Many of you may be aware, but just in case:
uBASIC is a most interesting / capable 'dialect' of BASIC which supports precision up to 2600 digits, rational and complex datatypes, list handling capabilities...
It is an older DOS era program, runs quite quickly and consequently very small.
http://archives.math.utk.edu/software/msdos/number.theory/ubasic/.html
TomC