f(x)modg(x)

[smslca]

I like to know

what is best known efficient algorithm to calculate f(x)modg(x) , in which the degrees of f(x) and g(x) are very very very large , and degree of f(x) >> degree of g(x).

[Stephen Tashi]

f and g are polynomials with integer coefficients? You know how to divide one polynomial into another, right?