# choose(n, k) as n approaches k

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## choose(n, k) as n approaches k

 This struck me as incorrect: > choose(3.999999, 4) [1] 0.9999979 > choose(3.9999999, 4) [1] 0 > choose(4, 4) [1] 1 > choose(4.0000001, 4) [1] 4 > choose(4.000001, 4) [1] 1.000002 Should base::choose(n, k) check whether n is within machine precision of k and return 1? Thanks, Erik *** sessionInfo() R version 3.6.0 beta (2019-04-15 r76395) Platform: x86_64-apple-darwin15.6.0 (64-bit) Running under: macOS High Sierra 10.13.6         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: choose(n, k) as n approaches k

 On 13/01/2020 6:33 p.m., Wright, Erik Scott wrote: > This struck me as incorrect: > >> choose(3.999999, 4) > [1] 0.9999979 >> choose(3.9999999, 4) > [1] 0 >> choose(4, 4) > [1] 1 >> choose(4.0000001, 4) > [1] 4 >> choose(4.000001, 4) > [1] 1.000002 > > Should base::choose(n, k) check whether n is within machine precision of k and return 1? I don't think that's the solution.  The current code checks whether n is within 1e-7 of an integer; if it is and n-k is smaller than k, it computes choose(n, n-k) instead.  The problem in your second example is that n-k < 0 which implies the answer should be zero.  In the 4th example n-k > 0 but it is not an integer; the code rounds k to an integer, but the transformation to n-k happens after that, so the code ends up working with a non-integer. I think a solution would be to force n to be an integer if it is very close to one. I note that the source to lchoose() seems to already do this:  it handles your examples nicely. Duncan Murdoch ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: choose(n, k) as n approaches k

 In reply to this post by Wright, Erik Scott Yep, that looks wrong (probably want to continue discussion over on R-devel) I think the culprit is here (in src/nmath/choose.c)      if (k < k_small_max) {         int j;         if(n-k < k && n >= 0 && R_IS_INT(n)) k = n-k; /* <- Symmetry */         if (k <  0) return 0.;         if (k == 0) return 1.;         /* else: k >= 1 */ if n is a near-integer, then k can become non-integer and negative. In your case, n == 4 - 1e-7 k == 4 n - k == -1e-7 < 4 n >= 0 R_IS_INT(n) = TRUE (relative diff < 1e-7 is allowed) so k gets set to n - k == -1e-7 which is less than 0, so we return 0. However, as you point out, 1 would be more reasonable and in accordance with the limit as n -> 4, e.g. > factorial(4 - 1e-10)/factorial(1e-10)/factorial(4) -1 [1] -9.289025e-11 I guess that the fix could be as simple as replacing n by R_forceint(n) in the k = n - k step. -pd > On 14 Jan 2020, at 00:33 , Wright, Erik Scott <[hidden email]> wrote: > > This struck me as incorrect: > >> choose(3.999999, 4) > [1] 0.9999979 >> choose(3.9999999, 4) > [1] 0 >> choose(4, 4) > [1] 1 >> choose(4.0000001, 4) > [1] 4 >> choose(4.000001, 4) > [1] 1.000002 > > Should base::choose(n, k) check whether n is within machine precision of k and return 1? > > Thanks, > Erik > > *** > sessionInfo() > R version 3.6.0 beta (2019-04-15 r76395) > Platform: x86_64-apple-darwin15.6.0 (64-bit) > Running under: macOS High Sierra 10.13.6 > > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] 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. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: [hidden email]  Priv: [hidden email] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.