Hyperbolic tangent different results on Windows and Mac

Rodrigo Zepeda <rzepeda17 at gmail.com>
    on Fri, 17 Mar 2017 12:56:06 -0600 writes:

    > Dear all,
    > We seem to have found a "strange" behaviour in the hyperbolic tangent
    > function tanh on Windows.
    > When running tanh(356 + 0i) the Windows result is NaN + 0.i while on Mac
    > the result is 1 + 0i. It doesn't seem to be a floating point error because
    > on Mac it is possible to run arbitrarily large numbers (say tanh(
    > 999999677873648767519238192348124812341234182374817239847812738481234871823+0i)
    > ) and still get 1 + 0i as result. This seems to be related to the imaginary
    > part as tanh(356) returns 1 in both Windows and Mac.

    > We have obtained those results in:
    > 1) Mac with El Capitan v 10.11.6 *processor: 2.7 GHz Intel Core i5*
    > - 2) Mac with Sierra v 10.12.3 *processor: 3.2 GHz Intel Core i5*
    > - 3) Windows 10 Home v 1607 *processor: Intel Core m3-SY30 CPU@ 0.90 GHz
    > 1.51 GHz*
    > - 4) Windows 7 Home Premium Service Pack 1 *processor: Intel Core i5-2410M
    > CPU @2.30 GHz 2.30GHz.*

(The hardware should not matter).

Yes, there is a bug here on Windows only, (several Linux
versions work correctly too).

    > ?In all cases we are using R version 3.3.3 (64 bits)?

    > - *Does anybody have a clue on why is this happening?*

    > ?PS: We have previously posted this issue in Stack Overflow (
    > http://stackoverflow.com/questions/42847414/hyperbolic-tangent-in-r-throws-nan-in-windows-but-not-in-mac).
    > A comment suggests it is related to a glibc bug.

Yes, that would have been my guess too... as indeed, R on
Windows which should work for quite old versions of Windows has
been using a relatively old (gcc / libc) toolchain.

The upcoming version of R 3.4.0 uses a considerably newer
toolchain *BUT* I've just checked the latest "R-devel" binary
and the bug is still present there.

Here's a slight extension of the answer I wrote to the
above SO question here:  http://stackoverflow.com/a/42923289/161921

... Windows uses somewhat old C libraries, and here it is the
"mathlib" part of glibc.

More specifically, according to the CRAN download page for R-devel for Windows
https://cran.r-project.org/bin/windows/base/rdevel.html ,
the R 3.3.z series uses the gcc 4.6.3 (March 2012) toolchain, whereas
"R-devel", the upcoming (not yet released!) R 3.4.z series uses
the gcc 4.9.3 (June 2015) toolchain.

According to Ben Bolker's comment on SO, the bug in glibc should have
been fixed in 2012 -- and so the change from 4.6.3 to 4.9.3
should have helped,
**however* I've just checked (installed the R-devel binary from CRAN on our Windows server virtual machine) and I see that the problem is still present there: In yesterday's version of R-devel, tanh(500+0i) still returns NaN+0i.

I now think a better solution would be to use R's internal
substitute (in R's src/main/complex.c): There, we have
------------------------------------------------
#ifndef HAVE_CTANH
#define ctanh R_ctanh
static double complex ctanh(double complex z)
{
    return -I * ctan(z * I); /* A&S 4.5.9 */
}
#endif
------------------------------------------------
and we should use it (by "#undef HAVE_CTAN" (or better by a
       	      	      configure check, using  ctanh("500 + 0i"),
as I see that on Windows,
   R> -1i * tan((500+0i)*1i)
gives
   [1] 1+0i
as it should for tanh(500+0i) --- but does not on Windows.

Martin Maechler
ETH Zurich and R Core