does there exist a multiple-precision C or C++ math library that could be used with Arduino?
Floating point? I don't think so. Most of the generic C/C++ "advanced math" packages will assume that you're starting with a real 64bit double, I think. Which avr-gcc doesn't have.
(depending on your definition of "could be used with", I guess. I found a couple of references to people trying to compile mpfr and/or gmp on AVR. Although they tend to be dwarfed by the hits about needing those to compile gcc itself.)
Do you actually need multiple-precision, or would 64bits be enough?
For fixed point, Nick Gammon ported a bignum (gnu "bc") project: http://www.gammon.com.au/forum/?id=11519