[Rd] Recent changes to as.complex(NA_real_)

[Martin Maechler]

>>>>> Gregory R Warnes 
>>>>>     on Sat, 23 Sep 2023 13:22:35 -0400 writes:

    > It sounds like we need to add arguments (with sensible
    > defaults) to complex(), Re(), Im(), is.na.complex() etc to
    > allow the user to specify the desired behavior.

I don't think I'd like such extra flexibility for all these, 
... ;-)  and even much less I'd like to be part of the group who
then has to *maintain* such behavior ;-)

    > --  
    > Change your thoughts and you change the world.
    > --Dr. Norman Vincent Peale

     ( .. *some* hybris from the last century ..)

Currently, I'm actually tending to *simplify* things
drastically, also because it means less surprises in the long
term and much less code reading / debugging in formatting /
printing and dealing with complex numbers.
NB: there *is* the re-opened PR#16752,
    https://bugs.r-project.org/show_bug.cgi?id=16752
where the investigation of the (C-level) R source is a major reason
for my current thinking ..

What if we decided to really treat complex numbers much more
than currently  as pairs of real (i.e. "double") numbers,
notably also when print()ing them?
Consequently, Re() and Im() would continue to return what they
do now (contrary to Hervé's original proposal) also in case of
non-finite numbers.

Of course, *no* change in arithmetic or other Ops (such as '==')
nor  is.na(), is.finite(), is.nan(), etc.

The current formatting and printing of complex numbers is
complicated in some cases unnecessarily inaccurate and in other
cases unnecessarily *ugly*.
I believe that formatting, we should change to basically format
the (vector of) real parts and imaginary parts separately.
E.g., it is really unnecessarily ugly to switch to exponential
format for both Re and Im, in a situation like this:

> (-1):2 + 1i*1e99
[1] 0e+00+1e+99i 0e+00+1e+99i 0e+00+1e+99i 0e+00+1e+99i

It is very ugly to use  exponential/scientific format for the Re()
even if we'd fix the confusing and inaccurate *joint* rounding
of Re and Im.

... and indeed (as discusses here previously:
While it makes some sense to print  NA
identically for logical, integer and double,
it seems often confusing *not* to show  <Re> + <Im>i
in the complex case; where that *does* happen for
Inf and NaN:

 > complex(, NA, ((-1):2))
 [1] NA NA NA NA
 > complex(, NaN, ((-1):2))
 [1] NaN-1i NaN+0i NaN+1i NaN+2i
 > complex(, c(-Inf,Inf), ((-1):2))
 [1] -Inf-1i  Inf+0i -Inf+1i  Inf+2i
 > 

where the first of these *does* keep the finite imaginary
values, but does not show them

> (cN <- complex(, NA, ((-1):2))); rbind(Re(cN), Im(cN))
[1] NA NA NA NA
     [,1] [,2] [,3] [,4]
[1,]   NA   NA   NA   NA
[2,]   -1    0    1    2
>