Error modelling of dual fixed-point arithmetic and its application in field programmable logic

Dual FiXed-point (DFX) is a new data representation which is an efficient compromise between fixed-point and floating-point representations. DFX has an implementation complexity similar to that of a fixed-point system with the improved dynamic range capability of a floating-point system. Automating the process of DFX scaling optimisation requires the knowledge of its truncation/rounding noise properties. This paper presents truncation and rounding error models for DFX arithmetic as traditional error models do not apply to DFX. The models were tested on a 159-tap FIR filter and the benefits of using DFX over floating-point are demonstrated with implementations on a Xilinx Virtex II Pro.