Approximate computing: Difference between revisions

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: Approximate arithmetic circuits:<ref>Jiang et al., "[http://www.ece.ualberta.ca/~jhan8/publications/survey.pdf Approximate Arithmetic Circuits: A Survey, Characterization, and Recent Applications]", the Proceedings of the IEEE, Vol. 108, No. 12, pp. 2108 - 2135, 2020.</ref> [[Adder (electronics)|adders]],<ref>J. Echavarria, et al. "FAU: Fast and Error-Optimized Approximate Adder Units on LUT-Based FPGAs", FPT, 2016.</ref><ref>J. Miao, et al. "[https://repositories.lib.utexas.edu/bitstream/handle/2152/19706/miao_thesis_201291.pdf?sequence=1 Modeling and synthesis of quality-energy optimal approximate adders]", ICCAD, 2012</ref> [[Binary multiplier|multipliers]]<ref>{{Cite book|last1=Rehman|first1=Semeen|last2=El-Harouni|first2=Walaa|last3=Shafique|first3=Muhammad|last4=Kumar|first4=Akash|last5=Henkel|first5=Jörg|date=2016-11-07|title=Architectural-space exploration of approximate multipliers|publisher=ACM|pages=80|doi=10.1145/2966986.2967005|isbn=9781450344661|s2cid=5326133}}</ref> and other [[logical circuit]]s can reduce hardware overhead.<ref>S. Venkataramani, et al. "[http://algos.inesc-id.pt/projectos/approx/FCT/Ref-15.pdf SALSA: systematic logic synthesis of approximate circuits]", DAC, 2012.</ref><ref>J. Miao, et al. "[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.453.7870&rep=rep1&type=pdf Approximate logic synthesis under general error magnitude and frequency constraints]", ICCAD, 2013</ref><ref>R. Hegde et al. "[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.8929&rep=rep1&type=pdf Energy-efficient signal processing via algorithmic noise-tolerance]", ISLPED, 1999.</ref> For example, an approximate multi-bit adder can ignore the [[carry chain]] and thus, allow all its sub-adders to perform addition operation in parallel.

; Approximate storage and memory

: Instead of [[Computer data storage|storing data]] values exactly, they can be stored approximately, e.g., by [[Data truncation|truncating]] the lower-bits in [[floating point]] data. Another method is to accept less reliable memory. For this, in [[DRAM]]<ref>{{Cite journal|last1=Raha|first1=A.|last2=Sutar|first2=S.|last3=Jayakumar|first3=H.|last4=Raghunathan|first4=V.|date=July 2017|title=Quality Configurable Approximate DRAM|journal=IEEE Transactions on Computers|volume=66|issue=7|pages=1172–1187|doi=10.1109/TC.2016.2640296|issn=0018-9340|doi-access=free}}</ref> and [[eDRAM]], [[refresh rate]] assignments can be lowered or controlled.<ref>{{Cite journal|last1=Kim|first1=Yongjune|last2=Choi|first2=Won Ho|last3=Guyot|first3=Cyril|last4=Cassuto|first4=Yuval|date=December 2019|title=On the Optimal Refresh Power Allocation for Energy-Efficient Memories|url=https://ieeexplore.ieee.org/document/9013465|journal=2019 IEEE Global Communications Conference (GLOBECOM)|___location=Waikoloa, HI, USA|publisher=IEEE|pages=1–6|doi=10.1109/GLOBECOM38437.2019.9013465|isbn=978-1-7281-0962-6|arxiv=1907.01112|s2cid=195776538}}</ref> In [[Static random-access memory|SRAM]], supply voltage can be lowered<ref>{{Cite journal|last1=Frustaci|first1=Fabio|last2=Blaauw|first2=David|last3=Sylvester|first3=Dennis|last4=Alioto|first4=Massimo|date=June 2016|title=Approximate SRAMs With Dynamic Energy-Quality Management|url=https://ieeexplore.ieee.org/document/7372479|journal=IEEE Transactions on Very Large Scale Integration (VLSI) Systems|volume=24|issue=6|pages=2128–2141|doi=10.1109/TVLSI.2015.2503733|s2cid=8051173|issn=1063-8210}}</ref> or controlled.<ref>{{Cite journal|last1=Kim|first1=Yongjune|last2=Kang|first2=Mingu|last3=Varshney|first3=Lav R.|last4=Shanbhag|first4=Naresh R.|date=2018|title=Generalized Water-filling for Source-aware Energy-efficient SRAMs|url=https://ieeexplore.ieee.org/document/8368137|journal=IEEE Transactions on Communications|volume=66|issue=10|pages=4826–4841|doi=10.1109/TCOMM.2018.2841406|issn=0090-6778|arxiv=1710.07153|s2cid=24512949}}</ref> Approximate storage can be applied to reduce [[Magnetoresistive random-access memory|MRAM]]'s high write energy consumption.<ref>{{Cite journal |lastlast1=Kim |firstfirst1=Yongjune |last2=Jeon |first2=Yoocharn |last3=Choi |first3=Hyeokjin |last4=Guyot |first4=Cyril |last5=Cassuto |first5=Yuval |date=2022 |title=Optimizing Write Fidelity of MRAMs by Alternating Water-filling Algorithm |url=https://ieeexplore.ieee.org/document/9829735/ |journal=IEEE Transactions on Communications |volume=70 |issue=9 |pages=1–15825–5836 |doi=10.1109/TCOMM.2022.3190868 |s2cid=250565077 |issn=0090-6778}}</ref> In general, any [[error detection and correction]] mechanisms should be disabled.

; Software-level approximation

: There are several ways to approximate at software level. [[Memoization]] can be applied. Some [[iteration]]s of [[Loop (computing)|loops]] can be skipped (termed as [[loop perforation]]) to achieve a result faster. Some tasks can also be skipped, for example when a run-time condition suggests that those tasks are not going to be useful ([[task skipping]]). [[Monte Carlo algorithm]]s and [[Randomized algorithm]]s trade correctness for execution time guarantees.<ref>C.Alippi, Intelligence for Embedded Systems: a Methodological approach, Springer, 2014, pp. 283</ref> The computation can be reformulated according to paradigms that allow easily the acceleration on specialized hardware, e.g. a neural processing unit.<ref>{{Cite conference|last1=Esmaeilzadeh|first1=Hadi|last2=Sampson|first2=Adrian|last3=Ceze|first3=Luis|last4=Burger|first4=Doug|title=Neural acceleration for general-purpose approximate programs|conference=45th Annual IEEE/ACM International Symposium on Microarchitecture|year=2012|doi=10.1109/MICRO.2012.48|publisher=IEEE|pages=449–460|___location=Vancouver, BC}}</ref>