When setup/hold times of bistable elements are violated, they may become metastable, i.e., enter a transient state that is neither digital 0 nor 1 . In general, metastability cannot be avoided, a problem that manifests whenever taking discrete measurements of analog values. Metastability of the output then reflects uncertainty as to whether a measurement should be rounded up or down to the next possible measurement outcome. Surprisingly, Lenzen & Medina (ASYNC 2016) showed that metastability can be contained, i.e., measurement values can be correctly sorted without resolving metastability first. However, both their work and the state of the art by Bund et al. (DATE 2017) leave open whether such a solution can be as small and fast as standard sorting networks. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Concretely, for 10-channel sorting networks and 16-bit wide inputs, we improve by 48.46% in delay and by 71.58% in area over Bund et al. Our simulations indicate that straightforward transistor-level optimization is likely to result in performance on par with standard (non-containing) solutions.
|Title of host publication||Proceedings of the 2018 Design, Automation and Test in Europe Conference and Exhibition, DATE 2018|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - 19 Apr 2018|
|Event||2018 Design, Automation and Test in Europe Conference and Exhibition, DATE 2018 - Dresden, Germany|
Duration: 19 Mar 2018 → 23 Mar 2018
|Name||Proceedings of the 2018 Design, Automation and Test in Europe Conference and Exhibition, DATE 2018|
|Conference||2018 Design, Automation and Test in Europe Conference and Exhibition, DATE 2018|
|Period||19/03/18 → 23/03/18|
Bibliographical noteFunding Information:
Acknowledgements: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 716562).
© 2018 EDAA.