Complex multiply-add and other related operators

In this work we present algorithms and schemes for computing several common arithmetic expressions dened in the complex domain as hardware-implemented operators. The operators include Complex Multiply-Add (CMA : ab +c), Complex Sum of Products (CSP : ab +ce +f), Complex Sum of Squares (CSS : a2 +b2), and Complex Integer Powers (CIPk : x2;x3;:::;xk). The proposed approach is to map the expression to a system of linear equations, apply a complex-to-real transform, and compute the solutions to the linear system using a digit-by-digit, the most signicant digit rst, recurrence method. The components of the solution vector corresponds to the expressions being evaluated. The number of digit cycles is about m for m-digit precision. The basic modules are similar to left-to-right multipliers. The interconnections between the modules are digit-wide.