mindcrime, thank you for your kind words. I kept my comment es short as possibly, as not to scare you off. Integer arithmetic is a huge and interesting topic, arguably worth a thread in the Microcontroller section.
One huge advantage of integers over floating point hasn't been mentioned yet:
The precision of integer arithmetics can be predicted more easily than that of floats. Automatic mantissa/exponent adjustment might be a good starting point for research.
This all leads to the classic fail, where a newbie compares two floats for identity to exit a loop...
T3sl4co1l, I like your extension to my remark.
I love the reference to 2.048V references even better, knowing that an ADR420A will come with 2.045..2.051V initial output voltage. In that context a REF2920 2.007..2.048..2.089V becomes outright hilarious, especially knowing that many designers won't read past the marketing text on page 1 of the datasheet.
Regarding accu size on integer machines - does anybody remember the DSP56K series? 24bit registers, leaving a lot of leeway for operations on 16bit audio. That was the bee's knees in 1990's embedded audio processing. I remember doing active noise cancelling with those. Taking DSP56K as a reference, doing DSP on a ARM Mx feels like a dream.