A function lookup table is a method by which you can approximate a function by a table with a finite number of points (X,Y). Function lookup tables are essential to many fixed-point applications. The function you want to approximate is called the ideal function. The X values of the lookup table are called the breakpoints. You approximate the value of the ideal function at a point by linearly interpolating between the two breakpoints closest to the point.
In creating the points for a function lookup table, you generally want to achieve one or both of the following goals:
Minimize the worst-case error for a specified maximum number of breakpoints
Minimize the number of breakpoints for a specified maximum allowed error
Create Lookup Tables for a Sine Function shows you how
to create function lookup tables using the function
fixpt_look1_func_approx. You can optimize
the lookup table to minimize the number of data points, the error,
or both. You can also restrict the spacing of the breakpoints to be
even or even powers of two to speed up computations using the table.