A Linear-System Operator Based Scheme for Evaluation of Multinomials

We present a radix-2 online computational scheme for evaluating multinomials in a fixed-point number representation system. Its main advantage is that it can adapt to any evaluation graph representing the multinomial. Evaluation graphs are efficient representations of multinomials in a factored form. The proposed scheme maps subgraphs of the evaluation graph using linear-system operators. These operators transform the expressions represented by the subgraphs into systems of linear equations. The linear equations are then solved in an online, most-significant-digitfirst fashion. The scheme produces, after an initial delay, one output digit per iteration for inputs within range. The iteration time is equal to the sum of the delays of a redundant adder, multiplexer, register and a selection unit and is independent of the size of the multinomial and the precision of the inputs/outputs. The initial delay is proportional to the diameter of the evaluation graph and the maximum number of ...

• Type: Conference
• Year: 2005
• Where: ARITH
• Authors: Pavan Adharapurapu, Milos D. Ercegovac
• Keywords: Applied Computing, ARITH 2005, Evaluation Graph, Initial Delay, Linear Equations