Significance-Driven Data Truncation for Preventing Timing Failures

Abstract

The continuous scaling of transistor sizes and the increased parametric variations render nanometer circuits more prone to timing failures. To protect circuits from such failures, typically designers adopt pessimistic timing margins, which are estimated under rare worst-case conditions. In this paper, we present a technique that mitigates such pessimistic margins by minimizing the number of timing failures. In particular, we propose a method that minimizes the number of long latency paths within each processor pipeline stage and constrains them in as few stages as possible. Such a method allows us not only to reduce the timing failures but also to limit the potential error-prone locations to only a few pipeline stages. To further reduce these failures, we exploit the path excitation dependence on data patterns and truncate the bitwidth of the operands in the few remaining long latency paths by setting a number of less significant bits (LSBs) to a constant value of zero. Such a truncation may incur quality loss, but this is limited since it is applied only to the LSBs of the few operands that may activate the confined error-prone long latency paths. To evaluate the efficiency of our method, we perform post-place and route dynamic timing analysis based on real operands extracted from a variety of applications. This helps to estimate the bit-error rate, while considering the data-dependent path excitation. When applied to an IEEE-754 compatible double precision floating point unit (FPU), the proposed approach reduces the timing failures by $216.25 {\times }$ on average compared to the reference FPU design under an assumed 8.1% variation-induced worst-case path delay increase in a 45-nm process. Our results show that the path shaping alone introduces a negligible 0.25% area and 5.7% power overheads with no performance cost. Finally, we demonstrate that by combining the path shaping with aggressive operand bitwidth truncation, we enable power savings up to 44.7% due to the substantially reduced switching activity at minimal quality loss.