Cost-Effective Error Detection Through Mersenne Modulo Shadow Datapaths

With technology scaling leading to reliability problems and a proliferation of hardware accelerators, there is a need for cost-effective techniques to detect errors in complex datapaths. Modulo (residue) arithmetic is useful for creating a shadow datapath to check the computation of an arithmetic datapath and involves three key steps: 1) reduction of the inputs to modulo shadow values; 2) computation with those shadow values; and 3) checking the outputs for consistency with the shadow outputs. The focus of this paper is new gate-level architectures and algorithms to reduce the cost of modulo shadow datapaths. We introduce new low-cost architectures for the functional units performing the aforementioned reduction, shadow computation, and checking operations. We compare our functional units to the previous state-of-the-art approach, observing a 12.5% reduction in area and a 47.1% reduction in delay for a 32-bit mod-3 reducer; that our reducer costs, which tend to dominate shadow datapath costs, do not increase with larger modulo bases; and that for modulo-15 and above, all of our functional units have better area and delay than their previous counterparts. To demonstrate the cost-effectiveness of our approach in computation-intensive accelerator applications, we design custom pipelined shadow datapaths for five compound functional units implementing a variety of vector and matrix operations. For a 32-bit main datapath and 2-bit shadow datapath, we observe area costs of 6%-10% and reliability improvements against single event transient errors of 3-61 $\times$. For an 8-bit shadow datapath, we observe area costs of 15%-20% and reliability gains of 121-2477 $\times$.