Modular Arithmetics

MODULAR ARITHMETIC:

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

expressions.

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

efficient maner.

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

MODULAR ARITHMETIC:

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

expressions.

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

efficient maner.

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