Towards Reversed Approximate Hardware Design

Approximate computing is an emerging design paradigm for trading off computational accuracy for computational effort. Due to their inherited error resilience many applications significantly benefit from approximate computing. To realize approximation, dedicated approximate circuits have been developed and provide a solid foundation for energy and time efficient computing. However, when it comes to the design and integration of the approximate HW, complex error analysis is required to determine the effect of the error with respect to application specific error norms. This frequently leads to sub-optimal results. In this work, we propose to reverse the typical design flow for approximate HW and demonstrate the new flow for a first application: LU-Factorization, which is one of the most basic and most popular numerical algorithm known. The general idea of the reversed flow for approximate HW design is to start with the application and determine the required computational accuracy such that the computational error of the result is below the application specific error bound. This allows us to push the approximate HW to its limits, while guaranteeing that the result is correct by construction wrt. the requirements. The effectiveness of our approach for LU-Factorization is shown on a well-known and large set of benchmarks.