Word-length optimization beyond straight line code

The silicon area benefits that result from word-length optimization have been widely reported by the FPGA community. However, to date, most approaches are restricted to straight line code, or code that can be converted into straight line code using techniques such as loop-unrolling. In this paper, we take the first steps towards creating analytical techniques to optimize the precision used throughout custom FPGA accelerators for algorithms that contain loops with data dependent exit conditions. To achieve this, we build on ideas emanating from the software verification community to prove program termination. Our idea is to apply word-length optimization techniques to find the minimum precision required to guarantee that a loop with data dependent exit conditions will terminate. Without techniques to analyze algorithms containing these types of loops, a hardware designer may elect to implement every arithmetic operator throughout a custom FPGA-based accelerator using IEEE-754 standard single or double precision arithmetic. With this approach, the FPGA accelerator would have comparable accuracy to a software implementation. However, we show that using our new technique to create custom fixed and floating point designs, we can obtain silicon area savings of up to 50% over IEEE standard single precision arithmetic, or 80% over IEEE standard double precision arithmetic, at the same time as providing guarantees that the created hardware designs will work in practice.