OK, I see what you mean. But in those cases, we don't get the catastrophic failures from the if (k < 0) return 0.; if (k == 0) return 1.; /* else: k >= 1 */ part, because at that point k is sure to be integer, possibly after rounding. It is when n-k is approximately but not exactly zero and we should return 1, that we either return 0 (negative case) or n (positive case; because the n(n-1)(n-2)... product has at least one factor). In the other cases, we get 1 or n(n-1)(n-2)...(n-k+1) which if n is near-integer gets rounded to produce an integer, due to the return R_IS_INT(n) ? R_forceint(r) : r; part. -pd> On 14 Jan 2020, at 17:02 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: > > On 14/01/2020 10:50 a.m., peter dalgaard wrote: >>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >>> >>> On 14/01/2020 10:07 a.m., peter dalgaard wrote: >>>> 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. >>> >>> I think that would break symmetry: you want choose(n, k) to equal choose(n, n-k) when n is very close to an integer. So I'd suggest the replacement whenever R_IS_INT(n) is true. >>> >> But choose() very deliberately ensures that k is integer, so choose(n, n-k) is ill-defined for non-integer n. > > That's only true if there's a big difference. I'd be worried about cases where n and k are close to integers (within 1e-7). In those cases, k is silently rounded to integer. As I read your suggestion, n would only be rounded to integer if k > n-k. I think both n and k should be rounded to integer in this near-integer situation, regardless of the value of k. > > I believe that lchoose(n, k) already does this. > > Duncan Murdoch > >> double r, k0 = k; >> k = R_forceint(k); >> ... >> if (fabs(k - k0) > 1e-7) >> MATHLIB_WARNING2(_("'k' (%.2f) must be integer, rounded to %.0f"), k0, k); >> >>> Duncan Murdoch >>> >>>> -pd >>>>> On 14 Jan 2020, at 00:33 , Wright, Erik Scott <ESWRIGHT at pitt.edu> 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]] >>>>> >>>>> ______________________________________________ >>>>> R-help at 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.-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
At the risk of throwing oil on a fire. If we are talking about fractional values of choose() doesn't it make sense to look to the gamma function for the correct analytic continuation? In particular k<0 may not imply the function should evaluate to zero until we get k<=-1. Example: ``` r choose(5, 4) #> [1] 5 gchoose <- function(n, k) { gamma(n+1)/(gamma(n+1-k) * gamma(k+1)) } gchoose(5, 4) #> [1] 5 gchoose(5, 0) #> [1] 1 gchoose(5, -0.5) #> [1] 0.2351727 ```> On Jan 14, 2020, at 10:20 AM, peter dalgaard <pdalgd at gmail.com> wrote: > > OK, I see what you mean. But in those cases, we don't get the catastrophic failures from the > > if (k < 0) return 0.; > if (k == 0) return 1.; > /* else: k >= 1 */ > > part, because at that point k is sure to be integer, possibly after rounding. > > It is when n-k is approximately but not exactly zero and we should return 1, that we either return 0 (negative case) or n (positive case; because the n(n-1)(n-2)... product has at least one factor). In the other cases, we get 1 or n(n-1)(n-2)...(n-k+1) which if n is near-integer gets rounded to produce an integer, due to the > > return R_IS_INT(n) ? R_forceint(r) : r; > > part. > > -pd > > > >> On 14 Jan 2020, at 17:02 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >> >> On 14/01/2020 10:50 a.m., peter dalgaard wrote: >>>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >>>> >>>> On 14/01/2020 10:07 a.m., peter dalgaard wrote: >>>>> 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. >>>> >>>> I think that would break symmetry: you want choose(n, k) to equal choose(n, n-k) when n is very close to an integer. So I'd suggest the replacement whenever R_IS_INT(n) is true. >>>> >>> But choose() very deliberately ensures that k is integer, so choose(n, n-k) is ill-defined for non-integer n. >> >> That's only true if there's a big difference. I'd be worried about cases where n and k are close to integers (within 1e-7). In those cases, k is silently rounded to integer. As I read your suggestion, n would only be rounded to integer if k > n-k. I think both n and k should be rounded to integer in this near-integer situation, regardless of the value of k. >> >> I believe that lchoose(n, k) already does this. >> >> Duncan Murdoch >> >>> double r, k0 = k; >>> k = R_forceint(k); >>> ... >>> if (fabs(k - k0) > 1e-7) >>> MATHLIB_WARNING2(_("'k' (%.2f) must be integer, rounded to %.0f"), k0, k); >>> >>>> Duncan Murdoch >>>> >>>>> -pd >>>>>> On 14 Jan 2020, at 00:33 , Wright, Erik Scott <ESWRIGHT at pitt.edu> 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]] >>>>>> >>>>>> ______________________________________________ >>>>>> R-help at 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. > > -- > Peter Dalgaard, Professor, > Center for Statistics, Copenhagen Business School > Solbjerg Plads 3, 2000 Frederiksberg, Denmark > Phone: (+45)38153501 > Office: A 4.23 > Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com > > ______________________________________________ > R-devel at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel--------------- John Mount http://www.win-vector.com/ <http://www.win-vector.com/> Our book: Practical Data Science with R http://practicaldatascience.com <http://practicaldatascience.com/> [[alternative HTML version deleted]]
That crossed my mind too, but presumably someone designed choose() to handle the near-integer cases specially. Otherwise, we already have beta() -- you just need to remember what the connection is ;-). I would expect that it has to do with the binomial and negative binomial distributions, but I can't offhand picture a calculation that leads to integer k, n plus/minus a tiny numerical error of the sort that one may encounter with, say, seq(). -pd ;-) choose(a,b) = 1/(beta(a-b+1,b+1)*(a+1)) or thereabouts> On 14 Jan 2020, at 19:36 , John Mount <jmount at win-vector.com> wrote: > > > At the risk of throwing oil on a fire. If we are talking about fractional values of choose() doesn't it make sense to look to the gamma function for the correct analytic continuation? In particular k<0 may not imply the function should evaluate to zero until we get k<=-1. > > Example: > > ``` r > choose(5, 4) > #> [1] 5 > > gchoose <- function(n, k) { > gamma(n+1)/(gamma(n+1-k) * gamma(k+1)) > } > > gchoose(5, 4) > #> [1] 5 > gchoose(5, 0) > #> [1] 1 > gchoose(5, -0.5) > #> [1] 0.2351727 > ``` > >> On Jan 14, 2020, at 10:20 AM, peter dalgaard <pdalgd at gmail.com> wrote: >> >> OK, I see what you mean. But in those cases, we don't get the catastrophic failures from the >> >> if (k < 0) return 0.; >> if (k == 0) return 1.; >> /* else: k >= 1 */ >> >> part, because at that point k is sure to be integer, possibly after rounding. >> >> It is when n-k is approximately but not exactly zero and we should return 1, that we either return 0 (negative case) or n (positive case; because the n(n-1)(n-2)... product has at least one factor). In the other cases, we get 1 or n(n-1)(n-2)...(n-k+1) which if n is near-integer gets rounded to produce an integer, due to the >> >> return R_IS_INT(n) ? R_forceint(r) : r; >> >> part. >> >> -pd >> >> >> >>> On 14 Jan 2020, at 17:02 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >>> >>> On 14/01/2020 10:50 a.m., peter dalgaard wrote: >>>>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >>>>> >>>>> On 14/01/2020 10:07 a.m., peter dalgaard wrote: >>>>>> 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. >>>>> >>>>> I think that would break symmetry: you want choose(n, k) to equal choose(n, n-k) when n is very close to an integer. So I'd suggest the replacement whenever R_IS_INT(n) is true. >>>>> >>>> But choose() very deliberately ensures that k is integer, so choose(n, n-k) is ill-defined for non-integer n. >>> >>> That's only true if there's a big difference. I'd be worried about cases where n and k are close to integers (within 1e-7). In those cases, k is silently rounded to integer. As I read your suggestion, n would only be rounded to integer if k > n-k. I think both n and k should be rounded to integer in this near-integer situation, regardless of the value of k. >>> >>> I believe that lchoose(n, k) already does this. >>> >>> Duncan Murdoch >>> >>>> double r, k0 = k; >>>> k = R_forceint(k); >>>> ... >>>> if (fabs(k - k0) > 1e-7) >>>> MATHLIB_WARNING2(_("'k' (%.2f) must be integer, rounded to %.0f"), k0, k); >>>> >>>>> Duncan Murdoch >>>>> >>>>>> -pd >>>>>>> On 14 Jan 2020, at 00:33 , Wright, Erik Scott <ESWRIGHT at pitt.edu> 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]] >>>>>>> >>>>>>> ______________________________________________ >>>>>>> R-help at 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. >> >> -- >> Peter Dalgaard, Professor, >> Center for Statistics, Copenhagen Business School >> Solbjerg Plads 3, 2000 Frederiksberg, Denmark >> Phone: (+45)38153501 >> Office: A 4.23 >> Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com >> >> ______________________________________________ >> R-devel at r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-devel > > --------------- > John Mount > http://www.win-vector.com/ > Our book: Practical Data Science with R > http://practicaldatascience.com > > > > >-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
Um, n(n-1)(n-2)...(n-k+1)/factorial(k), of course, but I think the argument still holds. Also, note that there are overflow conditions involved with computing n(n-1)(n-2)...(n-k+1)/factorial(k) as written, so it is computed in a loop with alternating multiply and divide steps. This introduces FP errors even if it is known that the result should be integer. I.e., we cannot remove the final "R_IS_INT(n) ? R_forceint(r) : r" if we want choose(n, k) to return an integer if n and k are integers. -pd> On 14 Jan 2020, at 19:20 , peter dalgaard <pdalgd at gmail.com> wrote: > > OK, I see what you mean. But in those cases, we don't get the catastrophic failures from the > > if (k < 0) return 0.; > if (k == 0) return 1.; > /* else: k >= 1 */ > > part, because at that point k is sure to be integer, possibly after rounding. > > It is when n-k is approximately but not exactly zero and we should return 1, that we either return 0 (negative case) or n (positive case; because the n(n-1)(n-2)... product has at least one factor). In the other cases, we get 1 or n(n-1)(n-2)...(n-k+1) which if n is near-integer gets rounded to produce an integer, due to the > > return R_IS_INT(n) ? R_forceint(r) : r; > > part. > > -pd > > > >> On 14 Jan 2020, at 17:02 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >> >> On 14/01/2020 10:50 a.m., peter dalgaard wrote: >>>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >>>> >>>> On 14/01/2020 10:07 a.m., peter dalgaard wrote: >>>>> 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. >>>> >>>> I think that would break symmetry: you want choose(n, k) to equal choose(n, n-k) when n is very close to an integer. So I'd suggest the replacement whenever R_IS_INT(n) is true. >>>> >>> But choose() very deliberately ensures that k is integer, so choose(n, n-k) is ill-defined for non-integer n. >> >> That's only true if there's a big difference. I'd be worried about cases where n and k are close to integers (within 1e-7). In those cases, k is silently rounded to integer. As I read your suggestion, n would only be rounded to integer if k > n-k. I think both n and k should be rounded to integer in this near-integer situation, regardless of the value of k. >> >> I believe that lchoose(n, k) already does this. >> >> Duncan Murdoch >> >>> double r, k0 = k; >>> k = R_forceint(k); >>> ... >>> if (fabs(k - k0) > 1e-7) >>> MATHLIB_WARNING2(_("'k' (%.2f) must be integer, rounded to %.0f"), k0, k); >>> >>>> Duncan Murdoch >>>> >>>>> -pd >>>>>> On 14 Jan 2020, at 00:33 , Wright, Erik Scott <ESWRIGHT at pitt.edu> 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]] >>>>>> >>>>>> ______________________________________________ >>>>>> R-help at 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. > > -- > Peter Dalgaard, Professor, > Center for Statistics, Copenhagen Business School > Solbjerg Plads 3, 2000 Frederiksberg, Denmark > Phone: (+45)38153501 > Office: A 4.23 > Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com > > > > > > > > >-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
Fix committed to R-devel w/regression test. I settled for just doing k = R_forceint(n - k) inside if(n-k < k && n >= 0 && R_IS_INT(n)) k = n-k; /* <- Symmetry */ so that k stays integer. In principle, you also could prefix this code r = n; for(j = 2; j <= k; j++) r *= (n-j+1)/j; return R_IS_INT(n) ? R_forceint(r) : r; /* might have got rounding errors */ with if(R_IS_INT(n)) n = R_forceint(n); but as I said, I believe that is really a no-op because of the rounding at the end. -pd> On 14 Jan 2020, at 19:20 , peter dalgaard <pdalgd at gmail.com> wrote: > > OK, I see what you mean. But in those cases, we don't get the catastrophic failures from the > > if (k < 0) return 0.; > if (k == 0) return 1.; > /* else: k >= 1 */ > > part, because at that point k is sure to be integer, possibly after rounding. > > It is when n-k is approximately but not exactly zero and we should return 1, that we either return 0 (negative case) or n (positive case; because the n(n-1)(n-2)... product has at least one factor). In the other cases, we get 1 or n(n-1)(n-2)...(n-k+1) which if n is near-integer gets rounded to produce an integer, due to the > > return R_IS_INT(n) ? R_forceint(r) : r; > > part. > > -pd > > > >> On 14 Jan 2020, at 17:02 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >> >> On 14/01/2020 10:50 a.m., peter dalgaard wrote: >>>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote: >>>> >>>> On 14/01/2020 10:07 a.m., peter dalgaard wrote: >>>>> 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. >>>> >>>> I think that would break symmetry: you want choose(n, k) to equal choose(n, n-k) when n is very close to an integer. So I'd suggest the replacement whenever R_IS_INT(n) is true. >>>> >>> But choose() very deliberately ensures that k is integer, so choose(n, n-k) is ill-defined for non-integer n. >> >> That's only true if there's a big difference. I'd be worried about cases where n and k are close to integers (within 1e-7). In those cases, k is silently rounded to integer. As I read your suggestion, n would only be rounded to integer if k > n-k. I think both n and k should be rounded to integer in this near-integer situation, regardless of the value of k. >> >> I believe that lchoose(n, k) already does this. >> >> Duncan Murdoch >> >>> double r, k0 = k; >>> k = R_forceint(k); >>> ... >>> if (fabs(k - k0) > 1e-7) >>> MATHLIB_WARNING2(_("'k' (%.2f) must be integer, rounded to %.0f"), k0, k); >>> >>>> Duncan Murdoch >>>> >>>>> -pd >>>>>> On 14 Jan 2020, at 00:33 , Wright, Erik Scott <ESWRIGHT at pitt.edu> 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]] >>>>>> >>>>>> ______________________________________________ >>>>>> R-help at 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. > > -- > Peter Dalgaard, Professor, > Center for Statistics, Copenhagen Business School > Solbjerg Plads 3, 2000 Frederiksberg, Denmark > Phone: (+45)38153501 > Office: A 4.23 > Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com > > > > > > > > >-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com