Use all.equal(tolerance=0, aa, bb) to check for exact equality: > aa <- 100*(23/40) > bb <- (100*23)/40 > all.equal(aa,bb) [1] TRUE > all.equal(aa,bb,tolerance=0) [1] "Mean relative difference: 1.235726e-16" > aa < bb [1] TRUE
The numbers there are rounded to 52 binary digits (16+ decimal digits) for storage and rounding is not a linear or associative operation. Think of doing arithmetic by hand where you store all numbers, include intermediate results, with only 2 significant decimal digits: (3 * 1) / 3 -> 3 / 3 -> 1 3 * (1/3) -> 3 * 0.33 -> 0.99 Bill Dunlap TIBCO Software wdunlap tibco.com On Thu, Apr 20, 2017 at 2:56 PM, Paul Johnson <pauljoh...@gmail.com> wrote: > Hello, R friends > > My student unearthed this quirk that might interest you. > > I wondered if this might be a bug in the R interpreter. If not a bug, > it certainly stands as a good example of the dangers of floating point > numbers in computing. > > What do you think? > > > 100*(23/40) > [1] 57.5 > > (100*23)/40 > [1] 57.5 > > round(100*(23/40)) > [1] 57 > > round((100*23)/40) > [1] 58 > > The result in the 2 rounds should be the same, I think. Clearly some > digital number devil is at work. I *guess* that when you put in whole > numbers and group them like this (100*23), the interpreter does > integer math, but if you group (23/40), you force a fractional > division and a floating point number. The results from the first 2 > calculations are not actually 57.5, they just appear that way. > > Before you close the books, look at this: > > > aa <- 100*(23/40) > > bb <- (100*23)/40 > > all.equal(aa,bb) > [1] TRUE > > round(aa) > [1] 57 > > round(bb) > [1] 58 > > I'm putting this one in my collection of "difficult to understand" > numerical calculations. > > If you have seen this before, I'm sorry to waste your time. > > pj > -- > Paul E. Johnson http://pj.freefaculty.org > Director, Center for Research Methods and Data Analysis > http://crmda.ku.edu > > To write to me directly, please address me at pauljohn at ku.edu. > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/ > posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
