Self-similar module for FP/LNS arithmetic in high-performance FPGA systems

The scientific community has gratefully embraced floating-point arithmetic to escape the close attention for accuracy and precision required in fixed-point computational styles. Though its deficiencies are well known, the role of the floating-point system as standard has kept other number representation systems from coming into practice. The paper discusses the relation between fixed and floating-point numbers from a pragmatic point of view that allows to mix both systems to optimize FPGA-based hardware accelerators. The method is developed for the Mitrion "processor on demand" technology, where a computationally intensive algorithm is transformed into a dedicated. The large gap in cycle time between fixed and floating-point operations and between direct and reverse operations makes the on-chip control for the fine-grain pipelines of parallel logic very complicated. Having alternative hardware realizations available can alleviate this. The paper uses a conjunctive notation, also known as DIGILOG, to introduce a flexible means in creating configurable arithmetic of arbitrary order using a single module type. This allows the Mitrion hardware compiler to match the hardware closer to the demands of the specific algorithm. Typical applications are in molecular simulation and real-time image analysis