whole_func_string: 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;
    }
func_code_string: 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;
    }
func_documentation_string: --------------------------------------------------------------------------------------------------- AHRS algorithm update