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

[Pavel Krivitsky]

Dear All,

Thanks for looking into it, and apologies for bumping this.

I think the strangest thing for me is that the C and the R
implementations on Windows yield different results. I don't know if it
warrants a deeper look.

Ultimately, I rewrote the code that relied on this behaviour. (I needed
something that was a finite number when squared but was still as big as
possible, so I divided it 1 + Machine epsilon, and it seems to work for
my particular situation.)

				Best,
				Pavel

On Tue, 2025-04-29 at 15:54 +0200, Tomas Kalibera wrote:
> 
> On 4/29/25 12:00, Martin Maechler wrote:
> > > > > > > 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$double.xmax)
> > [1] 1.797693e+308
> > > M+1 == M
> > [1] TRUE
> > > M*(1 + 2^-52)
> > [1] Inf
> > > print(1 + 2^-52, digits= 16)
> > [1] 1
> > > print(1 + 2^-52, digits= 17)
> > [1] 1.0000000000000002
> > What you see, I'd classify as quite related to R FAQ 7.31,
> >   := "the most frequently asked question about R
> >       among all the other frequently asked questions"
> > 
> > A nice reading is the README you get here
> >    https://github.com/ThinkR-open/seven31
> > which does link also to the R FAQ at
> >  
> > https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f
> > 
> > Of tangential interest only:
> > You mention that it is R 4.5.0 you use on Windows.
> > Would you (or anybody else) know if this is new behaviour or it
> > also happened e.g. in R 4.4.x versions on  Windows?
> 
> This depends on C math function sqrt. With sqrt implemented in mingw-
> w64 
> (mingwex), which is still the case of mingw-w64 v11, so still of 
> Rtools45, the result of sqrt(.Machine$double.xmax) is
> 
> "0x1p+512"
> 
> with mingw-w64 v12 (so with UCRT, and also on Linux, and also using
> mpfr 
> library) it is
> 
> "0x1.fffffffffffffp+511"
> 
> It is not required by any standard for the math functions in the C
> math 
> library to be precise (correctly rounded). But still, in this case,
> the 
> correctly rounded value would be returned once Rtools can switch to 
> mingw-w64 v12 (which could be no sooner than Rtools46, as mingw-w64
> is a 
> core component of the toolchain).
> 
> A bit of advertising -  I used Martin's Rmpfr package to compute this
> using mpfr.
> And there is a related blog post: 
> https://blog.r-project.org/2025/04/24/sensitivity-to-c-math-library-and-mingw-w64-v12
> 
> Best
> Tomas
> 
> 
> > 
> > 
> > Best regards,
> > Martin
> > 
> > --
> > Martin Maechler
> > ETH Zurich  and  R Core team
> > 
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