mpfr exceptions<'memory overflow'> is possible any time
mpfr runs out of memory.
<'bad mpfr specification'> will be returned
if an input argument recognizably violates the required specification.
<'mpfr error'> message is returned in the event of any
unexpected behavior or irregular status from the API.
<'mpfr overflow'> can be cause by the
nat2mp function if a natural number has too many bits to be
represented exactly as an mpfr number.