Very Fast Parallel Polynomial Arithmetic
Wayne Eberly · SIAM Journal on Computing · 1989
Parallel algorithms for polynomial arithmetic—multiplication of n polynomials of degree m, polynomial division with remainder, and polynomial interpolation—are presented. These algorithms can be implemented using polynomial time constructible families of Boolean circuits of polynomial size and optimal order depth, or log space constructible families of polynomial size and near optimal depth, for computations over $\mathbb{Z},\mathbb{Q}$, finite fields, and several other domains. Arithmetic circuits of polynomial size and optimal order depth are obtained for polynomial arithmetic over arbitrary fields.