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-digit-first 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 children of any addition node in the graph. The proposed method lends itself to implementation using simple, highly regular hardware with serial interconnections between modules.