{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T16:20:27Z","timestamp":1781886027315,"version":"3.54.5"},"reference-count":40,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"National Key Research and Development Project","award":["2018YFE0126300"],"award-info":[{"award-number":["2018YFE0126300"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61974133"],"award-info":[{"award-number":["61974133"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"crossref","award":["LD21F040003"],"award-info":[{"award-number":["LD21F040003"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. Emerg. Technol. Comput. Syst."],"published-print":{"date-parts":[[2021,10,31]]},"abstract":"<jats:p>\n            Multiplications have been commonly conducted in quantized CNNs, filters, and reconfigurable cores, and so on, which are widely deployed in mobile and embedded applications. Most multipliers are designed to perform multiplications with symmetric bit-widths, i.e.,\n            <jats:italic>n<\/jats:italic>\n            - by\n            <jats:italic>n<\/jats:italic>\n            -bit multiplication. Such features would cause extra area overhead and performance loss when\n            <jats:italic>m<\/jats:italic>\n            - by\n            <jats:italic>n<\/jats:italic>\n            -bit multiplications (\n            <jats:italic>m<\/jats:italic>\n            &gt;\n            <jats:italic>n<\/jats:italic>\n            ) are deployed in the same hardware design, resulting in inefficient multiplication operations. It is highly desired and challenging to propose a reconfigurable multiplier design to accommodate operands with both symmetric and asymmetric bit-widths. In this work, we propose a reconfigurable approximate multiplier to support multiplications at various precisions, i.e., bit-widths. Unlike prior works of approximate adders assuming a uniform weight distribution with bit-wise independence, scenarios like a quantized CNN may have a centralized weight distribution and hence follow a Gaussian-like distribution with correlated adjacent bits. Thus, a new block-based approximate adder is also proposed as part of the multiplier to ensure energy-efficient operation with an awareness of the bit-wise correlation. Our experimental results show that the proposed approximate adder significantly reduces the error rate by 76% to 98% over a state-of-the-art approximate adder for Gaussian-like distribution scenarios. Evaluation results show that the proposed multiplier is 19% faster and 22% more power saving than a Xilinx multiplier IP at the same bit precision and achieves a 23.94-dB peak signal-to-noise ratio, which is comparable to the accurate one of 24.10 dB when deployed in a Gaussian filter for image processing tasks.\n          <\/jats:p>","DOI":"10.1145\/3446213","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T19:37:47Z","timestamp":1625081867000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["A Reconfigurable Multiplier for Signed Multiplications with Asymmetric Bit-Widths"],"prefix":"10.1145","volume":"17","author":[{"given":"Chuliang","family":"Guo","sequence":"first","affiliation":[{"name":"Zhejing University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Zhang","sequence":"additional","affiliation":[{"name":"Zhejing University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xian","family":"Zhou","sequence":"additional","affiliation":[{"name":"Zhejing University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Grace Li","family":"Zhang","sequence":"additional","affiliation":[{"name":"Technical University of Munich"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bing","family":"Li","sequence":"additional","affiliation":[{"name":"Technical University of Munich"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weikang","family":"Qian","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xunzhao","family":"Yin","sequence":"additional","affiliation":[{"name":"Zhejing University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng","family":"Zhuo","sequence":"additional","affiliation":[{"name":"Zhejing University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2016.2561518"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/CICN.2011.86"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISQED.2014.6783335"},{"key":"e_1_2_1_4_1","unstructured":"Indranil Chakraborty Deboleena Roy Aayush Ankit and Kaushik Roy. 2019. Efficient hybrid network architectures for extremely quantized neural networks enabling intelligence at the edge. arxiv:1902.00460.  Indranil Chakraborty Deboleena Roy Aayush Ankit and Kaushik Roy. 2019. Efficient hybrid network architectures for extremely quantized neural networks enabling intelligence at the edge. arxiv:1902.00460."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3400302.3415702"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2017.2774288"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2463209.2488873"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2019.2957724"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.5555\/2016802.2016898"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/ETS.2013.6569370"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/3061639.3062306"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/3130379.3130725"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/3316781.3322475"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2228360.2228509"},{"key":"e_1_2_1_15_1","first-page":"683","article-title":"Implementation of modified Booth algorithm (Radix 4) and its comparison with Booth algorithm (Radix-2)","volume":"3","author":"Kaur Sukhmeet","year":"2013","journal-title":"Advances in Electronic and Electric Engineering"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/EDSSC.2010.5713751"},{"key":"e_1_2_1_17_1","volume-title":"Sanghyuck Ha, Changgwun Lee, and Inyup Kang.","author":"Kim Doyun","year":"2018"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.5555\/3130379.3130424"},{"key":"e_1_2_1_19_1","unstructured":"Raghuraman Krishnamoorthi. 2018. Quantizing deep convolutional networks for efficient inference: A whitepaper. arxiv:1806.08342.  Raghuraman Krishnamoorthi. 2018. Quantizing deep convolutional networks for efficient inference: A whitepaper. arxiv:1806.08342."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/VLSID.2011.51"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/JSSC.2018.2865489"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.5555\/2691365.2691468"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2017.2672976"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3273957"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/3240765.3240855"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2009.2027626"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2016.2605382"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISLPED.2015.7273520"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2744769.2744778"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/SOCDC.2008.4815685"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1403375.1403679"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1964.263830"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.5555\/2561828.2561838"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2018.2872012"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2017.2704610"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/2902961.2903012"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS45731.2020.9180844"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1109\/SOCDC.2010.5682905"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2019.2917844"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2018.2834438"}],"container-title":["ACM Journal on Emerging Technologies in Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3446213","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3446213","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:47:05Z","timestamp":1750193225000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3446213"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,30]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,10,31]]}},"alternative-id":["10.1145\/3446213"],"URL":"https:\/\/doi.org\/10.1145\/3446213","relation":{},"ISSN":["1550-4832","1550-4840"],"issn-type":[{"value":"1550-4832","type":"print"},{"value":"1550-4840","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,30]]},"assertion":[{"value":"2020-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-06-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}