{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T18:30:28Z","timestamp":1775845828700,"version":"3.50.1"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2015,10,12]],"date-time":"2015-10-12T00:00:00Z","timestamp":1444608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"CNRS\/JSPS Exchange Scientist"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2015,10,26]]},"abstract":"<jats:p>\n            In this article, we present an efficient algorithm to compute the faithful rounding of the\n            <jats:italic>l<\/jats:italic>\n            <jats:sub>2<\/jats:sub>\n            -norm of a floating-point vector. This means that the result is accurate to within 1 bit of the underlying floating-point type. This algorithm does not generate overflows or underflows spuriously, but does so when the final result calls for such a numerical exception to be raised. Moreover, the algorithm is well suited for parallel implementation and vectorization. The implementation runs up to 3 times faster than the netlib version on current processors.\n          <\/jats:p>","DOI":"10.1145\/2699469","type":"journal-article","created":{"date-parts":[[2015,10,13]],"date-time":"2015-10-13T22:31:00Z","timestamp":1444775460000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Efficient Calculations of Faithfully Rounded\n            <i>l<\/i>\n            <sub>2<\/sub>\n            -Norms of\n            <i>n<\/i>\n            -Vectors"],"prefix":"10.1145","volume":"41","author":[{"given":"Stef","family":"Graillat","sequence":"first","affiliation":[{"name":"Sorbonne Universit\u00e9s, UPMC Univ Paris 06, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christoph","family":"Lauter","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s, UPMC Univ Paris 06, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PING Tak Peter","family":"Tang","sequence":"additional","affiliation":[{"name":"Intel Corporation, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naoya","family":"Yamanaka","sequence":"additional","affiliation":[{"name":"Teikyo Heisei University\/CREST, JST, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin\u2019ichi","family":"Oishi","sequence":"additional","affiliation":[{"name":"Waseda University, Tokyo Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,10,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"E. 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