Hello Guys,

I have a problem with my current project reproducing the IMU Headtracker vom Gregory Pauls Hackaday Site (https://hackaday.io/project/8952/instructions)

Problem is, the MiniIMU board from Pololu changed in the meantime to v5, (https://www.pololu.com/product/2738) using a LSM6DS33 (3 axis gyro and 3 axis accelerometer) and a LIS3MDL (3 axis magnetometer). So we have now different sensors and the accelerometer is now integretated in the gyro and not in the magnetometer anymore.

I changed the code, integrating the new libraries (with a change from "int" to "float" for one parameter to match the smoothing function) and reading the Acc-data from the gyro (gyro.a.x instead of compass.a.x).

The code works in general pretty good, but it starts drifting soon (especially the yaw-anlge) - in my understanding the 3-axis-magnetometer should prevent the drift and reset the direction? Apperently this doesn´t work and i have no idea why.
It also seems, that there is no change to the drift if I delete the magnetometer-setup in the IMUInit-function. I calibrated the magnetmoter and put the values in the beginning headtracker-code.

Can someone help me please? Here is my altered code:

Code:
/*
  Code below comes from http://planetkris.com/2014/12/easier-better-arduino-imu-head-tracker/ with minors updates.

  Based on the Madgwick algorithm found at:
  See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/

  This code inherits all relevant licenses and may be freely modified and redistributed.
  The MinIMU v1 has a roughly +/- 10degree accuracy
  The MinIMU v2 has a roughly +/- 1 degree accuracy
*/

//Uncommenting following line will enable debugging output
#define DEBUG

#include <LIS3MDL.h>                                              //Änderung                                        
#include <LSM6.h>                                                 //Änderung
#include <Wire.h>

#define ToRad(x) ((x) * 0.01745329252)  // *pi/180
#define ToDeg(x) ((x) * 57.2957795131)  // *180/pi
#define PI_FLOAT     3.14159265f
#define PIBY2_FLOAT  1.5707963f
#define GYRO_SCALE 0.07f
#define betaDef    0.08f

/*
 * To find the calibration values, load the Calibrate sketch from LSM303 library in menu : examples > LSM303 > Calibrate
 * https://github.com/pololu/lsm303-arduino/blob/master/LSM303/examples/Calibrate/Calibrate.ino
 * Then put the calibration values below
 */
#define compassXMin -3472.0f
#define compassYMin -4107.0f
#define compassZMin -4935.0f
#define compassXMax 2880.0f
#define compassYMax 2889.0f
#define compassZMax 1572.0f
#define inverseXRange (float)(2.0 / (compassXMax - compassXMin))
#define inverseYRange (float)(2.0 / (compassYMax - compassYMin))
#define inverseZRange (float)(2.0 / (compassZMax - compassZMin))

#define headingtimeout 20000  //20 sec in ms
// Teensy 2.0 has the LED on pin 11
// Teensy++ 2.0 has the LED on pin 6
// Teensy 3.0 has the LED on pin 13
const int ledPin = 6;

LSM6 gyro;                                                                //Change
LIS3MDL compass;                                                          //Change

long timer, printTimer;
float G_Dt;
int loopCount;
int blinkCount;

float q0;
float q1;
float q2;
float q3;
float beta;

float magnitude;

float pitch, roll, yaw;

float gyroSumX, gyroSumY, gyroSumZ;
float offSetX, offSetY, offSetZ;

float floatMagX, floatMagY, floatMagZ;
float smoothAccX, smoothAccY, smoothAccZ;
float accToFilterX, accToFilterY, accToFilterZ;

int i;
int inithead;  //Store initial heading
boolean fixed;  //Lock in that heading
int newhead;  //360 degree transformation

void setup() {
#ifdef DEBUG
  Serial.begin(115200);
  Serial.println("Keeping the device still and level during startup will yield the best results");
#endif
  pinMode(ledPin, OUTPUT);
  digitalWrite(ledPin, HIGH);   // set the LED on
  delay(100);
  Wire.begin();
  TWBR = ((F_CPU / 400000) - 16) / 2;//set the I2C speed to 400KHz
  IMUinit();
#ifdef DEBUG
  Serial.println("IMUinit done");
#endif
  printTimer = millis();
  timer = micros();
  blinkCount = 0;
  inithead = yaw; // Grab an initial heading - expect this to change
  fixed = false;
}

void loop() {
  if (micros() - timer >= 5000) {
    
//this runs in 4ms on the MEGA 2560

    G_Dt = (micros() - timer) / 1000000.0;
    timer = micros();
    
    compass.read();
        floatMagX = ((float)compass.m.x - compassXMin) * inverseXRange - 1.0;
        floatMagY = ((float)compass.m.y - compassYMin) * inverseYRange - 1.0;
        floatMagZ = ((float)compass.m.z - compassZMin) * inverseZRange - 1.0;

    gyro.read();
        Smoothing(&gyro.a.x, &smoothAccX);                                                                       //Change
        Smoothing(&gyro.a.y, &smoothAccY);                                                                       //Change
        Smoothing(&gyro.a.z, &smoothAccZ);                                                                       //Change
        accToFilterX = smoothAccX;                                                                               //Change
        accToFilterY = smoothAccY;                                                                               //Change           
        accToFilterZ = smoothAccZ;                                                                               //Change
        AHRSupdate(&G_Dt);
        
//update the joystick heading coordinates
// modify degress for heading

    newhead = yaw - inithead;
    if (newhead > 180) {
      newhead = -360 + newhead;
    }
    else if (newhead < -180) {
      newhead = 360 + newhead;
    }
    if (newhead < 0) {
      newhead = fscale(-90, 0, 0, 512, newhead, 0);
    }
    else {
      newhead = fscale(0, 90, 512, 1023, newhead, 0);
    }
    if (newhead < 0) {
      newhead = 0;
    }
    if (newhead > 1023) {
      newhead = 1023;
    }
    Joystick.X(newhead);
  }

  
  if (millis() - printTimer > 10) {
    printTimer = millis();
    GetEuler();
    
    if (roll < 0) {
      roll = fscale(-90, 0, 0, 512, roll, 0);
    }
    else {
      roll = fscale(0, 90, 512, 1023, roll, 0);
    }
    if (roll < 0) {
      roll = 0;
    }
    if (roll > 1023) {
      roll = 1023;
    }
    Joystick.Z(roll);
    
    if (pitch < 0) {
      pitch = fscale(-90, 0, 0, 512, pitch, 0);
    }
    else {
      pitch = fscale(0, 90, 512, 1023, pitch, 0);
    }
    if (pitch < 0) {
      pitch = 0;
    }
    if (pitch > 1023) {
      pitch = 1023;
    }
    Joystick.Y(pitch);

#ifdef DEBUG
    Serial.print("newhead: ");
    Serial.print(newhead);
    Serial.print(", pitch: ");
    Serial.print(pitch);
    Serial.print(", roll: ");
    Serial.println(roll);
#endif

    if (fixed == false) {
      blinkCount++;
      if (blinkCount > 15) {
        digitalWrite(ledPin, HIGH);
      }
      if (blinkCount > 30) {
        digitalWrite(ledPin, LOW);
        blinkCount = 0;
      }
      if (printTimer > headingtimeout) {
        inithead = yaw;
        fixed = true;
        digitalWrite(ledPin, HIGH);   // set the LED on
      }
    }
  }
}

void IMUinit() {
  //init devices
  compass.init();
  gyro.init();
  
  gyro.writeReg(0x19, 0x38);                                                              //Change
  gyro.writeReg(0x11, 0x6C);                                                              //Change
  gyro.writeReg(0x0D, 0x02);                                                              //Change
                                                          
  gyro.writeReg(0x18, 0x38);                                                              //Change
  gyro.writeReg(0x10, 0x6C);                                                              //Change
  gyro.writeReg(0x0D, 0x01);                                                              //Change                                                            

 /compass.writeReg(0x20, 0xFC);                                                           //Change   
  compass.writeReg(0x21, 0x00);                                                           //Change  
  compass.writeReg(0x22, 0x00);                                                           //Change
  compass.writeReg(0x23, 0x0C);                                                           //Change

  beta = betaDef;
  //calculate initial quaternion
  //take an average of the gyro readings to remove the bias

  for (i = 0; i < 500; i++) {
    gyro.read();
    Smoothing(&gyro.a.x, &smoothAccX);                         //Change
    Smoothing(&gyro.a.y, &smoothAccY);                         //Change
    Smoothing(&gyro.a.z, &smoothAccZ);                         //Change
    compass.read();
    delay(3);
  }
  gyroSumX = 0;
  gyroSumY = 0;
  gyroSumZ = 0;
  for (i = 0; i < 500; i++) {
    gyro.read();                                              ///Change
    Smoothing(&gyro.a.x, &smoothAccX);                         //Change
    Smoothing(&gyro.a.y, &smoothAccY);                         //Change
    Smoothing(&gyro.a.z, &smoothAccZ);                         //Change
    compass.read();

    gyroSumX += (gyro.g.x);
    gyroSumY += (gyro.g.y);
    gyroSumZ += (gyro.g.z);
    delay(3);
  }
  offSetX = gyroSumX / 500.0;
  offSetY = gyroSumY / 500.0;
  offSetZ = gyroSumZ / 500.0;
  gyro.read();                                          //Change

  //calculate the initial quaternion
  //these are rough values. This calibration works a lot better if the device is kept as flat as possible
  //find the initial pitch and roll
  pitch = ToDeg(fastAtan2(gyro.a.x, sqrt(gyro.a.y * gyro.a.y + gyro.a.z * gyro.a.z)));                             //Change
  roll = ToDeg(fastAtan2(-1 * gyro.a.y, sqrt(gyro.a.x * gyro.a.x + gyro.a.z * gyro.a.z)));                         //Change


  if (gyro.a.z > 0) {                                                                                                    //Change
    if (gyro.a.x > 0) {                                                                                                      //Change
      pitch = 180.0 - pitch;
    }
    else {
      pitch = -180.0 - pitch;
    }
    if (gyro.a.y > 0) {                                                                                                    //Change
      roll = -180.0 - roll;
    }
    else {
      roll = 180.0 - roll;
    }
  }

  floatMagX = (compass.m.x - compassXMin) * inverseXRange - 1.0;
  floatMagY = (compass.m.y - compassYMin) * inverseYRange - 1.0;
  floatMagZ = (compass.m.z - compassZMin) * inverseZRange - 1.0;
  //tilt compensate the compass
  float xMag = (floatMagX * cos(ToRad(pitch))) + (floatMagZ * sin(ToRad(pitch)));
  float yMag = -1 * ((floatMagX * sin(ToRad(roll))  * sin(ToRad(pitch))) + (floatMagY * cos(ToRad(roll))) - (floatMagZ * sin(ToRad(roll)) * cos(ToRad(pitch))));

  yaw = ToDeg(fastAtan2(yMag, xMag));

  if (yaw < 0) {
    yaw += 360;
  }
  //calculate the rotation matrix
  float cosPitch = cos(ToRad(pitch));
  float sinPitch = sin(ToRad(pitch));

  float cosRoll = cos(ToRad(roll));
  float sinRoll = sin(ToRad(roll));

  float cosYaw = cos(ToRad(yaw));
  float sinYaw = sin(ToRad(yaw));

  //need the transpose of the rotation matrix
  float r11 = cosPitch * cosYaw;
  float r21 = cosPitch * sinYaw;
  float r31 = -1.0 * sinPitch;

  float r12 = -1.0 * (cosRoll * sinYaw) + (sinRoll * sinPitch * cosYaw);
  float r22 = (cosRoll * cosYaw) + (sinRoll * sinPitch * sinYaw);
  float r32 = sinRoll * cosPitch;

  float r13 = (sinRoll * sinYaw) + (cosRoll * sinPitch * cosYaw);
  float r23 = -1.0 * (sinRoll * cosYaw) + (cosRoll * sinPitch * sinYaw);
  float r33 = cosRoll * cosPitch;

  //convert to quaternion
  q0 = 0.5 * sqrt(1 + r11 + r22 + r33);
  q1 = (r32 - r23) / (4 * q0);
  q2 = (r13 - r31) / (4 * q0);
  q3 = (r21 - r12) / (4 * q0);
}

void IMUupdate(float *dt) {
  static float gx;
  static float gy;
  static float gz;
  static float ax;
  static float ay;
  static float az;

  static float recipNorm;
  static float s0, s1, s2, s3;
  static float qDot1, qDot2, qDot3, qDot4;
  static float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 , _8q1, _8q2, q0q0, q1q1, q2q2, q3q3;

  gx = ToRad((gyro.g.x - offSetX) * GYRO_SCALE);
  gy = ToRad((gyro.g.y - offSetY) * GYRO_SCALE);
  gz = ToRad((gyro.g.z - offSetZ) * GYRO_SCALE);

  ax = -1.0 * gyro.a.x;                                                                                                           //Change
  ay = -1.0 * gyro.a.y;                                                                                                    //Change
  az = -1.0 * gyro.a.z;                                                                                                    //Change
  // Rate of change of quaternion from gyroscope
  qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
  qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
  qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
  qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

  magnitude = sqrt(ax * ax + ay * ay + az * az);
  if ((magnitude > 384) || (magnitude < 128)) {
    ax = 0;
    ay = 0;
    az = 0;
  }

  // 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;

    // Auxiliary variables to avoid repeated arithmetic
    _2q0 = 2.0f * q0;
    _2q1 = 2.0f * q1;
    _2q2 = 2.0f * q2;
    _2q3 = 2.0f * q3;
    _4q0 = 4.0f * q0;
    _4q1 = 4.0f * q1;
    _4q2 = 4.0f * q2;
    _8q1 = 8.0f * q1;
    _8q2 = 8.0f * q2;
    q0q0 = q0 * q0;
    q1q1 = q1 * q1;
    q2q2 = q2 * q2;
    q3q3 = q3 * q3;

    // Gradient decent algorithm corrective step
    s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
    s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
    s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
    s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
    recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
    s0 *= recipNorm;
    s1 *= recipNorm;
    s2 *= recipNorm;
    s3 *= recipNorm;

    // Apply feedback step
    qDot1 -= beta * s0;
    qDot2 -= beta * s1;
    qDot3 -= beta * s2;
    qDot4 -= beta * s3;
  }

  // Integrate rate of change of quaternion to yield quaternion
  q0 += qDot1 * *dt;
  q1 += qDot2 * *dt;
  q2 += qDot3 * *dt;
  q3 += qDot4 * *dt;

  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;
}

void AHRSupdate(float *dt) {
  static float gx;
  static float gy;
  static float gz;
  static float ax;
  static float ay;
  static float az;
  static float mx;
  static float my;
  static float mz;

  static float recipNorm;
  static float s0, s1, s2, s3;
  static float qDot1, qDot2, qDot3, qDot4;
  static float hx, hy;
  static float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;

  gx = ToRad((gyro.g.x - offSetX) * GYRO_SCALE);
  gy = ToRad((gyro.g.y - offSetY) * GYRO_SCALE);
  gz = ToRad((gyro.g.z - offSetZ) * GYRO_SCALE);

  ax = -1.0 * gyro.a.x;
  ay = -1.0 * gyro.a.y;
  az = -1.0 * gyro.a.z;

  mx = floatMagX;
  my = floatMagY;
  mz = floatMagZ;
  // Rate of change of quaternion from gyroscope
  qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
  qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
  qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
  qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

  magnitude = sqrt(ax * ax + ay * ay + az * az);

  if ((magnitude > 384) || (magnitude < 128)) {
    ax = 0;
    ay = 0;
    az = 0;
  }

  // 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
    _2q0mx = 2.0f * q0 * mx;
    _2q0my = 2.0f * q0 * my;
    _2q0mz = 2.0f * q0 * mz;
    _2q1mx = 2.0f * q1 * mx;
    _2q0 = 2.0f * q0;
    _2q1 = 2.0f * q1;
    _2q2 = 2.0f * q2;
    _2q3 = 2.0f * q3;
    _2q0q2 = 2.0f * q0 * q2;
    _2q2q3 = 2.0f * q2 * q3;
    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 = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
    hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
    _2bx = sqrt(hx * hx + hy * hy);
    _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
    _4bx = 2.0f * _2bx;
    _4bz = 2.0f * _2bz;

    // Gradient decent algorithm corrective step
    s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
    s0 *= recipNorm;
    s1 *= recipNorm;
    s2 *= recipNorm;
    s3 *= recipNorm;

    // Apply feedback step
    qDot1 -= beta * s0;
    qDot2 -= beta * s1;
    qDot3 -= beta * s2;
    qDot4 -= beta * s3;
  }

  // Integrate rate of change of quaternion to yield quaternion
  q0 += qDot1 * *dt;
  q1 += qDot2 * *dt;
  q2 += qDot3 * *dt;
  q3 += qDot4 * *dt;

  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;
}

void GetEuler(void) {
  roll = ToDeg(fastAtan2(2 * (q0 * q1 + q2 * q3), 1 - 2 * (q1 * q1 + q2 * q2)));
  pitch = ToDeg(asin(2 * (q0 * q2 - q3 * q1)));
  yaw = ToDeg(fastAtan2(2 * (q0 * q3 + q1 * q2) , 1 - 2 * (q2 * q2 + q3 * q3)));
  if (yaw < 0) {
    yaw += 360;
  }

}
float fastAtan2( float y, float x)
{
  static float atan;
  static float z;
  if ( x == 0.0f )
  {
    if ( y > 0.0f ) return PIBY2_FLOAT;
    if ( y == 0.0f ) return 0.0f;
    return -PIBY2_FLOAT;
  }
  z = y / x;
  if ( fabs( z ) < 1.0f )
  {
    atan = z / (1.0f + 0.28f * z * z);
    if ( x < 0.0f )
    {
      if ( y < 0.0f ) return atan - PI_FLOAT;
      return atan + PI_FLOAT;
    }
  }
  else
  {
    atan = PIBY2_FLOAT - z / (z * z + 0.28f);
    if ( y < 0.0f ) return atan - PI_FLOAT;
  }
  return atan;
}

float invSqrt(float number) {
  volatile long i;
  volatile float x, y;
  volatile const float f = 1.5F;

  x = number * 0.5F;
  y = number;
  i = * ( long * ) &y;
  i = 0x5f375a86 - ( i >> 1 );
  y = * ( float * ) &i;
  y = y * ( f - ( x * y * y ) );
  return y;
}

void Smoothing(float *raw, float *smooth) {
  *smooth = (*raw * (0.15)) + (*smooth * 0.85);
}

float fscale( float originalMin, float originalMax, float newBegin, float newEnd, float inputValue, float curve) {
  float OriginalRange = 0;
  float NewRange = 0;
  float zeroRefCurVal = 0;
  float normalizedCurVal = 0;
  float rangedValue = 0;
  boolean invFlag = 0;


  // condition curve parameter
  // limit range

  if (curve > 10) curve = 10;
  if (curve < -10) curve = -10;

  curve = (curve * -.1) ; // - invert and scale - this seems more intuitive - postive numbers give more weight to high end on output
  curve = pow(10, curve); // convert linear scale into lograthimic exponent for other pow function

  // Check for out of range inputValues
  if (inputValue < originalMin) {
    inputValue = originalMin;
  }
  if (inputValue > originalMax) {
    inputValue = originalMax;
  }

  // Zero Refference the values
  OriginalRange = originalMax - originalMin;

  if (newEnd > newBegin) {
    NewRange = newEnd - newBegin;
  }
  else
  {
    NewRange = newBegin - newEnd;
    invFlag = 1;
  }

  zeroRefCurVal = inputValue - originalMin;
  normalizedCurVal  =  zeroRefCurVal / OriginalRange;   // normalize to 0 - 1 float

  // Check for originalMin > originalMax  - the math for all other cases i.e. negative numbers seems to work out fine
  if (originalMin > originalMax ) {
    return 0;
  }

  if (invFlag == 0) {
    rangedValue =  (pow(normalizedCurVal, curve) * NewRange) + newBegin;

  }
  else // invert the ranges
  {
    rangedValue =  newBegin - (pow(normalizedCurVal, curve) * NewRange);
  }

  return rangedValue;
}
Thank you very much,
Durzo