Efficient Evaluation of Large Polynomials
Minimizing the evaluation cost of a polynomial expression is a fundamental problem in computer science. We propose tools that, for a polynomial P given as the sum of its terms, compute a representation that permits a more efficient evaluation. Our algorithm runs in d(nt) O(1) bit operations plus dt O(1) operations in the base field where d, n and t are the total degree, number of variables and number of terms of P. Our experimental results show that our approach can handle much larger polynomials than other available software solutions. Moreover, our computed representation reduce the evaluation cost of P substantially.
KeywordsMultivariate polynomial evaluation code optimization Cilk++
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- 2.Leiserson, C.E., Li, L., Moreno Maza, M., Xie, Y.: Parallel computation of the minimal elements of a poset. In: Proc. PASCO 2010. ACM Press, New York (2010)Google Scholar
- 5.Intel Corporation. Cilk++., http://www.cilk.com/
- 7.Hosangadi, A., Fallah, F., Kastner, R.: Factoring and eliminating common subexpressions in polynomial expressions. In: ICCAD 2004, pp. 169–174. IEEE Computer Society, Los Alamitos (2004)Google Scholar