Broken integer rounding for `big(Inf)`

[Keno]

julia> round(Integer, Inf)
ERROR: InexactError: trunc(Int64, Inf)
Stacktrace:
 [1] trunc
   @ ./float.jl:781 [inlined]
 [2] trunc
   @ ./float.jl:354 [inlined]
 [3] round(#unused#::Type{Integer}, x::Float64)
   @ Base ./float.jl:359
 [4] top-level scope
   @ REPL[14]:1

julia> round(Integer, big(Inf))
0

[barucden]

Also:

julia> round(Integer, NaN)
ERROR: InexactError: trunc(Int64, NaN)
Stacktrace:
 [1] trunc
   @ ./float.jl:805 [inlined]
 [2] trunc
   @ ./float.jl:364 [inlined]
 [3] round(#unused#::Type{Integer}, x::Float64)
   @ Base ./float.jl:369
 [4] top-level scope
   @ REPL[16]:1

julia> round(Integer, big(NaN))
0

I think it is due to mpfr.jl#L280 calling mpfr_get_z which returns 0 in case of NaN or Inf:

If op is NaN or an infinity, the erange flag is set, rop is set to 0, and 0 is returned.

Is _unchecked_cast the correct place to check for NaN or Inf?

[Keno]

Presumably we should look at the erange flag after the operation and raise an appropriate error.

[barucden]

It seems that the logic is already there for Union{Signed, Unsigned}. It just does not get called, and this definition for BigInt (added in #33681) is used instead. Can we just remove the specific method for BigInt and keep the one for Union{Signed, Unsigned}?

[Keno]

The other method doesn't quite work for BigInt, because

julia> typemin(BigInt)
ERROR: MethodError: no method matching typemin(::Type{BigInt})

but yes, add the same logic for checking the erange flag.

[barucden]

Solved by #44676 (I just messed up the "fixes" keyword in the PR message)