21 September 2007 Complex multiply-add and other related operators
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Abstract
In this work we present algorithms and schemes for computing several common arithmetic expressions defined 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 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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Miloš D. Ercegovac, Jean-Michel Muller, "Complex multiply-add and other related operators", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 66970S (21 September 2007); doi: 10.1117/12.734841; https://doi.org/10.1117/12.734841
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