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.dun...@gmail.com> wrote:
>
> On 14/01/2020 10:50 a.m., peter dalgaard wrote:
>>> On 14 Jan 2020, at 16:21 , Duncan Murdoch <murdoch.dun...@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 <eswri...@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-h...@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....@cbs.dk Priv: pda...@gmail.com
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