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+//=============================================================================================
+// Adafruit_Mahony.c
+//=============================================================================================
+//
+// Madgwick's implementation of Mayhony's AHRS algorithm.
+// See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/
+//
+// From the x-io website "Open-source resources available on this website are
+// provided under the GNU General Public Licence unless an alternative licence
+// is provided in source."
+//
+// Date			Author			Notes
+// 29/09/2011	SOH Madgwick    Initial release
+// 02/10/2011	SOH Madgwick	Optimised for reduced CPU load
+//
+// Algorithm paper:
+// http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934
+//
+//=============================================================================================
+
+//-------------------------------------------------------------------------------------------
+// Header files
+
+#include "Adafruit_AHRS_Mahony.h"
+#include <math.h>
+
+//-------------------------------------------------------------------------------------------
+// Definitions
+
+#define DEFAULT_SAMPLE_FREQ 100.0f // sample frequency in Hz
+#define twoKpDef (2.0f * 12.5f)     // 2 * proportional gain
+#define twoKiDef (2.0f * 0.0f)     // 2 * integral gain
+
+//============================================================================================
+// Functions
+
+//-------------------------------------------------------------------------------------------
+// AHRS algorithm update
+
+Adafruit_Mahony::Adafruit_Mahony() : Adafruit_Mahony(twoKpDef, twoKiDef) {}
+
+Adafruit_Mahony::Adafruit_Mahony(float prop_gain, float int_gain) {
+  twoKp = prop_gain; // 2 * proportional gain (Kp)
+  twoKi = int_gain;  // 2 * integral gain (Ki)
+  q0 = 1.0f;
+  q1 = 0.0f;
+  q2 = 0.0f;
+  q3 = 0.0f;
+  integralFBx = 0.0f;
+  integralFBy = 0.0f;
+  integralFBz = 0.0f;
+  anglesComputed = false;
+  invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ;
+}
+
+void Adafruit_Mahony::update(float gx, float gy, float gz, float ax, float ay,
+                             float az, float mx, float my, float mz, float dt) {
+  float recipNorm;
+  float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
+  float hx, hy, bx, bz;
+  float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
+  float halfex, halfey, halfez;
+  float qa, qb, qc;
+
+  // Use IMU algorithm if magnetometer measurement invalid
+  // (avoids NaN in magnetometer normalisation)
+  if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
+    updateIMU(gx, gy, gz, ax, ay, az, dt);
+    return;
+  }
+
+  // Convert gyroscope degrees/sec to radians/sec
+  //gx *= 0.0174533f;
+  //gy *= 0.0174533f;
+  //gz *= 0.0174533f;
+
+  // Compute feedback only if accelerometer measurement valid
+  // (avoids NaN in accelerometer normalisation)
+  if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
+
+    // Normalise accelerometer measurement
+    recipNorm = invSqrt(ax * ax + ay * ay + az * az);
+    ax *= recipNorm;
+    ay *= recipNorm;
+    az *= recipNorm;
+
+    // Normalise magnetometer measurement
+    recipNorm = invSqrt(mx * mx + my * my + mz * mz);
+    mx *= recipNorm;
+    my *= recipNorm;
+    mz *= recipNorm;
+
+    // Auxiliary variables to avoid repeated arithmetic
+    q0q0 = q0 * q0;
+    q0q1 = q0 * q1;
+    q0q2 = q0 * q2;
+    q0q3 = q0 * q3;
+    q1q1 = q1 * q1;
+    q1q2 = q1 * q2;
+    q1q3 = q1 * q3;
+    q2q2 = q2 * q2;
+    q2q3 = q2 * q3;
+    q3q3 = q3 * q3;
+
+    // Reference direction of Earth's magnetic field
+    hx = 2.0f *
+         (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
+    hy = 2.0f *
+         (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
+    bx = sqrtf(hx * hx + hy * hy);
+    bz = 2.0f *
+         (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
+
+    // Estimated direction of gravity and magnetic field
+    halfvx = q1q3 - q0q2;
+    halfvy = q0q1 + q2q3;
+    halfvz = q0q0 - 0.5f + q3q3;
+    halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
+    halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
+    halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);
+
+    // Error is sum of cross product between estimated direction
+    // and measured direction of field vectors
+    halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy);
+    halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz);
+    halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx);
+
+    // Compute and apply integral feedback if enabled
+    if (twoKi > 0.0f) {
+      // integral error scaled by Ki
+      integralFBx += twoKi * halfex * dt;
+      integralFBy += twoKi * halfey * dt;
+      integralFBz += twoKi * halfez * dt;
+      gx += integralFBx; // apply integral feedback
+      gy += integralFBy;
+      gz += integralFBz;
+    } else {
+      integralFBx = 0.0f; // prevent integral windup
+      integralFBy = 0.0f;
+      integralFBz = 0.0f;
+    }
+
+    // Apply proportional feedback
+    gx += twoKp * halfex;
+    gy += twoKp * halfey;
+    gz += twoKp * halfez;
+  }
+
+  // Integrate rate of change of quaternion
+  gx *= (0.5f * dt); // pre-multiply common factors
+  gy *= (0.5f * dt);
+  gz *= (0.5f * dt);
+  qa = q0;
+  qb = q1;
+  qc = q2;
+  q0 += (-qb * gx - qc * gy - q3 * gz);
+  q1 += (qa * gx + qc * gz - q3 * gy);
+  q2 += (qa * gy - qb * gz + q3 * gx);
+  q3 += (qa * gz + qb * gy - qc * gx);
+
+  // Normalise quaternion
+  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+  q0 *= recipNorm;
+  q1 *= recipNorm;
+  q2 *= recipNorm;
+  q3 *= recipNorm;
+  anglesComputed = 0;
+}
+
+//-------------------------------------------------------------------------------------------
+// IMU algorithm update
+
+void Adafruit_Mahony::updateIMU(float gx, float gy, float gz, float ax,
+                                float ay, float az, float dt) {
+  float recipNorm;
+  float halfvx, halfvy, halfvz;
+  float halfex, halfey, halfez;
+  float qa, qb, qc;
+
+  // Convert gyroscope degrees/sec to radians/sec
+  //gx *= 0.0174533f;
+  //gy *= 0.0174533f;
+  //gz *= 0.0174533f;
+
+  // Compute feedback only if accelerometer measurement valid
+  // (avoids NaN in accelerometer normalisation)
+  if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
+
+    // Normalise accelerometer measurement
+    recipNorm = invSqrt(ax * ax + ay * ay + az * az);
+    ax *= recipNorm;
+    ay *= recipNorm;
+    az *= recipNorm;
+
+    // Estimated direction of gravity
+    halfvx = q1 * q3 - q0 * q2;
+    halfvy = q0 * q1 + q2 * q3;
+    halfvz = q0 * q0 - 0.5f + q3 * q3;
+
+    // Error is sum of cross product between estimated
+    // and measured direction of gravity
+    halfex = (ay * halfvz - az * halfvy);
+    halfey = (az * halfvx - ax * halfvz);
+    halfez = (ax * halfvy - ay * halfvx);
+
+    // Compute and apply integral feedback if enabled
+    if (twoKi > 0.0f) {
+      // integral error scaled by Ki
+      integralFBx += twoKi * halfex * dt;
+      integralFBy += twoKi * halfey * dt;
+      integralFBz += twoKi * halfez * dt;
+      gx += integralFBx; // apply integral feedback
+      gy += integralFBy;
+      gz += integralFBz;
+    } else {
+      integralFBx = 0.0f; // prevent integral windup
+      integralFBy = 0.0f;
+      integralFBz = 0.0f;
+    }
+
+    // Apply proportional feedback
+    gx += twoKp * halfex;
+    gy += twoKp * halfey;
+    gz += twoKp * halfez;
+  }
+
+  // Integrate rate of change of quaternion
+  gx *= (0.5f * dt); // pre-multiply common factors
+  gy *= (0.5f * dt);
+  gz *= (0.5f * dt);
+  qa = q0;
+  qb = q1;
+  qc = q2;
+  q0 += (-qb * gx - qc * gy - q3 * gz);
+  q1 += (qa * gx + qc * gz - q3 * gy);
+  q2 += (qa * gy - qb * gz + q3 * gx);
+  q3 += (qa * gz + qb * gy - qc * gx);
+
+  // Normalise quaternion
+  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+  q0 *= recipNorm;
+  q1 *= recipNorm;
+  q2 *= recipNorm;
+  q3 *= recipNorm;
+  anglesComputed = 0;
+}
+
+//-------------------------------------------------------------------------------------------
+// Fast inverse square-root
+// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
+
+float Adafruit_Mahony::invSqrt(float x) {
+  float halfx = 0.5f * x;
+  float y = x;
+  long i = *(long *)&y;
+  i = 0x5f3759df - (i >> 1);
+  y = *(float *)&i;
+  y = y * (1.5f - (halfx * y * y));
+  y = y * (1.5f - (halfx * y * y));
+  return y;
+}
+
+//-------------------------------------------------------------------------------------------
+
+void Adafruit_Mahony::computeAngles() {
+  roll = atan2f(q0 * q1 + q2 * q3, 0.5f - q1 * q1 - q2 * q2);
+  pitch = asinf(-2.0f * (q1 * q3 - q0 * q2));
+  yaw = atan2f(q1 * q2 + q0 * q3, 0.5f - q2 * q2 - q3 * q3);
+  grav[0] = 2.0f * (q1 * q3 - q0 * q2);
+  grav[1] = 2.0f * (q0 * q1 + q2 * q3);
+  grav[2] = 2.0f * (q1 * q0 - 0.5f + q3 * q3);
+  anglesComputed = 1;
+}
+
+//============================================================================================
+// END OF CODE
+//============================================================================================