[Rd] Problem following an R bug fix to integrate()

[Hans W Borchers]

I have been told by the CRAN administrators that the following code generated
an error on 64-bit Fedora Linux (gcc, clang) and on Solaris machines (sparc,
x86), but runs well on all other systems):

    > fn <- function(x, y) ifelse(x^2 + y^2 <= 1, 1 - x^2 - y^2, 0)

    > tol <- 1.5e-8
    > fy <- function(x) integrate(function(y) fn(x, y), 0, 1,
                            subdivisions = 300, rel.tol = tol)$value
    > Fy <- Vectorize(fy)

    > xa <- -1; xb <- 1
    > Q  <- integrate(Fy, xa, xb,
                subdivisions = 300, rel.tol = tol)$value

    Error in integrate(Fy, xa, xb, subdivisions = 300, rel.tol = tol) :
    roundoff error was detected

Obviously, this realizes a double integration, split up into two 1-dimensional
integrations, and the result shall be pi/4. I wonder what a 'roundoff error'
means in this situation.

In my package, this test worked well, w/o error or warnings, since July 2011,
on Windows, Max OS X, and Ubuntu Linux. I have no chance to test it on one of
the above mentioned systems. Of course, I can simply disable these tests, but
I would not like to do so w/o good reason.

If there is a connection to a bug fix to integrate(), with NEWS item

    "integrate() reverts to the pre-2.12.0 behaviour.  (PR#15219)",

then I do not understand what this pre-2.12.0 behavior really means.

Thanks for any help or a hint to what shall be changed.
Hans W Borchers

PS:
This kind of tricky definition in function 'fn' has caused some discussion on
this list in July 2009. I still think it should be allowed to proceed in this
way.