{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T01:49:08Z","timestamp":1742953748747,"version":"3.40.3"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030955601"},{"type":"electronic","value":"9783030955618"}],"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.springer.com\/tdm"},{"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.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-030-95561-8_10","type":"book-chapter","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T19:04:21Z","timestamp":1645470261000},"page":"165-181","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Efficient Summation Algorithm for\u00a0the\u00a0Accuracy, Convergence and\u00a0Reproducibility of\u00a0Parallel Numerical Methods"],"prefix":"10.1007","author":[{"given":"Farah","family":"Benmouhoub","sequence":"first","affiliation":[]},{"given":"Pierre-Loic","family":"Garoche","sequence":"additional","affiliation":[]},{"given":"Matthieu","family":"Martel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,22]]},"reference":[{"key":"10_CR1","unstructured":"ANSI\/IEEE. IEEE Standard for Binary Floating-Point Arithmetic. SIAM (2008)"},{"key":"10_CR2","series-title":"Lecture Notes in Networks and Systems","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/978-3-030-80119-9_21","volume-title":"Intelligent Computing","author":"F Benmouhoub","year":"2022","unstructured":"Benmouhoub, F., Garoche, P.-L., Martel, M.: Parallel accurate and reproducible summation. In: Arai, K. (ed.) Intelligent Computing. LNNS, vol. 283, pp. 363\u2013382. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-80119-9_21"},{"issue":"7","key":"10_CR3","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1109\/TC.1977.1674894","volume":"26","author":"G Bohlender","year":"1977","unstructured":"Bohlender, G.: Floating-point computation of functions with maximum accuracy. IEEE Trans. Comput. 26(7), 621\u2013632 (1977)","journal-title":"IEEE Trans. Comput."},{"key":"10_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/978-3-319-27436-2_9","volume-title":"Logic-Based Program Synthesis and Transformation","author":"N Damouche","year":"2015","unstructured":"Damouche, N., Martel, M., Chapoutot, A.: Impact of accuracy optimization on the convergence of numerical iterative\u00a0methods. In: Falaschi, M. (ed.) LOPSTR 2015. LNCS, vol. 9527, pp. 143\u2013160. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-27436-2_9"},{"key":"10_CR5","unstructured":"Demmel, J., Hida, Y.: Accurate floating point summation. Technical Report UCB\/CSD-02-1180, EECS Department, University of California, Berkeley, May 2002"},{"issue":"4","key":"10_CR6","doi-asserted-by":"publisher","first-page":"1214","DOI":"10.1137\/S1064827502407627","volume":"25","author":"J Demmel","year":"2003","unstructured":"Demmel, J., Hida, Y.: Accurate and efficient floating point summation. SIAM J. Sci. Comput. 25(4), 1214\u20131248 (2003)","journal-title":"SIAM J. Sci. Comput."},{"issue":"7","key":"10_CR7","doi-asserted-by":"publisher","first-page":"2060","DOI":"10.1109\/TC.2014.2345391","volume":"64","author":"J Demmel","year":"2015","unstructured":"Demmel, J., Nguyen, H.D.: Parallel reproducible summation. IEEE Trans. Comput. 64(7), 2060\u20132070 (2015)","journal-title":"IEEE Trans. Comput."},{"issue":"1","key":"10_CR8","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1145\/103162.103163","volume":"23","author":"D Goldberg","year":"1991","unstructured":"Goldberg, D.: What every computer scientist should know about floating-point arithmetic. ACM Comput. Surv. 23(1), 5\u201348 (1991)","journal-title":"ACM Comput. Surv."},{"issue":"2\u20133","key":"10_CR9","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF03186531","volume":"26","author":"S Graillat","year":"2009","unstructured":"Graillat, S., Langlois, P., Louvet, N.: Algorithms for accurate, validated and fast polynomial evaluation. Jpn. J. Ind. Appl. Math. 26(2\u20133), 191\u2013214 (2009)","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"10_CR10","unstructured":"Graillat, S., M\u00e9nissier-Morain, V.: Compensated Horner scheme in complex floating point arithmetic. In: Proceedings 8th Conference on Real Numbers and Computers, Santiago de Compostela, Spain, pp. 133\u2013146 (2008)"},{"issue":"4","key":"10_CR11","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1137\/0914050","volume":"14","author":"N Higham","year":"1993","unstructured":"Higham, N.: The accuracy of floating point summation. SIAM J. Sci. Comput. 14(4), 783\u2013799 (1993)","journal-title":"SIAM J. Sci. Comput."},{"key":"10_CR12","unstructured":"Higham, N.: Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics (1996)"},{"key":"10_CR13","unstructured":"Kahan, W.: A survey of error analysis. In: IFIP Congress (1971)"},{"key":"10_CR14","doi-asserted-by":"crossref","unstructured":"Langlois, P., Martel, M., Th\u00e9venoux, L.: Accuracy versus time: a case study with summation algorithms. In: Proceedings of the 4th International Workshop on Parallel and Symbolic Computation, PASCO \u201910, New York, NY, USA, pp. 121\u2013130. Association for Computing Machinery (2010)","DOI":"10.1145\/1837210.1837229"},{"issue":"2","key":"10_CR15","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/BF02241816","volume":"28","author":"H Leuprecht","year":"1982","unstructured":"Leuprecht, H., Oberaigner, W.: Parallel algorithms for the rounding exact summation of floating point numbers. Computing 28(2), 89\u2013104 (1982). https:\/\/doi.org\/10.1007\/BF02241816","journal-title":"Computing"},{"issue":"11","key":"10_CR16","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1145\/362854.362889","volume":"14","author":"M Malcolm","year":"1971","unstructured":"Malcolm, M.: On accurate floating-point summation. Commun. ACM 14(11), 731\u2013736 (1971)","journal-title":"Commun. ACM"},{"key":"10_CR17","doi-asserted-by":"crossref","unstructured":"Muller, J.M., et al.: Handbook of Floating-Point Arithmetic, Birkh\u00e4user (2010)","DOI":"10.1007\/978-0-8176-4705-6"},{"issue":"6","key":"10_CR18","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.1137\/030601818","volume":"26","author":"T Ogita","year":"2005","unstructured":"Ogita, T., Rump, S., Oishi, S.: Accurate sum and dot product. SIAM J. Sci. Comput. 26(6), 1955\u20131988 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"10_CR19","volume-title":"An Introduction to Parallel Programming","author":"P Pacheco","year":"2011","unstructured":"Pacheco, P.: An Introduction to Parallel Programming, 1st edn. Morgan Kaufmann Publishers Inc., San Francisco (2011)","edition":"1"},{"issue":"5","key":"10_CR20","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1007\/BF01404922","volume":"19","author":"M Pichat","year":"1972","unstructured":"Pichat, M.: Correction d\u2019une somme en arithmetique a virgule flottante. Numer. Math. 19(5), 400\u2013406 (1972). https:\/\/doi.org\/10.1007\/BF01404922","journal-title":"Numer. Math."},{"issue":"5","key":"10_CR21","doi-asserted-by":"publisher","first-page":"3466","DOI":"10.1137\/080738490","volume":"31","author":"S Rump","year":"2009","unstructured":"Rump, S.: Ultimately fast accurate summation. SIAM J. Sci. Comput. 31(5), 3466\u20133502 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"10_CR22","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1587\/nolta.1.2","volume":"1","author":"S Rump","year":"2010","unstructured":"Rump, S., Ogita, T.: Fast high precision summation. Nonlinear Theory Appl. IEICE 1, 2\u201324 (2010)","journal-title":"Nonlinear Theory Appl. IEICE"},{"issue":"1","key":"10_CR23","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1137\/050645671","volume":"31","author":"S Rump","year":"2008","unstructured":"Rump, S., Ogita, T., Oishi, S.: Accurate floating-point summation part I: faithful rounding. SIAM J. Sci. Comput, 31(1), 189\u2013224 (2008)","journal-title":"SIAM J. Sci. Comput,"},{"issue":"7","key":"10_CR24","doi-asserted-by":"publisher","first-page":"e3953","DOI":"10.1002\/cpe.3953","volume":"29","author":"L Th\u00e9venoux","year":"2017","unstructured":"Th\u00e9venoux, L., Langlois, P., Martel, M.: Automatic source-to-source error compensation of floating-point programs: code synthesis to optimize accuracy and time. Concurr. Comput.: Pract. Exp. 29(7), e3953 (2017)","journal-title":"Concurr. Comput.: Pract. Exp."}],"container-title":["Lecture Notes in Computer Science","Software Verification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-95561-8_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T19:06:12Z","timestamp":1645470372000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-95561-8_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783030955601","9783030955618"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-95561-8_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"22 February 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"NSV","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Numerical Software Verification","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 July 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 July 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"nsv2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/nsv2021.github.io\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-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":"3","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":"3","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":"100% - 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":"3,7","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":"1","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":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}