{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T19:41:53Z","timestamp":1785872513904,"version":"3.56.0"},"reference-count":40,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2007,6,1]],"date-time":"2007-06-01T00:00:00Z","timestamp":1180656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:p>\n            This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas from the IEEE 754 standard, by providing\n            <jats:italic>correct rounding<\/jats:italic>\n            and\n            <jats:italic>exceptions<\/jats:italic>\n            . We demonstrate how these strong semantics are achieved---with no significant slowdown with respect to other arbitrary-precision tools---and discuss a few applications where such a library can be useful.\n          <\/jats:p>","DOI":"10.1145\/1236463.1236468","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":686,"title":["MPFR"],"prefix":"10.1145","volume":"33","author":[{"given":"Laurent","family":"Fousse","sequence":"first","affiliation":[{"name":"LORIA, Nancy Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guillaume","family":"Hanrot","sequence":"additional","affiliation":[{"name":"LORIA, Nancy Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincent","family":"Lef\u00e8vre","sequence":"additional","affiliation":[{"name":"LORIA, Nancy Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick","family":"P\u00e9lissier","sequence":"additional","affiliation":[{"name":"LORIA, Nancy Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Zimmermann","sequence":"additional","affiliation":[{"name":"LORIA, Nancy Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2007,6]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Batut C. Belabas K. Bernardi D. Cohen H. and Olivier M. 2000. User's Guide to PARI\/GP. http:\/\/pari.math.u-bordeaux.fr\/pub\/pari\/manuals\/2.1.6\/users.pdf.  Batut C. Belabas K. Bernardi D. Cohen H. and Olivier M. 2000. User's Guide to PARI\/GP. http:\/\/pari.math.u-bordeaux.fr\/pub\/pari\/manuals\/2.1.6\/users.pdf."},{"key":"e_1_2_1_2_1","unstructured":"Booker A. R. 2005. Artin's conjecture Turing's method and the Riemann hypothesis. http:\/\/www.arxiv.org\/abs\/math.NT\/0507502. 37 pages.  Booker A. R. 2005. Artin's conjecture Turing's method and the Riemann hypothesis. http:\/\/www.arxiv.org\/abs\/math.NT\/0507502. 37 pages."},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"Booker A. R. Str\u00f6mbergsson A. and Venkatesh A. 2006. Effective computation of Maass cusp forms. http:\/\/www.math.uu.se\/~astrombe\/papers\/papers.html. Preprint. 29 pages.  Booker A. R. Str\u00f6mbergsson A. and Venkatesh A. 2006. Effective computation of Maass cusp forms. http:\/\/www.math.uu.se\/~astrombe\/papers\/papers.html. Preprint. 29 pages.","DOI":"10.1155\/IMRN\/2006\/71281"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/355769.355775"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"Char B. W. Geddes K. O. Gonnet G. H. Leong B. L. Monagan M. B. and Watt S. M. 1991. Maple V: Language Reference Manual. Springer-Verlag.  Char B. W. Geddes K. O. Gonnet G. H. Leong B. L. Monagan M. B. and Watt S. M. 1991. Maple V: Language Reference Manual. Springer-Verlag.","DOI":"10.1007\/978-1-4615-7386-9"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/93542.93557"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/345542.345585"},{"key":"e_1_2_1_10_1","volume-title":"The decNumber C library, 3.32 ed. IBM UK Laboratories. 55","author":"Cowlishaw M.","unstructured":"Cowlishaw , M. 2005. The decNumber C library, 3.32 ed. IBM UK Laboratories. 55 pp. Cowlishaw, M. 2005. The decNumber C library, 3.32 ed. IBM UK Laboratories. 55 pp."},{"key":"e_1_2_1_11_1","unstructured":"Cuyt A. Kuterna P. Verdonk B. and Vervloet J. 2001. Arithmos: a reliable integrated computational environment. http:\/\/www.cant.ua.ac.be\/arithmos\/index.html.  Cuyt A. Kuterna P. Verdonk B. and Vervloet J. 2001. Arithmos: a reliable integrated computational environment. http:\/\/www.cant.ua.ac.be\/arithmos\/index.html."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.2005.46"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:NUMA.0000049482.38935.0b"},{"key":"e_1_2_1_14_1","unstructured":"Gay D. M. 1990. Correctly rounded binary-decimal and decimal-binary conversions. Numerical Analysis Manuscript 90-10 AT&T Bell Laboratories.  Gay D. M. 1990. Correctly rounded binary-decimal and decimal-binary conversions. Numerical Analysis Manuscript 90-10 AT&T Bell Laboratories."},{"key":"e_1_2_1_15_1","series-title":"Lecture Notes in Computer Science","volume-title":"Proceedings of SAS'01","author":"Goubault E.","unstructured":"Goubault , E. 2001. Static analyses of the precision of floating-point operations . In Proceedings of SAS'01 . Lecture Notes in Computer Science , vol. 2126 . Springer-Verlag , 234--259. Goubault, E. 2001. Static analyses of the precision of floating-point operations. In Proceedings of SAS'01. Lecture Notes in Computer Science, vol. 2126. Springer-Verlag, 234--259."},{"key":"e_1_2_1_16_1","volume-title":"GNU MP","author":"Granlund T.","year":"2004","unstructured":"Granlund , T. 2004 . GNU MP : The GNU Multiple Precision Arithmetic Library , 4.1.4 ed. http:\/\/gmplib.org\/. Granlund, T. 2004. GNU MP: The GNU Multiple Precision Arithmetic Library, 4.1.4 ed. http:\/\/gmplib.org\/."},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the 6th Conference Real Numbers and Computers (RNC'6)","author":"Hack M.","year":"2004","unstructured":"Hack , M. 2004 . On intermediate precision required for correctly-rounding decimal-to-binary floating-point conversion . In Proceedings of the 6th Conference Real Numbers and Computers (RNC'6) . Schloss Dagstuhl, Germany. Hack, M. 2004. On intermediate precision required for correctly-rounding decimal-to-binary floating-point conversion. In Proceedings of the 6th Conference Real Numbers and Computers (RNC'6). Schloss Dagstuhl, Germany."},{"key":"e_1_2_1_18_1","unstructured":"Haible B. and Kreckel R. 2005. CLN a class library for numbers. http:\/\/www.ginac.de\/CLN\/. Version 1.1.11.  Haible B. and Kreckel R. 2005. CLN a class library for numbers. http:\/\/www.ginac.de\/CLN\/. Version 1.1.11."},{"key":"e_1_2_1_19_1","volume-title":"Tech. Rep. TI-7\/97","author":"Haible B.","year":"1997","unstructured":"Haible , B. and Papanikolaou , T . 1997 . Fast multiprecision evaluation of series of rational numbers. Tech. Rep. TI-7\/97 , Darmstadt University of Technology . Haible, B. and Papanikolaou, T. 1997. Fast multiprecision evaluation of series of rational numbers. Tech. Rep. TI-7\/97, Darmstadt University of Technology."},{"key":"e_1_2_1_20_1","unstructured":"Hanrot G. Lef\u00e8vre V. P\u00e9lissier P. and Zimmermann P. 2005. The MPFR library. http:\/\/www.mpfr.org\/. Version 2.2.0.  Hanrot G. Lef\u00e8vre V. P\u00e9lissier P. and Zimmermann P. 2005. The MPFR library. http:\/\/www.mpfr.org\/. Version 2.2.0."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1978.6155780"},{"key":"e_1_2_1_22_1","first-page":"754","article-title":"IEEE standard for binary floating-point arithmetic","author":"IEEE.","year":"1985","unstructured":"IEEE. 1985 . IEEE standard for binary floating-point arithmetic . ANSI\/IEEE Std 754 - 1985 . IEEE. 1985. IEEE standard for binary floating-point arithmetic. ANSI\/IEEE Std 754-1985.","journal-title":"ANSI\/IEEE Std"},{"key":"e_1_2_1_23_1","volume-title":"Lecture notes on the status of IEEE standard 754 for binary floating-point arithmetic","author":"Kahan W.","unstructured":"Kahan , W. 1996. Lecture notes on the status of IEEE standard 754 for binary floating-point arithmetic . http:\/\/http.cs.berkeley.edu\/~wkahan\/ieee754status\/ieee754.ps. 30 pp. Kahan, W. 1996. Lecture notes on the status of IEEE standard 754 for binary floating-point arithmetic. http:\/\/http.cs.berkeley.edu\/~wkahan\/ieee754status\/ieee754.ps. 30 pp."},{"key":"e_1_2_1_24_1","volume-title":"Proceedings of the 11th IEEE Symposium on Computer Arithmetic (Arith'11)","author":"Krandick W.","unstructured":"Krandick , W. and Johnson , J. R . 1993. Efficient multiprecision floating point multiplication with optimal directional rounding . In Proceedings of the 11th IEEE Symposium on Computer Arithmetic (Arith'11) . Windsor, Ontario. Krandick, W. and Johnson, J. R. 1993. Efficient multiprecision floating point multiplication with optimal directional rounding. In Proceedings of the 11th IEEE Symposium on Computer Arithmetic (Arith'11). Windsor, Ontario."},{"key":"e_1_2_1_25_1","unstructured":"Kreinovich V. and Rump S. 2006. Towards optimal use of multi-precision arithmetic: A remark. http:\/\/www.ti3.tu-harburg.de\/~rump\/. 4 pp.  Kreinovich V. and Rump S. 2006. Towards optimal use of multi-precision arithmetic: A remark. http:\/\/www.ti3.tu-harburg.de\/~rump\/. 4 pp."},{"key":"e_1_2_1_26_1","volume-title":"Proceedings of 6th Conference on Real Numbers and Computers (RNC'6)","author":"Lef\u00e8vre V.","year":"2004","unstructured":"Lef\u00e8vre , V. 2004 . The generic multiple-precision floating-point addition with exact rounding (as in the MPFR library) . In Proceedings of 6th Conference on Real Numbers and Computers (RNC'6) . Schloss Dagstuhl, Germany. Lef\u00e8vre, V. 2004. The generic multiple-precision floating-point addition with exact rounding (as in the MPFR library). In Proceedings of 6th Conference on Real Numbers and Computers (RNC'6). Schloss Dagstuhl, Germany."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s002000000037"},{"key":"e_1_2_1_28_1","volume-title":"Elementary Functions. Algorithms and Implementation","author":"Muller J.-M.","unstructured":"Muller , J.-M. 2005. Elementary Functions. Algorithms and Implementation , 2 nd ed. Birkh\u00e4user . Muller, J.-M. 2005. Elementary Functions. Algorithms and Implementation, 2nd ed. Birkh\u00e4user.","edition":"2"},{"key":"e_1_2_1_29_1","volume-title":"Proceedings of the 6th International Conference on Numerical Analysis. Plovdiv.","author":"M\u00fcller N. T.","year":"1997","unstructured":"M\u00fcller , N. T. 1997 . Towards a real RealRAM: a prototype using C&plus;&plus; . In Proceedings of the 6th International Conference on Numerical Analysis. Plovdiv. M\u00fcller, N. T. 1997. Towards a real RealRAM: a prototype using C&plus;&plus;. In Proceedings of the 6th International Conference on Numerical Analysis. Plovdiv."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/11426639_13"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/ARITH.1991.145549"},{"key":"e_1_2_1_32_1","unstructured":"Revol N. and Rouillier F. 2005. MPFI a multiple precision interval arithmetic library based on MPFR. http:\/\/mpfi.gforge.inria.fr\/.  Revol N. and Rouillier F. 2005. MPFI a multiple precision interval arithmetic library based on MPFR. http:\/\/mpfi.gforge.inria.fr\/."},{"key":"e_1_2_1_33_1","volume-title":"NTL: A library for doing number theory","author":"Shoup V.","year":"2005","unstructured":"Shoup , V. 2005 . NTL: A library for doing number theory . http:\/\/www.shoup.net\/ntl\/. Version 5.4. Shoup, V. 2005. NTL: A library for doing number theory. http:\/\/www.shoup.net\/ntl\/. Version 5.4."},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/108556.108585"},{"key":"e_1_2_1_35_1","first-page":"113","article-title":"Precise numerical computation. Journal of Logic and Algebraic Programming","volume":"64","author":"Sofroniou M.","year":"2005","unstructured":"Sofroniou , M. and Spaletta , G. 2005 . Precise numerical computation. Journal of Logic and Algebraic Programming . Special Issue on Practical Development of Exact Real Number Computation 64 , 1, 113 -- 134 . Sofroniou, M. and Spaletta, G. 2005. Precise numerical computation. Journal of Logic and Algebraic Programming. Special Issue on Practical Development of Exact Real Number Computation 64, 1, 113--134.","journal-title":"Special Issue on Practical Development of Exact Real Number Computation"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/93542.93559"},{"key":"e_1_2_1_37_1","volume-title":"20 Years of the ACM\/SIGPLAN Conference on Programming Language Design and Implementation (1979--1999)","author":"Steele G. L.","unstructured":"Steele , G. L. and White , J. L . 2003. How to print floating-point numbers accurately . In 20 Years of the ACM\/SIGPLAN Conference on Programming Language Design and Implementation (1979--1999) : A Selection. Retrospective. 3 pp. Steele, G. L. and White, J. L. 2003. How to print floating-point numbers accurately. In 20 Years of the ACM\/SIGPLAN Conference on Programming Language Design and Implementation (1979--1999): A Selection. Retrospective. 3 pp."},{"key":"e_1_2_1_38_1","unstructured":"Sun Microsystems. 2004. Libmcr 0.9 beta: A reference correctly-rounded library of basic double-precision transcendental elementary functions. http:\/\/www.sun.com\/download\/products.xml?id=41797765.  Sun Microsystems. 2004. Libmcr 0.9 beta: A reference correctly-rounded library of basic double-precision transcendental elementary functions. http:\/\/www.sun.com\/download\/products.xml?id=41797765."},{"key":"e_1_2_1_39_1","unstructured":"The Arenaire project. 2005. CR-Libm a library of correctly rounded elementary functions in double-precision. http:\/\/lipforge.ens-lyon.fr\/projects\/crlibm\/. Version 0.8.  The Arenaire project. 2005. CR-Libm a library of correctly rounded elementary functions in double-precision. http:\/\/lipforge.ens-lyon.fr\/projects\/crlibm\/. Version 0.8."},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/382043.382404"},{"key":"e_1_2_1_41_1","volume-title":"The Mathematica Book","author":"Wolfram S.","unstructured":"Wolfram , S. 1996. The Mathematica Book , 3 rd ed. Cambridge University Press . Wolfram, S. 1996. The Mathematica Book, 3rd ed. Cambridge University Press.","edition":"3"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/114697.116813"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1236463.1236468","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1236463.1236468","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:52:07Z","timestamp":1750258327000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1236463.1236468"}},"subtitle":["A multiple-precision binary floating-point library with correct rounding"],"short-title":[],"issued":{"date-parts":[[2007,6]]},"references-count":40,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1145\/1236463.1236468"],"URL":"https:\/\/doi.org\/10.1145\/1236463.1236468","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6]]},"assertion":[{"value":"2007-06-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}