Fast Parallel Computation of the Polynomial Shift

Given an n-degree polynomial fx over an arbitrary ring, the shift of fx by c is the operation which computes coefficients of the polynomial fx + c. In this paper we consider the case when the shift by given constant c has to be performed several times (repeatedly). We propose a parallel algorithm suited for SIMD architecture to perform the shift in O1 time if we have On2  Processor Elements available. Proposed algorithm is easy to generalize to multivariate polynomials shift. The possibility of applying this algorithm to polynomials with coefficients from non-commutative rings is discussed as well as the bit-wise complexity of the algorithm.

• Type: Conference
• Year: 1997
• Where: IPPS
• Authors: Eugene V. Zima
• Keywords: Algorithm, Distributed And Parallel Computing, IPPS 1997, N-degree Polynomial Fx, Polynomials