prod(0, 1:1000) ; 0 * Inf etc

I definitely do agree with you.
Basically, I see two different ways to proceed:

   1. one could first check if there are any 0 in the vector and then
      return 0 without computing the product
That would fail for prod(0,Inf), which should return the same
thing as 0*Inf=NaN.  Similarly for prod(0,NA) and prod(0,NaN).
Scanning for all these things might well be slower than just
doing the multiplications.  Scanning also means that 0 is treated
more commutatively than other numbers.
   2. or convert prod(x1, x2, x3) in prod(c(x1, x2, x3))
c() can convert values of classy objects in undesirable ways.
E.g.,
   > now<-Sys.time()
   > min(now-file.info(".")$mtime, now-file.info("..")$mtime)
   Time difference of 3787.759 secs
   > min(c(now-file.info(".")$mtime, now-file.info("..")$mtime))
   [1] 1.052155

This may be considered a bug in c(), at least for class
"timediff" (and  "factor" and "ordered"), but c() removes
attributes.
Martin Maechler a ?crit :
I think most of us would expect  prod(0:1000)  to return 0, and ...

... it does.

However, many of us also expect
  prod(x1, x2)    to be equivalent to
  prod(c(x1,x2))
the same as we can expect that for min(), max(), sum() and such
members of the "Summary" group.

Consequently, prod(0, 1:1000) should also return 0,
but as you see, it gives  NaN  which may be a bit puzzling...
The explanation is relatively simple:

1) The internal implementation uses

     prod(x1, x2) := prod(x1) * prod(x2)

   which in this case is

2)  0 * Inf    and that is not 0, but NaN;

  not necessarily because we would want that, but I think just
  because the underlying C math library does so.

I would personally like to change both behaviors,
but am currently only proposing to change  prod() such as to
return 0 in such cases.
This would be S-plus compatible, in case that matters.

Opinions?

Martin Maechler, ETH Zurich & R-core

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prod(0, 1:1000) ; 0 * Inf etc

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