Converting Arduino compass signal to useable heading - function

Question

Background
I bought an Arduino magnetometer/compass with a QMC5883 chip from Amazon, however the bearing output I'm getting doesn't tally with the calculations I've found online. The serial output seems to be plausible (sinusoids with a phase difference of 90°), but the numbers I'm getting for the calculated bearing don't match what they are supposed to. I stored the serial output as a .csv file to graph the magnetometer response when turned through 360° in Excel:
Response was roughly as expected - Z remaining roughly steady (apart from a few wobbles caused by the cable!), X and Y varying sinusoidaly through 360°. (Bear in mind I couldn't turn the magnetometer at a constant speed with my hand which is why the curves are so unsteady).
However below is the graph of what heading was calculated; results were supposed to be between -180° and +180°:
As you can see it only varies around -60° to -160°, and each bearing reading is not unique as it is given by two different rotations of the magnetometer. The specific calculation in the code used (in full at the bottom) is:
bearing =180*atan2(y,x)/3.141592654; //values will range from +180 to -180°
bearing +=0-(19/60); //Adjust for local magnetic declination
Question
I can't figure out what's wrong with the calculation as it is used in a few different sources, and I would like to know how to convert the readings I'm getting to a usable range which is one to one instead of many to one, such as -180° to +180° or 0° to 360°.
Here is the code:
//There are several differences between the QMC5883L and the HMC5883L chips
//Differences in address: 0x0D for QMC5883L; 0x1E for HMC5883L
//Differences in register map (compare datasheets)
//Output data register differences include location of x,y,z and MSB and LSB for these parameters
//Control registers are also different (so location and values for settings change)
#include <Wire.h> //I2C Arduino Library
#define addr 0x0D //I2C Address for The QMC5883L (0x1E for HMC5883)
double scale=1.0;
void setup() {
// double scaleValues[9]={0.00,0.73,0.92,1.22,1.52,2.27,2.56,3.03,4.35};
// scale=scaleValues[2];
//initialize serial and I2C communications
Serial.begin(9600);
Wire.begin();
Wire.beginTransmission(addr); //start talking to slave
Wire.write(0x0B);
Wire.write(0x01);
Wire.endTransmission();
Wire.beginTransmission(addr); //start talking to slave
Wire.write(0x09);
Wire.write(0x1D);
Wire.endTransmission();
}
void loop() {
int x, y, z; //triple axis data
//Tell the QMC what regist to begin writing data into
Wire.beginTransmission(addr);
Wire.write(0x00); //start with register 00H for QMC5883L
Wire.endTransmission();
double bearing=0.00;
//Read the data.. 2, 8 bit bytes for each axis.. 6 total bytes
Wire.requestFrom(addr, 6);
//read 6 registers in order; register location (i.e.00H)indexes by one once read
if (6 <= Wire.available()) {
//note the order of following statements matters
//as each register will be read in sequence starting from data register 00H to 05H
//where order is xLSB,xMSB,yLSB,yMSB,zLSB,zMSB
//this is different from HMC5883L!
//data registers are 03 to 08
//where order is xMSB,xLSB,zMSB,zLSB,yMSB,yLSB
x = Wire.read(); //LSB x;
x |= Wire.read()<<8; //MSB x; bitshift left 8, then bitwise OR to make "x"
// x*=scale;
y = Wire.read(); //LSB y
y |= Wire.read()<<8; //MSB y;
// y*=scale;
z = Wire.read(); //LSB z; irrelevant for compass
z |= Wire.read()<<8; //MSB z;
// z*=scale;
bearing =180*atan2(y,x)/3.141592654;//values will range from +180 to -180 degrees
bearing +=0-(19/60);//Adjust for local magnetic declination
}
// Show Values
//Serial.print("X:");
Serial.print(x);
//Serial.print(" Y: ");
Serial.print(",");
Serial.print(y);
//Serial.print(" Z: ");
Serial.print(",");
Serial.print(z);
//Serial.print(" B: ");
Serial.print(",");
Serial.println(bearing);
delay(500);
}

Answer 1

For others reading this question:
The OP forgot to implement a x,y,z smoothing and an out of scope value removal. How this can be achieved and how its done look into the source code of this QMC5883 compass library:
QMC5883L Compass is an Arduino library for using QMC5583L series chip boards as a compass.
It supports:
Getting values of XYZ axis.
Calculating Azimuth.
Getting 16 point Azimuth bearing direction (0 - 15).
Getting 16 point Azimuth bearing Names (N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW)
Smoothing of XYZ readings via rolling averaging and min / max removal.