Ok, I read through a bunch of their tech docs. First, there is no "tell me when the sun will rise" function that I can find. (Nor any reference to anything of the sort) I've seen examples for calculating time, position of the planets, etc. Definitely not using a table as everything is using a calculations to determine time/position. Which frankly, is sort of to be expected. You aren't going to have a database of positions/times going out an arbitrary amount of time because you'd have to calculate those at some point anyways. The math is definitely going to be quicker than doing a data read from a table and you save storage space.

In terms of accuracy, their software is accurate down to the microarcsecond. To give you an example of that, take the circle of the sky, divide it up into 3600 degrees. That is an arcsecond. Now, take one of those 3600 slices and divide that into a million tiny slices. (pie shaped to be exact) That is the accuracy they are dealing with. Extremely accurate.