{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:38:17Z","timestamp":1750307897931,"version":"3.41.0"},"reference-count":38,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T00:00:00Z","timestamp":1188604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Des. Autom. Electron. Syst."],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:p>\n            This article presents an approach to area optimization of arithmetic datapaths at register-transfer level (RTL). The focus is on those designs that perform polynomial computations (add, mult) over finite word-length operands (bit-vectors). We model such polynomial computations over\n            <jats:italic>m<\/jats:italic>\n            -bit vectors as algebra over finite integer rings of residue classes\n            <jats:italic>Z<\/jats:italic>\n            <jats:sub>2<\/jats:sub>\n            <jats:sup>\n              <jats:italic>m<\/jats:italic>\n            <\/jats:sup>\n            . Subsequently, we use the number-theoretic and algebraic properties of such rings to transform a given datapath computation into another, bit-true equivalent computation. We also derive a cost model to estimate, at RTL, the area cost of the computation. Using the transformation procedure along with the cost model, we devise algorithmic procedures to search for a lower-cost implementation. We show how these theoretical concepts can be applied to RTL optimization of arithmetic datapaths within practical CAD settings. Experiments conducted over a variety of benchmarks demonstrate substantial optimizations using our approach.\n          <\/jats:p>","DOI":"10.1145\/1278349.1278362","type":"journal-article","created":{"date-parts":[[2007,10,14]],"date-time":"2007-10-14T12:41:11Z","timestamp":1192365671000},"page":"49","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimization of polynomial datapaths using finite ring algebra"],"prefix":"10.1145","volume":"12","author":[{"given":"Sivaram","family":"Gopalakrishnan","sequence":"first","affiliation":[{"name":"University of Utah, Salt Lake City, UT"}]},{"given":"Priyank","family":"Kalla","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, UT"}]}],"member":"320","published-online":{"date-parts":[[2007,9]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Allenby R. J. B. T. 1983. Rings Fields and Groups: An Introduction to Abstract Algebra. E. J. Arnold.  Allenby R. J. B. T. 1983. Rings Fields and Groups: An Introduction to Abstract Algebra. E. J. Arnold."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/40.768501"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/49.926359"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(95)00305-G"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)E0162-W"},{"volume-title":"Proceedings of the Design Automation and Test in Europe (DATE)","author":"Constantinides G.","key":"e_1_2_1_6_1"},{"volume-title":"Synthesis and Optimization of Digital Circuits","author":"DeMicheli G.","key":"e_1_2_1_7_1"},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","unstructured":"Groute I. A. and Keane K. 2000. M(VH)DL: A Matlab to VHDL conversion toolbox for digital control. In IFAC Symposiun on Computer-Aided Control System Design (Salford UK).  Groute I. A. and Keane K. 2000. M(VH)DL: A Matlab to VHDL conversion toolbox for digital control. In IFAC Symposiun on Computer-Aided Control System Design (Salford UK).","DOI":"10.1016\/S1474-6670(17)36861-1"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.5555\/1128020.1128563"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICVD.2005.90"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD.2004.1382566"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/43.913756"},{"key":"e_1_2_1_13_1","article-title":"A generalization of the smarandache function to several variables. Integers","volume":"6","author":"Hungerbuhler N.","year":"2006","journal-title":"Electron. J. Combin. Num. Theory"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-68-03589-8"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1921-1501173-4"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1918.11998418"},{"key":"e_1_2_1_18_1","unstructured":"Koren I. 2002. Computer Arithmetic Algorithms. A. K. Peters.   Koren I. 2002. Computer Arithmetic Algorithms. A. K. Peters."},{"volume-title":"International Workshop Signal Processing Systems (SIPS)","author":"Kum K.","key":"e_1_2_1_19_1"},{"key":"e_1_2_1_20_1","first-page":"232","article-title":"Question nr. 288","volume":"3","author":"Lucas E.","year":"1883","journal-title":"Mathesis"},{"key":"e_1_2_1_21_1","unstructured":"Maple. 2007. Maple. http:\/\/www.maplesoft.com.  Maple. 2007. Maple. http:\/\/www.maplesoft.com."},{"key":"e_1_2_1_22_1","unstructured":"Mathews V. J. and Sicuranza G. L. 2000. Polynomial Signal Processing. Wiley-Interscience New York.  Mathews V. J. and Sicuranza G. L. 2000. Polynomial Signal Processing. Wiley-Interscience New York."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/581630.581674"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2003.816213"},{"key":"e_1_2_1_25_1","first-page":"1","article-title":"Java concurrent program for the smarandache function","volume":"13","author":"Power D.","year":"2002","journal-title":"Smarandache Notions J."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1978.1675077"},{"volume-title":"Proceedings of the IEEE International High Level Design Validation and Test Workshop (HLDVT)","author":"Pradhan D.","key":"e_1_2_1_27_1"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/HLDVT.2004.1431237"},{"volume-title":"Proceedings of the Design Automation and Test in Europe (DATE)","author":"Shekhar N.","key":"e_1_2_1_29_1"},{"volume-title":"Proceedings of the International Conference on Computer Aided Design (ICCAD)","author":"Shekhar N.","key":"e_1_2_1_30_1"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(74)90031-6"},{"key":"e_1_2_1_32_1","first-page":"79","article-title":"A function in number theory","volume":"1","author":"Smarandache F.","year":"1980","journal-title":"Analele Univ. Timisoara, Fascicle"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/92.974892"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/307418.307492"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/288548.289115"},{"key":"e_1_2_1_36_1","unstructured":"Synopsys. 2007. Synopsys module compiler and designware library. htpp:\/\/www.synopsys.com.  Synopsys. 2007. Synopsys module compiler and designware library. htpp:\/\/www.synopsys.com."},{"key":"e_1_2_1_37_1","doi-asserted-by":"crossref","unstructured":"Thornton M. Drechsler R. and Miller D. M. 2001. Spectral Techniques in VLSI CAD. Kluwer Academic Hingham MA.   Thornton M. Drechsler R. and Miller D. M. 2001. Spectral Techniques in VLSI CAD. Kluwer Academic Hingham MA.","DOI":"10.1007\/978-1-4615-1425-1"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1146909.1147027"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD.2004.1382683"}],"container-title":["ACM Transactions on Design Automation of Electronic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1278349.1278362","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1278349.1278362","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:47:29Z","timestamp":1750258049000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1278349.1278362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1145\/1278349.1278362"],"URL":"https:\/\/doi.org\/10.1145\/1278349.1278362","relation":{},"ISSN":["1084-4309","1557-7309"],"issn-type":[{"type":"print","value":"1084-4309"},{"type":"electronic","value":"1557-7309"}],"subject":[],"published":{"date-parts":[[2007,9]]},"assertion":[{"value":"2007-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}