{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,31]],"date-time":"2025-08-31T10:18:18Z","timestamp":1756635498710,"version":"3.37.3"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T00:00:00Z","timestamp":1558656000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T00:00:00Z","timestamp":1558656000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s11075-019-00711-z","type":"journal-article","created":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T04:21:47Z","timestamp":1558671707000},"page":"957-986","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimal inverse projection of floating-point addition"],"prefix":"10.1007","volume":"83","author":[{"given":"Diane","family":"Gallois-Wong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1970-3019","authenticated-orcid":false,"given":"Sylvie","family":"Boldo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Cuoq","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,5,24]]},"reference":[{"issue":"2","key":"711_CR1","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1002\/stvr.333","volume":"16","author":"B Botella","year":"2006","unstructured":"Botella, B., Gotlieb, A., Michel, C.: Symbolic execution of floating-point computations. Software Testing Verification and Reliability 16(2), 97\u2013121 (2006). \nhttps:\/\/doi.org\/10.1002\/stvr.333","journal-title":"Software Testing Verification and Reliability"},{"key":"711_CR2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-540-89330-1_2","volume-title":"Programming Languages and Systems","author":"Liqian Chen","year":"2008","unstructured":"Chen, L., Min\u00e9, A., Cousot, P.: A sound floating-point polyhedra abstract domain. In: Ramalingam, G. (ed.) Programming Languages and Systems, pp 3\u201318. Springer, Berlin (2008)"},{"key":"711_CR3","unstructured":"Cousot, P., Cousot, R.: Static determination of dynamic properties of programs. In: Proceedings of the Second International Symposium on Programming, pp 106\u2013130. Dunod, Paris, France (1976)"},{"key":"711_CR4","doi-asserted-by":"publisher","unstructured":"Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Sethi, R. (ed.) Proceedings of the 4th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (POPL), pp 238\u2013252. ACM, Los Angeles, CA, USA (1977), \nhttps:\/\/doi.org\/10.1145\/512950.512973","DOI":"10.1145\/512950.512973"},{"key":"711_CR5","doi-asserted-by":"publisher","unstructured":"IEEE Computer Society: IEEE standard for floating-point arithmetic. Tech. Rep. 754-2008. \nhttps:\/\/doi.org\/10.1109\/IEEESTD.2008.4610935\n\n (2008)","DOI":"10.1109\/IEEESTD.2008.4610935"},{"key":"711_CR6","unstructured":"ISO: International standard ISO\/IEC 9899:2011 Programming languages \u2013 C (2011)"},{"key":"711_CR7","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1007\/978-3-642-15396-9_30","volume-title":"Principles and Practice of Constraint Programming \u2013 CP 2010","author":"Bruno Marre","year":"2010","unstructured":"Marre, B., Michel, C.: Improving the floating point addition and subtraction constraints. In: Cohen, D. (ed.) Principles and Practice of Constraint Programming \u2013 CP 2010, pp 360\u2013367. Springer, Berlin (2010)"},{"key":"711_CR8","unstructured":"Michel, C.: Exact projection functions for floating point number constraints. In: International Symposium on Artificial Intelligence and Mathematics. Fort Lauderdale, Florida, USA (2002). Http:\/\/Rutcor.Rutgers.Edu\/ Amai\/Aimath02\/PAPERS\/21.Ps. (AI&m (2002)"},{"key":"711_CR9","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1007\/3-540-45578-7_36","volume-title":"Principles and Practice of Constraint Programming \u2014 CP 2001","author":"C. Michel","year":"2001","unstructured":"Michel, C., Rueher, M., Lebbah, Y.: Solving constraints over floating-point numbers. In: Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming, CP \u201901, pp 524\u2013538. Springer, London (2001). \nhttp:\/\/dl.acm.org\/citation.cfm?id=647488.726803"},{"key":"711_CR10","doi-asserted-by":"crossref","unstructured":"Min\u00e9, A.: Relational abstract domains for the detection of floating-point run-time errors. In: Schmidt, D. (ed.) Programming Languages and Systems, pp 3\u201317. Springer, Berlin (2004)","DOI":"10.1007\/978-3-540-24725-8_2"},{"issue":"3","key":"711_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1353445.1353446","volume":"30","author":"D Monniaux","year":"2008","unstructured":"Monniaux, D.: The pitfalls of verifying floating-point computations. ACM Trans. Program. Lang. Syst. 30(3), 1\u201341 (2008). \nhttps:\/\/doi.org\/10.1145\/1353445.1353446","journal-title":"ACM Trans. Program. Lang. Syst."},{"key":"711_CR12","volume-title":"Interval analysis","author":"RE Moore","year":"1963","unstructured":"Moore, R.E.: Interval analysis. Prentice-Hall, Englewood Cliffs (1963)"},{"key":"711_CR13","unstructured":"Muller, J.M.: On the definition of ulp(x). Tech. Rep. RR-5504, INRIA. \nhttps:\/\/hal.inria.fr\/inria-00070503\n\n (2005)"},{"issue":"2","key":"711_CR14","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s10543-009-0218-z","volume":"49","author":"SM Rump","year":"2009","unstructured":"Rump, S.M., Zimmermann, P., Boldo, S., Melquiond, G.: Computing predecessor and successor in rounding to nearest. BIT 49(2), 419\u2013431 (2009). \nhttps:\/\/doi.org\/10.1007\/s10543-009-0218-z\n\n. \nhttp:\/\/hal.inria.fr\/inria-00337537\/fr\/","journal-title":"BIT"},{"key":"711_CR15","unstructured":"Sterbenz, P.H.: Floating point computation. Prentice Hall (1974)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-019-00711-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-019-00711-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-019-00711-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,22]],"date-time":"2020-05-22T23:15:56Z","timestamp":1590189356000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-019-00711-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,24]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["711"],"URL":"https:\/\/doi.org\/10.1007\/s11075-019-00711-z","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2019,5,24]]},"assertion":[{"value":"7 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 May 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}