use quaternions instead of MRPs

also use correct time propagation equation
disable the fused sensors when gyro is not present since
they were unusable in practice.

Change-Id: Iad797425784e67dc6c5690e97c71c583418cc5b5
diff --git a/services/sensorservice/quat.h b/services/sensorservice/quat.h
new file mode 100644
index 0000000..fea1afe
--- /dev/null
+++ b/services/sensorservice/quat.h
@@ -0,0 +1,98 @@
+/*
+ * Copyright (C) 2011 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef ANDROID_QUAT_H
+#define ANDROID_QUAT_H
+
+#include <math.h>
+
+#include "vec.h"
+#include "mat.h"
+
+// -----------------------------------------------------------------------
+namespace android {
+// -----------------------------------------------------------------------
+
+template <typename TYPE>
+mat<TYPE, 3, 3> quatToMatrix(const vec<TYPE, 4>& q) {
+    mat<TYPE, 3, 3> R;
+    TYPE q0(q.w);
+    TYPE q1(q.x);
+    TYPE q2(q.y);
+    TYPE q3(q.z);
+    TYPE sq_q1 = 2 * q1 * q1;
+    TYPE sq_q2 = 2 * q2 * q2;
+    TYPE sq_q3 = 2 * q3 * q3;
+    TYPE q1_q2 = 2 * q1 * q2;
+    TYPE q3_q0 = 2 * q3 * q0;
+    TYPE q1_q3 = 2 * q1 * q3;
+    TYPE q2_q0 = 2 * q2 * q0;
+    TYPE q2_q3 = 2 * q2 * q3;
+    TYPE q1_q0 = 2 * q1 * q0;
+    R[0][0] = 1 - sq_q2 - sq_q3;
+    R[0][1] = q1_q2 - q3_q0;
+    R[0][2] = q1_q3 + q2_q0;
+    R[1][0] = q1_q2 + q3_q0;
+    R[1][1] = 1 - sq_q1 - sq_q3;
+    R[1][2] = q2_q3 - q1_q0;
+    R[2][0] = q1_q3 - q2_q0;
+    R[2][1] = q2_q3 + q1_q0;
+    R[2][2] = 1 - sq_q1 - sq_q2;
+    return R;
+}
+
+template <typename TYPE>
+vec<TYPE, 4> matrixToQuat(const mat<TYPE, 3, 3>& R) {
+    // matrix to quaternion
+
+    struct {
+        inline TYPE operator()(TYPE v) {
+            return v < 0 ? 0 : v;
+        }
+    } clamp;
+
+    vec<TYPE, 4> q;
+    const float Hx = R[0].x;
+    const float My = R[1].y;
+    const float Az = R[2].z;
+    q.x = sqrtf( clamp( Hx - My - Az + 1) * 0.25f );
+    q.y = sqrtf( clamp(-Hx + My - Az + 1) * 0.25f );
+    q.z = sqrtf( clamp(-Hx - My + Az + 1) * 0.25f );
+    q.w = sqrtf( clamp( Hx + My + Az + 1) * 0.25f );
+    q.x = copysignf(q.x, R[2].y - R[1].z);
+    q.y = copysignf(q.y, R[0].z - R[2].x);
+    q.z = copysignf(q.z, R[1].x - R[0].y);
+    // guaranteed to be unit-quaternion
+    return q;
+}
+
+template <typename TYPE>
+vec<TYPE, 4> normalize_quat(const vec<TYPE, 4>& q) {
+    vec<TYPE, 4> r(q);
+    if (r.w < 0) {
+        r = -r;
+    }
+    return normalize(r);
+}
+
+// -----------------------------------------------------------------------
+
+typedef vec4_t quat_t;
+
+// -----------------------------------------------------------------------
+}; // namespace android
+
+#endif /* ANDROID_QUAT_H */