Method of fast arctangent calculation pre and post processing

A method of calculating an arctangent for a point located on a plane by an x-value and a y-value of a Cartesian coordinate system, the method comprising:

• establishing an index in a memory of a controller, wherein the index includes a 3-bit binary value;
• coding a y-bit of the index to indicate a sign of the y-value;
• coding an x-bit of the index to indicate a sign of the x-value;
• clearing a sign bit of a binary value representing the y-value to define a cleared y-value;
• clearing a sign bit of a binary value representing the x-value to define a cleared x-value;
• comparing the cleared x-value to cleared y-value to determine if the cleared x-value is greater than the cleared y-value, or if cleared x-value is equal to or less than cleared y-value;
• returning a calculated arctangent output value equal to zero when the cleared y-value is equal to zero;
• calculating the arctangent of the quotient of the cleared x-value divided by the cleared y-value to define a calculated arctangent output value, when the cleared x-value is equal to or less than the cleared y-value;
• swapping the cleared x-value for the cleared y-value to define a swapped x-value, and swapping the cleared y-value for the cleared x-value to define a swapped y-value, when the cleared x-value is greater than cleared y-value;
• coding a swap bit of the index to indicate that the cleared x-value and the cleared y-value were swapped to define the swapped x-value and the swapped y-value respectively;
• calculating the arctangent of the quotient of the swapped x-value divided by the swapped y-value to define a calculated arctangent output value, when the cleared x-value is greater than the cleared y-value;
• looking up a segment base angle from an angle adjustment table, based on the coded x-bit, the coded y-bit, and the coded swap bit of the index;
• extracting a numerical sign from a reverse bit coded into the segment base angle;
• applying the extracted numerical sign from the reverse bit to the calculated arctangent output value to define a corrected arctangent value;
• clearing the reverse bit of the extracted segment base angle to define an cleared segment base angle;
• and
• adding the corrected arctangent value to the cleared segment base angle to define the arctangent of the point.