Modular arithmetic can be used to compute
exactly, at low cost, a set of simple computations.
These include most geometric predicates, that
need to be checked exactly, and especially, the
sign of determinants and more general polynomial
Modular arithmetic resides on the Chinese
Remainder Theorem, which states that, when
computing an integer expression, you only have to
compute it modulo several relatively prime integers
called the modulis. The true integer value can then
be deduced, but also only its sign, in a simple and
The main drawback with modular arithmetic is its
static nature, because we need to have a bound on
the result to be sure that we preserve ourselves
from overflows (that can't be detected easily
while computing). The smaller this known bound is,
the less computations we have to do.
We have developped a set of efficient tools to deal
with these problems, and we propose a...