fast computation for extended precision floating point for number theory application

fast computation for extended precision floating point for number theory
application

I am a graduate student in mathematics working on a research project that
involves calculating the norms of algebraic integers in very high degree
number fields. Essentially, that would involve multiplying 100 more more
floating point numbers together to get an integer. I am programming in C.
The problem I am encountering is that I'm beginning to need to calculate
norms which exceed 1e20 = 10^20, which exceeds both the integer and the
floating point precision of my hardware (Macbook).
I could attempt to use some kind of software emulation to do extended
precision, but my understanding is this is about 300x slower than hardware
floating point calculation. This would mean that the calculations I do
that currently take several days would instead take several years, which
isn't acceptable.
I have two questions: Q1: Is my estimation of 300x slower for software
emulation of extended precision (say to 10^36 precision, about twice the
precision of hardware) unduly pessimistic?
Q2: Is I had many thousands of dollars to throw at the problem, what kind
of hardware solutions might be available?