//=============================================================================================
// 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
//============================================================================================