Cost-Effective Error Detection Through Mersenne Modulo Shadow Datapaths

Keith Campbell, Chen Hsuan Lin, Deming Chen

Research output: Contribution to journalArticlepeer-review


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 $\times$.

Original languageEnglish (US)
Article number8356040
Pages (from-to)1056-1069
Number of pages14
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number6
StatePublished - Jun 2019


  • Cost-effective
  • Mersenne number
  • error detection
  • functional unit
  • gate-level
  • modulo arithmetic
  • reliability
  • shadow datapath

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


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