Construction of Parallel Addition Algorithms by the Extending Window Method - results

An algebraic number \(\beta \in \mathbb{C}\) with no conjugate of modulus 1 can serve as the base of a numeration system \((\beta, \mathcal{A})\) with parallel addition, i.e., the sum of two operands represented in base \(\beta\) with digits from \(\mathcal{A}\) is calculated in constant time, irrespective of the length of the operands.

In the paper Construction of Algorithms for Parallel Addition, a so-called Extending Window Method is introduced. This method is an algorithm to construct Parallel Addition algorithms. See the paper for the details, or the project website.

We present here the results of this method for selected numeration systems, see the implementation.