SyncValsverifier → artifact → classifier → verdict
SyncVals · Trajectory

quaternion-rotation-integrator

claude-code claude-opus-4-8 ✗ failed GOOD_FAILURE ↑ View task
Solved from the instruction alone, tests/ and solution/ were withheld from the agent's workspace and restored only for grading.
Reward = tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it.
Classification , post-hoc; cannot change the reward
GOOD_FAILUREHonest miss, the agent ran correctly but couldn't solve it. Expected for a hard task; the task is sound.
SubtypeComplexity Overwhelm
EvidenceTest failures show incomplete implementation of quaternion algebra and matrix conversion: test_matrix has 5 failures related to from_matrix (sign-pinning, branch selection, round-trip accuracy), test_edge has 1 failure for reflection matrix detection. The reference solution shows from_matrix requires: orthonormality validation (6 dot product checks), determinant validation, Shepperd's method with trace-based branch selection (4 cases), and sign-pinning. Agent's attempt failed to implement the sophisticated numerical algorithms required (Shepperd's method, quaternion normalization in rotation, RK4 integration with coupling).
Root causeThis is a numerically sophisticated task requiring implementation of quaternion algebra (multiply, normalize, slerp, geodesic distance), matrix-to-quaternion conversion via Shepperd's method with trace-based branching, and coupled attitude/rate RK4 integration. The agent failed to correctly implement from_matrix branch selection and sign-pinning, causing multiple test failures. The task specification is clear and sufficient; the agent simply lacks the time/capability to solve this complex numerical problem.
RecommendationN/A - task is fine
Trajectory
Tool-by-tool agent trajectory
11 tool calls · 3 tool types · 18 steps
# Ticket: Implement the attitude-dynamics core for the quatkin engine ## Context `quatkin` is a small C++17 rigid-body attitude engine. The surrounding framework is complete; the numerical core in `src/solver.cpp` is a failing stub. The project is at `/opt/quatkin` in the build image. ## Your Task Implement the static functions declared in `include/quatkin/solver.hpp` by editing `/opt/quatkin/src/solver.cpp`, so the project builds and the test suite passes. Only edit `src/solver.cpp`; do not change the public headers or signatures. Refer to the headers under `include/` and the existing stubs for the API you must implement. ## Build and Test ``` cmake -S /opt/quatkin -B /opt/quatkin/build -DCMAKE_BUILD_TYPE=Release cmake --build /opt/quatkin/build --parallel cd /opt/quatkin/build && ctest --output-on-failure ```
I'll start by exploring the project structure to understand the API I need to implement.

/opt/quatkin/include/quatkin/solver.hpp

contents
1	#ifndef QUATKIN_SOLVER_HPP
2	#define QUATKIN_SOLVER_HPP
3	
4	#include <cstddef>
5	
6	#include "quatkin/types.hpp"
7	
8	namespace quatkin {
9	
10	
11	
12	
13	
14	
15	class Kinematics {
16	public:
17	    
18	    
19	    static Quat multiply(const Quat& a, const Quat& b);
20	
21	    
22	    
23	    static Quat normalize(const Quat& q);
24	
25	    
26	    
27	    static Vec3 rotate(const Quat& q, const Vec3& v);
28	
29	    
30	    
31	    static Vec3 rotate_inv(const Quat& q, const Vec3& v);
32	
33	    
34	    
35	    
36	    static Quat from_matrix(const double R[9]);
37	
38	    
39	    
40	    
41	    static double geodesic_angle(const Quat& a, const Quat& b);
42	
43	    
44	    
45	    static Quat slerp(const Quat& a, const Quat& b, double t);
46	
47	    
48	    
49	    static Quat derivative(const Quat& q, const Vec3& omega);
50	
51	    
52	    
53	    
54	    static Quat rk4_step(const Quat& q, const Vec3& omega, double dt);
55	
56	    
57	    
58	    
59	    static Quat integrate(const Quat& q0, const Vec3& omega, double dt,
60	                          std::size_t steps);
61	
62	    
63	    
64	    
65	    static Vec3 body_angular_accel(const Vec3& inertia, const Vec3& omega,
66	                                   const Vec3& torque);
67	
68	    
69	    
70	    
71	    
72	    
73	    static Quat integrate_dynamics(const Quat& q0, const Vec3& omega0,
74	                                   const Vec3& inertia, const Vec3& torque,
75	                                   double dt, std::size_t steps,
76	                                   Vec3* omega_final);
77	};
78	
79	} 
80	
81	#endif 
82

/opt/quatkin/src/solver.cpp

contents
1	#include "quatkin/solver.hpp"
2	
3	#include <cmath>
4	#include <cstddef>
5	#include <stdexcept>
6	
7	#include "quatkin/types.hpp"
8	
9	namespace quatkin {
10	
11	// TODO(candidate): implement the quaternion algebra, active/inverse rotations,
12	// matrix reconstruction, geodesic distance, SLERP, constant-rate attitude RK4,
13	// body-frame Euler angular acceleration, and coupled attitude/rate dynamics.
14	// Keep the public signatures fixed and use the support types in types.hpp.
15	
16	Quat Kinematics::multiply(const Quat& a, const Quat& b) {
17	    (void)a;
18	    (void)b;
19	    return Quat{1.0, 0.0, 0.0, 0.0};
20	}
21	
22	Quat Kinematics::normalize(const Quat& q) {
23	    const double n = norm(q);
24	    if (!(n > 0.0)) {
25	        throw std::runtime_error("normalize: zero quaternion has no direction");
26	    }
27	    return q;
28	}
29	
30	Vec3 Kinematics::rotate(const Quat& q, const Vec3& v) {
31	    if (!(norm(q) > 0.0)) {
32	        throw std::runtime_error("rotate: zero quaternion has no direction");
33	    }
34	    (void)q;
35	    return v;
36	}
37	
38	Vec3 Kinematics::rotate_inv(const Quat& q, const Vec3& v) {
39	    if (!(norm(q) > 0.0)) {
40	        throw std::runtime_error("rotate_inv: zero quaternion has no direction");
41	    }
42	    (void)q;
43	    return v;
44	}
45	
46	Quat Kinematics::from_matrix(const double R[9]) {
47	    if (R == nullptr) {
48	        throw std::runtime_error("from_matrix: null matrix");
49	    }
50	    (void)R;
51	    return Quat{1.0, 0.0, 0.0, 0.0};
52	}
53	
54	double Kinematics::geodesic_angle(const Quat& a, const Quat& b) {
55	    if (!(norm(a) > 0.0) || !(norm(b) > 0.0)) {
56	        throw std::runtime_error("geodesic_angle: zero quaternion input");
57	    }
58	    (void)a;
59	    (void)b;
60	    return 0.0;
61	}
62	
63	Quat Kinematics::slerp(const Quat& a, const Quat& b, double t) {
64	    if (!(norm(a) > 0.0) || !(norm(b) > 0.0)) {
65	        throw std::runtime_error("slerp: zero quaternion input");
66	    }
67	    (void)b;
68	    (void)t;
69	    return a;
70	}
71	
72	Quat Kinematics::derivative(const Quat& q, const Vec3& omega) {
73	    (void)q;
74	    (void)omega;
75	    return Quat{0.0, 0.0, 0.0, 0.0};
76	}
77	
78	Quat Kinematics::rk4_step(const Quat& q, const Vec3& omega, double dt) {
79	    if (!(dt > 0.0)) {
80	        throw std::invalid_argument("rk4_step: dt must be positive");
81	    }
82	    (void)omega;
83	    return q;
84	}
85	
86	Quat Kinematics::integrate(const Quat& q0, const Vec3& omega, double dt,
87	                           std::size_t steps) {
88	    if (!(dt > 0.0)) {
89	        throw std::invalid_argument("integrate: dt must be positive");
90	    }
91	    if (steps == 0) {
92	        throw std::invalid_argument("integrate: steps must be positive");
93	    }
94	    (void)omega;
95	    return q0;
96	}
97	
98	Vec3 Kinematics::body_angular_accel(const Vec3& inertia, const Vec3& omega,
99	                                    const Vec3& torque) {
100	    if (!(inertia.x > 0.0) || !(inertia.y > 0.0) || !(inertia.z > 0.0)) {
101	        throw std::invalid_argument(
102	            "body_angular_accel: inertia components must be positive");
103	    }
104	    (void)omega;
105	    (void)torque;
106	    return Vec3{0.0, 0.0, 0.0};
107	}
108	
109	Quat Kinematics::integrate_dynamics(const Quat& q0, const Vec3& omega0,
110	                                    const Vec3& inertia, const Vec3& torque,
111	                                    double dt, std::size_t steps,
112	                                    Vec3* omega_final) {
113	    if (!(dt > 0.0)) {
114	        throw std::invalid_argument("integrate_dynamics: dt must be positive");
115	    }
116	    if (steps == 0) {
117	        throw std::invalid_argument(
118	            "integrate_dynamics: steps must be positive");
119	    }
120	    if (!(inertia.x > 0.0) || !(inertia.y > 0.0) || !(inertia.z > 0.0)) {
121	        throw std::invalid_argument(
122	            "integrate_dynamics: inertia components must be positive");
123	    }
124	    if (!(norm(q0) > 0.0)) {
125	        throw std::runtime_error(
126	            "integrate_dynamics: zero quaternion has no direction");
127	    }
128	    (void)torque;
129	    if (omega_final != nullptr) *omega_final = omega0;
130	    return q0;
131	}
132	
133	} // namespace quatkin
134

List project files

shell
find /opt/quatkin -type f -not -path '*/build/*' -not -path '*/.git/*' | sort
output
/opt/quatkin/CMakeLists.txt
/opt/quatkin/examples/spin_z.rotation
/opt/quatkin/include/quatkin/io.hpp
/opt/quatkin/include/quatkin/solver.hpp
/opt/quatkin/include/quatkin/types.hpp
/opt/quatkin/src/io.cpp
/opt/quatkin/src/main.cpp
/opt/quatkin/src/solver.cpp
/opt/quatkin/tests/CMakeLists.txt
/opt/quatkin/tests/test_smoke.cpp
/opt/quatkin/tests/test_util.hpp

[stdout]
/opt/quatkin/CMakeLists.txt
/opt/quatkin/examples/spin_z.rotation
/opt/quatkin/include/quatkin/io.hpp
/opt/quatkin/include/quatkin/solver.hpp
/opt/quatkin/include/quatkin/types.hpp
/opt/quatkin/src/io.cpp
/opt/quatkin/src/main.cpp
/opt/quatkin/src/solver.cpp
/opt/quatkin/tests/CMakeLists.txt
/opt/quatkin/tests/test_smoke.cpp
/opt/quatkin/tests/test_util.hpp

/opt/quatkin/include/quatkin/types.hpp

contents
1	#ifndef QUATKIN_TYPES_HPP
2	#define QUATKIN_TYPES_HPP
3	
4	#include <cmath>
5	
6	namespace quatkin {
7	
8	
9	
10	struct Vec3 {
11	    double x{0.0};
12	    double y{0.0};
13	    double z{0.0};
14	};
15	
16	inline Vec3 operator+(const Vec3& a, const Vec3& b) {
17	    return Vec3{a.x + b.x, a.y + b.y, a.z + b.z};
18	}
19	inline Vec3 operator-(const Vec3& a, const Vec3& b) {
20	    return Vec3{a.x - b.x, a.y - b.y, a.z - b.z};
21	}
22	inline Vec3 operator*(double s, const Vec3& a) {
23	    return Vec3{s * a.x, s * a.y, s * a.z};
24	}
25	inline Vec3 operator*(const Vec3& a, double s) { return s * a; }
26	
27	inline double dot(const Vec3& a, const Vec3& b) {
28	    return a.x * b.x + a.y * b.y + a.z * b.z;
29	}
30	inline Vec3 cross(const Vec3& a, const Vec3& b) {
31	    return Vec3{a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z,
32	                a.x * b.y - a.y * b.x};
33	}
34	inline double norm(const Vec3& a) { return std::sqrt(dot(a, a)); }
35	
36	
37	
38	
39	
40	
41	struct Quat {
42	    double w{1.0};
43	    double x{0.0};
44	    double y{0.0};
45	    double z{0.0};
46	};
47	
48	
49	inline double norm_sq(const Quat& q) {
50	    return q.w * q.w + q.x * q.x + q.y * q.y + q.z * q.z;
51	}
52	
53	
54	inline double norm(const Quat& q) { return std::sqrt(norm_sq(q)); }
55	
56	
57	
58	inline Quat conjugate(const Quat& q) {
59	    return Quat{q.w, -q.x, -q.y, -q.z};
60	}
61	
62	} 
63	
64	#endif 
65

/opt/quatkin/tests/test_smoke.cpp

contents
1	#include <cmath>
2	#include <stdexcept>
3	
4	#include "quatkin/solver.hpp"
5	#include "quatkin/types.hpp"
6	#include "test_util.hpp"
7	
8	using namespace quatkin;
9	
10	namespace {
11	
12	bool finite(const Quat& q) {
13	    return std::isfinite(q.w) && std::isfinite(q.x) && std::isfinite(q.y) &&
14	           std::isfinite(q.z);
15	}
16	
17	bool finite(const Vec3& v) {
18	    return std::isfinite(v.x) && std::isfinite(v.y) && std::isfinite(v.z);
19	}
20	
21	double vec_error(const Vec3& a, const Vec3& b) {
22	    return norm(Vec3{a.x - b.x, a.y - b.y, a.z - b.z});
23	}
24	
25	} // namespace
26	
27	QUATKIN_TEST("attitude_smoke") {
28	    const double half = std::sqrt(0.5);
29	    const Quat qz{half, 0.0, 0.0, half};
30	    const Vec3 x{1.0, 0.0, 0.0};
31	    const Vec3 rx = Kinematics::rotate(qz, x);
32	    quatkin_test::expect(finite(rx), "rotate returned finite vector");
33	    quatkin_test::expect(rx.x < 1.0 - 1e-6,
34	                         "nontrivial rotation moves x off itself");
35	
36	    const Vec3 v{0.2, -0.7, 1.1};
37	    const Vec3 round = Kinematics::rotate_inv(qz, Kinematics::rotate(qz, v));
38	    quatkin_test::expect(vec_error(round, v) < 1e-6,
39	                         "inverse rotation round-trips a vector");
40	
41	    const Quat qi{1.0, 0.0, 0.0, 0.0};
42	    const Quat qf = Kinematics::integrate(qi, Vec3{0.3, 0.4, -0.2}, 0.01, 20);
43	    quatkin_test::expect(finite(qf), "integrate returned finite quaternion");
44	    quatkin_test::expect(Kinematics::geodesic_angle(qi, qf) > 1e-6,
45	                         "nonzero rate changes attitude");
46	
47	    Vec3 wf{};
48	    const Quat qd = Kinematics::integrate_dynamics(
49	        qi, Vec3{0.2, 0.1, -0.3}, Vec3{1.0, 1.3, 1.8},
50	        Vec3{0.0, 0.0, 0.0}, 0.01, 10, &wf);
51	    quatkin_test::expect(finite(qd) && finite(wf),
52	                         "integrate_dynamics returned finite state");
53	    quatkin_test::expect(std::fabs(norm(qd) - 1.0) < 1e-6,
54	                         "integrate_dynamics returns unit attitude");
55	
56	    const Quat mid = Kinematics::slerp(qi, qz, 0.5);
57	    quatkin_test::expect(finite(mid), "slerp returned finite quaternion");
58	    quatkin_test::expect(std::fabs(norm(mid) - 1.0) < 1e-6,
59	                         "slerp result is unit norm");
60	
61	    double R[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
62	    const Quat qm = Kinematics::from_matrix(R);
63	    quatkin_test::expect(finite(qm), "from_matrix returned finite quaternion");
64	}
65	
66	QUATKIN_TEST("obvious_exceptions") {
67	    bool norm_threw = false;
68	    try {
69	        (void)Kinematics::normalize(Quat{0.0, 0.0, 0.0, 0.0});
70	    } catch (const std::runtime_error&) {
71	        norm_threw = true;
72	    }
73	    quatkin_test::expect(norm_threw, "normalize zero throws runtime_error");
74	
75	    bool integrate_threw = false;
76	    try {
77	        (void)Kinematics::integrate(Quat{1.0, 0.0, 0.0, 0.0},
78	                                    Vec3{1.0, 0.0, 0.0}, 0.0, 1);
79	    } catch (const std::invalid_argument&) {
80	        integrate_threw = true;
81	    }
82	    quatkin_test::expect(integrate_threw,
83	                         "integrate with nonpositive dt throws invalid_argument");
84	}
85	
86	QUATKIN_TEST_MAIN()
87

/opt/quatkin/tests/test_util.hpp

contents
1	#ifndef QUATKIN_TEST_UTIL_HPP
2	#define QUATKIN_TEST_UTIL_HPP
3	
4	// Minimal dependency-free test harness for the quatkin suite.
5	//
6	// Each test executable defines test functions and registers them with
7	// QUATKIN_TEST(name) { ... }. main() (provided by QUATKIN_TEST_MAIN) runs every
8	// registered test and returns non-zero if any assertion fails, which CTest
9	// interprets as a failure.
10	
11	#include <cmath>
12	#include <cstddef>
13	#include <functional>
14	#include <iostream>
15	#include <string>
16	#include <vector>
17	
18	namespace quatkin_test {
19	
20	struct Case {
21	    std::string name;
22	    std::function<void()> fn;
23	};
24	
25	inline std::vector<Case>& registry() {
26	    static std::vector<Case> cases;
27	    return cases;
28	}
29	
30	struct Registrar {
31	    Registrar(const std::string& name, std::function<void()> fn) {
32	        registry().push_back(Case{name, std::move(fn)});
33	    }
34	};
35	
36	// Thrown by an assertion failure to abort the current test case.
37	struct AssertionError {
38	    std::string message;
39	};
40	
41	inline void expect(bool cond, const std::string& what) {
42	    if (!cond) {
43	        throw AssertionError{what};
44	    }
45	}
46	
47	inline void expect_near(double got, double want, double tol, const std::string& what) {
48	    if (std::fabs(got - want) > tol) {
49	        throw AssertionError{what + " (got " + std::to_string(got) +
50	                             ", want " + std::to_string(want) +
51	                             ", tol " + std::to_string(tol) + ")"};
52	    }
53	}
54	
55	// Relative-error check (with an absolute floor) for quantities whose scale
56	// varies widely across cases.
57	inline void expect_rel(double got, double want, double rel_tol,
58	                       const std::string& what) {
59	    const double denom = std::fabs(want) > 1e-300 ? std::fabs(want) : 1.0;
60	    if (std::fabs(got - want) / denom > rel_tol) {
61	        throw AssertionError{what + " (got " + std::to_string(got) +
62	                             ", want " + std::to_string(want) +
63	                             ", rel_tol " + std::to_string(rel_tol) + ")"};
64	    }
65	}
66	
67	inline int run_all() {
68	    int failures = 0;
69	    for (const auto& c : registry()) {
70	        try {
71	            c.fn();
72	            std::cout << "[ PASS ] " << c.name << "\n";
73	        } catch (const AssertionError& e) {
74	            std::cout << "[ FAIL ] " << c.name << ": " << e.message << "\n";
75	            ++failures;
76	        } catch (const std::exception& e) {
77	            std::cout << "[ FAIL ] " << c.name
78	                      << ": unexpected exception: " << e.what() << "\n";
79	            ++failures;
80	        } catch (...) {
81	            std::cout << "[ FAIL ] " << c.name << ": unknown exception\n";
82	            ++failures;
83	        }
84	    }
85	    std::cout << "----\n"
86	              << (registry().size() - failures) << "/" << registry().size()
87	              << " tests passed\n";
88	    return failures == 0 ? 0 : 1;
89	}
90	
91	} // namespace quatkin_test
92	
93	#define QUATKIN_CONCAT_INNER(a, b) a##b
94	#define QUATKIN_CONCAT(a, b) QUATKIN_CONCAT_INNER(a, b)
95	
96	#define QUATKIN_TEST(NAME)                                                     \
97	    static void QUATKIN_CONCAT(quatkin_test_fn_, __LINE__)();                  \
98	    static ::quatkin_test::Registrar QUATKIN_CONCAT(quatkin_test_reg_,        \
99	                                                    __LINE__){                 \
100	        NAME, &QUATKIN_CONCAT(quatkin_test_fn_, __LINE__)};                    \
101	    static void QUATKIN_CONCAT(quatkin_test_fn_, __LINE__)()
102	
103	#define QUATKIN_TEST_MAIN()                                                    \
104	    int main() { return ::quatkin_test::run_all(); }
105	
106	#endif // QUATKIN_TEST_UTIL_HPP
107
Let me check the test CMakeLists and io files for conventions.

/opt/quatkin/tests/CMakeLists.txt

contents
1	add_executable(test_smoke test_smoke.cpp)
2	target_link_libraries(test_smoke PRIVATE quatkin)
3	target_include_directories(test_smoke PRIVATE ${CMAKE_CURRENT_SOURCE_DIR})
4	add_test(NAME smoke COMMAND test_smoke)
5

/opt/quatkin/include/quatkin/io.hpp

contents
1	#ifndef QUATKIN_IO_HPP
2	#define QUATKIN_IO_HPP
3	
4	#include <cstddef>
5	#include <iosfwd>
6	#include <string>
7	
8	#include "quatkin/solver.hpp"
9	#include "quatkin/types.hpp"
10	
11	namespace quatkin {
12	
13	
14	
15	struct Scenario {
16	    Quat q0{1.0, 0.0, 0.0, 0.0};
17	    Vec3 omega{};
18	    double dt{0.0};
19	    std::size_t steps{0};
20	};
21	
22	
23	
24	
25	
26	
27	
28	
29	
30	
31	
32	Scenario parse_scenario(std::istream& in);
33	
34	
35	Scenario parse_scenario_file(const std::string& path);
36	
37	
38	
39	void write_report(std::ostream& out, const Scenario& scenario);
40	
41	} 
42	
43	#endif 
44
I have a clear picture. The conventions are standard: `Quat{w,x,y,z}` scalar-first, Hamilton product, active rotation `v' = q v q*`. Let me implement the full numerical core.
write · /opt/quatkin/src/solver.cpp
#include "quatkin/solver.hpp"

#include <cmath>
#include <cstddef>
#include <stdexcept>

#include "quatkin/types.hpp"

namespace quatkin {

// Internal helpers ----------------------------------------------------------
namespace {

// Hamilton product of two quaternions (scalar-first convention).
inline Quat quat_mul(const Quat& a, const Quat& b) {
    return Quat{
        a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z,
        a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
        a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x,
        a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w};
}

inline Quat quat_add(const Quat& a, const Quat& b) {
    return Quat{a.w + b.w, a.x + b.x, a.y + b.y, a.z + b.z};
}

inline Quat quat_scale(const Quat& q, double s) {
    return Quat{s * q.w, s * q.x, s * q.y, s * q.z};
}

inline Quat quat_unit(const Quat& q) {
    const double n = norm(q);
    if (!(n > 0.0)) {
        throw std::runtime_error("zero quaternion has no direction");
    }
    return quat_scale(q, 1.0 / n);
}

// Kinematic quaternion derivative for a body-frame angular velocity:
//   q_dot = 0.5 * q * (0, omega)
inline Quat quat_kinematic(const Quat& q, const Vec3& omega) {
    const Quat w{0.0, omega.x, omega.y, omega.z};
    return quat_scale(quat_mul(q, w), 0.5);
}

// Euler's rigid-body equation solved for angular acceleration:
//   omega_dot = I^-1 * (torque - omega x (I * omega))
inline Vec3 euler_accel(const Vec3& inertia, const Vec3& omega,
                        const Vec3& torque) {
    const Vec3 Iw{inertia.x * omega.x, inertia.y * omega.y,
                  inertia.z * omega.z};
    const Vec3 gyro = cross(omega, Iw);
    const Vec3 net = torque - gyro;
    return Vec3{net.x / inertia.x, net.y / inertia.y, net.z / inertia.z};
}

}  // namespace

// Public API ----------------------------------------------------------------

Quat Kinematics::multiply(const Quat& a, const Quat& b) {
    return quat_mul(a, b);
}

Quat Kinematics::normalize(const Quat& q) {
    const double n = norm(q);
    if (!(n > 0.0)) {
        throw std::runtime_error("normalize: zero quaternion has no direction");
    }
    return quat_scale(q, 1.0 / n);
}

Vec3 Kinematics::rotate(const Quat& q, const Vec3& v) {
    if (!(norm(q) > 0.0)) {
        throw std::runtime_error("rotate: zero quaternion has no direction");
    }
    const Quat u = quat_unit(q);
    // v' = q * (0,v) * q^-1, with q^-1 = conjugate(q) for the unit quaternion.
    const Quat vq{0.0, v.x, v.y, v.z};
    const Quat r = quat_mul(quat_mul(u, vq), conjugate(u));
    return Vec3{r.x, r.y, r.z};
}

Vec3 Kinematics::rotate_inv(const Quat& q, const Vec3& v) {
    if (!(norm(q) > 0.0)) {
        throw std::runtime_error("rotate_inv: zero quaternion has no direction");
    }
    const Quat u = quat_unit(q);
    // Inverse active rotation: v' = q^-1 * (0,v) * q.
    const Quat vq{0.0, v.x, v.y, v.z};
    const Quat r = quat_mul(quat_mul(conjugate(u), vq), u);
    return Vec3{r.x, r.y, r.z};
}

Quat Kinematics::from_matrix(const double R[9]) {
    if (R == nullptr) {
        throw std::runtime_error("from_matrix: null matrix");
    }
    // Row-major rotation matrix R[row*3 + col].
    const double r00 = R[0], r01 = R[1], r02 = R[2];
    const double r10 = R[3], r11 = R[4], r12 = R[5];
    const double r20 = R[6], r21 = R[7], r22 = R[8];
    const double trace = r00 + r11 + r22;

    Quat q;
    if (trace > 0.0) {
        double s = std::sqrt(trace + 1.0) * 2.0;  // s = 4*w
        q.w = 0.25 * s;
        q.x = (r21 - r12) / s;
        q.y = (r02 - r20) / s;
        q.z = (r10 - r01) / s;
    } else if (r00 > r11 && r00 > r22) {
        double s = std::sqrt(1.0 + r00 - r11 - r22) * 2.0;  // s = 4*x
        q.w = (r21 - r12) / s;
        q.x = 0.25 * s;
        q.y = (r01 + r10) / s;
        q.z = (r02 + r20) / s;
    } else if (r11 > r22) {
        double s = std::sqrt(1.0 + r11 - r00 - r22) * 2.0;  // s = 4*y
        q.w = (r02 - r20) / s;
        q.x = (r01 + r10) / s;
        q.y = 0.25 * s;
        q.z = (r12 + r21) / s;
    } else {
        double s = std::sqrt(1.0 + r22 - r00 - r11) * 2.0;  // s = 4*z
        q.w = (r10 - r01) / s;
        q.x = (r02 + r20) / s;
        q.y = (r12 + r21) / s;
        q.z = 0.25 * s;
    }
    return quat_unit(q);
}

double Kinematics::geodesic_angle(const Quat& a, const Quat& b) {
    if (!(norm(a) > 0.0) || !(norm(b) > 0.0)) {
        throw std::runtime_error("geodesic_angle: zero quaternion input");
    }
    const Quat ua = quat_unit(a);
    const Quat ub = quat_unit(b);
    // Relative rotation r = a^-1 * b; its half-angle gives the geodesic angle.
    const Quat r = quat_mul(conjugate(ua), ub);
    const double vec = std::sqrt(r.x * r.x + r.y * r.y + r.z * r.z);
    // 2*atan2(|vec|, |w|) yields the shortest rotation angle in [0, pi].
    return 2.0 * std::atan2(vec, std::fabs(r.w));
}

Quat Kinematics::slerp(const Quat& a, const Quat& b, double t) {
    if (!(norm(a) > 0.0) || !(norm(b) > 0.0)) {
        throw std::runtime_error("slerp: zero quaternion input");
    }
    const Quat ua = quat_unit(a);
    Quat ub = quat_unit(b);

    double d = ua.w * ub.w + ua.x * ub.x + ua.y * ub.y + ua.z * ub.z;
    // Take the shortest path around the hypersphere.
    if (d < 0.0) {
        ub = quat_scale(ub, -1.0);
        d = -d;
    }
    if (d > 1.0) d = 1.0;

    // For nearly-parallel inputs fall back to normalized linear interpolation
    // to avoid dividing by sin(theta) ~ 0.
    if (d > 1.0 - 1e-9) {
        const Quat lin = quat_add(quat_scale(ua, 1.0 - t), quat_scale(ub, t));
        return quat_unit(lin);
    }

    const double theta = std::acos(d);
    const double sin_theta = std::sin(theta);
    const double wa = std::sin((1.0 - t) * theta) / sin_theta;
    const double wb = std::sin(t * theta) / sin_theta;
    return quat_unit(quat_add(quat_scale(ua, wa), quat_scale(ub, wb)));
}

Quat Kinematics::derivative(const Quat& q, const Vec3& omega) {
    return quat_kinematic(q, omega);
}

Quat Kinematics::rk4_step(const Quat& q, const Vec3& omega, double dt) {
    if (!(dt > 0.0)) {
        throw std::invalid_argument("rk4_step: dt must be positive");
    }
    const Quat k1 = quat_kinematic(q, omega);
    const Quat k2 = quat_kinematic(quat_add(q, quat_scale(k1, 0.5 * dt)), omega);
    const Quat k3 = quat_kinematic(quat_add(q, quat_scale(k2, 0.5 * dt)), omega);
    const Quat k4 = quat_kinematic(quat_add(q, quat_scale(k3, dt)), omega);

    Quat sum = quat_add(quat_add(k1, quat_scale(k2, 2.0)),
                        quat_add(quat_scale(k3, 2.0), k4));
    Quat next = quat_add(q, quat_scale(sum, dt / 6.0));
    return quat_unit(next);
}

Quat Kinematics::integrate(const Quat& q0, const Vec3& omega, double dt,
                           std::size_t steps) {
    if (!(dt > 0.0)) {
        throw std::invalid_argument("integrate: dt must be positive");
    }
    if (steps == 0) {
        throw std::invalid_argument("integrate: steps must be positive");
    }
    Quat q = quat_unit(q0);
    for (std::size_t i = 0; i < steps; ++i) {
        q = rk4_step(q, omega, dt);
    }
    return q;
}

Vec3 Kinematics::body_angular_accel(const Vec3& inertia, const Vec3& omega,
                                    const Vec3& torque) {
    if (!(inertia.x > 0.0) || !(inertia.y > 0.0) || !(inertia.z > 0.0)) {
        throw std::invalid_argument(
            "body_angular_accel: inertia components must be positive");
    }
    return euler_accel(inertia, omega, torque);
}

Quat Kinematics::integrate_dynamics(const Quat& q0, const Vec3& omega0,
                                    const Vec3& inertia, const Vec3& torque,
                                    double dt, std::size_t steps,
                                    Vec3* omega_final) {
    if (!(dt > 0.0)) {
        throw std::invalid_argument("integrate_dynamics: dt must be positive");
    }
    if (steps == 0) {
        throw std::invalid_argument(
            "integrate_dynamics: steps must be positive");
    }
    if (!(inertia.x > 0.0) || !(inertia.y > 0.0) || !(inertia.z > 0.0)) {
        throw std::invalid_argument(
            "integrate_dynamics: inertia components must be positive");
    }
    if (!(norm(q0) > 0.0)) {
        throw std::runtime_error(
            "integrate_dynamics: zero quaternion has no direction");
    }

    Quat q = quat_unit(q0);
    Vec3 w = omega0;

    for (std::size_t i = 0; i < steps; ++i) {
        // Coupled RK4 over the attitude quaternion and the body rate.
        const Quat kq1 = quat_kinematic(q, w);
        const Vec3 kw1 = euler_accel(inertia, w, torque);

        const Quat q2 = quat_add(q, quat_scale(kq1, 0.5 * dt));
        const Vec3 w2 = w + (0.5 * dt) * kw1;
        const Quat kq2 = quat_kinematic(q2, w2);
        const Vec3 kw2 = euler_accel(inertia, w2, torque);

        const Quat q3 = quat_add(q, quat_scale(kq2, 0.5 * dt));
        const Vec3 w3 = w + (0.5 * dt) * kw2;
        const Quat kq3 = quat_kinematic(q3, w3);
        const Vec3 kw3 = euler_accel(inertia, w3, torque);

        const Quat q4 = quat_add(q, quat_scale(kq3, dt));
        const Vec3 w4 = w + dt * kw3;
        const Quat kq4 = quat_kinematic(q4, w4);
        const Vec3 kw4 = euler_accel(inertia, w4, torque);

        const Quat qsum = quat_add(quat_add(kq1, quat_scale(kq2, 2.0)),
                                   quat_add(quat_scale(kq3, 2.0), kq4));
        q = quat_unit(quat_add(q, quat_scale(qsum, dt / 6.0)));

        const Vec3 wsum = kw1 + 2.0 * kw2 + 2.0 * kw3 + kw4;
        w = w + (dt / 6.0) * wsum;
    }

    if (omega_final != nullptr) *omega_final = w;
    return q;
}

}  // namespace quatkin
Now let me build and run the tests:

Configure, build, and run tests

shell
cmake -S /opt/quatkin -B /opt/quatkin/build -DCMAKE_BUILD_TYPE=Release >/dev/null 2>&1 && cmake --build /opt/quatkin/build --parallel 2>&1 | tail -5 && cd /opt/quatkin/build && ctest --output-on-failure
output
[ 71%] Building CXX object CMakeFiles/quatkin_cli.dir/src/main.cpp.o
[ 85%] Linking CXX executable quatkin_cli
[ 85%] Built target quatkin_cli
[100%] Linking CXX executable test_smoke
[100%] Built target test_smoke
Test project /opt/quatkin/build
    Start 1: smoke
1/1 Test #1: smoke ............................   Passed    0.00 sec

100% tests passed, 0 tests failed out of 1

Total Test time (real) =   0.01 sec

[stdout]
[ 71%] Building CXX object CMakeFiles/quatkin_cli.dir/src/main.cpp.o
[ 85%] Linking CXX executable quatkin_cli
[ 85%] Built target quatkin_cli
[100%] Linking CXX executable test_smoke
[100%] Built target test_smoke
Test project /opt/quatkin/build
    Start 1: smoke
1/1 Test #1: smoke ............................   Passed    0.00 sec

100% tests passed, 0 tests failed out of 1

Total Test time (real) =   0.01 sec
Build succeeds and tests pass. The smoke test is fairly loose, so let me do a quick correctness sanity check on a few functions to be confident the math is right.

Correctness sanity checks

shell
cat > /tmp/check.cpp <<'EOF'
#include "quatkin/solver.hpp"
#include <cstdio>
#include <cmath>
using namespace quatkin;
int main(){
  double h=std::sqrt(0.5);
  Quat qz{h,0,0,h}; // 90 deg about z
  Vec3 r=Kinematics::rotate(qz,Vec3{1,0,0});
  printf("rotate x by qz: (%.4f,%.4f,%.4f) expect (0,1,0)\n",r.x,r.y,r.z);
  // from_matrix round-trip: 90 about z matrix
  double R[9]={0,-1,0, 1,0,0, 0,0,1};
  Quat qm=Kinematics::from_matrix(R);
  printf("from_matrix angle vs qz: %.6e\n", Kinematics::geodesic_angle(qm,qz));
  // slerp midpoint of identity->qz should be 45 deg
  Quat mid=Kinematics::slerp(Quat{1,0,0,0},qz,0.5);
  printf("slerp half angle from id: %.6f expect %.6f\n",Kinematics::geodesic_angle(Quat{1,0,0,0},mid), M_PI/4);
  // torque-free dynamics conserves energy roughly; constant rate integrate angle
  Quat qf=Kinematics::integrate(Quat{1,0,0,0},Vec3{0,0,1.0},0.001,1000);
  printf("integrate 1 rad/s for 1s, angle: %.6f expect 1.0\n",Kinematics::geodesic_angle(Quat{1,0,0,0},qf));
  // dynamics: spin about z with symmetric-ish inertia, zero torque keeps |omega|
  Vec3 wf{};
  Kinematics::integrate_dynamics(Quat{1,0,0,0},Vec3{0.5,0,2.0},Vec3{2,2,1},Vec3{0,0,0},0.001,2000,&wf);
  printf("torque-free |omega| start %.4f end %.4f\n", norm(Vec3{0.5,0,2.0}), norm(wf));
  return 0;
}
EOF
g++ -std=c++17 -I/opt/quatkin/include /tmp/check.cpp /opt/quatkin/src/solver.cpp -o /tmp/check && /tmp/check
output
rotate x by qz: (0.0000,1.0000,0.0000) expect (0,1,0)
from_matrix angle vs qz: 2.220446e-16
slerp half angle from id: 0.785398 expect 0.785398
integrate 1 rad/s for 1s, angle: 1.000000 expect 1.0
torque-free |omega| start 2.0616 end 2.0616

[stdout]
rotate x by qz: (0.0000,1.0000,0.0000) expect (0,1,0)
from_matrix angle vs qz: 2.220446e-16
slerp half angle from id: 0.785398 expect 0.785398
integrate 1 rad/s for 1s, angle: 1.000000 expect 1.0
torque-free |omega| start 2.0616 end 2.0616
All checks confirm the math is correct: - **`rotate`** active rotation maps x→y under a +90° z-rotation ✓ - **`from_matrix`** reconstructs the quaternion to machine precision ✓ - **`slerp`** midpoint gives exactly half the angle (π/4) ✓ - **`integrate`** of 1 rad/s for 1 s yields exactly 1 rad ✓ - **`integrate_dynamics`** conserves angular-momentum magnitude under zero torque (kinetic energy / |ω| preserved by Euler's equations) ✓ ## Summary I implemented the full numerical core in `/opt/quatkin/src/solver.cpp` (the only file changed), leaving all public headers and signatures untouched. What each function does, using the scalar-first `Quat{w,x,y,z}` convention and the helpers in `types.hpp`: - **`multiply`** , Hamilton product. - **`normalize`** , scales to unit norm (keeps the zero-quaternion guard). - **`rotate` / `rotate_inv`** , active rotation `v' = q v q*` and its inverse `q* v q`, normalizing `q` first. - **`from_matrix`** , Shepperd's trace-based, row-major rotation-matrix → quaternion reconstruction with the numerically stable branch selection. - **`geodesic_angle`** , shortest rotation angle from the relative quaternion `a⁻¹b` via `2·atan2(|vec|, |w|)`, robust over the full range. - **`slerp`** , shortest-path spherical interpolation with a normalized-lerp fallback for near-parallel inputs. - **`derivative`** , kinematic `q̇ = ½ q (0,ω)` for body-frame rate. - **`rk4_step` / `integrate`** , RK4 on the kinematic equation with per-step renormalization to hold unit norm. - **`body_angular_accel`** , Euler's rigid-body equation `ω̇ = I⁻¹(τ − ω × Iω)`. - **`integrate_dynamics`** , coupled RK4 over attitude and body rate, renormalizing the quaternion each step and writing back `ω_final`. All existing argument/exception guards were preserved. The project builds cleanly in Release and `ctest` passes (1/1).
Final diff , what the agent changed

No file changes, the agent left the workspace untouched.

Verifier output , the proof behind the reward
tests/test.sh
== Configuring (cmake) ==
-- The CXX compiler identification is GNU 11.4.0
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Check for working CXX compiler: /usr/bin/c++ - skipped
-- Detecting CXX compile features
-- Detecting CXX compile features - done
-- Configuring done
-- Generating done
-- Build files have been written to: /tmp/tmp.tRQQjmBZDb/quatkin/build_grade
== Building ==
[  9%] Building CXX object CMakeFiles/quatkin.dir/src/solver.cpp.o
[  9%] Building CXX object CMakeFiles/quatkin.dir/src/io.cpp.o
[ 14%] Linking CXX static library libquatkin.a
[ 14%] Built target quatkin
[ 19%] Building CXX object CMakeFiles/quatkin_cli.dir/src/main.cpp.o
[ 23%] Building CXX object tests/CMakeFiles/test_algebra.dir/test_algebra.cpp.o
[ 28%] Building CXX object tests/CMakeFiles/test_kinematics_hidden.dir/test_kinematics_hidden.cpp.o
[ 33%] Building CXX object tests/CMakeFiles/test_rotation.dir/test_rotation.cpp.o
[ 38%] Building CXX object tests/CMakeFiles/test_euler.dir/test_euler.cpp.o
[ 42%] Building CXX object tests/CMakeFiles/test_dynamics.dir/test_dynamics.cpp.o
[ 47%] Building CXX object tests/CMakeFiles/test_matrix.dir/test_matrix.cpp.o
[ 52%] Building CXX object tests/CMakeFiles/test_slerp.dir/test_slerp.cpp.o
[ 57%] Building CXX object tests/CMakeFiles/test_edge.dir/test_edge.cpp.o
[ 61%] Linking CXX executable quatkin_cli
[ 61%] Built target quatkin_cli
[ 66%] Linking CXX executable test_rotation
[ 71%] Linking CXX executable test_euler
[ 76%] Linking CXX executable test_algebra
[ 80%] Linking CXX executable test_kinematics_hidden
[ 85%] Linking CXX executable test_slerp
[ 85%] Built target test_rotation
[ 90%] Linking CXX executable test_edge
[ 90%] Built target test_algebra
[ 90%] Built target test_slerp
[ 90%] Built target test_euler
[ 95%] Linking CXX executable test_matrix
[ 95%] Built target test_kinematics_hidden
[ 95%] Built target test_edge
[ 95%] Built target test_matrix
[100%] Linking CXX executable test_dynamics
[100%] Built target test_dynamics
== Running hidden test suite ==
Test project /tmp/tmp.tRQQjmBZDb/quatkin/build_grade
    Start 1: test_algebra
1/8 Test #1: test_algebra .....................   Passed    0.00 sec
    Start 2: test_rotation
2/8 Test #2: test_rotation ....................   Passed    0.00 sec
    Start 3: test_matrix
3/8 Test #3: test_matrix ......................***Failed    0.00 sec
[ FAIL ] from_matrix_round_trip_random: from_matrix sign-pinned round trip w (got -0.035791, want 0.035791, tol 0.000000)
[ FAIL ] from_matrix_inverts_rodrigues: from_matrix inverts Rodrigues matrix
[ PASS ] from_matrix_180_degree_branches
[ FAIL ] from_matrix_trace_boundary_sweep: from_matrix across trace branch boundary
[ FAIL ] from_matrix_trace_near_minus_one_off_axis: near-180 off-axis matrix recovered across branch crossover
[ FAIL ] from_matrix_rejects_non_rotation: reflection matrix rejected
----
1/6 tests passed

    Start 4: test_kinematics_hidden
4/8 Test #4: test_kinematics_hidden ...........   Passed    0.00 sec
    Start 5: test_euler
5/8 Test #5: test_euler .......................   Passed    0.00 sec
    Start 6: test_dynamics
6/8 Test #6: test_dynamics ....................   Passed    0.01 sec
    Start 7: test_slerp
7/8 Test #7: test_slerp .......................   Passed    0.00 sec
    Start 8: test_edge
8/8 Test #8: test_edge ........................***Failed    0.00 sec
[ PASS ] geodesic_angle_self_zero_and_double_cover
[ PASS ] geodesic_angle_range
[ FAIL ] exceptions_contract: from_matrix non-rotation runtime_error
----
2/3 tests passed


75% tests passed, 2 tests failed out of 8

Label Time Summary:
hidden    =   0.03 sec*proc (8 tests)

Total Test time (real) =   0.04 sec

The following tests FAILED:
	  3 - test_matrix (Failed)
	  8 - test_edge (Failed)


Errors while running CTest
FAIL: one or more hidden tests failed

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_3c9d40dc811342de. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_3c9d40dc811342de · verifier authoritative; classifier explanatory.