trueskill-tt/tests/non_finite_results.rs

//! Inference must report numerical breakdown rather than call it convergence.
//!
//! The boundary rejects inputs that are *not numbers*, but finite inputs can
//! still overflow during inference — `beta.powi(2)` at 1e300 is infinite, and
//! infinity minus infinity is NaN. `NonFiniteResult` is the guard for that, and
//! it matters because the alternative is silent: NaN fails every comparison, so
//! a naive `step < epsilon` check reads a NaN step as *converged*.
//!
//! That is why the crate has `step_converged` / `step_is_finite` rather than
//! `!tuple_gt(..)`. These tests pin the guard from outside.

use smallvec::smallvec;
use trueskill_tt::{
    ConstantDrift, Event, Gaussian, History, InferenceError, Member, Outcome, Team,
};

fn scored_fit(
    sigma: f64,
    beta: f64,
    score_sigma: f64,
    scores: [f64; 2],
) -> Result<bool, InferenceError> {
    let mut h = History::builder()
        .mu(0.0)
        .sigma(sigma)
        .beta(beta)
        .score_sigma(score_sigma)
        .build();
    h.add_events(vec![Event {
        time: 1i64,
        teams: smallvec![
            Team::with_members([Member::new("a")]),
            Team::with_members([Member::new("b")]),
        ],
        outcome: Outcome::scores(scores),
    }])?;
    h.converge().map(|r| r.converged)
}

/// Every one of these is built from finite, individually legal parameters. The
/// overflow happens inside inference, which is exactly the case the boundary
/// checks cannot catch.
///
/// Matched rather than merely `is_err()`: an assertion that only checks "some
/// error" would keep passing if these started failing at the boundary for an
/// unrelated reason, and would then be testing nothing.
#[test]
fn overflow_during_inference_is_reported_not_hidden() {
    let cases: [(&str, f64, f64, f64, [f64; 2]); 5] = [
        ("huge sigma", 1e300, 1.0, 1.0, [3.0, 1.0]),
        ("huge beta", 6.0, 1e300, 1.0, [3.0, 1.0]),
        ("tiny sigma", 1e-300, 1.0, 1.0, [3.0, 1.0]),
        ("tiny score_sigma", 6.0, 1.0, 1e-300, [3.0, 1.0]),
        ("huge scores", 6.0, 1.0, 1.0, [1e308, -1e308]),
    ];

    for (name, sigma, beta, score_sigma, scores) in cases {
        match scored_fit(sigma, beta, score_sigma, scores) {
            Err(InferenceError::NonFiniteStep { context, step, .. }) => {
                assert_eq!(context, "History::converge", "{name}");
                assert!(
                    !step.0.is_finite() || !step.1.is_finite(),
                    "{name}: reported NonFiniteResult with a finite step {step:?}"
                );
            }
            other => panic!("{name}: expected NonFiniteResult, got {other:?}"),
        }
    }
}

/// The trap the invariant exists for: NaN fails every comparison, so a naive
/// `step < epsilon` test reads a NaN step as converged. A breakdown must never
/// come back as a successful fit.
#[test]
fn a_broken_fit_is_never_reported_as_converged() {
    let mut h = History::builder().build();
    h.add_events(vec![Event {
        time: 1i64,
        teams: smallvec![
            Team::with_members([Member::new("a").with_prior(Gaussian::from_ms(1e300, 1e-300))]),
            Team::with_members([Member::new("b")]),
        ],
        outcome: Outcome::winner(0, 2),
    }])
    .unwrap();

    let err = h.converge().unwrap_err();
    assert!(
        matches!(err, InferenceError::NonFiniteStep { .. }),
        "a breakdown must not be reported as convergence: {err:?}"
    );

    // `converge_partial` must not launder it into an `Ok` either — the
    // permissive path is permissive about *stopping short*, not about NaN.
    let mut h2 = History::builder().build();
    h2.add_events(vec![Event {
        time: 1i64,
        teams: smallvec![
            Team::with_members([Member::new("a").with_prior(Gaussian::from_ms(1e300, 1e-300))]),
            Team::with_members([Member::new("b")]),
        ],
        outcome: Outcome::winner(0, 2),
    }])
    .unwrap();
    assert!(matches!(
        h2.converge_partial().unwrap_err(),
        InferenceError::NonFiniteStep { .. }
    ));
}

/// The neighbouring case, so the tests above cannot pass by the fit simply
/// always failing: ordinary extreme-but-workable parameters still converge.
#[test]
fn merely_extreme_parameters_still_converge() {
    assert!(scored_fit(1e6, 1.0, 1.0, [3.0, 1.0]).unwrap());
    assert!(scored_fit(1e-6, 1.0, 1.0, [3.0, 1.0]).unwrap());
    assert!(scored_fit(6.0, 1.0, 1e6, [3.0, 1.0]).unwrap());
    assert!(scored_fit(6.0, 1.0, 1.0, [1e150, -1e150]).unwrap());
}

/// A NaN in one competitor must not be masked by a healthy competitor reduced
/// after it.
///
/// The convergence step is a fold over a `HashMap`, so which competitor is
/// reduced last is per-process hash order. Before the fix, `tuple_max` dropped
/// a NaN accumulator in favour of the next finite delta and this returned
/// `Ok(converged: true)` with a NaN posterior in **16 of 30 runs** on identical
/// input. Deterministic now, but note this test can only ever sample one hash
/// order per run — the ordering guarantee itself is pinned by
/// `tuple_max_propagates_a_nan_from_any_position` in the crate's unit tests.
#[test]
fn a_nan_competitor_is_not_masked_by_a_healthy_one() {
    let mut h = History::builder()
        .mu(0.0)
        .sigma(6.0)
        .beta(1.0)
        .p_draw(0.1)
        .build();
    h.add_events(vec![
        Event {
            time: 1i64,
            teams: smallvec![
                Team::with_members([Member::new("a").with_prior(Gaussian::from_ms(0.0, 1e-200))]),
                Team::with_members([Member::new("b")]),
            ],
            outcome: Outcome::winner(0, 2),
        },
        // A healthy pair in the same slice, to be reduced alongside the NaN.
        Event {
            time: 1i64,
            teams: smallvec![
                Team::with_members([Member::new("c")]),
                Team::with_members([Member::new("d")]),
            ],
            outcome: Outcome::winner(0, 2),
        },
    ])
    .unwrap();

    let err = h
        .converge()
        .expect_err("a NaN fit must never be reported as converged");
    assert!(
        matches!(err, InferenceError::NonFiniteStep { .. }),
        "{err:?}"
    );
}

/// A tie observed with a narrow draw margin between far-apart competitors must
/// produce a fit, not NaN skills.
///
/// The tie branch forms the truncated variance from `v^2 - u`, and both grow as
/// `alpha^2` while their difference stays `O(1)`. Deep enough into the tail
/// that subtraction had four digits left: measured, it returned `1 - w`
/// negative and `sqrt` of it was NaN. The half-line escape hatch did not cover
/// it, because that keys on how many window-widths from the mean the window
/// sits and a narrow window fails that however deep it is.
///
/// These parameters are ordinary for a precise-scoring domain, and the
/// neighbouring wider-margin case always worked — so this was a cliff, not
/// "extreme inputs break".
#[test]
fn a_narrow_draw_margin_far_into_the_tail_still_fits() {
    for (beta, p_draw, sd, gap) in [
        (1e-2, 1e-8, 1e-2, 10.0),
        (1e-3, 1e-9, 1e-3, 1.0),
        (1e-4, 1e-12, 1e-4, 1.0),
    ] {
        let mut h = History::builder()
            .mu(0.0)
            .sigma(sd)
            .beta(beta)
            .p_draw(p_draw)
            .drift(ConstantDrift::new(0.0))
            .build();
        h.add_events(vec![Event {
            time: 1i64,
            teams: smallvec![
                Team::with_members([Member::new("a").with_prior(Gaussian::from_ms(0.0, sd))]),
                Team::with_members([Member::new("b").with_prior(Gaussian::from_ms(gap, sd))]),
            ],
            outcome: Outcome::draw(2),
        }])
        .unwrap();

        let report = h
            .converge()
            .unwrap_or_else(|e| panic!("beta {beta:e}, p_draw {p_draw:e}: {e:?}"));
        assert!(report.converged);

        let skill = h.current_skill(&"a").unwrap();
        assert!(
            skill.mu().is_finite() && skill.sigma().is_finite() && skill.sigma() > 0.0,
            "beta {beta:e}, p_draw {p_draw:e}: {skill:?}"
        );
    }
}