Add tests for complex division corner cases, issue #22983

[giordano]

No description provided.

[giordano]

@stevengj I assume complex(1) / complex(1) is currently giving a "wrong" results (the only issue being the sign of imaginary part), right?

[stevengj]

@giordano, no

julia> complex(1)/complex(1)
1.0 + 0.0im

is correct. ISO/IEC 10967-3:2006(E) section 5.2.6.3 says that the result should be

(1.0+0.0im)/(1.0+0.0im)
= Complex(1.0*1.0+0.0*0.0, 0.0*1.0-1.0*0.0) / (1.0*1.0 + 0.0*0.0)
= Complex(1.0, 0.0) / 1.0
= Complex(1.0, 0.0)
= 1.0 + 0.0im

since 0.0 - 0.0 = +0.0 according to IEEE 754.

If you think of it as (1+x*im) / (1 + y*im) in the limit as x and y go to zero from above, then whether it is 1 + 0.0im or 1 - 0.0im (with the "sign of 0" taken as the direction from which zero is approached) depends on the order of the limits, so the former choice is a valid option.

[stevengj]

(It's also pretty sensible that z/z give one(z) for any nonzero z, and we've defined one to be 1.0+0.0im, although actually this doesn't always happen due to roundoff errors.)

[giordano]

Oh, right, thanks! I added the test for one(Complex{T}) / one(Complex{T}) and slightly reorganized the test to avoid defining variables.