Datapath synthesis for overclocking: Online arithmetic for latency-accuracy trade-offs

Digital circuits are currently designed to ensure timing closure. Releasing this constraint by allowing timing violations could lead to significant performance improvements, but conventional forms of computer arithmetic do not fail gracefully when pushed beyond deterministic operation. In this paper we take a fresh look at Online Arithmetic, originally proposed for digit serial operation, and synthesize unrolled digit parallel online operators to allow for graceful degradation. We quantify the impact of timing violation on key arithmetic primitives, and show that substantial performance benefits can be obtained in comparison to binary arithmetic. Since timing errors are caused by long carry chains, these result in errors in least significant digits with online arithmetic, causing less impact than conventional implementations. Using analytical models and empirical FPGA results from an image processing application, we demonstrate an error reduction over 89% and an improvement in SNR of over 20dB for the same clock rate.