polynomial: Improving tests for double/triple roots in order 3

src/lol/math/polynomial.h

@@ -225,20 +225,22 @@ struct polynomial
                 solutions[i] = u_norm * cos(u_angle) + v_norm * cos(v_angle);
             }
 
-            if (delta < 0) // 3 real solutions
-                return array<T> { solutions[0] - k,
-                                  solutions[1] - k,
-                                  solutions[2] - k };
-
-            if (delta > 0) // 1 real solution
+            if (a == d && b == c && b == T(3)*a) // triple solution
                 return array<T> { solutions[0] - k };
 
-            if (u_norm > 0) // 2 real solutions
-                return array<T> { solutions[0] - k,
-                                  solutions[1] - k };
+            // if root of the derivative is also root of the current polynomial, we have a double root.
+            for (auto root : polynomial<T>{c, T(2)*b, T(3)*a}.roots())
+                if (eval(root) == T(0))
+                    return array<T> { solutions[0] - k,
+                                      solutions[1] - k };
 
-            // one triple solution
-            return array<T> { solutions[0] - k };
+            // we have 3 or 1 root depending on delta sign
+            if (delta > 0)
+                return array<T> { solutions[0] - k };
+            else // if (delta < 0) 3 real solutions
+                return array<T> { solutions[0] - k,
+                                  solutions[1] - k,
+                                  solutions[2] - k };
         }
 
         /* It is an error to reach this point. */

src/t/math/polynomial.cpp

@@ -287,10 +287,9 @@ lolunit_declare_fixture(polynomial_test)
         auto roots1 = p.roots();
 
         // Should have 2 solutions only, but precision leads to 3 solutions
-        lolunit_assert_equal(roots1.count(), 3);
+        lolunit_assert_equal(roots1.count(), 2);
         lolunit_assert_doubles_equal(roots1[0], -1, 1e-3);
         lolunit_assert_doubles_equal(roots1[1], -2, 1e-6);
-        lolunit_assert_doubles_equal(roots1[2], -1, 1e-3);
     }
 
     lolunit_declare_test(degree_3_three_roots)