diff --git a/src/lol/math/polynomial.h b/src/lol/math/polynomial.h index e5ccc9c7..5695ecb1 100644 --- a/src/lol/math/polynomial.h +++ b/src/lol/math/polynomial.h @@ -23,10 +23,6 @@ // #define ENABLE_3SOLVE // #include -#ifdef ENABLE_3SOLVE -#include -#endif - namespace lol { @@ -160,7 +156,7 @@ struct polynomial return array { -k }; } } -#ifdef ENABLE_3SOLVE // Development in progress +#ifdef ENABLE_3SOLVE else if (degree() == 3) { /* p(x) = ax³ + bx² + cx + d */ @@ -174,8 +170,6 @@ struct polynomial T const m = 3 * a * k * k - 2 * b * k + c; T const n = -a * k * k * k + b * k * k - c * k + d; - std::cout << "k,m,n: " << k << ", " << m << ", " << n << std::endl; - /* Assuming X = u + v and 3uv = -m, then * p2(u + v) = a(u + v) + n * @@ -190,7 +184,7 @@ struct polynomial * u³ = (-n/a + √((n/a)² + 4m³/27))/2 * v³ = (-n/a - √((n/a)² + 4m³/27))/2 */ - T const delta = (n * n) / (a * a) + 4 * m * m * m / 27; + T const delta = (n * n) / (a * a) + 4.f * m * m * m / 27.f; /* Because 3×u×v = -m and m is not complex * angle(u³) + angle(v³) must equal 0. @@ -203,9 +197,9 @@ struct polynomial if (delta < 0) { - v3_norm = u3_norm = sqrt((-n/(2.0f*a)) * (-n/(2.0f*a)) + abs(delta)) / 2.f; + v3_norm = u3_norm = sqrt((-n/a) * (-n/a) + abs(delta)) / 2.f; - u3_angle = atan2(sqrt(abs(delta)), (-n/(2.0f*a))); + u3_angle = atan2(sqrt(abs(delta)), (-n/(2.f*a))); v3_angle = -u3_angle; } else @@ -220,23 +214,31 @@ struct polynomial v3_norm = abs(v3_norm); } - std::complex complex_solutions[3]; + T solutions[3]; for (int i = 0 ; i < 3 ; ++i) { T u_angle = u3_angle / 3.f + i * 2.f * M_PI / 3.f; T v_angle = v3_angle / 3.f - i * 2.f * M_PI / 3.f; - complex_solutions[i] = - pow(u3_norm, 1.f / 3.f) * std::complex(cos(u_angle), sin(u_angle)) + - pow(v3_norm, 1.f / 3.f) * std::complex(cos(v_angle), sin(v_angle)); + solutions[i] = + pow(u3_norm, 1.f / 3.f) * cos(u_angle) + + pow(v3_norm, 1.f / 3.f) * cos(v_angle); } - std::cout << "delta: " << delta << std::endl; - - std::cout << "complex_solutions: " << complex_solutions[0] << ", " << complex_solutions[1] << ", " << complex_solutions[2] << std::endl; - - return array {complex_solutions[0].real() - k, complex_solutions[1].real() - k, complex_solutions[2].real() - k}; + if (delta < 0) + return array {solutions[0] - k, solutions[1] - k, solutions[2] - k}; + else + { + if (u3_norm > 0) + { + return array {solutions[0] - k, solutions[1] - k}; + } + else + { + return array {solutions[0] - k}; + } + } } #endif diff --git a/src/t/math/polynomial.cpp b/src/t/math/polynomial.cpp index 5a2b7ae7..fd02772d 100644 --- a/src/t/math/polynomial.cpp +++ b/src/t/math/polynomial.cpp @@ -272,25 +272,29 @@ lolunit_declare_fixture(PolynomialTest) lolunit_assert_equal(roots2[1], 7.f); } -#ifdef ENABLE_3SOLVE // Development in progress - lolunit_declare_test(RootsDegree3) +#ifdef ENABLE_3SOLVE + lolunit_declare_test(RootsDegree3TripleSolution) { - polynomial p { 1.f, 0.f, 0.f, 1.f }; + polynomial p { 1.f, 3.f, 3.f, 1.f }; auto roots1 = p.roots(); lolunit_assert_equal(roots1.count(), 3); - - std::cout << roots1[0] << ", " << roots1[1] << ", " << roots1[2] << std::endl; } - lolunit_declare_test(RootsDegree3_2) + lolunit_declare_test(RootsDegree3DoubleSolution) { - polynomial p { 0.f, -2.f, 0.f, 1.f }; + polynomial p { 2.f, 5.f, 4.f, 1.f }; auto roots1 = p.roots(); lolunit_assert_equal(roots1.count(), 3); + } + + lolunit_declare_test(RootsDegree3SingleSolutions) + { + polynomial p { 6.f, 11.f, 6.f, 1.f }; + auto roots1 = p.roots(); - std::cout << roots1[0] << ", " << roots1[1] << ", " << roots1[2] << std::endl; + lolunit_assert_equal(roots1.count(), 3); } #endif