{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T12:18:58Z","timestamp":1770466738830,"version":"3.49.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T00:00:00Z","timestamp":1683763200000},"content-version":"unspecified","delay-in-days":10,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Acta Numerica"],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p>Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as early as 1985. In particular, floating-point operations should be performed as if their results were first computed with an infinite precision and then rounded to the target format. A consequence is that floating-point arithmetic satisfies the \u2018standard model\u2019 that is often used for analysing the accuracy of floating-point algorithms. But that is only scraping the surface, and floating-point arithmetic offers much more.<\/jats:p><jats:p>In this survey we recall the history of floating-point arithmetic as well as its specification mandated by the IEEE-754 Standard. We also recall what properties it entails and what every programmer should know when designing a floating-point algorithm. We provide various basic blocks that can be implemented with floating-point arithmetic. In particular, one can actually compute the rounding error caused by some floating-point operations, which paves the way to designing more accurate algorithms. More generally, properties of floating-point arithmetic make it possible to extend the accuracy of computations beyond working precision.<\/jats:p>","DOI":"10.1017\/s0962492922000101","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T10:25:58Z","timestamp":1683800758000},"page":"203-290","source":"Crossref","is-referenced-by-count":24,"title":["Floating-point arithmetic"],"prefix":"10.1017","volume":"32","author":[{"given":"Sylvie","family":"Boldo","sequence":"first","affiliation":[]},{"given":"Claude-Pierre","family":"Jeannerod","sequence":"additional","affiliation":[]},{"given":"Guillaume","family":"Melquiond","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3588-0047","authenticated-orcid":false,"given":"Jean-Michel","family":"Muller","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,5,11]]},"container-title":["Acta Numerica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0962492922000101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T10:26:07Z","timestamp":1683800767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0962492922000101\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5]]},"references-count":0,"alternative-id":["S0962492922000101"],"URL":"https:\/\/doi.org\/10.1017\/s0962492922000101","relation":{},"ISSN":["0962-4929","1474-0508"],"issn-type":[{"value":"0962-4929","type":"print"},{"value":"1474-0508","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5]]}}}