`rounding(::Type{Float16})`

[nsajko]

On my system, which doesn't have native Float16, the method for rounding(Float16) doesn't exist. As far as I see effectively the rounding mode is RoundNearest, no? So I guess the method should be defined and it should return RoundNearest.

[giordano]

On my system, which doesn't have native Float16

I don't think having native hardware support for Float16 is relevant here, since I get

julia> rounding(Float16)
ERROR: MethodError: no method matching rounding(::Type{Float16})
The function `rounding` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  rounding(::Type{BigFloat})
   @ Base mpfr.jl:169
  rounding(::Type{T}) where T<:Union{Float32, Float64}
   @ Base rounding.jl:222

also on Apple Silicon. And in general I think we should treat Float16 as first-class floating point type, and not as an exception (related to #53745)