By floating I assume you mean piers or caissons with void form. Typically it's done with piers placed at a depth to bear on bedrock on which are placed grade beams. Then foundation walls are placed on that and slab inside the walls bearing on the grade beams. Void form depth will depend on what the soils report tells you about how expansive the soils are. I've seen 6" void up to 16" void - so it just depends.
You'll want an engineer to review anything you do. Wouldn't be real good if you didn't get the caissons deep enough and have it heave in the middle of your slab.
This is also called a "Mat" foundation and used a lot where water tables are high and "pumping"action common. it's also sometimes cheaper than a sprread footing foundation. needs to be designed by an engineer. not quite as simple as doing calcs for a common standard spread footing.