A Hardware-Oriented Method for Evaluating Complex Polynomials

A hardware-oriented method for evaluating complex polynomials by solving iteratively a system of linear equations is proposed. Its implementation uses a digit-serial iterations on simple and highly regular hardware. The operations involved are defined over the reals. We describe a complex-to-real transform, a complex polynomial evaluation algorithm, the convergence conditions, and a corresponding design and implementation. The latency and the area are estimated for the radix-2 case. The main features of the method are: the latency of about m cycles for an m-bit precision; the cycle time independent of the precision; a design consisting of identical modules; and a digit-serial connections between the modules. The number of modules, each roughly corresponding to serial-parallel multiplier without a carry-propagate adder, is 2(n + I) for evaluating an n-th degree complex polynomial. The method can also be used to compute all successive integer powers of the complex argument with the same latency and a similar implementation cost.