[Rd] sqrt(.Machine$double.xmax)^2 == Inf, but only on Windows in R

[Martin Maechler]

>>>>> Pavel Krivitsky via R-devel 
>>>>>     on Mon, 28 Apr 2025 05:13:41 +0000 writes:

    > Hello, Under R 4.5.0 on Windows (x86-64), I get:

    >> sqrt(.Machine$double.xmax)^2
    > [1] Inf
    >> sqrt(.Machine$double.xmax)*sqrt(.Machine$double.xmax)
    > [1] Inf

    > On other hand on other platforms, including Debian Linux
    > (x86-64), I get:

    d> sqrt(.Machine$double.xmax)^2
    > [1] 1.797693134862315508561e+308
    d> sqrt(.Machine$double.xmax)*sqrt(.Machine$double.xmax)
    > [1] 1.797693134862315508561e+308

    > Windows is running inside a VirtualBox instance on the
    > same host as Linux. I don't have direct results from the
    > MacOS platforms, but based on the symptoms that had led me
    > to investigate, the behaviour is as the Linux.

    > Adding to the mystery, if I implement the same operation in C, e.g.,

    > library(inline)
    > sqrsqrt <- cfunction(sig = c(x = "numeric"), language = "C", "
    > double sqrtx = sqrt(Rf_asReal(x));
    > return Rf_ScalarReal(sqrtx*sqrtx);
    > ")

    > R on Linux yields:

    d> sqrsqrt(.Machine$double.xmax)
    > [1] 1.797693134862315508561e+308

    > i.e., the same number, whereas R on Windows yields:

    d> sqrsqrt(.Machine$double.xmax)
    > [1] 1.797693134862315508804e+308

    > which is not Inf but not the same as Linux either.

    > Lastly, on both platforms,

    d> sqrsqrt(.Machine$double.xmax) < .Machine$double.xmax
    > [1] TRUE

    > I am not sure if this is a bug, intended behaviour, or something else.

"something else":  It is not a bug, nor intended, but should
also *not* be surprising nor a mistery:  The largest possible
double precision number is by definition "very close to
infinity" (in the space of double precision numbers)
[R 4.5.0 patched on Linux (Fedora 40; x86_64)] :

> (M <- .Machine$double.xmax)
[1] 1.797693e+308
> M+1 == M
[1] TRUE
> M*(1 + 2^-52)
[1] Inf
> print(1 + 2^-52, digits= 16)
[1] 1
> print(1 + 2^-52, digits= 17)
[1] 1.0000000000000002
> 

What you see, I'd classify as quite related to R FAQ 7.31,
 := "the most frequently asked question about R
     among all the other frequently asked questions"

A nice reading is the README you get here
  https://github.com/ThinkR-open/seven31
which does link also to the R FAQ at
 https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

Of tangential interest only:
You mention that it is R 4.5.0 you use on Windows.
Would you (or anybody else) know if this is new behaviour or it
also happened e.g. in R 4.4.x versions on  Windows?


Best regards,
Martin

--
Martin Maechler
ETH Zurich  and  R Core team