    /// Number of distinct time slices in the history.
    #[must_use]
    pub fn time_slices_len(&self) -> usize {
        self.time_slices.len()
    }

    /// Learning curves for all competitors, keyed by their user-facing key.
    pub fn learning_curves(&self) -> HashMap<K, Vec<(T, Gaussian)>> {
        #[cfg(feature = "rayon")]
        {
            use rayon::prelude::*;

            let per_slice: Vec<Vec<(Index, T, Gaussian)>> = self
                .time_slices
                .par_iter()
                .map(|ts| {
                    ts.skills
                        .iter()
                        .map(|(idx, sk)| (idx, ts.time, sk.posterior()))
                        .collect()
                })
                .collect();

            let mut data: HashMap<K, Vec<(T, Gaussian)>> = HashMap::new();
            for slice_contrib in per_slice {
                for (idx, t, g) in slice_contrib {
                    if let Some(key) = self.keys.key(idx).cloned() {
                        data.entry(key).or_default().push((t, g));
                    }
                }
            }
            data
        }
        #[cfg(not(feature = "rayon"))]
        {
            let mut data: HashMap<K, Vec<(T, Gaussian)>> = HashMap::new();
            for slice in &self.time_slices {
                for (idx, skill) in slice.skills.iter() {
                    if let Some(key) = self.keys.key(idx).cloned() {
                        data.entry(key)
                            .or_default()
                            .push((slice.time, skill.posterior()));
                    }
                }
            }
            data
        }
    }

    /// Skill estimate at the latest time slice the competitor appears in.
    pub fn current_skill<Q>(&self, key: &Q) -> Option<Gaussian>
    where
        K: std::borrow::Borrow<Q>,
        Q: std::hash::Hash + Eq + ?Sized,
    {
        let idx = self.keys.get(key)?;
        self.time_slices
            .iter()
            .rev()
            .find_map(|ts| ts.skills.get(idx).map(|sk| sk.posterior()))
    }

    /// Learning curve for a single key: (time, posterior) pairs in time order.
    pub fn learning_curve<Q>(&self, key: &Q) -> Vec<(T, Gaussian)>
    where
        K: std::borrow::Borrow<Q>,
        Q: std::hash::Hash + Eq + ?Sized,
    {
        let Some(idx) = self.keys.get(key) else {
            return Vec::new();
        };
        self.time_slices
            .iter()
            .filter_map(|ts| ts.skills.get(idx).map(|sk| (ts.time, sk.posterior())))
            .collect()
    }

    /// Filtered learning curves for all competitors, keyed by user-facing key.
    ///
    /// Each point is the posterior using only events up to and including that
    /// time — "what we knew then". Contrast `learning_curves`, whose points
    /// are smoothed and so incorporate rounds played later.
    ///
    /// Runs a full forward pass per call and caches nothing. This is the
    /// entry point for multi-key work — see `filtered_learning_curve` for
    /// why calling that once per key is far more expensive.
    pub fn filtered_learning_curves(&self) -> HashMap<K, Vec<(T, Gaussian)>> {
        let mut data: HashMap<K, Vec<(T, Gaussian)>> = HashMap::new();

        for (time, step) in self.filtered_pass() {
            for (agent, posterior) in step.posteriors {
                if let Some(key) = self.keys.key(agent).cloned() {
                    data.entry(key).or_default().push((time, posterior));
                }
            }
        }

        data
    }

    /// Filtered learning curve for a single key: (time, posterior) pairs in
    /// time order.
    ///
    /// Despite mirroring `learning_curve`'s signature, this is not the cheap
    /// per-key lookup that method is: it runs a full forward pass, O(events),
    /// discarding every posterior but the requested key's. N keys fetched
    /// this way costs O(N * events); use `filtered_learning_curves` for
    /// multi-key work instead — it computes the same pass once.
    pub fn filtered_learning_curve<Q>(&self, key: &Q) -> Vec<(T, Gaussian)>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ?Sized,
    {
        let Some(idx) = self.keys.get(key) else {
            return Vec::new();
        };

        self.filtered_pass()
            .into_iter()
            .filter_map(|(time, step)| {
                step.posteriors
                    .iter()
                    .find(|(agent, _)| *agent == idx)
                    .map(|&(_, posterior)| (time, posterior))
            })
            .collect()
    }

    /// Sum per-slice evidence.
    ///
    /// `forward` selects `skill.forward` as each event's prior instead of the
    /// cavity. That is a genuine forward-only (filtering) quantity ONLY on a
    /// history that has never been converged: `iteration` alternates backward
    /// and forward sweeps, so from the second iteration onward the likelihood
    /// feeding the forward message has already absorbed backward information.
    /// For a filtering quantity that holds after convergence, use
    /// `filtered_log_evidence`.
    pub(crate) fn log_evidence_internal(&self, forward: bool, targets: &[Index]) -> f64 {
        // Bound before the closure so it captures the store rather than all of
        // `&self`: capturing `&History` would drag `KeyTable<K>` in and demand
        // `K: Sync` from every caller, which the key type need not satisfy.
        let agents = &self.agents;

        #[cfg(feature = "rayon")]
        {
            use rayon::prelude::*;
            let per_slice: Vec<f64> = self
                .time_slices
                .par_iter()
                .map(|ts| ts.log_evidence(targets, forward, agents))
                .collect();
            per_slice.into_iter().sum()
        }
        #[cfg(not(feature = "rayon"))]
        {
            self.time_slices
                .iter()
                .map(|ts| ts.log_evidence(targets, forward, agents))
                .sum()
        }
    }

    /// Total log-evidence across the history.
    pub fn log_evidence(&self) -> f64 {
        self.log_evidence_internal(false, &[])
    }

    /// Log-evidence restricted to time slices containing at least one of the
    /// given keys. Useful for leave-one-out cross-validation.
    pub fn log_evidence_for<Q>(&self, keys: &[&Q]) -> f64
    where
        K: std::borrow::Borrow<Q>,
        Q: std::hash::Hash + Eq + ?Sized,
    {
        let targets: Vec<Index> = keys.iter().filter_map(|k| self.keys.get(*k)).collect();
        self.log_evidence_internal(false, &targets)
    }

    /// Walk the slices in time order carrying forward messages only.
    ///
    /// This is the forward half of `iteration` with the backward half never
    /// run. It reads `self` and mutates nothing.
    fn filtered_pass(&self) -> Vec<(T, FilteredStep)> {
        let mut messages: HashMap<Index, Gaussian> = HashMap::new();

        let mut pass = Vec::with_capacity(self.time_slices.len());

        for slice in &self.time_slices {
            let step = slice.filtered_step(&messages, &self.agents);

            for &(agent, posterior) in &step.posteriors {
                messages.insert(agent, posterior);
            }

            pass.push((slice.time, step));
        }

        pass
    }

    /// Total log-evidence under forward-only (filtering) information.
    ///
    /// Each event is scored using only what was known before that *time*,
    /// which is the right quantity for prequential scoring and model
    /// comparison. Events sharing a timestamp still inform each other
    /// through the within-slice sweep, so within one slice this is not a
    /// guarantee that event A is scored independently of simultaneous event
    /// B. Contrast `log_evidence`, whose per-event priors carry information
    /// from events that had not happened yet.
    ///
    /// Runs a full forward pass per call and caches nothing. The result does
    /// not depend on whether `converge` has been called.
    #[must_use]
    pub fn filtered_log_evidence(&self) -> f64 {
        self.filtered_pass()
            .iter()
            .map(|(_, step)| step.log_evidence)
            .sum()
    }

    /// The configured observer.
    ///
    /// `History` takes its observer by value, so this is how a caller inspects
    /// one it did not keep a handle to. For an observer that accumulates
    /// state, prefer passing an `Arc` and keeping a clone — see the
    /// [`Observer`] docs.
    #[must_use]
    pub fn observer(&self) -> &O {
        &self.observer
    }

    /// Consume the history and return its observer.
    ///
    /// Useful for reclaiming a non-shared observer's accumulated state after
    /// `converge` without needing interior mutability.
    #[must_use]
    pub fn into_observer(self) -> O {
        self.observer
    }

    /// Every team's member skills, validated.
    ///
    /// # Errors
    ///
    /// `NotEnoughTeams`, `EmptyTeam`, or `UnknownKey`. Unknown keys are
    /// reported rather than dropped — silently skipping them would turn a team
    /// of strangers into a confident-looking prediction about nobody, which is
    /// the failure this replaced.
    fn member_skills(&self, teams: &[&[&K]]) -> Result<Vec<Vec<Gaussian>>, InferenceError>
    where
        K: std::fmt::Debug,
    {
        if teams.len() < 2 {
            return Err(InferenceError::NotEnoughTeams { got: teams.len() });
        }

        let mut gathered = Vec::with_capacity(teams.len());

        for (team_idx, team) in teams.iter().enumerate() {
            if team.is_empty() {
                return Err(InferenceError::EmptyTeam { team: team_idx });
            }

            let mut members = Vec::with_capacity(team.len());
            for (member_idx, key) in team.iter().enumerate() {
                let unknown = InferenceError::UnknownKey {
                    team: team_idx,
                    member: member_idx,
                    key: format!("{key:?}"),
                };
                let index = self.keys.get(*key).ok_or(unknown.clone())?;
                members.push(
                    self.time_slices
                        .iter()
                        .rev()
                        .find_map(|ts| ts.skills.get(index).map(|s| s.posterior()))
                        .ok_or(unknown)?,
                );
            }

            gathered.push(members);
        }

        Ok(gathered)
    }

    /// Each team's performance Gaussian, and its member count.
    ///
    /// Performance is skill inflated by `beta`: the question a prediction
    /// answers is "how will they do today", not "how good are they".
    ///
    /// # Errors
    ///
    /// As [`History::member_skills`].
    fn performances(&self, teams: &[&[&K]]) -> Result<(Vec<Gaussian>, Vec<usize>), InferenceError>
    where
        K: std::fmt::Debug,
    {
        let skills = self.member_skills(teams)?;

        let performances = skills
            .iter()
            .map(|team| {
                team.iter()
                    .fold(crate::N00, |acc, s| acc + s.forget(self.beta.powi(2)))
            })
            .collect();
        let sizes = skills.iter().map(Vec::len).collect();

        Ok((performances, sizes))
    }

    /// Draw margins per team pair.
    ///
    /// Inference derives the margin per rank-adjacent pair from those two
    /// teams' betas (`Game::likelihoods`), so prediction must too — a single
    /// game-wide margin would describe a different model than the one that
    /// will actually be fitted.
    fn margins(&self, sizes: &[usize]) -> crate::predict::Margins {
        let beta_sq = self.beta.powi(2);
        let p_draw = self.p_draw;

        crate::predict::Margins::new(sizes.len(), |i, j| {
            if p_draw == 0.0 {
                0.0
            } else {
                let sd = ((sizes[i] + sizes[j]) as f64 * beta_sq).sqrt();
                crate::compute_margin(p_draw, sd)
            }
        })
    }

    /// Draw-probability quality metric for the given teams (key slices).
    ///
    /// Values range roughly `[0, 1]`; 1 == perfectly matched. Supports any
    /// number of teams.
    ///
    /// Note this answers "is this matchup *fair*", which is not the same as
    /// "is this matchup *informative*" — the two coincide for two evenly
    /// matched teams and diverge elsewhere.
    ///
    /// # Preconditions
    ///
    /// Every key must already be known to the history — that is, must have
    /// appeared in an ingested event. An unknown key is `UnknownKey`, not a
    /// silently dropped member. If your caller cannot guarantee that, pre-filter
    /// with [`History::lookup`] or [`History::current_skill`]; treating the
    /// error as "no information" and substituting a neutral value turns a
    /// whole-team miss into a plausible constant, which is invisible to any
    /// test that does not assert on variation.
    ///
    /// # Errors
    ///
    /// `NotEnoughTeams`, `EmptyTeam`, or `UnknownKey`.
    pub fn predict_quality(&self, teams: &[&[&K]]) -> Result<f64, InferenceError>
    where
        K: std::fmt::Debug,
    {
        let groups = self.member_skills(teams)?;
        let group_refs: Vec<&[Gaussian]> = groups.iter().map(Vec::as_slice).collect();
        Ok(crate::quality(&group_refs, self.beta))
    }

    /// Expected information gain of running this matchup, in nats.
    ///
    /// Answers "which comparison should I run next" rather than "who will
    /// win": the outcome-weighted divergence between current beliefs and the
    /// beliefs each possible result would produce. Higher means the result
    /// would teach you more.
    ///
    /// Uses each competitor's current skill as the prior, and the history's
    /// own `beta`, `drift` and `p_draw`, so the outcomes weighted here are the
    /// ones that would actually be fitted if the matchup were played and
    /// recorded.
    ///
    /// Distinct from [`History::predict_quality`], which measures *fairness*.
    /// The two coincide for two evenly matched competitors and diverge
    /// elsewhere. See [`expected_information_gain`](crate::expected_information_gain)
    /// for the scale, the analytic `ln k` ceiling, and the cost.
    ///
    /// # Errors
    ///
    /// # Preconditions
    ///
    /// Every key must already be known to the history — that is, must have
    /// appeared in an ingested event. An unknown key is `UnknownKey`, not a
    /// silently dropped member. If your caller cannot guarantee that, pre-filter
    /// with [`History::lookup`] or [`History::current_skill`]; treating the
    /// error as "no information" and substituting a neutral value turns a
    /// whole-team miss into a plausible constant, which is invisible to any
    /// test that does not assert on variation.
    ///
    /// As [`History::member_skills`], plus `TooManyTeams` and anything
    /// inference returns for a hypothetical outcome.
    pub fn expected_information_gain(&self, teams: &[&[&K]]) -> Result<f64, InferenceError>
    where
        K: std::fmt::Debug,
    {
        let skills = self.member_skills(teams)?;

        let ratings: Vec<Vec<Rating<T, D>>> = skills
            .iter()
            .map(|team| {
                team.iter()
                    .map(|&skill| Rating::new(skill, self.beta, self.drift))
                    .collect()
            })
            .collect();
        let team_refs: Vec<&[Rating<T, D>]> = ratings.iter().map(Vec::as_slice).collect();

        crate::expected_information_gain(
            &team_refs,
            &crate::GameOptions {
                p_draw: self.p_draw,
                score_sigma: self.score_sigma,
                convergence: self.convergence,
            },
        )
    }

    /// `P(team i finishes strictly first)`, for every team.
    ///
    /// Supports any number of teams. Because performances are independent
    /// Gaussians, this separates into a one-dimensional integral per team —
    /// no multivariate orthant probability is involved — and is evaluated by
    /// adaptive quadrature to within the precision of the underlying normal
    /// CDF (~1e-8).
    ///
    /// With a zero `p_draw` these sum to one. With a positive `p_draw` the
    /// shortfall is the probability that the top place is shared.
    ///
    /// Cheap at any team count: cost grows as the square of the team count,
    /// not factorially. Prefer this to [`History::predict_outcome`] when you
    /// only need to know who wins.
    ///
    /// # Preconditions
    ///
    /// Every key must already be known to the history — that is, must have
    /// appeared in an ingested event. An unknown key is `UnknownKey`, not a
    /// silently dropped member. If your caller cannot guarantee that, pre-filter
    /// with [`History::lookup`] or [`History::current_skill`]; treating the
    /// error as "no information" and substituting a neutral value turns a
    /// whole-team miss into a plausible constant, which is invisible to any
    /// test that does not assert on variation.
    ///
    /// # Errors
    ///
    /// `NotEnoughTeams`, `EmptyTeam`, or `UnknownKey`.
    pub fn predict_win_probabilities(&self, teams: &[&[&K]]) -> Result<Vec<f64>, InferenceError>
    where
        K: std::fmt::Debug,
    {
        let (performances, sizes) = self.performances(teams)?;
        Ok(crate::predict::win_probabilities(
            &performances,
            &self.margins(&sizes),
        ))
    }

    /// The full distribution over finishing orders.
    ///
    /// Every entry is a rank vector — the shape [`crate::Outcome::ranking`]
    /// takes, equal ranks meaning a tie — paired with its probability. The
    /// entries are exhaustive and disjoint, so they sum to one; that identity
    /// is the strongest available check on the numerics and is worth asserting
    /// in tests via [`Prediction::total`].
    ///
    /// Accounts for `p_draw`: with a positive draw probability, tied outcomes
    /// carry real mass rather than being silently omitted.
    ///
    /// # Cost
    ///
    /// This enumerates the outcome space, which holds `n! * 2^(n-1)` events —
    /// 24 at three teams, 192 at four, 1_920 at five, 23_040 at six. Each
    /// costs one `O(teams * grid)` pass, so this is milliseconds at three or
    /// four teams and seconds at six. Above
    /// [`MAX_TEAMS_FOR_DISTRIBUTION`](crate::MAX_PREDICTED_TEAMS) it returns
    /// `TooManyTeams` rather than hanging. When you need one specific ordering
    /// use [`History::predict_ranking`], and when you only need the winner use
    /// [`History::predict_win_probabilities`]; both stay cheap at any size.
    ///
    /// # Preconditions
    ///
    /// Every key must already be known to the history — that is, must have
    /// appeared in an ingested event. An unknown key is `UnknownKey`, not a
    /// silently dropped member. If your caller cannot guarantee that, pre-filter
    /// with [`History::lookup`] or [`History::current_skill`]; treating the
    /// error as "no information" and substituting a neutral value turns a
    /// whole-team miss into a plausible constant, which is invisible to any
    /// test that does not assert on variation.
    ///
    /// # Errors
    ///
    /// `NotEnoughTeams`, `EmptyTeam`, `UnknownKey`, or `TooManyTeams`.
    pub fn predict_outcome(&self, teams: &[&[&K]]) -> Result<Prediction, InferenceError>
    where
        K: std::fmt::Debug,
    {
        if teams.len() > crate::MAX_PREDICTED_TEAMS {
            return Err(InferenceError::TooManyTeams {
                got: teams.len(),
                max: crate::MAX_PREDICTED_TEAMS,
            });
        }

        let (performances, sizes) = self.performances(teams)?;
        Ok(Prediction::new(crate::predict::outcome_distribution(
            &performances,
            &self.margins(&sizes),
        )))
    }

    /// Probability of one specific finishing order.
    ///
    /// `ranks` follows [`crate::Outcome::ranking`]: lower is better, and equal
    /// values mean those teams tied. Teams sharing a rank may finish in any
    /// internal order, so this sums over those orders rather than picking one.
    ///
    /// Unlike [`History::predict_outcome`] this does not enumerate the outcome
    /// space, so it stays cheap at any team count — use it when you know which
    /// orderings you care about.
    ///
    /// # Errors
    ///
    /// # Preconditions
    ///
    /// Every key must already be known to the history — that is, must have
    /// appeared in an ingested event. An unknown key is `UnknownKey`, not a
    /// silently dropped member. If your caller cannot guarantee that, pre-filter
    /// with [`History::lookup`] or [`History::current_skill`]; treating the
    /// error as "no information" and substituting a neutral value turns a
    /// whole-team miss into a plausible constant, which is invisible to any
    /// test that does not assert on variation.
    ///
    /// `NotEnoughTeams`, `EmptyTeam`, `UnknownKey`, or `MismatchedShape` if
    /// `ranks` does not have one entry per team.
    pub fn predict_ranking(&self, teams: &[&[&K]], ranks: &[u32]) -> Result<f64, InferenceError>
    where
        K: std::fmt::Debug,
    {
        if ranks.len() != teams.len() {
            return Err(InferenceError::MismatchedShape {
                kind: "ranks vs teams",
                expected: teams.len(),
                got: ranks.len(),
            });
        }

        let (performances, sizes) = self.performances(teams)?;
        Ok(crate::predict::ranking_probability(
            &performances,
            &self.margins(&sizes),
            ranks,
        ))
    }

    /// Run the full forward+backward convergence loop and return a summary.
    ///
    /// Failing to reach `epsilon` within `max_iter` is not an error: the
    /// returned report carries `converged: false` and the final step.
    ///
    /// # Errors
    ///
    /// `NonFiniteResult` if a sweep produces a NaN or infinite step. EP has
    /// broken down at that point and further iterations cannot recover, so the
    /// loop stops rather than reporting a NaN step as convergence.
    pub fn converge(&mut self) -> Result<ConvergenceReport, InferenceError> {
        use std::time::Instant;

        use smallvec::SmallVec;

        let opts = self.convergence;

        if self.time_slices.is_empty() {
            return Ok(ConvergenceReport {
                iterations: 0,
                final_step: (0.0, 0.0),
                log_evidence: 0.0,
                converged: true,
                per_iteration_time: SmallVec::new(),
            });
        }

        let mut step = (f64::INFINITY, f64::INFINITY);
        let mut i = 0;
        let mut per_iter: SmallVec<[std::time::Duration; 32]> = SmallVec::new();
        while tuple_gt(step, opts.epsilon) && i < opts.max_iter {
            let t0 = Instant::now();
            step = self.iteration();
            per_iter.push(t0.elapsed());
            i += 1;
            self.observer.on_iteration_end(i, step);

            // A non-finite step means EP has broken down; further iterations
            // cannot recover, and `tuple_gt` would read NaN as converged.
            if !crate::step_is_finite(step) {
                break;
            }
        }

        if !crate::step_is_finite(step) {
            self.observer.on_converged(i, step, false);

            return Err(InferenceError::NonFiniteResult {
                context: "History::converge",
                step,
            });
        }

        let converged = crate::step_converged(step, opts.epsilon);
        let log_evidence = self.log_evidence_internal(false, &[]);
        self.observer.on_converged(i, step, converged);
        Ok(ConvergenceReport {
            iterations: i,
            final_step: step,
            log_evidence,
            converged,
            per_iteration_time: per_iter,
        })
    }
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
    pub(crate) fn add_events_with_prior(
        &mut self,
        mut composition: Vec<Vec<Vec<Index>>>,
        mut results: Option<Vec<Vec<f64>>>,
        times: Vec<T>,
        mut weights: Option<Vec<Vec<Vec<f64>>>>,
        kinds: Vec<EventKind>,
        priors: HashMap<Index, CompetitorConfig>,
    ) -> Result<(), InferenceError> {
        if results
            .as_ref()
            .is_some_and(|r| r.len() != composition.len())
        {
            let got = results.as_ref().map_or(0, Vec::len);

            return Err(InferenceError::MismatchedShape {
                kind: "results",
                expected: composition.len(),
                got,
            });
        }
        if times.len() != composition.len() {
            return Err(InferenceError::MismatchedShape {
                kind: "times",
                expected: composition.len(),
                got: times.len(),
            });
        }
        if weights
            .as_ref()
            .is_some_and(|w| w.len() != composition.len())
        {
            let got = weights.as_ref().map_or(0, Vec::len);

            return Err(InferenceError::MismatchedShape {
                kind: "weights",
                expected: composition.len(),
                got,
            });
        }
        if kinds.len() != composition.len() {
            return Err(InferenceError::MismatchedShape {
                kind: "kinds",
                expected: composition.len(),
                got: kinds.len(),
            });
        }

        // Chokepoint for tie validation: every ingestion route lands here,
        // including `record_draw`, which builds its results directly rather
        // than going through `Outcome`.
        if self.p_draw == 0.0 {
            for (event_results, kind) in results.iter().flatten().zip(kinds.iter()) {
                if !matches!(kind, EventKind::Ranked) {
                    continue;
                }

                if let Some(teams) = crate::first_tied_output(event_results) {
                    return Err(InferenceError::TieWithoutDrawProbability { teams });
                }
            }
        }

        competitor::clean(self.agents.values_mut(), true);

        let mut this_agent = Vec::with_capacity(1024);

        for agent in composition.iter().flatten().flatten() {
            if this_agent.contains(agent) {
                continue;
            }

            this_agent.push(*agent);

            let config = priors.get(agent).copied().unwrap_or_default();

            if self.agents.contains(*agent) {
                // Seeding a competitor the history already knows. This used to
                // be dropped on the floor: `remove` was only reached on the
                // create path, so a prior applied on a competitor's very first
                // event and was silently ignored ever after.
                if config.is_empty() {
                    continue;
                }

                let rating = &mut self.agents.get_mut(*agent).unwrap().rating;
                if let Some(prior) = config.prior {
                    rating.prior = prior;
                }
                if let Some(scale) = config.drift_scale {
                    rating.drift_scale = scale;
                }
                let seeded = rating.prior;

                if config.prior.is_some() {
                    // The prior is not re-derived every pass the way drift is.
                    // A competitor's earliest slice has its forward message set
                    // to the prior once, at ingestion, and `iteration` refreshes
                    // only slices after the first — so without this, a late
                    // prior would reach the drift terms and nothing else, which
                    // is a subtler version of the silent drop this replaced.
                    //
                    // `clean` has just nulled every message, so the earliest
                    // slice's forward is exactly the prior.
                    for slice in &mut self.time_slices {
                        if let Some(skill) = slice.skills.get_mut(*agent) {
                            skill.forward = seeded;
                            break;
                        }
                    }
                }
            } else {
                let mut rating = Rating::new(
                    Gaussian::from_ms(self.mu, self.sigma),
                    self.beta,
                    self.drift,
                );
                if let Some(prior) = config.prior {
                    rating.prior = prior;
                }
                if let Some(scale) = config.drift_scale {
                    rating.drift_scale = scale;
                }

                self.agents.insert(
                    *agent,
                    Competitor {
                        rating,
                        message: None,
                        last_time: None,
                    },
                );
            }
        }

        let n = composition.len();
        let o = sort_time(&times, false);

        // The chunking loop below MOVES each event's data out of `composition`,
        // `results` and `weights` instead of cloning it. That is only sound
        // because `o` is a permutation, so every index is visited exactly once
        // — visiting one twice would silently yield an empty event rather than
        // failing.
        debug_assert!(
            {
                let mut seen = vec![false; n];
                o.iter()
                    .all(|&idx| !std::mem::replace(&mut seen[idx], true))
            },
            "sort_time must return a permutation of 0..{n}"
        );

        let mut i = 0;
        let mut k = 0;

        while i < n {
            let mut j = i + 1;
            let t = times[o[i]];

            while j < n && times[o[j]] == t {
                j += 1;
            }

            while self.time_slices.len() > k && self.time_slices[k].time < t {
                let time_slice = &mut self.time_slices[k];

                if k > 0 {
                    time_slice.new_forward_info(&self.agents);
                }

                for agent_idx in &this_agent {
                    if let Some(skill) = time_slice.skills.get_mut(*agent_idx) {
                        skill.elapsed = time_slice::compute_elapsed(
                            self.agents[*agent_idx].last_time.as_ref(),
                            &time_slice.time,
                        );

                        let agent = self.agents.get_mut(*agent_idx).unwrap();

                        agent.last_time = Some(time_slice.time);
                        agent.message = Some(time_slice.forward_prior_out(agent_idx));
                    }
                }

                k += 1;
            }

            let composition = (i..j)
                .map(|e| std::mem::take(&mut composition[o[e]]))
                .collect::<Vec<_>>();

            let results = results.as_mut().map(|results| {
                (i..j)
                    .map(|e| std::mem::take(&mut results[o[e]]))
                    .collect::<Vec<_>>()
            });

            let weights = weights.as_mut().map(|weights| {
                (i..j)
                    .map(|e| std::mem::take(&mut weights[o[e]]))
                    .collect::<Vec<_>>()
            });

            let kinds_chunk: Vec<EventKind> = (i..j).map(|e| kinds[o[e]]).collect();

            if self.time_slices.len() > k && self.time_slices[k].time == t {
                let time_slice = &mut self.time_slices[k];
                time_slice.add_events(composition, results, weights, kinds_chunk, &self.agents);

                for agent_idx in time_slice.skills.keys() {
                    let agent = self.agents.get_mut(agent_idx).unwrap();

                    agent.last_time = Some(t);
                    agent.message = Some(time_slice.forward_prior_out(&agent_idx));
                }

                k += 1;
            } else {
                let mut time_slice = TimeSlice::new(t, self.p_draw, self.convergence);
                time_slice.add_events(composition, results, weights, kinds_chunk, &self.agents);

                self.time_slices.insert(k, time_slice);

                let time_slice = &self.time_slices[k];

                for agent_idx in time_slice.skills.keys() {
                    let agent = self.agents.get_mut(agent_idx).unwrap();

                    agent.last_time = Some(t);
                    agent.message = Some(time_slice.forward_prior_out(&agent_idx));
                }

                k += 1;
            }

            i = j;
        }

        while self.time_slices.len() > k {
            let time_slice = &mut self.time_slices[k];

            time_slice.new_forward_info(&self.agents);

            for agent_idx in &this_agent {
                if let Some(skill) = time_slice.skills.get_mut(*agent_idx) {
                    skill.elapsed = time_slice::compute_elapsed(
                        self.agents[*agent_idx].last_time.as_ref(),
                        &time_slice.time,
                    );

                    let agent = self.agents.get_mut(*agent_idx).unwrap();

                    agent.last_time = Some(time_slice.time);
                    agent.message = Some(time_slice.forward_prior_out(agent_idx));
                }
            }

            k += 1;
        }

        self.size += n;
        Ok(())
    }

    /// Record a single two-competitor event that `winner` won.
    ///
    /// # Errors
    ///
    /// Ingests through the same path as [`History::add_events`], so it returns
    /// the same errors. A two-team decisive outcome cannot tie, so
    /// `TieWithoutDrawProbability` is not reachable here.
    pub fn record_winner<Q>(&mut self, winner: &Q, loser: &Q, time: T) -> Result<(), InferenceError>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        let w = self.intern(winner);
        let l = self.intern(loser);
        self.add_events_with_prior(
            vec![vec![vec![w], vec![l]]],
            Some(vec![vec![1.0, 0.0]]),
            vec![time],
            None,
            vec![EventKind::Ranked],
            HashMap::new(),
        )
    }

    /// Record a single two-competitor event that ended level.
    ///
    /// # Errors
    ///
    /// Ingests through the same path as [`History::add_events`]. Note
    /// `TieWithoutDrawProbability` *is* reachable here: a draw needs a
    /// positive `p_draw`.
    pub fn record_draw<Q>(&mut self, a: &Q, b: &Q, time: T) -> Result<(), InferenceError>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        let a_idx = self.intern(a);
        let b_idx = self.intern(b);
        self.add_events_with_prior(
            vec![vec![vec![a_idx], vec![b_idx]]],
            Some(vec![vec![0.0, 0.0]]),
            vec![time],
            None,
            vec![EventKind::Ranked],
            HashMap::new(),
        )
    }

    /// Start a fluent event builder for a single match at `time`.
    pub fn event(&mut self, time: T) -> crate::event_builder::EventBuilder<'_, T, D, O, K> {
        crate::event_builder::EventBuilder::new(self, time)
    }

    /// Bulk-ingest typed events.
    ///
    /// # Errors
    ///
    /// - `MismatchedShape` if an event's outcome does not describe the same
    ///   number of teams the event has, or if per-member weights do not match
    ///   the team's membership.
    /// - `InvalidParameter` if a per-event `score_sigma` override is not
    ///   strictly positive.
    /// - `TieWithoutDrawProbability` if an event ties two teams while the
    ///   history's `p_draw` is zero. This includes `Outcome::winner(w, n)` for
    ///   `n >= 3`, which ties every loser.
    pub fn add_events<I>(&mut self, events: I) -> Result<(), InferenceError>
    where
        I: IntoIterator<Item = crate::event::Event<T, K>>,
    {
        use crate::event::Event;
        let events: Vec<Event<T, K>> = events.into_iter().collect();
        if events.is_empty() {
            return Ok(());
        }

        let mut composition: Vec<Vec<Vec<Index>>> = Vec::with_capacity(events.len());
        let mut results: Vec<Vec<f64>> = Vec::with_capacity(events.len());
        let mut times: Vec<T> = Vec::with_capacity(events.len());
        let mut weights: Vec<Vec<Vec<f64>>> = Vec::with_capacity(events.len());
        let mut kinds: Vec<EventKind> = Vec::with_capacity(events.len());
        let mut priors: HashMap<Index, CompetitorConfig> = HashMap::new();

        for ev in events {
            if ev.outcome.team_count() != ev.teams.len() {
                return Err(InferenceError::MismatchedShape {
                    kind: "outcome vs teams",
                    expected: ev.teams.len(),
                    got: ev.outcome.team_count(),
                });
            }

            let mut event_comp: Vec<Vec<Index>> = Vec::with_capacity(ev.teams.len());
            let mut event_weights: Vec<Vec<f64>> = Vec::with_capacity(ev.teams.len());

            for team in ev.teams {
                let mut team_indices: Vec<Index> = Vec::with_capacity(team.members.len());
                let mut team_weights: Vec<f64> = Vec::with_capacity(team.members.len());
                for member in team.members {
                    let idx = self.keys.get_or_create(&member.key);
                    team_indices.push(idx);
                    team_weights.push(member.weight);

                    if let Some(scale) = member.drift_scale {
                        // Squaring would make a negative scale behave as its
                        // absolute value, so reject rather than silently
                        // accept a sign the caller cannot have meant.
                        if !scale.is_finite() || scale < 0.0 {
                            return Err(InferenceError::InvalidParameter {
                                name: "drift_scale",
                                value: scale,
                            });
                        }
                    }

                    // `prior` and `drift_scale` configure the competitor, not
                    // the event. Both land in the same entry so a member may
                    // set either alone.
                    //
                    // Events within a batch are not ordered, so a batch that
                    // sets one field twice with different values has no
                    // well-defined result — "last one wins" would depend on
                    // iteration order, which `tests/ingestion_equivalence.rs`
                    // exists to rule out. Repeating the *same* value is fine,
                    // and is the expected shape when the configuration is a
                    // property of the domain rather than of one event.
                    if member.prior.is_some() || member.drift_scale.is_some() {
                        let entry = priors.entry(idx).or_default();

                        if let Some(prior) = member.prior {
                            if entry.prior.is_some_and(|held| held != prior) {
                                return Err(InferenceError::ConflictingCompetitorConfig {
                                    competitor: idx.get(),
                                    field: "prior",
                                });
                            }
                            entry.prior = Some(prior);
                        }
                        if let Some(scale) = member.drift_scale {
                            if entry.drift_scale.is_some_and(|held| held != scale) {
                                return Err(InferenceError::ConflictingCompetitorConfig {
                                    competitor: idx.get(),
                                    field: "drift_scale",
                                });
                            }
                            entry.drift_scale = Some(scale);
                        }
                    }
                }
                event_comp.push(team_indices);
                event_weights.push(team_weights);
            }
            composition.push(event_comp);
            weights.push(event_weights);

            let event_result: Vec<f64> = match &ev.outcome {
                crate::Outcome::Ranked(ranks) => {
                    let max_rank = ranks.iter().copied().max().unwrap_or(0) as f64;
                    kinds.push(EventKind::Ranked);
                    ranks.iter().map(|&r| max_rank - r as f64).collect()
                }
                crate::Outcome::Scored { scores, sigma } => {
                    let resolved = sigma.unwrap_or(self.score_sigma);
                    if resolved <= 0.0 || resolved.is_nan() {
                        return Err(InferenceError::InvalidParameter {
                            name: "score_sigma",
                            value: resolved,
                        });
                    }

                    kinds.push(EventKind::Scored {
                        score_sigma: resolved,
                    });
                    scores.to_vec()
                }
            };
            results.push(event_result);
            times.push(ev.time);
        }

        let weights = if weights.is_empty() {
            None
        } else {
            Some(weights)
        };

        self.add_events_with_prior(composition, Some(results), times, weights, kinds, priors)
    }
}

#[cfg(test)]
mod tests {
    use approx::assert_ulps_eq;
    use smallvec::smallvec;

    use super::*;
    use crate::{
        ConstantDrift, EPSILON, Event, Game, Gaussian, Member, Outcome, P_DRAW, Team,
        arena::ScratchArena,
    };

    /// #17: a slice's footprint must be O(competitors in the slice), not
    /// O(largest global index it touches). The store used to be a dense
    /// `Vec<Skill>` indexed by `Index.0`, so the same two-competitor games cost
    /// 20,000 slots per slice when the competitors sat at the top of a large
    /// roster. Measured end to end, peak RSS was 309 MB against 52 MB.
    #[test]
    fn per_slice_footprint_is_independent_of_index_magnitude() {
        fn total_skill_slots(high_indices: bool) -> usize {
            let mut h: History<i64, ConstantDrift, NullObserver, String> =
                History::builder_with_key().build();

            for i in 0..2_000 {
                h.intern(&format!("k{i:05}"));
            }

            let (a, b) = if high_indices {
                ("k01998".to_string(), "k01999".to_string())
            } else {
                ("k00000".to_string(), "k00001".to_string())
            };

            for time in 1..=20i64 {
                h.record_winner(&a, &b, time).unwrap();
            }

            h.time_slices
                .iter()
                .map(|ts| ts.skills.allocated_slots())
                .sum()
        }

        let low = total_skill_slots(false);
        let high = total_skill_slots(true);

        assert_eq!(low, high, "footprint must not depend on index magnitude");

        // A dense store over a 2,000-key roster would allocate 20 x 2,000.
        assert!(
            high < 1_000,
            "20 slices of 2 competitors allocated {high} slots"
        );
    }

    fn make_events_1v1(
        pairs: &[(&'static str, &'static str)],
        outcomes: &[Outcome],
        times: &[i64],
    ) -> Vec<Event<i64, &'static str>> {
        pairs
            .iter()
            .copied()
            .zip(outcomes.iter().cloned())
            .zip(times.iter().copied())
            .map(|(((a, b), outcome), time)| Event {
                time,
                teams: smallvec![
                    Team::with_members([Member::new(a)]),
                    Team::with_members([Member::new(b)]),
                ],
                outcome,
            })
            .collect()
    }

    #[test]
    fn test_init() {
        let mut h = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(0.15 * 25.0 / 3.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        let p0 = h.time_slices[0].posteriors();

        assert_ulps_eq!(
            p0[&a],
            Gaussian::from_ms(29.205220, 7.194481),
            epsilon = 1e-6
        );

        let observed = h.time_slices[1].skills.get(a).unwrap().forward.sigma();
        let gamma: f64 = 0.15 * 25.0 / 3.0;
        let expected = (gamma.powi(2)
            + h.time_slices[0]
                .skills
                .get(a)
                .unwrap()
                .posterior()
                .sigma()
                .powi(2))
        .sqrt();

        assert_ulps_eq!(observed, expected, epsilon = 0.000001);

        let observed = h.time_slices[1].skills.get(a).unwrap().posterior();

        let w = [vec![1.0], vec![1.0]];
        let p = Game::ranked_with_arena(
            h.time_slices[1].events[0].within_priors(false, &h.time_slices[1].skills, &h.agents),
            &[0.0, 1.0],
            &w,
            P_DRAW,
            crate::ConvergenceOptions::default(),
            &mut ScratchArena::new(),
        )
        .posteriors();
        let expected = p[0][0];

        assert_ulps_eq!(observed, expected, epsilon = 1e-6);

        let _ = (b, c);
    }

    #[test]
    fn test_one_batch() {
        let mut h1 = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(0.15 * 25.0 / 3.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "c"), ("c", "a")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 1, 1],
        );
        h1.add_events(events).unwrap();

        let a = h1.keys.get("a").unwrap();
        let c = h1.keys.get("c").unwrap();

        assert_ulps_eq!(
            h1.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(22.904409, 6.010330),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h1.time_slices[0].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.110318, 5.866311),
            epsilon = 1e-6
        );

        let _ = h1.converge().unwrap();

        assert_ulps_eq!(
            h1.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h1.time_slices[0].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );

        let mut h2 = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(25.0 / 300.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "c"), ("c", "a")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h2.add_events(events).unwrap();

        let a = h2.keys.get("a").unwrap();
        let c = h2.keys.get("c").unwrap();

        assert_ulps_eq!(
            h2.time_slices[2].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(22.903522, 6.011017),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h2.time_slices[2].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.110702, 5.866811),
            epsilon = 1e-6
        );

        let _ = h2.converge().unwrap();

        assert_ulps_eq!(
            h2.time_slices[2].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(24.998668, 5.420053),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h2.time_slices[2].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.000532, 5.419827),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_learning_curves() {
        let mut h = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(25.0 / 300.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "c"), ("c", "a")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[5, 6, 7],
        );
        h.add_events(events).unwrap();
        let _ = h.converge().unwrap();

        let lc_a = h.learning_curve("a");
        let lc_c = h.learning_curve("c");

        let aj_e = lc_a.len();
        let cj_e = lc_c.len();

        assert_eq!(lc_a[0].0, 5);
        assert_eq!(lc_a[aj_e - 1].0, 7);

        assert_ulps_eq!(
            lc_a[aj_e - 1].1,
            Gaussian::from_ms(24.998668, 5.420053),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_c[cj_e - 1].1,
            Gaussian::from_ms(25.000532, 5.419827),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_env_ttt() {
        let mut h = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(25.0 / 300.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();
        let _ = h.converge().unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        assert_eq!(h.time_slices[2].skills.get(b).unwrap().elapsed, 2);
        assert_eq!(h.time_slices[2].skills.get(c).unwrap().elapsed, 1);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(25.000267, 5.419423),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(24.999197939, 5.419510957),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(25.001331690, 5.420052840),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_teams() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(6.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events: Vec<Event<i64, &'static str>> = vec![
            Event {
                time: 1,
                teams: smallvec![
                    Team::with_members([Member::new("a"), Member::new("b")]),
                    Team::with_members([Member::new("c"), Member::new("d")]),
                ],
                outcome: Outcome::winner(0, 2),
            },
            Event {
                time: 2,
                teams: smallvec![
                    Team::with_members([Member::new("e"), Member::new("f")]),
                    Team::with_members([Member::new("b"), Member::new("c")]),
                ],
                outcome: Outcome::winner(1, 2),
            },
            Event {
                time: 3,
                teams: smallvec![
                    Team::with_members([Member::new("a"), Member::new("d")]),
                    Team::with_members([Member::new("e"), Member::new("f")]),
                ],
                outcome: Outcome::winner(0, 2),
            },
        ];
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();
        let d = h.keys.get("d").unwrap();
        let e = h.keys.get("e").unwrap();
        let f = h.keys.get("f").unwrap();

        let trueskill_log_evidence = h.log_evidence_internal(false, &[]);
        let trueskill_log_evidence_forward = h.log_evidence_internal(true, &[]);

        assert_ulps_eq!(
            trueskill_log_evidence,
            trueskill_log_evidence_forward,
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior().mu(),
            -h.time_slices[0].skills.get(c).unwrap().posterior().mu(),
            epsilon = 1e-6
        );

        let evidence_second_event = h.log_evidence_internal(false, &[b]).exp() * 2.0;
        assert_ulps_eq!(0.5, evidence_second_event, epsilon = 1e-6);

        let evidence_third_event = h.log_evidence_internal(false, &[a]).exp() * 2.0;
        assert_ulps_eq!(0.669885, evidence_third_event, epsilon = 1e-6);

        let _ = h.converge().unwrap();

        let loocv_hat = h.log_evidence_internal(false, &[]).exp();
        let p_d_m_hat = h.log_evidence_internal(true, &[]).exp();

        assert_ulps_eq!(loocv_hat, 0.241027, epsilon = 1e-6);
        assert_ulps_eq!(p_d_m_hat, 0.172432, epsilon = 1e-6);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            h.time_slices[0].skills.get(d).unwrap().posterior(),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[1].skills.get(e).unwrap().posterior(),
            h.time_slices[1].skills.get(f).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(4.084902, 5.106919),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(-0.533029, 5.106919),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(e).unwrap().posterior(),
            Gaussian::from_ms(-3.551872, 5.154569),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_add_events() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        let _ = h.converge().unwrap();

        assert_eq!(h.time_slices[2].skills.get(b).unwrap().elapsed, 2);
        assert_eq!(h.time_slices[2].skills.get(c).unwrap().elapsed, 1);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );

        let events2 = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[4, 5, 6],
        );
        h.add_events(events2).unwrap();

        assert_eq!(h.time_slices.len(), 6);

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        let _ = h.converge().unwrap();

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[5].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_only_add_events() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        let _ = h.converge().unwrap();

        assert_eq!(h.time_slices[2].skills.get(b).unwrap().elapsed, 2);
        assert_eq!(h.time_slices[2].skills.get(c).unwrap().elapsed, 1);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );

        let events2 = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[4, 5, 6],
        );
        h.add_events(events2).unwrap();

        assert_eq!(h.time_slices.len(), 6);

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        let _ = h.converge().unwrap();

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[5].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_log_evidence() {
        use crate::ConvergenceOptions;

        let mut h: History<i64, _, _, &'static str> = History::builder().build();

        // empty results in the old API = team 0 wins; reproduce with Outcome::winner(0,2)
        let events = make_events_1v1(
            &[("a", "b"), ("b", "a")],
            &[Outcome::winner(0, 2), Outcome::winner(0, 2)],
            &[1, 2],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();

        let p_d_m_2 = h.log_evidence_internal(false, &[]).exp() * 2.0;

        assert_ulps_eq!(p_d_m_2, 0.17650911, epsilon = 1e-6);
        assert_ulps_eq!(
            p_d_m_2,
            h.log_evidence_internal(true, &[]).exp() * 2.0,
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            p_d_m_2,
            h.log_evidence_internal(true, &[a]).exp() * 2.0,
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            p_d_m_2,
            h.log_evidence_internal(false, &[a]).exp() * 2.0,
            epsilon = 1e-6
        );

        // run exactly 11 iterations (old test used convergence(11, ...))
        h.convergence = ConvergenceOptions {
            max_iter: 11,
            epsilon: EPSILON,
            alpha: 1.0,
        };
        let _ = h.converge().unwrap();

        let loocv_approx_2 = h.log_evidence_internal(false, &[]).exp().sqrt();

        assert_ulps_eq!(loocv_approx_2, 0.001976774, epsilon = 0.000001);

        let p_d_m_approx_2 = h.log_evidence_internal(true, &[]).exp() * 2.0;

        assert!(loocv_approx_2 - p_d_m_approx_2 < 1e-4);

        assert_ulps_eq!(
            loocv_approx_2,
            h.log_evidence_internal(true, &[b]).exp() * 2.0,
            epsilon = 1e-4
        );

        let mut h2: History<i64, _, _, &'static str> = History::builder().build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "a")],
            &[Outcome::winner(0, 2), Outcome::winner(0, 2)],
            &[1, 2],
        );
        h2.add_events(events).unwrap();

        assert_ulps_eq!(
            ((0.5f64 * 0.1765).ln() / 2.0).exp(),
            (h2.log_evidence_internal(false, &[]) / 2.0).exp(),
            epsilon = 1e-4
        );
    }

    #[test]
    fn test_add_events_with_time() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[0, 10, 20],
        );
        h.add_events(events).unwrap();
        let _ = h.converge().unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        let events2 = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[15, 10, 0],
        );
        h.add_events(events2).unwrap();

        assert_eq!(h.time_slices.len(), 4);

        assert_eq!(
            h.time_slices
                .iter()
                .map(|ts| ts.events.len())
                .collect::<Vec<_>>(),
            vec![2, 2, 1, 1]
        );

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]], vec![vec![b], vec![c]]],
                vec![vec![vec![a], vec![c]], vec![vec![a], vec![c]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_results())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![1.0, 0.0], vec![1.0, 0.0]],
                vec![vec![0.0, 1.0], vec![0.0, 1.0]],
                vec![vec![1.0, 0.0]],
                vec![vec![1.0, 0.0]]
            ]
        );

        let end = h.time_slices.len() - 1;

        assert_eq!(h.time_slices[0].skills.get(c).unwrap().elapsed, 0);
        assert_eq!(h.time_slices[end].skills.get(c).unwrap().elapsed, 10);

        assert_eq!(h.time_slices[0].skills.get(a).unwrap().elapsed, 0);
        assert_eq!(h.time_slices[2].skills.get(a).unwrap().elapsed, 5);

        assert_eq!(h.time_slices[0].skills.get(b).unwrap().elapsed, 0);
        assert_eq!(h.time_slices[end].skills.get(b).unwrap().elapsed, 5);

        let _ = h.converge().unwrap();

        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            h.time_slices[end].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            h.time_slices[end].skills.get(c).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );

        // second scenario: team-0 wins (empty results in old API), different composition order

        let mut h2: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("c", "a"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[0, 10, 20],
        );
        h2.add_events(events).unwrap();
        let _ = h2.converge().unwrap();

        let a = h2.keys.get("a").unwrap();
        let b = h2.keys.get("b").unwrap();
        let c = h2.keys.get("c").unwrap();

        let events2 = make_events_1v1(
            &[("a", "b"), ("c", "a"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[15, 10, 0],
        );
        h2.add_events(events2).unwrap();

        assert_eq!(h2.time_slices.len(), 4);

        assert_eq!(
            h2.time_slices
                .iter()
                .map(|ts| ts.events.len())
                .collect::<Vec<_>>(),
            vec![2, 2, 1, 1]
        );

        assert_eq!(
            h2.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]], vec![vec![b], vec![c]]],
                vec![vec![vec![c], vec![a]], vec![vec![c], vec![a]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        assert_eq!(
            h2.time_slices
                .iter()
                .map(|b| b.get_results())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![1.0, 0.0], vec![1.0, 0.0]],
                vec![vec![1.0, 0.0], vec![1.0, 0.0]],
                vec![vec![1.0, 0.0]],
                vec![vec![1.0, 0.0]]
            ]
        );

        let end = h2.time_slices.len() - 1;

        assert_eq!(h2.time_slices[0].skills.get(c).unwrap().elapsed, 0);
        assert_eq!(h2.time_slices[end].skills.get(c).unwrap().elapsed, 10);

        assert_eq!(h2.time_slices[0].skills.get(a).unwrap().elapsed, 0);
        assert_eq!(h2.time_slices[2].skills.get(a).unwrap().elapsed, 5);

        assert_eq!(h2.time_slices[0].skills.get(b).unwrap().elapsed, 0);
        assert_eq!(h2.time_slices[end].skills.get(b).unwrap().elapsed, 5);

        let _ = h2.converge().unwrap();

        assert_ulps_eq!(
            h2.time_slices[0].skills.get(b).unwrap().posterior(),
            h2.time_slices[end].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h2.time_slices[0].skills.get(c).unwrap().posterior(),
            h2.time_slices[end].skills.get(c).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h2.time_slices[0].skills.get(c).unwrap().posterior(),
            h2.time_slices[0].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_1vs1_weighted() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(2.0)
            .sigma(6.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        // empty results in old API = team 0 wins: a wins event 1, b wins event 2
        let events: Vec<Event<i64, &'static str>> = vec![
            Event {
                time: 1,
                teams: smallvec![
                    Team::with_members([Member::new("a").with_weight(5.0)]),
                    Team::with_members([Member::new("b").with_weight(4.0)]),
                ],
                outcome: Outcome::winner(0, 2),
            },
            Event {
                time: 2,
                teams: smallvec![
                    Team::with_members([Member::new("b").with_weight(5.0)]),
                    Team::with_members([Member::new("a").with_weight(4.0)]),
                ],
                outcome: Outcome::winner(0, 2),
            },
        ];
        h.add_events(events).unwrap();

        let lc_a = h.learning_curve("a");
        let lc_b = h.learning_curve("b");

        assert_ulps_eq!(
            lc_a[0].1,
            Gaussian::from_ms(5.537659, 4.758722),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_b[0].1,
            Gaussian::from_ms(-0.830127, 5.239568),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_a[1].1,
            Gaussian::from_ms(1.792278067, 4.099566582),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_b[1].1,
            Gaussian::from_ms(4.845533, 3.747616),
            epsilon = 1e-6
        );

        let _ = h.converge().unwrap();

        let lc_a = h.learning_curve("a");
        let lc_b = h.learning_curve("b");

        assert_ulps_eq!(lc_a[0].1, lc_a[0].1, epsilon = 1e-6);
        assert_ulps_eq!(lc_b[0].1, lc_a[0].1, epsilon = 1e-6);
        assert_ulps_eq!(lc_a[1].1, lc_a[0].1, epsilon = 1e-6);
        assert_ulps_eq!(lc_b[1].1, lc_a[0].1, epsilon = 1e-6);
    }

    #[test]
    fn test_converge_returns_report() {
        use crate::ConvergenceOptions;

        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .convergence(ConvergenceOptions {
                max_iter: 30,
                epsilon: 1e-6,
                alpha: 1.0,
            })
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let report = h.converge().unwrap();
        assert!(report.converged);
        assert!(report.iterations > 0);
        assert!(report.iterations < 30);
        assert!(report.final_step.0 <= 1e-6);
    }

    #[test]
    #[should_panic(expected = "score_sigma must be positive")]
    fn history_builder_rejects_zero_score_sigma() {
        let _ = History::builder().score_sigma(0.0).build();
    }

    #[test]
    fn history_propagates_convergence_to_inner_run_chain() {
        use crate::ConvergenceOptions;

        let events_for =
            |h: &mut History<i64, ConstantDrift, crate::observer::NullObserver, &'static str>| {
                h.event(0)
                    .team(["a"])
                    .team(["b"])
                    .team(["c"])
                    .team(["d"])
                    .ranking([0u32, 1, 2, 3])
                    .commit()
                    .unwrap();
            };

        let mut h_capped: History<i64, _, _, &'static str> = History::builder()
            .convergence(ConvergenceOptions {
                max_iter: 1,
                ..ConvergenceOptions::default()
            })
            .build();
        events_for(&mut h_capped);
        let _ = h_capped.converge().unwrap();

        let mut h_full: History<i64, _, _, &'static str> = History::builder().build();
        events_for(&mut h_full);
        let _ = h_full.converge().unwrap();

        let curves_capped = h_capped.learning_curves();
        let curves_full = h_full.learning_curves();

        let mut max_diff: f64 = 0.0;
        for (key, capped_pts) in curves_capped.iter() {
            let full_pts = curves_full.get(key).expect("agent missing in full");
            for (capped, full) in capped_pts.iter().zip(full_pts.iter()) {
                max_diff = max_diff.max((capped.1.mu() - full.1.mu()).abs());
                max_diff = max_diff.max((capped.1.sigma() - full.1.sigma()).abs());
            }
        }
        assert!(
            max_diff > 1e-6,
            "max_iter=1 inner loop should differ from default; max_diff={max_diff}"
        );
    }

    #[test]
    fn history_with_damping_reaches_same_fixed_point_as_undamped() {
        use crate::ConvergenceOptions;

        let events_for =
            |h: &mut History<i64, ConstantDrift, crate::observer::NullObserver, &'static str>| {
                h.event(0)
                    .team(["a"])
                    .team(["b"])
                    .team(["c"])
                    .team(["d"])
                    .ranking([0u32, 1, 2, 3])
                    .commit()
                    .unwrap();
            };

        let mut h_undamped: History<i64, _, _, &'static str> = History::builder().build();
        events_for(&mut h_undamped);
        let _ = h_undamped.converge().unwrap();

        let mut h_damped: History<i64, _, _, &'static str> = History::builder()
            .convergence(ConvergenceOptions {
                alpha: 0.5,
                max_iter: 200,
                ..ConvergenceOptions::default()
            })
            .build();
        events_for(&mut h_damped);
        let _ = h_damped.converge().unwrap();

        let curves_u = h_undamped.learning_curves();
        let curves_d = h_damped.learning_curves();

        let mut max_diff: f64 = 0.0;
        for (key, u_pts) in curves_u.iter() {
            let d_pts = curves_d.get(key).expect("agent missing in damped");
            for (u, d) in u_pts.iter().zip(d_pts.iter()) {
                max_diff = max_diff.max((u.1.mu() - d.1.mu()).abs());
                max_diff = max_diff.max((u.1.sigma() - d.1.sigma()).abs());
            }
        }
        assert!(
            max_diff < 1e-3,
            "α=0.5 should reach the same fixed point as α=1.0; max_diff={max_diff}"
        );
    }

    #[test]
    fn outcome_scores_default_sigma_uses_history_default() {
        use crate::Outcome;

        // Path A: explicit sigma=0.5 via override.
        let mut h_a = crate::History::builder().score_sigma(0.5).build();
        h_a.add_events([crate::Event {
            time: 0_i64,
            teams: smallvec::smallvec![
                crate::Team::with_members([crate::Member::new("a")]),
                crate::Team::with_members([crate::Member::new("b")]),
            ],
            outcome: Outcome::scores_with_sigma([3.0, 1.0], 0.5),
        }])
        .unwrap();
        let _ = h_a.converge().unwrap();

        // Path B: history-wide default 0.5, no per-event override.
        let mut h_b = crate::History::builder().score_sigma(0.5).build();
        h_b.add_events([crate::Event {
            time: 0_i64,
            teams: smallvec::smallvec![
                crate::Team::with_members([crate::Member::new("a")]),
                crate::Team::with_members([crate::Member::new("b")]),
            ],
            outcome: Outcome::scores([3.0, 1.0]),
        }])
        .unwrap();
        let _ = h_b.converge().unwrap();

        // Inheritance: posteriors must be bit-equal.
        let curves_a = h_a.learning_curves();
        let curves_b = h_b.learning_curves();
        for (key, a_pts) in curves_a.iter() {
            let b_pts = curves_b.get(key).expect("agent missing in path B");
            for (a, b) in a_pts.iter().zip(b_pts.iter()) {
                assert_eq!(a.1.pi(), b.1.pi(), "mismatch at agent {key:?}");
                assert_eq!(a.1.tau(), b.1.tau(), "mismatch at agent {key:?}");
            }
        }
    }

    #[test]
    fn outcome_scores_with_sigma_overrides_history_default() {
        use crate::Outcome;

        // Path A: history-wide default 0.5, per-event override 2.0.
        let mut h_a = crate::History::builder().score_sigma(0.5).build();
        h_a.add_events([crate::Event {
            time: 0_i64,
            teams: smallvec::smallvec![
                crate::Team::with_members([crate::Member::new("a")]),
                crate::Team::with_members([crate::Member::new("b")]),
            ],
            outcome: Outcome::scores_with_sigma([3.0, 1.0], 2.0),
        }])
        .unwrap();
        let _ = h_a.converge().unwrap();

        // Path B: history-wide default 2.0, no per-event override.
        let mut h_b = crate::History::builder().score_sigma(2.0).build();
        h_b.add_events([crate::Event {
            time: 0_i64,
            teams: smallvec::smallvec![
                crate::Team::with_members([crate::Member::new("a")]),
                crate::Team::with_members([crate::Member::new("b")]),
            ],
            outcome: Outcome::scores([3.0, 1.0]),
        }])
        .unwrap();
        let _ = h_b.converge().unwrap();

        // Override == default-set-to-the-override-value: bit-equal.
        let curves_a = h_a.learning_curves();
        let curves_b = h_b.learning_curves();
        for (key, a_pts) in curves_a.iter() {
            let b_pts = curves_b.get(key).expect("agent missing in path B");
            for (a, b) in a_pts.iter().zip(b_pts.iter()) {
                assert_eq!(a.1.pi(), b.1.pi(), "mismatch at agent {key:?}");
                assert_eq!(a.1.tau(), b.1.tau(), "mismatch at agent {key:?}");
            }
        }

        // Path C: history-wide default 0.5, no override. Different sigma → different posteriors.
        let mut h_c = crate::History::builder().score_sigma(0.5).build();
        h_c.add_events([crate::Event {
            time: 0_i64,
            teams: smallvec::smallvec![
                crate::Team::with_members([crate::Member::new("a")]),
                crate::Team::with_members([crate::Member::new("b")]),
            ],
            outcome: Outcome::scores([3.0, 1.0]),
        }])
        .unwrap();
        let _ = h_c.converge().unwrap();

        let curves_c = h_c.learning_curves();
        let mut max_diff: f64 = 0.0;
        for (key, a_pts) in curves_a.iter() {
            let c_pts = curves_c.get(key).expect("agent missing in path C");
            for (a, c) in a_pts.iter().zip(c_pts.iter()) {
                max_diff = max_diff.max((a.1.mu() - c.1.mu()).abs());
                max_diff = max_diff.max((a.1.sigma() - c.1.sigma()).abs());
            }
        }
        assert!(
            max_diff > 1e-6,
            "override should produce different posteriors from inherited default; max_diff={max_diff}"
        );
    }

    #[test]
    fn event_builder_scores_with_sigma_threading() {
        use crate::Outcome;

        // Path A: builder fluent API with sigma override.
        let mut h_a = crate::History::builder().score_sigma(0.5).build();
        h_a.event(0_i64)
            .team(["a"])
            .team(["b"])
            .scores_with_sigma([3.0, 1.0], 2.0)
            .commit()
            .unwrap();
        let _ = h_a.converge().unwrap();

        // Path B: same outcome via the explicit Outcome constructor.
        let mut h_b = crate::History::builder().score_sigma(0.5).build();
        h_b.add_events([crate::Event {
            time: 0_i64,
            teams: smallvec::smallvec![
                crate::Team::with_members([crate::Member::new("a")]),
                crate::Team::with_members([crate::Member::new("b")]),
            ],
            outcome: Outcome::scores_with_sigma([3.0, 1.0], 2.0),
        }])
        .unwrap();
        let _ = h_b.converge().unwrap();

        let curves_a = h_a.learning_curves();
        let curves_b = h_b.learning_curves();
        for (key, a_pts) in curves_a.iter() {
            let b_pts = curves_b.get(key).expect("agent missing");
            for (a, b) in a_pts.iter().zip(b_pts.iter()) {
                assert_eq!(a.1.pi(), b.1.pi(), "mismatch at agent {key:?}");
                assert_eq!(a.1.tau(), b.1.tau(), "mismatch at agent {key:?}");
            }
        }
    }
}