High Dynamic Range (HDR)

Image modes

32 bits = 256 levels per color component (standard)
64 bits = 2^16 levels per color component (65536 levels)
128 bits = 2^32 levels for each color (that's a lot, aka. a shitload or 4+ billions)

128 bits operations gives you much greater accuracy and is much less destructive.
Just try this:

Take a picture, reduce it's luminosity to 10% of what it was (apply the filter).
Now try to take it back to its original luminosity.

You'll see that with 128 bits floating-point precision you can get back pretty much your original image without loss. With good old 32 bits trying to get back to the original luminosity would get you an awfully posterized image. Note that not all formats will allow you to save in such a color depth. OpenEXR (used by the movie industry and supported by OSX) allows it and so does ChocoFlop's native format (which uses TIFFs). Even if you wish to save a GIF (256 colors) in the end, it's always better to work in this mode and convert to 256 colors only when saving. Speed however can be impacted severely depending on the performance of your graphics card.

For more, read "Why is HDR so cool?".