How Fast Can We Compute Products?

In this paper we consider the problem of fast computation of n-ary products, for large n, over arbitrary precision integer or rational number domains. The combination of loop unrolling, chains of recurrences techniques and analogs of binary powering allows us to obtain order-of-magnitude speed improvements for such computations. Three di erent implementations of the technique (in Maple, C++ and Java) are described. Many examples together with timings are given.

• Type: Conference
• Year: 1999
• Where: ISSAC
• Authors: V. Kislenkov, V. Mitrofanov, Eugene V. Zima
• Keywords: Arbitrary Precision Integer, Di Erent Implementations, ISSAC 1999, Mathematics, Rational Number Domains