{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T09:24:03Z","timestamp":1768296243507,"version":"3.49.0"},"publisher-location":"Cham","reference-count":12,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030935702","type":"print"},{"value":"9783030935719","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-030-93571-9_6","type":"book-chapter","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T11:02:52Z","timestamp":1642071772000},"page":"64-75","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Class of\u00a0Fast and\u00a0Accurate Multi-layer Block Summation and\u00a0Dot Product Algorithms"],"prefix":"10.1007","author":[{"given":"Kang","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"Barrio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tongxiang","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Qi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"issue":"3","key":"6_CR1","doi-asserted-by":"publisher","first-page":"A1541","DOI":"10.1137\/19M1257780","volume":"42","author":"P Blanchard","year":"2020","unstructured":"Blanchard, P., Higham, N.J., Mary, T.: A class of fast and accurate summation algorithms. SIAM J. Sci. Comput. 42(3), A1541\u2013A1557 (2020)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"6_CR2","doi-asserted-by":"publisher","first-page":"1156","DOI":"10.1137\/070679946","volume":"31","author":"AM Castaldo","year":"2009","unstructured":"Castaldo, A.M., Whaley, C.R., Chronopoulos, A.T.: Reducing floating point error in dot product using the superblock family of algorithms. SIAM J. Sci. Comput. 31(2), 1156\u20131174 (2009)","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"6_CR3","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1145\/361573.361584","volume":"15","author":"J Gregory","year":"1972","unstructured":"Gregory, J.: A comparison of floating point summation methods. Commun. ACM 15(9), 838 (1972)","journal-title":"Commun. ACM"},{"issue":"2","key":"6_CR4","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/BF01932946","volume":"14","author":"S Linnainmaa","year":"1974","unstructured":"Linnainmaa, S.: Analysis of some known methods of improving the accuracy of floating-point sums. BIT Numer. Math. 14(2), 167\u2013202 (1974)","journal-title":"BIT Numer. Math."},{"issue":"1","key":"6_CR5","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1145\/42288.42343","volume":"14","author":"TG Robertazzi","year":"1988","unstructured":"Robertazzi, T.G., Schwartz, S.C.: Best \u201cordering\u2019\u2019 for floating-point addition. ACM Trans. Math. Softw. (TOMS) 14(1), 101\u2013110 (1988)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"issue":"4","key":"6_CR6","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1137\/0914050","volume":"14","author":"NJ Higham","year":"1993","unstructured":"Higham, N.J.: The accuracy of floating point summation. SIAM J. Sci. Comput. 14(4), 783\u2013799 (1993)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"6_CR7","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1145\/363707.363723","volume":"8","author":"W Kahan","year":"1965","unstructured":"Kahan, W.: Pracniques: further remarks on reducing truncation errors. Commun. ACM 8(1), 40 (1965)","journal-title":"Commun. ACM"},{"issue":"6","key":"6_CR8","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.1137\/030601818","volume":"26","author":"T Ogita","year":"2005","unstructured":"Ogita, T., Rump, S.M., Oishi, S.: Accurate sum and dot product. SIAM J. Sci. Comput. 26(6), 1955\u20131988 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"6_CR9","doi-asserted-by":"crossref","unstructured":"Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, PA, USA (2002)","DOI":"10.1137\/1.9780898718027"},{"issue":"1","key":"6_CR10","first-page":"5","volume":"23","author":"D Goldberg","year":"1991","unstructured":"Goldberg, D.: What every computer scientist should know about floating-point arithmetic. SIAM J. Sci. Comput. 23(1), 5\u201348 (1991)","journal-title":"SIAM J. Sci. Comput."},{"key":"6_CR11","doi-asserted-by":"crossref","unstructured":"Zimmermann, P.: Reliable computing with GNU MPFR. In: International Congress on Mathematical Software, pp. 42\u201345 (2010)","DOI":"10.1007\/978-3-642-15582-6_8"},{"issue":"5","key":"6_CR12","doi-asserted-by":"publisher","first-page":"C585","DOI":"10.1137\/19M1251308","volume":"41","author":"NJ Higham","year":"2019","unstructured":"Higham, N.J., Pranesh, S.: Simulating low precision floating-point arithmetic. SIAM J. Sci. Comput. 41(5), C585\u2013C602 (2019)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Lecture Notes in Computer Science","Network and Parallel Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-93571-9_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T01:02:55Z","timestamp":1768266175000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-93571-9_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783030935702","9783030935719"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-93571-9_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"13 January 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"NPC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"IFIP International Conference on Network and Parallel Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paris","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 November 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 November 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"npc2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/npc2021.dnac.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"62","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"20","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"32% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}