mach: math lib adding test for multiplication

src/math.zig

@@ -1063,3 +1063,55 @@ test "mat.rotateZ" {
         }
     }
 }
+
+test "mat.mul" {
+    {
+        const tolerance = 1e-6;
+        const t = Vec3{ 1, 2, -3 };
+        const T = mat.translate3d(t);
+        const s = Vec3{ 3, 1, -5 };
+        const S = mat.scale3d(s);
+        const r = Vec3{ 30, -40, 235 };
+        const R_x = mat.rotateX(degreesToRadians(f32, r[0]));
+        const R_y = mat.rotateY(degreesToRadians(f32, r[1]));
+        const R_z = mat.rotateZ(degreesToRadians(f32, r[2]));
+
+        const R_yz = mat.mul(R_y, R_z);
+        // NOTE: This values are calculated by hand with help of matrix calculator: https://matrix.reshish.com/multCalculation.php
+        const expected_R_yz = mat.set_3d_matrix(&[_]f32{
+            -0.43938504177070496278, -0.8191520442889918, -0.36868782649461236545, 0,
+            0.62750687159713312638,  -0.573576436351046,  0.52654078451836329713,  0,
+            -0.6427876096865394,     0,                   0.766044443118978,       0,
+            0,                       0,                   0,                       1,
+        });
+        try expect(mat.equalsApproximately(R_yz, expected_R_yz, tolerance));
+
+        const R_xyz = mat.mul(R_x, R_yz);
+        const expected_R_xyz = mat.set_3d_matrix(&[_]f32{
+            -0.439385041770705,  -0.52506256666891627986, -0.72886904595489960019, 0,
+            0.6275068715971331,  -0.76000215715133560834, 0.16920947734596765363,  0,
+            -0.6427876096865394, -0.383022221559489,      0.66341394816893832989,  0,
+            0,                   0,                       0,                       1,
+        });
+        try expect(mat.equalsApproximately(R_xyz, expected_R_xyz, tolerance));
+
+        const SR = mat.mul(S, R_xyz);
+        const expected_SR = mat.set_3d_matrix(&[_]f32{
+            -1.318155125312115,  -0.5250625666689163, 3.6443452297744985,  0,
+            1.8825206147913993,  -0.7600021571513356, -0.8460473867298382, 0,
+            -1.9283628290596182, -0.383022221559489,  -3.3170697408446915, 0,
+            0,                   0,                   0,                   1,
+        });
+        try expect(mat.equalsApproximately(SR, expected_SR, tolerance));
+
+        const TSR = mat.mul(T, SR);
+        const expected_TSR = mat.set_3d_matrix(&[_]f32{
+            -1.318155125312115,  -0.5250625666689163, 3.6443452297744985,  0,
+            1.8825206147913993,  -0.7600021571513356, -0.8460473867298382, 0,
+            -1.9283628290596182, -0.383022221559489,  -3.3170697408446914, 0,
+            1,                   2,                   -3,                  1,
+        });
+
+        try expect(mat.equalsApproximately(TSR, expected_TSR, tolerance));
+    }
+}