Physics (and more generally numerical simulations) is the killer app for Julia Language. No other language makes it as easy to work with arbitrary precision math. Whatever precision you need/want, just call setprecision(), Initialize variables/constants as BigInt/BitFloat, then do all your math just like you would in C.
Just remember to put the value in quotes when initializing:
BigFloat("1.0") NOT BigFloat(1.0). Without quotes it's silently initialized as double precision (!)