{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:36:19Z","timestamp":1750307779076,"version":"3.41.0"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T00:00:00Z","timestamp":1188604800000},"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 Commun. Comput. Algebra"],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:p>Most of us have taken the exact rational and approximate numbers in our computer algebra systems for granted for a long time, not thinking to ask if they could be significantly better. With exact rational arithmetic and adjustable-precision floating-point arithmetic to precision limited only by the total computer memory or our patience, what more could we want for such numbers? It turns out that there is much more that can be done that permits us to obtain exact results more often, more intelligible results, approximate results guaranteed to have requested error bounds, and recovery of exact results from approximate ones.<\/jats:p>","DOI":"10.1145\/1358190.1358192","type":"journal-article","created":{"date-parts":[[2008,4,8]],"date-time":"2008-04-08T15:40:00Z","timestamp":1207669200000},"page":"75-99","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Useful computations need useful numbers"],"prefix":"10.1145","volume":"41","author":[{"given":"David R.","family":"Stoutemyer","sequence":"first","affiliation":[{"name":"Stoutemyer Consultants LLC"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2007,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/220346.220351"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"J. Borwein and P. Borwein. A Dictionary of Real Numbers. Wadsworth &amp; Brooks Cole 1990.  J. Borwein and P. Borwein. A Dictionary of Real Numbers. Wadsworth &amp; Brooks Cole 1990.","DOI":"10.1007\/978-1-4615-8510-7"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1005285.1005298"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/143242.143314"},{"key":"e_1_2_1_6_1","unstructured":"R. W. Gosper Continued fraction arithmetic http:\/\/www.tweedledum.com\/rwg\/cfup.htm  R. W. Gosper Continued fraction arithmetic http:\/\/www.tweedledum.com\/rwg\/cfup.htm"},{"key":"e_1_2_1_7_1","first-page":"41","volume-title":"Kluwer Academic\/Plenum Publishers","author":"Hyv\u00f6nen E.","year":"2001"},{"key":"e_1_2_1_8_1","unstructured":"IEEE standard for binary floating-point arithmetic. ANSI\/IEEE Std 754--1985. (See also IEEE 854--1987 for radix independent floating point.)  IEEE standard for binary floating-point arithmetic. ANSI\/IEEE Std 754--1985. (See also IEEE 854--1987 for radix independent floating point.)"},{"key":"e_1_2_1_9_1","unstructured":"Interval arithmetic: http:\/\/www.cs.utep.edu\/interval-comp\/  Interval arithmetic: http:\/\/www.cs.utep.edu\/interval-comp\/"},{"key":"e_1_2_1_10_1","unstructured":"Inverse Symbolic Calculator: http:\/\/oldweb.cecm.sfu.ca\/projects\/ISC\/  Inverse Symbolic Calculator: http:\/\/oldweb.cecm.sfu.ca\/projects\/ISC\/"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1040034.1040036"},{"key":"e_1_2_1_12_1","unstructured":"Maple 11.0.1 on-line help.  Maple 11.0.1 on-line help."},{"key":"e_1_2_1_13_1","unstructured":"MapleSoft Application Center. http:\/\/www.maplesoft.com\/applications\/?p=maple11  MapleSoft Application Center. http:\/\/www.maplesoft.com\/applications\/?p=maple11"},{"key":"e_1_2_1_14_1","unstructured":"Mathematica 6.0.1.0 on-line help.  Mathematica 6.0.1.0 on-line help."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(02)00146-2"},{"key":"e_1_2_1_16_1","first-page":"94720","article-title":"Mathematical Constants, UCRL-20418, Lawrence Radiation Laboratory, University of California","author":"Robinson H. P.","year":"1971","journal-title":"Berkeley CA"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718157.ch10"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(00)00195-6"},{"key":"e_1_2_1_19_1","unstructured":"S. M. Rump. INTLAB the MATLAB interval toolbox down-loadable from http:\/\/www.ti3.tu-harburg.de\/rump\/  S. M. Rump. INTLAB the MATLAB interval toolbox down-loadable from http:\/\/www.ti3.tu-harburg.de\/rump\/"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11155-006-9007-4"},{"key":"e_1_2_1_21_1","first-page":"135","volume-title":"Proc. Comp. Methods for Algebraic Spline Surfaces","author":"Shou H.","year":"2003"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383267"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/12.57047"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1358190.1358192","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1358190.1358192","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:56:04Z","timestamp":1750254964000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1358190.1358192"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1145\/1358190.1358192"],"URL":"https:\/\/doi.org\/10.1145\/1358190.1358192","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2007,9]]},"assertion":[{"value":"2007-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}