**6. Summary**

The assumptions and optimization targets for NTC circuit design are different from the conventional super-threshold design, due to large impact of variabilities as well as comparable contributions of leakage power and dynamic power. This paper presented two cross-layer design optimization approaches for NTC circuits to co-optimize energy-efficiency, reliability, and performance.

In the *instruction multi-cycling* approach, the idle time of the functional units is reduced by executing slow instructions in multiple clock cycles and fast instructions in one clock cycle. This approach consists of

circuit redesign for smoother slack distribution across instructions (circuit level), multi-cycle execution of slow instructions (architecture level) and code replacement (compiler level). Our experimental results show that this approach achieves significant energy (34%) and performance (19%) improvement while providing orders of magnitude reduction of timing failure rate.

The proposed functional unit partitioning approach improves the energy efficiency and reliability of functional units by exploiting fine-grained power-gating. For this purpose, a large functional unit like an ALU is partitioned into several smaller (and faster) units based on the instruction usage pattern of the running applications and inherent similarity of the instructions. As a result, the smaller functional units can be power-gated whenever they are not used for a long time. Our simulation results show that the energy efficiency of an ALU can be improved by up to 43.4% in the NTV region. Additionally, the performance can be improved by at least 7.0%, or the reliability can be improved by 11.5 times in the NTV region.

Therefore, by revisiting the design of functional units as important components of data paths and utilizing cross-layer approaches, it is possible to optimize the energy-efficiency, performance, and reliability of NTC designs.

**Author Contributions:** Conceptualization and methodology, M.S.G. and M.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
