Data-Flow Transformations to Maximize the Use of Carry-Save Representation in Arithmetic Circuits

The increasing importance of datapath circuits in complex systems-on-chip calls for special arithmetic optimizations. The goal is to automatically achieve the handcrafted results which escape classic logic optimizations. Some work has been done in the recent years to infer the use of the carry-save representation in the synthesis of arithmetic circuits. Yet, many cases of practical interest cannot be handled due to the scattering of logic operations among the arithmetic ones - particularly in arithmetic computations which are originally described at the bit level in high-level languages such as C. We therefore introduce an algorithm to restructure dataflow graphs so that they can be synthesized as high-quality arithmetic circuits, close to those that an expert designer would conceive. On typical embedded software benchmarks which could be advantageously implemented with hardware accelerators, our technique always reduces tangibly the critical path by up to 46% and generally achieves the quality of manual implementations. In many cases, our algorithm also manages to reduce the cell area by up to 10%-20%.