internal: fix flakiness of accidentally quadratic test

crates/test_utils/src/assert_linear.rs

@@ -0,0 +1,112 @@
+//! Checks that a set of measurements looks like a linear function rather than
+//! like a quadratic function. Algorithm:
+//!
+//! 1. Linearly scale input to be in [0; 1)
+//! 2. Using linear regression, compute the best linear function approximating
+//!    the input.
+//! 3. Compute RMSE and  maximal absolute error.
+//! 4. Check that errors are within tolerances and that the constant term is not
+//!    too negative.
+//!
+//! Ideally, we should use a proper "model selection" to directly compare
+//! quadratic and linear models, but that sounds rather complicated:
+//!
+//!     https://stats.stackexchange.com/questions/21844/selecting-best-model-based-on-linear-quadratic-and-cubic-fit-of-data
+//!
+//! We might get false positives on a VM, but never false negatives. So, if the
+//! first round fails, we repeat the ordeal three more times and fail only if
+//! every time there's a fault.
+use stdx::format_to;
+
+#[derive(Default)]
+pub struct AssertLinear {
+    rounds: Vec<Round>,
+}
+
+#[derive(Default)]
+struct Round {
+    samples: Vec<(f64, f64)>,
+    plot: String,
+    linear: bool,
+}
+
+impl AssertLinear {
+    pub fn next_round(&mut self) -> bool {
+        if let Some(round) = self.rounds.last_mut() {
+            round.finish();
+        }
+        if self.rounds.iter().any(|it| it.linear) || self.rounds.len() == 4 {
+            return false;
+        }
+        self.rounds.push(Round::default());
+        true
+    }
+
+    pub fn sample(&mut self, x: f64, y: f64) {
+        self.rounds.last_mut().unwrap().samples.push((x, y))
+    }
+}
+
+impl Drop for AssertLinear {
+    fn drop(&mut self) {
+        assert!(!self.rounds.is_empty());
+        if self.rounds.iter().all(|it| !it.linear) {
+            for round in &self.rounds {
+                eprintln!("\n{}", round.plot);
+            }
+            panic!("Doesn't look linear!")
+        }
+    }
+}
+
+impl Round {
+    fn finish(&mut self) {
+        let (mut xs, mut ys): (Vec<_>, Vec<_>) = self.samples.iter().copied().unzip();
+        normalize(&mut xs);
+        normalize(&mut ys);
+        let xy = xs.iter().copied().zip(ys.iter().copied());
+
+        // Linear regression: finding a and b to fit y = a + b*x.
+
+        let mean_x = mean(&xs);
+        let mean_y = mean(&ys);
+
+        let b = {
+            let mut num = 0.0;
+            let mut denom = 0.0;
+            for (x, y) in xy.clone() {
+                num += (x - mean_x) * (y - mean_y);
+                denom += (x - mean_x).powi(2);
+            }
+            num / denom
+        };
+
+        let a = mean_y - b * mean_x;
+
+        self.plot = format!("y_pred = {:.3} + {:.3} * x\n\nx     y     y_pred\n", a, b);
+
+        let mut se = 0.0;
+        let mut max_error = 0.0f64;
+        for (x, y) in xy {
+            let y_pred = a + b * x;
+            se += (y - y_pred).powi(2);
+            max_error = max_error.max((y_pred - y).abs());
+
+            format_to!(self.plot, "{:.3} {:.3} {:.3}\n", x, y, y_pred);
+        }
+
+        let rmse = (se / xs.len() as f64).sqrt();
+        format_to!(self.plot, "\nrmse = {:.3} max error = {:.3}", rmse, max_error);
+
+        self.linear = rmse < 0.05 && max_error < 0.1 && a > -0.1;
+
+        fn normalize(xs: &mut Vec<f64>) {
+            let max = xs.iter().copied().max_by(|a, b| a.partial_cmp(b).unwrap()).unwrap();
+            xs.iter_mut().for_each(|it| *it /= max);
+        }
+
+        fn mean(xs: &[f64]) -> f64 {
+            xs.iter().copied().sum::<f64>() / (xs.len() as f64)
+        }
+    }
+}