{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T07:21:00Z","timestamp":1768029660870,"version":"3.49.0"},"reference-count":24,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T00:00:00Z","timestamp":1594166400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> Recently some scientific computing users have discovered that they can replace 64-bit with 32-bit operations for carefully selected portions of the computation, and still retain acceptable accuracy in the final results. In addition, developers of some emerging applications such as machine learning have discovered that they can achieve acceptable results with only 16-bit precision in certain portions of the code. At the other end of the precision spectrum, some users have explored using 128-bit arithmetic in some particularly demanding applications, while others have done computations using much higher precision\u2014hundreds or even thousands of digits. Such work has underscored the need to develop new mathematical and software frameworks to support a dynamically variable level of precision, and, more generally, to rethink what \u201creproducibility\u201d means in a variable precision environment. This article summarizes some of the work being done in this arena, and lists research problems that need to be solved. <\/jats:p>","DOI":"10.1177\/1094342020938424","type":"journal-article","created":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T11:38:12Z","timestamp":1594208292000},"page":"483-490","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Reproducibility and variable precision computing"],"prefix":"10.1177","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7574-8342","authenticated-orcid":false,"given":"David H","family":"Bailey","sequence":"first","affiliation":[{"name":"Lawrence Berkeley National Laboratory (Retired), Berkeley, CA, USA"},{"name":"Department of Computer Science, University of California, Davis, CA, USA"}]}],"member":"179","published-online":{"date-parts":[[2020,7,8]]},"reference":[{"key":"bibr1-1094342020938424","volume-title":"Efficient Reproducible Floating Point Summation and BLAS","author":"Ahrens P","year":"2016"},{"key":"bibr2-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719604"},{"key":"bibr3-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2008.11.005"},{"key":"bibr4-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.03.087"},{"key":"bibr5-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/46\/11\/115201"},{"key":"bibr6-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2016.1180565"},{"key":"bibr7-1094342020938424","unstructured":"Bailey DH, Borwein JM, Martin U, et al. (2014) Opportunities and challenges in 21st century experimental mathematical computation. Available at: https:\/\/www.davidhbailey.com\/dhbpapers\/ICERM-2014.pdf (accessed 24 June 2020). ICERM workshop report."},{"key":"bibr8-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-00-01278-3"},{"key":"bibr9-1094342020938424","unstructured":"Bailey DH, Burgess N, Dongarra J, et al. (2019) Variable precision in mathematical and scientific computing. Available at: https:\/\/www.davidhbailey.com\/dhbpapers\/icerm-varprec-prop.pdf (accessed 24 June 2020). Proposal for an ICERM workshop."},{"key":"bibr10-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1145\/1377596.1377597"},{"key":"bibr11-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479804440335"},{"key":"bibr12-1094342020938424","unstructured":"Diffenderfer J, Fox A, Hittinger J, et al. (2018) Error analysis of ZFP compression for floating-point data. Available at: https:\/\/arxiv.org\/abs\/1805.00546 (accessed 24 June 2020)."},{"key":"bibr13-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-00995-3"},{"key":"bibr14-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1145\/1236463.1236468"},{"key":"bibr15-1094342020938424","unstructured":"Gustafson J, Yonemoto I (2017) Beating floating point at its own game: posit arithmetic. Available at: http:\/\/www.johngustafson.net\/pdfs\/BeatingFloatingPoint.pdf (accessed 24 June 2020)."},{"key":"bibr16-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1109\/SC.2018.00050"},{"key":"bibr17-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2001.930115"},{"key":"bibr18-1094342020938424","unstructured":"Higham NJ, Mary T (2018) A new approach to probabilistic rounding error analysis. Available at: http:\/\/eprints.maths.manchester.ac.uk\/2673\/.MIMS\u00a0Preprint\u00a02018.33 (accessed 24 June 2020)."},{"key":"bibr19-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2346458"},{"key":"bibr20-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1145\/3190339.3190344"},{"key":"bibr21-1094342020938424","unstructured":"Ma D, Saunders M (2017) Solving multiscale linear programs using the simplex method in quadruple precision. In: Al-Baali M, Grandinetti L, Purnama A (eds) Recent Developments in Numerical Analysis and Optimization. New York, NY: Springer. Available at: http:\/\/web.stanford.edu\/group\/SOL\/reports\/quadLP3.pdf (accessed 24 June 2020)."},{"key":"bibr22-1094342020938424","volume-title":"38th International Conference on Software Engineering (ICSE 2016)","author":"Nguyen C","year":"2016"},{"key":"bibr23-1094342020938424","unstructured":"NVIDIA (2019) Deep learning SDK documentation. Technical report, NVIDIA. Available at: https:\/\/docs.nvidia.com\/deeplearning\/sdk\/index.html (accessed 24 June 2020)."},{"key":"bibr24-1094342020938424","doi-asserted-by":"publisher","DOI":"10.1145\/2503210.2503296"}],"container-title":["The International Journal of High Performance Computing Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1094342020938424","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1094342020938424","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1094342020938424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T19:00:02Z","timestamp":1740855602000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1094342020938424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,8]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1177\/1094342020938424"],"URL":"https:\/\/doi.org\/10.1177\/1094342020938424","relation":{},"ISSN":["1094-3420","1741-2846"],"issn-type":[{"value":"1094-3420","type":"print"},{"value":"1741-2846","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,8]]}}}