A Universal Methodology of Complex Number Computation for Low-Complexity and High-Speed Implementation

In complex-valued neural network (CVNN) applications, complex number calculations require high performance rather than high precision. However, most previous studies focused on high-precision approaches, which have low speed and high hardware costs. This paper proposes a universal methodology of complex number computation for low-complexity and high-speed implementation. The proposed methodology is based on the piecewise linear (PWL) method and can be used for different types of complex number computations. Considering that multiplication operations consume considerable resources, multiplication, fused square-add (FSA) and fused multiply-add (FMA) operations are the focus of optimization. The partial products of the square operation are reduced by folding and merging techniques because of their symmetry in the FSA operation. The partial products of the multiplication and FMA operations are reduced via Booth encoding. In addition, the partial products are further reduced by the proposed step-by-step truncation method. The proposed segmenter, which simulates the hardware implementation, automatically divides the nonlinear functions in the complex number computations into the smallest number of segments according to the required precision. The results show that the proposed approach improves performance and reduces hardware costs compared with the state-of-the-art methods for complex number calculations involving square roots, reciprocals and logarithms.