Mahony.js
function mahonyAHRSupdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltaTimeSec) {
    recipSampleFreq = deltaTimeSec || recipSampleFreq;
    let recipNorm;
    let q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
    let hx, hy, bx, bz;
    let halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
    let halfex, halfey, halfez;

    // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
    if (mx === undefined || my === undefined || mz === undefined || (mx === 0 && my === 0 && mz === 0)) {
      mahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az);
      return;
    }

    // Compute feedback only if accelerometer measurement valid (afunctions NaN in accelerometer normalisation)
    if (ax !== 0 && ay !== 0 && az !== 0) {
      // Normalise accelerometer measurement
      recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
      ax *= recipNorm;
      ay *= recipNorm;
      az *= recipNorm;

      // Normalise magnetometer measurement
      recipNorm = (mx * mx + my * my + mz * mz) ** -0.5;
      mx *= recipNorm;
      my *= recipNorm;
      mz *= recipNorm;

      // Auxiliary variables to afunction 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 = 2.0 * (mx * (0.5 - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
      hy = 2.0 * (mx * (q1q2 + q0q3) + my * (0.5 - q1q1 - q3q3) + mz * (q2q3 - q0q1));
      bx = Math.sqrt(hx * hx + hy * hy);
      bz = 2.0 * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5 - q1q1 - q2q2));

      // Estimated direction of gravity and magnetic field
      halfvx = q1q3 - q0q2;
      halfvy = q0q1 + q2q3;
      halfvz = q0q0 - 0.5 + q3q3;
      halfwx = bx * (0.5 - q2q2 - q3q3) + bz * (q1q3 - q0q2);
      halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
      halfwz = bx * (q0q2 + q1q3) + bz * (0.5 - 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 > 0.0) {
        integralFBx += twoKi * halfex * recipSampleFreq; // integral error scaled by Ki
        integralFBy += twoKi * halfey * recipSampleFreq;
        integralFBz += twoKi * halfez * recipSampleFreq;
        gx += integralFBx; // apply integral feedback
        gy += integralFBy;
        gz += integralFBz;
      } else {
        integralFBx = 0.0; // prevent integral windup
        integralFBy = 0.0;
        integralFBz = 0.0;
      }

      // Apply proportional feedback
      gx += twoKp * halfex;
      gy += twoKp * halfey;
      gz += twoKp * halfez;
    }

    // Integrate rate of change of quaternion
    gx *= 0.5 * recipSampleFreq; // pre-multiply common factors
    gy *= 0.5 * recipSampleFreq;
    gz *= 0.5 * recipSampleFreq;
    const qa = q0;
    const qb = q1;
    const 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 = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;
  }
function mahonyAHRSupdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltaTimeSec) {
    recipSampleFreq = deltaTimeSec || recipSampleFreq;
    let recipNorm;
    let q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
    let hx, hy, bx, bz;
    let halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
    let halfex, halfey, halfez;

    // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
    if (mx === undefined || my === undefined || mz === undefined || (mx === 0 && my === 0 && mz === 0)) {
      mahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az);
      return;
    }

    // Compute feedback only if accelerometer measurement valid (afunctions NaN in accelerometer normalisation)
    if (ax !== 0 && ay !== 0 && az !== 0) {
      // Normalise accelerometer measurement
      recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
      ax *= recipNorm;
      ay *= recipNorm;
      az *= recipNorm;

      // Normalise magnetometer measurement
      recipNorm = (mx * mx + my * my + mz * mz) ** -0.5;
      mx *= recipNorm;
      my *= recipNorm;
      mz *= recipNorm;

      // Auxiliary variables to afunction 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 = 2.0 * (mx * (0.5 - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
      hy = 2.0 * (mx * (q1q2 + q0q3) + my * (0.5 - q1q1 - q3q3) + mz * (q2q3 - q0q1));
      bx = Math.sqrt(hx * hx + hy * hy);
      bz = 2.0 * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5 - q1q1 - q2q2));

      // Estimated direction of gravity and magnetic field
      halfvx = q1q3 - q0q2;
      halfvy = q0q1 + q2q3;
      halfvz = q0q0 - 0.5 + q3q3;
      halfwx = bx * (0.5 - q2q2 - q3q3) + bz * (q1q3 - q0q2);
      halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
      halfwz = bx * (q0q2 + q1q3) + bz * (0.5 - 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 > 0.0) {
        integralFBx += twoKi * halfex * recipSampleFreq; // integral error scaled by Ki
        integralFBy += twoKi * halfey * recipSampleFreq;
        integralFBz += twoKi * halfez * recipSampleFreq;
        gx += integralFBx; // apply integral feedback
        gy += integralFBy;
        gz += integralFBz;
      } else {
        integralFBx = 0.0; // prevent integral windup
        integralFBy = 0.0;
        integralFBz = 0.0;
      }

      // Apply proportional feedback
      gx += twoKp * halfex;
      gy += twoKp * halfey;
      gz += twoKp * halfez;
    }

    // Integrate rate of change of quaternion
    gx *= 0.5 * recipSampleFreq; // pre-multiply common factors
    gy *= 0.5 * recipSampleFreq;
    gz *= 0.5 * recipSampleFreq;
    const qa = q0;
    const qb = q1;
    const 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 = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;
  }
--------------------------------------------------------------------------------------------------- AHRS algorithm update