[Rd] pmin(), pmax() - slower than necessary for common cases

[Martin Maechler]

A few hours ago, I was making a small point on the R-SIG-robust
mailing list on the point that  ifelse() was not too efficient
in a situation where  pmax() could easily be used instead.

However, this has reminded me of some timing experiments that I
did 13 years ago with S-plus -- where I found that pmin() /
pmax() were really relatively slow for the most common case
where they are used with only two arguments {and typically one
of the arguments is a scalar; but that's not even important here}.
The main reason is that the function accept an arbitrary number
of arguments and that they do recycling.
Their source is at
  https://svn.R-project.org/R/trunk/src/library/base/R/pmax.R

In April 2001 (as I see), I had repeated my timings with R (1.2.2)
which confirmed the picture more or less,  but for some reason I
never drew "proper" consequences of my findings.
Of course one can argue  pmax() & pmin() are still quite fast
functions; OTOH the experiment below shows that -- at least the
special case with 2 (matching) arguments could be made faster by
about a factor of 19 ...

I don't have yet a constructive proposition; just note the fact that

  pmin. <- function(k,x) (x+k - abs(x-k))/2
  pmax. <- function(k,x) (x+k + abs(x-k))/2

are probably the fastest way of computing  pmin() and pmax() of
two arguments {yes, they "suffer" from rounding error of about 1
to 2 bits...} currently in R. 
One "solution" could be to provide  pmin2() and pmax2()
functions based on trival .Internal() versions.

The experiments below are for the special case of  k=0  where I
found the above mentioned factor of 19 which is a bit
overoptimistic for the general case; here is my  pmax-ex.R  source file
(as text/plain attachment ASCII-code --> easy cut & paste)
demonstrating what I claim above.

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Martin Maechler, ETH Zurich