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.
SubtypeIncomplete Implementation
EvidenceAgent left all 11 Kinematics functions as failing stubs. Test output shows 75% passing overall but critical failures in test_matrix (1/6 tests passed): from_matrix_round_trip_random (sign-pinned round trip w component), from_matrix_inverts_rodrigues, from_matrix_trace_boundary_sweep, from_matrix_trace_near_minus_one_off_axis. The agent's solver.cpp returns identity quaternions (multiply, from_matrix) and zero/identity responses for all other functions. The reference solution (fix.patch) implements 11 complete functions with proper quaternion algebra, matrix-to-quaternion conversion with multi-branch numerical stability, derivative calculation, RK4 integration, and body dynamics.
Root causeAgent read the instruction and headers but did not attempt any implementation of the core algorithms. The stub implementations were left in place, causing the 11 required functions to fail all non-trivial tests. This is a complex C++ task requiring understanding of quaternion algebra, rotation matrices, and numerical stability that the agent did not pursue.
RecommendationN/A - task is fine. This is expected hard-task behavior (implementation task with complex numerical algorithms). The agent needed to implement multiply, normalize, rotate, rotate_inv, from_matrix (the hardest - requires trace-based branching and matrix validation), geodesic_angle, slerp, derivative, rk4_step, integrate, body_angular_accel, and integrate_dynamics functions. All were left as stubs."
Trajectory
Tool-by-tool agent trajectory
9 tool calls · 3 tool types · 14 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 ```

/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/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/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
Let me look at the tests to understand the exact conventions expected.

List project files

shell
find /opt/quatkin -type f -not -path '*/build/*' | head -50
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/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/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

/opt/quatkin/src/io.cpp

contents
1	#include "quatkin/io.hpp"
2	
3	#include <cmath>
4	#include <fstream>
5	#include <iomanip>
6	#include <optional>
7	#include <sstream>
8	#include <stdexcept>
9	#include <string>
10	
11	namespace quatkin {
12	
13	namespace {
14	
15	[[noreturn]] void fail(std::size_t line_no, const std::string& msg) {
16	    std::ostringstream oss;
17	    oss << "parse_scenario: line " << line_no << ": " << msg;
18	    throw std::runtime_error(oss.str());
19	}
20	
21	} // namespace
22	
23	Scenario parse_scenario(std::istream& in) {
24	    Quat q0{1.0, 0.0, 0.0, 0.0};
25	    std::optional<Vec3> omega;
26	    std::optional<double> dt;
27	    std::optional<long long> steps;
28	
29	    std::string line;
30	    std::size_t line_no = 0;
31	    while (std::getline(in, line)) {
32	        ++line_no;
33	        const auto hash = line.find('#');
34	        if (hash != std::string::npos) line.erase(hash);
35	        std::istringstream ls(line);
36	        std::string tag;
37	        if (!(ls >> tag)) continue;
38	
39	        if (tag == "q0") {
40	            Quat q;
41	            if (!(ls >> q.w >> q.x >> q.y >> q.z))
42	                fail(line_no, "record 'q0' needs w x y z");
43	            q0 = q;
44	        } else if (tag == "omega") {
45	            Vec3 w;
46	            if (!(ls >> w.x >> w.y >> w.z))
47	                fail(line_no, "record 'omega' needs wx wy wz");
48	            omega = w;
49	        } else if (tag == "dt") {
50	            double v;
51	            if (!(ls >> v)) fail(line_no, "record 'dt' needs a value");
52	            dt = v;
53	        } else if (tag == "steps") {
54	            long long v;
55	            if (!(ls >> v)) fail(line_no, "record 'steps' needs an integer");
56	            steps = v;
57	        } else {
58	            fail(line_no, "unknown record '" + tag + "'");
59	        }
60	    }
61	
62	    if (!omega) fail(line_no, "missing required record: omega");
63	    if (!dt) fail(line_no, "missing required record: dt");
64	    if (!steps) fail(line_no, "missing required record: steps");
65	    if (*steps <= 0) fail(line_no, "steps must be positive");
66	
67	    Scenario sc{q0, *omega, *dt, static_cast<std::size_t>(*steps)};
68	    return sc;
69	}
70	
71	Scenario parse_scenario_file(const std::string& path) {
72	    std::ifstream in(path);
73	    if (!in) {
74	        throw std::runtime_error("parse_scenario_file: cannot open '" + path +
75	                                 "'");
76	    }
77	    return parse_scenario(in);
78	}
79	
80	void write_report(std::ostream& out, const Scenario& scenario) {
81	    const Quat qf = Kinematics::integrate(scenario.q0, scenario.omega,
82	                                          scenario.dt, scenario.steps);
83	    // Recovered rotation angle theta from the scalar part of the unit
84	    // quaternion: w = cos(theta/2).
85	    const double w_clamped = std::fmax(-1.0, std::fmin(1.0, qf.w));
86	    const double angle = 2.0 * std::acos(w_clamped);
87	
88	    out << std::scientific << std::setprecision(6);
89	    out << "# quaternion attitude-propagation report\n";
90	    out << "omega=(" << scenario.omega.x << ", " << scenario.omega.y << ", "
91	        << scenario.omega.z << ") t_final=" << scenario.dt * scenario.steps
92	        << "\n";
93	    out << "q_final=(" << qf.w << ", " << qf.x << ", " << qf.y << ", " << qf.z
94	        << ")\n";
95	    out << "norm=" << norm(qf) << " angle_rad=" << angle << "\n";
96	}
97	
98	} // namespace quatkin
99
I now understand the conventions (scalar-first quaternions, body-frame angular velocity, active rotation). Let me implement the core.
write · /opt/quatkin/src/solver.cpp
#include "quatkin/solver.hpp"

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

#include "quatkin/types.hpp"

namespace quatkin {

namespace {

// Quaternion vector-space helpers (the public API keeps Quat free of operators).
Quat qadd(const Quat& a, const Quat& b) {
    return Quat{a.w + b.w, a.x + b.x, a.y + b.y, a.z + b.z};
}
Quat qscale(const Quat& q, double s) {
    return Quat{s * q.w, s * q.x, s * q.y, s * q.z};
}

} // namespace

Quat Kinematics::multiply(const Quat& a, const Quat& b) {
    // Hamilton product, scalar-first convention.
    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};
}

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");
    }
    const double inv = 1.0 / n;
    return Quat{q.w * inv, q.x * inv, q.y * inv, q.z * inv};
}

Vec3 Kinematics::rotate(const Quat& q, const Vec3& v) {
    if (!(norm(q) > 0.0)) {
        throw std::runtime_error("rotate: zero quaternion has no direction");
    }
    // Active rotation v' = q (0,v) q* using a unit quaternion.
    const Quat u = normalize(q);
    const Quat vq{0.0, v.x, v.y, v.z};
    const Quat r = multiply(multiply(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");
    }
    // Inverse (passive) rotation v' = q* (0,v) q.
    const Quat u = normalize(q);
    const Quat vq{0.0, v.x, v.y, v.z};
    const Quat r = multiply(multiply(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");
    }
    // R is row-major: R[3*row + col]. Shepperd's method for numerical safety.
    const double m00 = R[0], m01 = R[1], m02 = R[2];
    const double m10 = R[3], m11 = R[4], m12 = R[5];
    const double m20 = R[6], m21 = R[7], m22 = R[8];
    const double trace = m00 + m11 + m22;

    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 = (m21 - m12) / s;
        q.y = (m02 - m20) / s;
        q.z = (m10 - m01) / s;
    } else if (m00 > m11 && m00 > m22) {
        double s = std::sqrt(1.0 + m00 - m11 - m22) * 2.0; // s = 4*x
        q.w = (m21 - m12) / s;
        q.x = 0.25 * s;
        q.y = (m01 + m10) / s;
        q.z = (m02 + m20) / s;
    } else if (m11 > m22) {
        double s = std::sqrt(1.0 + m11 - m00 - m22) * 2.0; // s = 4*y
        q.w = (m02 - m20) / s;
        q.x = (m01 + m10) / s;
        q.y = 0.25 * s;
        q.z = (m12 + m21) / s;
    } else {
        double s = std::sqrt(1.0 + m22 - m00 - m11) * 2.0; // s = 4*z
        q.w = (m10 - m01) / s;
        q.x = (m02 + m20) / s;
        q.y = (m12 + m21) / s;
        q.z = 0.25 * s;
    }
    return normalize(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 = normalize(a);
    const Quat ub = normalize(b);
    double d = ua.w * ub.w + ua.x * ub.x + ua.y * ub.y + ua.z * ub.z;
    // q and -q are the same orientation; take the shorter arc.
    d = std::fabs(d);
    if (d > 1.0) d = 1.0;
    return 2.0 * std::acos(d);
}

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");
    }
    Quat ua = normalize(a);
    Quat ub = normalize(b);
    double cos_theta = ua.w * ub.w + ua.x * ub.x + ua.y * ub.y + ua.z * ub.z;
    // Choose the shorter arc by flipping one endpoint if needed.
    if (cos_theta < 0.0) {
        ub = qscale(ub, -1.0);
        cos_theta = -cos_theta;
    }
    if (cos_theta > 1.0) cos_theta = 1.0;

    // Nearly colinear: fall back to normalized linear interpolation.
    if (cos_theta > 1.0 - 1e-12) {
        return normalize(qadd(qscale(ua, 1.0 - t), qscale(ub, t)));
    }

    const double theta = std::acos(cos_theta);
    const double sin_theta = std::sin(theta);
    const double sa = std::sin((1.0 - t) * theta) / sin_theta;
    const double sb = std::sin(t * theta) / sin_theta;
    return normalize(qadd(qscale(ua, sa), qscale(ub, sb)));
}

Quat Kinematics::derivative(const Quat& q, const Vec3& omega) {
    // Body-frame rate kinematics: q_dot = 0.5 * q * (0, omega).
    const Quat omega_q{0.0, omega.x, omega.y, omega.z};
    return qscale(multiply(q, omega_q), 0.5);
}

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");
    }
    // Classic RK4 with constant angular velocity over the step.
    const Quat k1 = derivative(q, omega);
    const Quat k2 = derivative(qadd(q, qscale(k1, 0.5 * dt)), omega);
    const Quat k3 = derivative(qadd(q, qscale(k2, 0.5 * dt)), omega);
    const Quat k4 = derivative(qadd(q, qscale(k3, dt)), omega);
    Quat sum = qadd(qadd(k1, qscale(k2, 2.0)), qadd(qscale(k3, 2.0), k4));
    return normalize(qadd(q, qscale(sum, dt / 6.0)));
}

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 = normalize(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");
    }
    // Euler's rigid-body equation: I*w_dot = tau - w x (I*w).
    const Vec3 Iw{inertia.x * omega.x, inertia.y * omega.y, inertia.z * omega.z};
    const Vec3 gyro = cross(omega, Iw);
    return Vec3{(torque.x - gyro.x) / inertia.x,
                (torque.y - gyro.y) / inertia.y,
                (torque.z - gyro.z) / inertia.z};
}

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 = normalize(q0);
    Vec3 w = omega0;

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

        const Quat q2 = qadd(q, qscale(kq1, 0.5 * dt));
        const Vec3 w2 = w + (0.5 * dt) * kw1;
        const Quat kq2 = derivative(q2, w2);
        const Vec3 kw2 = body_angular_accel(inertia, w2, torque);

        const Quat q3 = qadd(q, qscale(kq2, 0.5 * dt));
        const Vec3 w3 = w + (0.5 * dt) * kw2;
        const Quat kq3 = derivative(q3, w3);
        const Vec3 kw3 = body_angular_accel(inertia, w3, torque);

        const Quat q4 = qadd(q, qscale(kq3, dt));
        const Vec3 w4 = w + dt * kw3;
        const Quat kq4 = derivative(q4, w4);
        const Vec3 kw4 = body_angular_accel(inertia, w4, torque);

        const Quat qsum =
            qadd(qadd(kq1, qscale(kq2, 2.0)), qadd(qscale(kq3, 2.0), kq4));
        q = normalize(qadd(q, qscale(qsum, dt / 6.0)));
        w = w + (dt / 6.0) * (kw1 + 2.0 * kw2 + 2.0 * kw3 + kw4);
    }

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

} // namespace quatkin
Now let me build and test.

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 2>&1 | tail -20
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    0.01 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    0.01 sec

100% tests passed, 0 tests failed out of 1

Total Test time (real) =   0.01 sec
The implementation builds cleanly and the test suite passes. I implemented the numerical core in `src/solver.cpp` using standard rigid-body attitude conventions (scalar-first quaternions, active rotations, body-frame angular velocity): - **`multiply`** , Hamilton product - **`normalize`** , division by norm (keeps the existing zero-quaternion guard) - **`rotate` / `rotate_inv`** , active sandwich `q(0,v)q*` and its inverse `q*(0,v)q` - **`from_matrix`** , Shepperd's branch-selecting reconstruction (row-major `R`), numerically stable across all trace cases - **`geodesic_angle`** , `2·acos(|⟨a,b⟩|)`, treating `q` and `−q` as the same orientation - **`slerp`** , shorter-arc spherical interpolation with a normalized-lerp fallback for nearly-colinear inputs - **`derivative`** , kinematics `q̇ = ½ q (0,ω)` - **`rk4_step` / `integrate`** , classic RK4 with constant rate, re-normalizing each step - **`body_angular_accel`** , Euler's equation `ω̇ = I⁻¹(τ − ω×Iω)` - **`integrate_dynamics`** , coupled RK4 over the joint `(attitude, body-rate)` state I only touched `src/solver.cpp`; the headers and signatures are unchanged, and all the original input-validation guards are preserved.
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.Inr96WTNwg/quatkin/build_grade
== Building ==
[  4%] Building CXX object CMakeFiles/quatkin.dir/src/io.cpp.o
[  9%] Building CXX object CMakeFiles/quatkin.dir/src/solver.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_matrix.dir/test_matrix.cpp.o
[ 38%] Building CXX object tests/CMakeFiles/test_euler.dir/test_euler.cpp.o
[ 42%] Building CXX object tests/CMakeFiles/test_rotation.dir/test_rotation.cpp.o
[ 47%] Building CXX object tests/CMakeFiles/test_dynamics.dir/test_dynamics.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_algebra
[ 71%] Linking CXX executable test_edge
[ 76%] Linking CXX executable test_kinematics_hidden
[ 80%] Linking CXX executable test_slerp
[ 85%] Linking CXX executable test_euler
[ 90%] Linking CXX executable test_rotation
[ 90%] Built target test_kinematics_hidden
[ 90%] Built target test_slerp
[ 95%] Linking CXX executable test_matrix
[ 95%] Built target test_edge
[ 95%] Built target test_algebra
[ 95%] Built target test_euler
[ 95%] Built target test_rotation
[ 95%] Built target test_matrix
[100%] Linking CXX executable test_dynamics
[100%] Built target test_dynamics
== Running hidden test suite ==
Test project /tmp/tmp.Inr96WTNwg/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) =   0.03 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_b2ae917fc4464d12. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_b2ae917fc4464d12 · verifier authoritative; classifier explanatory.