what are floating point accelerators and how do they work?

Answer 1

Floating point, or even integer accelerators use additional hardware and algorithms to speed up calculations. Consider standard long multiplication. When you were taught in school, you started with the one's digit, followed by the 10's digit, etc.
http://en.wikipedia.org/wiki/Multiplication_ALU

You could design a computer that would dedicate hardware so that you had multiple multipliers, each one responsible for multiplying a specific digit. This would ,for long numbers, speed up the calculation.

Likewise, there are algorithms inplemented in hardware to speed up multiplications:
http://en.wikipedia.org/wiki/Wallace_tree