Int8(8) // Int8(100)im == -50im due to overflow

[nhz2]

The current method for // on Integer and Complex{<:Integer} can overflow, silently giving an incorrect answer. For example:

julia> Int8(8) // Int8(100)im
0//1 - 50//1*im

The expected answer is 0//1 - 2//25*im

The issue is caused by abs2 and conj on Complex{Int8} silently overflowing in:

julia/base/rational.jl

Line 101 in ccba6c9

//(x::Number, y::Complex) = x*conj(y)//abs2(y)

One solution could be to specialize this method on the many different combinations of Complex{<:Rational}, Complex{<:Integer}, Rational, Integer, and Number for the inputs, and check for overflow when doing any Integer math. Maybe there is a nicer way to fix this issue.

[nsajko]

The offending oneliner is buggy in other ways, too: #56245.