"I see that there is a tendancy to use C code with double variables"

That may be down to nothing more than the fact that the standard 'C' math library functions expect and return doubles. I do a lot of not entirely dissimilar stuff with 32 bit floats and have not had any trouble with excessive loss of precision.

"How long would something like this take to compute on a bog standard 12 clocker 89C52 at say 11.0592 MHz?"

If you post a link to some code or a decent description of the math I'll try it. Keil's implementation is surprisingly efficient.