diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 572b57448..3812a7f6a 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -22,6 +22,7 @@ set(tests
     tests_pacing
     tests_quatexpmap
     tests_quat_change_of_basis
+    tests_quat_swing_twist
     tests_rational
     tests_vector
     tests_worker
@@ -66,8 +67,10 @@ target_link_libraries(tests_quatexpmap PRIVATE aux_math)
 target_link_libraries(tests_rational PRIVATE aux_math)
 target_link_libraries(tests_pose PRIVATE aux_math)
 target_link_libraries(tests_quat_change_of_basis PRIVATE aux_math)
+target_link_libraries(tests_quat_swing_twist PRIVATE aux_math)
 
 target_include_directories(tests_quat_change_of_basis SYSTEM PRIVATE ${EIGEN3_INCLUDE_DIR})
+target_include_directories(tests_quat_swing_twist SYSTEM PRIVATE ${EIGEN3_INCLUDE_DIR})
 
 if(XRT_BUILD_DRIVER_HANDTRACKING)
 	target_link_libraries(
diff --git a/tests/tests_quat_swing_twist.cpp b/tests/tests_quat_swing_twist.cpp
new file mode 100644
index 000000000..227971686
--- /dev/null
+++ b/tests/tests_quat_swing_twist.cpp
@@ -0,0 +1,103 @@
+// Copyright 2022, Collabora, Inc.
+// SPDX-License-Identifier: BSL-1.0
+/*!
+ * @file
+ * @brief Test for the quaternion swing-twist composition.
+ * @author Moses Turner <moses@collabora.com>
+ */
+#include "math/m_api.h"
+#include "xrt/xrt_defines.h"
+#include <util/u_worker.hpp>
+#include <util/u_logging.h>
+#include <math/m_space.h>
+#include <math/m_vec3.h>
+
+
+#include "catch/catch.hpp"
+
+#include <random>
+
+
+#include "math/m_eigen_interop.hpp"
+#include <Eigen/Core>
+
+float
+quat_difference(xrt_quat q1, xrt_quat q2)
+{
+	// https://math.stackexchange.com/a/90098
+	// d(q1,q2)=1−⟨q1,q2⟩2
+
+	float inner_product = (q1.w * q2.w) + (q1.x * q2.x) + (q1.y * q2.y) + (q1.z * q2.z);
+	return 1.0 - (inner_product * inner_product);
+}
+
+TEST_CASE("SwingTwistTriviallyInvertibleIn180DegreeHemisphere")
+
+{
+	std::random_device dev;
+
+	auto mt = std::mt19937(dev());
+
+	auto rd = std::uniform_real_distribution<float>(-M_PI / 2, M_PI / 2);
+
+	for (int i = 0; i < 20; i++) {
+		xrt_vec2 swing = {rd(mt), rd(mt)};
+		float twist = rd(mt);
+
+		xrt_quat combquat;
+
+		math_quat_from_swing_twist(&swing, twist, &combquat);
+
+		xrt_vec2 recovered_swing;
+		float recovered_twist;
+
+		math_quat_to_swing_twist(&combquat, &recovered_swing, &recovered_twist);
+
+		bool success = (fabsf(swing.x - recovered_swing.x) <= 0.001) &&
+		               (fabsf(swing.y - recovered_swing.y) <= 0.001) &&
+		               (fabsf(twist - recovered_twist) <= 0.001);
+
+		if (!success) {
+			U_LOG_E("Fail! Used swing %f %f, twist %f", swing.x, swing.y, twist);
+		}
+		CHECK(success);
+	}
+}
+
+
+TEST_CASE("SwingTwistAlwaysInvertibleIfYouUseSoundRotationEqualities")
+
+{
+	std::random_device dev;
+
+	auto mt = std::mt19937(dev());
+
+	auto rd = std::uniform_real_distribution<float>(-1000, 1000);
+
+	for (int i = 0; i < 20; i++) {
+
+		xrt_vec2 swing = {rd(mt), rd(mt)};
+		float twist = rd(mt);
+
+		xrt_quat combquat;
+
+		math_quat_from_swing_twist(&swing, twist, &combquat);
+
+		xrt_vec2 recovered_swing;
+		float recovered_twist;
+
+		math_quat_to_swing_twist(&combquat, &recovered_swing, &recovered_twist);
+
+		xrt_quat recovered_quat;
+
+		math_quat_from_swing_twist(&recovered_swing, recovered_twist, &recovered_quat);
+
+		bool success = quat_difference(combquat, recovered_quat) <= 0.001;
+
+		if (!success) {
+			// Test failed
+			U_LOG_E("Fail! Used swing %f %f, twist %f", swing.x, swing.y, twist);
+		}
+		CHECK(success);
+	}
+}