Test TubeX as well

src/bin/flat/main.rs

@@ -666,7 +666,33 @@ mod fns {
 
 	#[cfg(test)]
 	mod test {
-		use approx::{abs_diff_eq, assert_abs_diff_eq};
+		use approx::{abs_diff_eq, AbsDiffEq, assert_abs_diff_eq};
+
+		#[test]
+		fn test_tube_x() {
+			let testee = super::TubeX { min: 20.0, max: 30.0 };
+			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(0., testee.min, 10) {
+				assert_abs_diff_eq!(testee.value(x), 0., epsilon = ε);
+				assert_abs_diff_eq!(testee.value(-x), 0., epsilon = ε);
+			}
+			for x in itertools_num::linspace(testee.max, mul * testee.max, 10) {
+				assert_abs_diff_eq!(testee.value(x), 1., epsilon = ε);
+				assert_abs_diff_eq!(testee.value(-x), 1., epsilon = ε);
+			}
+			for x in itertools_num::linspace(-mul * testee.max, mul * testee.max, 100) {
+				// Currently, the derivative is discontinuous at ±min and ±max... let’s just skip these for now.
+				if x.abs().abs_diff_eq(&testee.min, δ) || x.abs().abs_diff_eq(&testee.max, δ) {
+					continue;
+				}
+				let df_num = (testee.value(x + δ) - testee.value(x - δ)) / (2. * δ);
+				let df_expl = testee.derivative(x);
+				assert!(abs_diff_eq!(df_expl, df_num, epsilon = ε), "At x={}, df/dx:\nnumerical: {}\nexplicit:  {}\n", x, df_num, df_expl);
+			}
+		}
 
 		#[test]
 		fn test_tube_y() {