> Need some notion of optimization/resolution/speed criteria.
> Interpolation, <abbreviated>series expansion and CORDICS
> seem to be the obvious candidates. Maybe we should 'choose sides'
> and publish all, targeted toward the 8bit territory. I'll do
> (at least) one of them. _I guess I mean the elementary trig
> functions to solve just this range of problems_.


The problem I'm trying to solve, is to "de-noise" an input that gives me an
8 bit "bearing" value. (0-255)  over a full circle of rotation.

I may only get a very short burst of samples, (16 is my minimum) or a lot
more, and I intend to use all that I can get.

Each sample is converted to rectangular notation (by sin/cos table lookup)
and I average in four layers of 16 sample pairs, down to a final XY pair.
In the first layer, I use a radius of "1", scaled to 127 to keep the X and Y
values within signed 8 bit values.  When the first layer bearings are
averaged into a single entry in the second layer, (also true for 2>3 and
3>4) the X and Y values then carry radus information that will end up as
<=1. If the bearing is very noisy, then the radius will be rather a lot less
than 1, and if quiet, it will closely approach 1.

The final pair are signed bytes, which represent sin and cos on a circle of
radius which is almost certainly not 1.  The conventional operation of
A=csc(X/Radius) performs the scaling of X out to the unit circle.

Speed, in my application isn't a huge issue, all the averaging is done
between samples at 300-4000 samples/sec, but this final step is done when
either the input signal stops, or when I have 65000 samples collected, so I
can afford to miss a few while I process.