Test that new code

src/bin/flat/main.rs

@@ -558,6 +558,9 @@ impl Rect {
 mod fns {
 	use crate::FloatExt2;
 
+	#[cfg(test)]
+	use approx::abs_diff_eq;
+
 	pub struct RectX {
 		pub min: f32,
 		pub max: f32,
@@ -594,6 +597,32 @@ mod fns {
 		pub fn du(&self, x: f32) -> f32 { extend_const(x, |x| 1.0 / self.root(x), self.external, 1.0) }
 		pub fn d2u(&self, x: f32) -> f32 { extend_const(x, |x| -2.0 * x.signum() * self.a() * self.root(x).powi(-3), self.external, 0.0) }
 	}
+
+	#[test]
+	fn test_rect_y() {
+		let testee = RectY { internal: 100.0, external: 150.0 };
+		let ε = 1.0e-4f32;
+		let δ = 1.0 / 8.0; // Mathematically, you want this to be small. Computationally, you don’t.
+		let margin = 1.0 / 16.0;
+		let mul = 1.0 + margin;
+		for x in itertools_num::linspace(-mul * testee.external, mul * testee.external, 100) {
+			let u = testee.u(x);
+			assert!(abs_diff_eq!(x, testee.x(u), epsilon = ε), "At x={}:\nu(x):    {}\nx(u(x)): {}\n", x, u, testee.x(u));
+
+			let du = (testee.u(x + δ) - testee.u(x - δ)) / (2. * δ);
+			assert!(abs_diff_eq!(du, testee.du(x), epsilon = ε), "At x={}, u':\nexpected: {}\nactual:   {}\n", x, du, testee.du(x));
+
+			let d2u = (testee.du(x + δ) - testee.du(x - δ)) / (2. * δ);
+			assert!(abs_diff_eq!(d2u, testee.d2u(x), epsilon = ε), "At x={}, u'':\nexpected: {}\nactual:   {}\n", x, d2u, testee.d2u(x));
+		}
+		for u in itertools_num::linspace(-mul * testee.internal, mul * testee.internal, 100) {
+			let x = testee.x(u);
+			assert!(abs_diff_eq!(x, testee.x(u), epsilon = ε), "At u={}:\nx(u):    {}\nu(x(u)): {}\n", u, x, testee.u(x));
+
+			let dx = (testee.x(u + δ) - testee.x(u - δ)) / (2. * δ);
+			assert!(abs_diff_eq!(dx, testee.dx(u), epsilon = ε), "At u={}, x':\nexpected: {}\nactual:   {}\n", u, dx, testee.dx(u));
+		}
+	}
 }
 
 #[test]