[Rd] RFC: lchoose() vs lfactorial() etc
Martin Maechler
maechler at stat.math.ethz.ch
Thu Dec 17 15:10:49 CET 2009
>>>>> "MM" == Martin Maechler <maechler at stat.math.ethz.ch>
>>>>> on Tue, 15 Dec 2009 14:54:18 +0100 writes:
>>>>> "PS" == Petr Savicky <savicky at cs.cas.cz>
>>>>> on Tue, 15 Dec 2009 10:52:43 +0100 writes:
PS> On Tue, Dec 15, 2009 at 09:49:28AM +0100, Martin Maechler wrote:
>>> lgamma(x) and lfactorial(x) are defined to return
>>>
>>> ln|Gamma(x)| {= log(abs(gamma(x)))} or ln|Gamma(x+1)| respectively.
>>>
>>> Unfortunately, we haven't chosen the analogous definition for
>>> lchoose().
>>>
>>> So, currently
>>>
>>> > lchoose(1/2, 1:10)
>>> [1] -0.6931472 -2.0794415 NaN -3.2425924 NaN -3.8869494
>>> [7] NaN -4.3357508 NaN -4.6805913
>>> Warning message:
>>> In lchoose(n, k) : NaNs produced
>>> >
>>>
>>> which (the NaN's) is not particularly useful.
>>> (I have use case where I really have to workaround those NaNs.)
>>>
>>> I herebey propose to *amend* the definition of lchoose() such
>>> that it behaves analogously to lgamma() and lfactorial(),
>>> i.e., to return
>>>
>>> log(abs(choose(.,.))
>>>
>>> Your comments are welcome.
>>> Martin Maechler, ETH Zurich
PS> I do not have a strong opinion, whether lchoose() should be log(choose(.,.))
PS> or log(abs(choose(.,.))), although i would slightly prefere the latter (with abs()).
PS> One of the reasons is that this would simplify the code of the function
PS> lchoose() in src/nmath/choose.c. It produces the NA by explicit testing
PS> the sign, so this test could be simply removed.
PS> Let me also point out that the current implementation seems to contain
PS> a bug, which causes that it is neither log(choose(.,.)) nor log(abs(choose(.,.))).
PS> x <- choose(1/2, 1:10)
PS> y <- lchoose(1/2, 1:10)
PS> cbind(choose=x, lchoose=y, log.choose=log(abs(x)))
PS> choose lchoose log.choose
PS> # [1,] 0.500000000 -0.6931472 -0.6931472
PS> # [2,] -0.125000000 -2.0794415 -2.0794415
PS> # [3,] 0.062500000 NaN -2.7725887
PS> # [4,] -0.039062500 -3.2425924 -3.2425924
PS> # [5,] 0.027343750 NaN -3.5992673
PS> # [6,] -0.020507812 -3.8869494 -3.8869494
PS> # [7,] 0.016113281 NaN -4.1281114
PS> # [8,] -0.013092041 -4.3357508 -4.3357508
PS> # [9,] 0.010910034 NaN -4.5180723
PS> # [10,] -0.009273529 -4.6805913 -4.6805913
PS> So, besides x[1], we get NA for those cases, when choose() is positive.
PS> The reason seems to be the test at line 89 of src/nmath/choose.c, which is
PS> if (fmod(floor(n-k+1), 2.) == 0) /* choose() < 0 */
PS> return ML_NAN;
PS> but it should be negated. I tested it using
PS> if (fmod(floor(n-k+1), 2.) != 0) /* choose() < 0 */
PS> return ML_NAN;
MM> Indeed !!!
MM> Pretty "interesting" that this thinko has not been detected for
MM> quite a few years....
MM> This, of course, is an even more compelling reason to implement
MM> the change of return log(abs(choose(.,.)),
MM> and at the moment, I'd even plan to "backport" that to R "2.10.1
MM> patched", as the current behavior is clearly bugous.
This has now happened;
svn revisions 50775 and 50776 {R-devel and R-patched}.
Martin
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