[Rd] Complex numbers and negative zeroes

[Mikael Jagan]

0 and 0i are parsed as constants with 'positive zero' real and imaginary parts,
whereas <uop>0, <uop>0i, and <uop>0<bop>0i are parsed as *calls*:

     <uop>0        ~ <uop>(      0     )
           <uop>0i ~ <uop>(          0i)
     <uop>0<bop>0i ~ <bop>(<uop>(0), 0i)

Keeping in mind R's usual arithmetic conversions and the IEEE 754 standard which
defines exactly how arithmetic on signed zeros should work, I see nothing odd in
your output.

Mikael

> Date: Sat, 26 Apr 2025 11:10:00 +0200
> From: Antoine Fabri<antoine.fabri using gmail.com>
> 
> Dear r-devel,
> 
> In R `sign(0)` and `sign(-0)` both return `0` but negative zeroes do exist
> in the sense that dividing by them gives `-Inf`
> Complex numbers behave oddly with negative 0s, see below:
> 
> ``` r
> 1 / Re(0 + 0i)
> #> [1] Inf
> 1 / Im(0 + 0i)
> #> [1] Inf
> 1 / Re(0 - 0i)
> #> [1] Inf
> 1 / Im(0 - 0i) # negating the imaginary part alone does nothing
> #> [1] Inf
> 1 / Re(-0 + 0i) # negating the real part alone does nothing
> #> [1] Inf
> 1 / Im(-0 + 0i)
> #> [1] Inf
> 1 / Re(-0 - 0i)  # negating both parts works on the real part
> #> [1] -Inf
> 1 / Im(-0 - 0i) # but not on the imaginary part
> #> [1] Inf
> 1 / Im(0i)
> #> [1] Inf
> 1 / Re(0i)
> #> [1] Inf
> 1 / Re(-0i) # negating the imaginary part without explicitly providing the
> real part negates the real part
> #> [1] -Inf
> 1 / Im(-0i) # and the imaginary part too
> #> [1] -Inf
> ``` r
> 
> Defined with `complex()` it seems to work ok
> 
> ``` r
> 1 / Re(complex(real = 0, imaginary = 0))
> #> [1] Inf
> 1 / Im(complex(real = 0, imaginary = 0))
> #> [1] Inf
> 1 / Re(complex(real = -0, imaginary = 0))
> #> [1] -Inf
> 1 / Im(complex(real = -0, imaginary = 0))
> #> [1] Inf
> 1 / Re(complex(real = 0, imaginary = -0))
> #> [1] Inf
> 1 / Im(complex(real = 0, imaginary = -0))
> #> [1] -Inf
> 1 / Re(complex(real = -0, imaginary = -0))
> #> [1] -Inf
> 1 / Im(complex(real = -0, imaginary = -0))
> #> [1] -Inf
> ```
> 
> Thanks,
> 
> Antoine
> 
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