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Softw."],"published-print":{"date-parts":[[2023,3,31]]},"abstract":"<jats:p>\n            We consider the computation of the Euclidean (or L2) norm of an\n            <jats:italic>n<\/jats:italic>\n            -dimensional vector in floating-point arithmetic. We review the classical solutions used to avoid spurious overflow or underflow and\/or to obtain very accurate results. We modify a recently published algorithm (that uses double-word arithmetic) to allow for a very accurate solution, free of spurious overflows and underflows. To that purpose, we use a double-word square-root algorithm of which we provide a tight error analysis. The returned L2 norm will be within very slightly more than 0.5 ulp from the exact result, which means that we will almost always provide correct rounding.\n          <\/jats:p>","DOI":"10.1145\/3568672","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T13:25:57Z","timestamp":1666704357000},"page":"1-34","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Accurate Calculation of Euclidean Norms Using Double-word Arithmetic"],"prefix":"10.1145","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4045-8273","authenticated-orcid":false,"given":"Vincent","family":"Lef\u00e8vre","sequence":"first","affiliation":[{"name":"Inria, LIP, Universit\u00e9 de Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5861-0819","authenticated-orcid":false,"given":"Nicolas","family":"Louvet","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Claude Bernard Lyon 1, LIP, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3588-0047","authenticated-orcid":false,"given":"Jean-Michel","family":"Muller","sequence":"additional","affiliation":[{"name":"CNRS, LIP, Universit\u00e9 de Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1403-5429","authenticated-orcid":false,"given":"Joris","family":"Picot","sequence":"additional","affiliation":[{"name":"\u00c9cole Normale Sup\u00e9rieure de Lyon, LIP, Universit\u00e9 de Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5049-0242","authenticated-orcid":false,"given":"Laurence","family":"Rideau","sequence":"additional","affiliation":[{"name":"Inria Sophia Antipolis, Universit\u00e9 C\u00f4te d\u2019Azur, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/3061665"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-64110-2"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.5555\/993954"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/355769.355771"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1991.145529"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2003.1207663"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/3054947"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10817-014-9317-x"},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2020.3002702"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129514000437"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2011.40"},{"key":"e_1_3_3_13_2","volume-title":"Computer Arithmetic and Formal Proofs: Verifying Floating-point Algorithms with the Coq System","author":"Boldo S.","year":"2017","unstructured":"S. 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