[Rd] 1/tan(-0) != 1/tan(0)

[Martin Maechler]

Testing the code that Morten Welinder suggested for improving
extreme tail behavior of  qcauchy(),
I found what you can read in the subject.
namely that the tan() + floating-point implementation on all
four different versions of Redhat linux, I have access to on
i686 and amd64 architectures,

    > 1/tan(c(-0,0))
gives
    -Inf  Inf

and of course, that can well be considered a feature, since
after all, the tan() function does jump from -Inf to +Inf at 0. 
I was still surprised that this even happens on the R level,
and I wonder if this distinction of "-0" and "0" shouldn't be
mentioned in some place(s) of the R documentation.

For the real problem, the R source (in C), It's simple
to work around the fact that
    qcauchy(0, log=TRUE)
for Morten's code proposal gives -Inf instead of +Inf.

Martin


>>>>> "MM" == Martin Maechler <maechler at stat.math.ethz.ch>
>>>>>     on Wed,  1 Jun 2005 08:57:18 +0200 (CEST) writes:

>>>>> "Morten" == Morten Welinder <mwelinder at gmail.com>
>>>>>     on Fri, 27 May 2005 20:24:36 +0200 (CEST) writes:

	  .............

    Morten> Now that pcauchy has been fixed, it is becoming
    Morten> clear that qcauchy suffers from the same problems.

    Morten> 
    Morten> qcauchy(pcauchy(1e100,0,1,FALSE,TRUE),0,1,FALSE,TRUE)

    Morten> should yield 1e100 back, but I get 1.633178e+16.
    Morten> The code below does much better.  Notes:

    Morten> 1. p need not be finite.  -Inf is ok in the log_p
    Morten> case and R_Q_P01_check already checks things.

    MM> yes

    Morten> 2. No need to disallow scale=0 and infinite
    Morten> location.

    MM> yes

    Morten> 3. The code below uses isnan and finite directly.
    Morten> It needs to be adapted to the R way of doing that.

    MM> I've done this, and started testing the new code; a version will
    MM> be put into the next version of R.

    MM> Thank you for the suggestions.

    >>> double
    >>> qcauchy (double p, double location, double scale, int lower_tail, int log_p)
    >>> {
    >>> if (isnan(p) || isnan(location) || isnan(scale))
    >>> return p + location + scale;

    >>> R_Q_P01_check(p);
    >>> if (scale < 0 || !finite(scale)) ML_ERR_return_NAN;

    >>> if (log_p) {
    >>> if (p > -1)
    >>> lower_tail = !lower_tail, p = -expm1 (p);
    >>> else
    >>> p = exp (p);
    >>> }
    >>> if (lower_tail) scale = -scale;
    >>> return location + scale / tan(M_PI * p);
    >>> }