faster impl of atan2 in java...

Specifically, I have an Angle class and a Vector class, and I'd like to
be able to convert between them quickly...

----Context----
The Angle class stores its value as a 8 bit integer value representing
"bygrees" (byte degrees). each "bygree" is 1/256th of a circle, with 0
starting at 12:00 going clockwise.
The Vector class stores its value as a pair of floating (double
precision) values.

After running it through a profiler, I've optimized the angle class to
precompute all 256 possible values, including sine, cosine, radian
conversion, etc...Good speed increase :-)

But, now my application is bottlenecking on an Math.atan2 call,
converting a vector's direction to an Angle object.

----One solution----
I'm trying to think of ways to speed up the conversion of Vectors to
Angles, but the only way I can think to precompute this is to make a 2d
array of Angle objects. and return
angleFor[normalizeForLookup(x)][normalizeForLookup(y)]. Where
normalizeForLookup would handle rounding and bound's checking.

OR, I could use an atan lookup for int((y/x) * k) (k to be determined),
but I would have to find a suitable k, and maybe some other tricks.

On the plus side, I can determine that the largest magnetude of any
vector would be sqrt(2) * 1000, and accuracy isn't extremely important.

The downside to this would be creating an array of approximitly
4,000,000 elements. Although most of those elements point to a subset
of 256 objects, 4 megs of references is non negligible. Not to mention
the init time required.

----Another possible solution----

So, the other alternative I see is to find a faster implementation of
atan2 (or atan), and use it in place of Math.atan2, but I wouldn't know
where to start. a quick search on google returned nothing, but I'm not
very good at finding keywords to search.

Thanks in advance,
Daniel.