{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T08:45:56Z","timestamp":1759826756979},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[1985,12,1]],"date-time":"1985-12-01T00:00:00Z","timestamp":502243200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1985,12]]},"DOI":"10.1007\/bf02251833","type":"journal-article","created":{"date-parts":[[2005,11,15]],"date-time":"2005-11-15T13:19:43Z","timestamp":1132060783000},"page":"325-347","source":"Crossref","is-referenced-by-count":36,"title":["On roundoff error distributions in floating point and logarithmic arithmetic"],"prefix":"10.1007","volume":"34","author":[{"given":"J. L.","family":"Barlow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. H.","family":"Bareiss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02251833_CR1","doi-asserted-by":"crossref","unstructured":"Bareiss, E. H., Barlow, J. L.: Probabilistic error analysis of computer arithmetics. Northwestern University DOE Report COO-2280-37 (December 1978).","DOI":"10.2172\/6226823"},{"key":"BF02251833_CR2","unstructured":"Bareiss, E. H., Grau, A. A.: Basics of the CRD computer. Northwestern University ERDA Report COO-2280-35 (August 1977)."},{"key":"BF02251833_CR3","volume-title":"Probabilistic error analysis of floating point and CRD arithmetics","author":"J. L. Barlow","year":"1981","unstructured":"Barlow, J. L.: Probabilistic error analysis of floating point and CRD arithmetics. Ph. D. Thesis, Northwestern University, Evanston, Illinois (June 1981 [a])."},{"key":"BF02251833_CR4","unstructured":"Barlow, J. L.: On the distribution of accumulated roundoff error in floating point arithmetic. Proc. Fifth IEEE Symposium on Computer Arithmetic, Ann Arbor, Michigan (1981 [b])."},{"key":"BF02251833_CR5","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF02251834","volume":"34","author":"J. L. Barlow","year":"1985","unstructured":"Barlow, J. L., Bareiss, E. H.: Probabilistic error analysis of Gaussian elimination in floating point and logarithmic arithmetic. Computing34, 349\u2013364 (1985).","journal-title":"Computing"},{"key":"BF02251833_CR6","first-page":"551","volume":"78","author":"F. Benford","year":"1938","unstructured":"Benford, F.: The law of anomalous numbers. Proc. Amer. Phil. Soc.78, 551\u2013572 (1938).","journal-title":"Proc. Amer. Phil. Soc."},{"issue":"No. 4","key":"BF02251833_CR7","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1145\/322154.322162","volume":"26","author":"J. Bustoz","year":"1979","unstructured":"Bustoz, J., Feldstein, A., Goodman, R., Linnainmaa, S.: Improved trailing digit estimates applied to optimal computer arithmetic. JACM26, No. 4, 716\u2013730 (1979).","journal-title":"JACM"},{"key":"BF02251833_CR8","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1145\/62.322429","volume":"31","author":"C. W. Clenshaw","year":"1984","unstructured":"Clenshaw, C. W., Olver, F. W. I.: Beyond floating point. JACM31, 319\u2013328 (1984).","journal-title":"JACM"},{"key":"BF02251833_CR9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1145\/321941.321948","volume":"23","author":"A. Feldstein","year":"1976","unstructured":"Feldstein, A., Goodman, R.: Convergence estimates for the distribution of trailing digits. JACM23, 287\u2013297 (1976).","journal-title":"JACM"},{"key":"BF02251833_CR10","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1080\/00029890.1966.11970894","volume":"73","author":"B. J. Flehinger","year":"1966","unstructured":"Flehinger, B. J.: On the probability that a random integer has initial digit A. Amer. Math. Monthly73, 105\u2013161 (1966).","journal-title":"Amer. Math. Monthly"},{"key":"BF02251833_CR11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF02243619","volume":"18","author":"R. Goodman","year":"1977","unstructured":"Goodman, R., Feldstein, A.: Effects of guard digits and normalization options on floating point multiplications. Computing18, 93\u2013106 (1977).","journal-title":"Computing"},{"key":"BF02251833_CR12","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF02242373","volume":"15","author":"R. Goodman","year":"1975","unstructured":"Goodman, R., Feldstein, A.: Roundoff error in products. Computing15, 263\u2013273 (1975).","journal-title":"Computing"},{"issue":"4","key":"BF02251833_CR13","first-page":"328","volume":"31","author":"R. Goodman","year":"1982","unstructured":"Goodman, R., Feldstein, A.: Loss of significance in floating point subtraction and addition. IEEE Trans. on ComputersC-31 (4), 328\u2013335 (1982).","journal-title":"IEEE Trans. on Computers C"},{"key":"BF02251833_CR14","unstructured":"Grau, A. A., Bareiss, E. H.: Statistical aspects of machine rounding. Northwestern University ERDA Report COO-2280-34 (August 1977)."},{"issue":"No. 8","key":"BF02251833_CR15","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1002\/j.1538-7305.1970.tb04281.x","volume":"49","author":"R. W. Hamming","year":"1970","unstructured":"Hamming, R. W.: On the distribution of numbers. Bell System Technical Journal49, No. 8, 1609\u20131625 (1970).","journal-title":"Bell System Technical Journal"},{"key":"BF02251833_CR16","volume-title":"Introduction to Mathematical Statistics","author":"R. V. Hogg","year":"1970","unstructured":"Hogg, R. V., Craig, A. T.: Introduction to Mathematical Statistics, Third Edition. New York: Macmillan 1970.","edition":"Third Edition"},{"key":"BF02251833_CR17","first-page":"238","volume-title":"The art of computer programming, Vol. 2","author":"D. E. Knuth","year":"1981","unstructured":"Knuth, D. E.: The art of computer programming, Vol. 2, Second Ed.: Seminumerical Algorithms, pp. 238\u2013250. Reading, Mass.: Addison-Wesley 1981.","edition":"Second Ed."},{"key":"BF02251833_CR18","volume-title":"Probabilistic distribution of the most significant digit in computer represented numbers and its behavior under iterated fixed and floating point operations","author":"L. H. Nathan","year":"1973","unstructured":"Nathan, L. H.: Probabilistic distribution of the most significant digit in computer represented numbers and its behavior under iterated fixed and floating point operations. M. S. Thesis, Northwestern University, Evanston, Illinois (August 1973)."},{"key":"BF02251833_CR19","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1214\/aoms\/1177704862","volume":"32","author":"R. S. Pinkham","year":"1961","unstructured":"Pinkham, R. S.: On the distribution of first significant digits. Ann. Math. Stat.32, 1223\u20131230 (1961).","journal-title":"Ann. Math. Stat."},{"issue":"No. 2","key":"BF02251833_CR20","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1080\/00029890.1969.12000215","volume":"74","author":"R. A. Raimi","year":"1969","unstructured":"Raimi, R. A.: On the distribution of first significant digits. Amer. Math. Monthly74, No. 2, 342\u2013348 (1969).","journal-title":"Amer. Math. Monthly"},{"key":"BF02251833_CR21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1147\/sj.41.0031","volume":"4","author":"D. Sweeney","year":"1965","unstructured":"Sweeney, D.: An analysis of floating point addition. IBM Systems Journal4, 31\u201342 (1965).","journal-title":"IBM Systems Journal"},{"key":"BF02251833_CR22","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1093\/imanum\/2.4.407","volume":"2","author":"P. R. Turner","year":"1982","unstructured":"Turner, P. R.: The distribution of leading significant digits. IMA J. of Num. Anal.2, 407\u2013412 (1982).","journal-title":"IMA J. of Num. Anal."},{"key":"BF02251833_CR23","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1093\/imanum\/4.2.225","volume":"4","author":"P. R. Turner","year":"1984","unstructured":"Turner, P. R.: Further revelations on l.s.d. IMA J. of Num. Anal.4, 225\u2013231 (1984).","journal-title":"IMA J. of Num. Anal."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02251833.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02251833\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02251833","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T23:21:32Z","timestamp":1586560892000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02251833"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,12]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1985,12]]}},"alternative-id":["BF02251833"],"URL":"https:\/\/doi.org\/10.1007\/bf02251833","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,12]]}}}