Complex Multiply-Add and Other Related Operators

Abstract : In this work, we present algorithms and schemes for computing common arithmetic expressions defined in the complex domain as hardware-implemented operators.The operators include Complex Multiply-Add (CMA: ab+c), Complex Sum of Producrs (CSP: ab+ce+f), Complex Sum of Squares (CSS: a^2+b^2) and complex Integer Powers. 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 significant digit first, 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.
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Milos Ercegovac, Jean-Michel Muller. Complex Multiply-Add and Other Related Operators. Franklin T. Luk. SPIE Conf. Advanced Signal Processing Algorithms, Architectures and Implementation XVII, 6697, Aug 2007, San Diego, United States. SPIE, 2007. 〈ensl-00167372〉

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