Inconsistent floattype result to float

[johnnychen94]

FixedPointNumbers.floattype seems inconsistent to Base.float

julia> float(Int8)
Float64

julia> floattype(Int8)
Float32

Should we update accordingly?

[timholy]

Good observation and question. Wth this package it's designed to convert to the smallest type that can store it exactly. For Int8 technically that's Float16, but Float16 has bad compute performance so we use either Float32 or Float64.

Base consistency is important, but so too is the goal of ensuring that images don't blow up to something much bigger than necessary. The right choice seems either (1) to change this package or (2) submit a PR to Base, tagged for Julia 2.0, that changes float(Int8) to Float32. I'm unsure about which of these to pick.

[johnnychen94]

I imagine we could break floattype down to float and accumulatortype

float(Int) = Float64
floattype(Int) = float(Int)
floattype(:+, Int) = accumulatortype(:+, Int)

But I'm not sure how broadly floattype(:+, Int) can be used externally.

[johnnychen94]

The fact that floattype(Int) == BigFloat seems troublesome when adopting LoopVectorization in JuliaImages.
Sometimes, the output array is pre-allocated via similar(img, floattype(eltype(img)). With floattype(Int) == BigFloat, this is either extremely inefficient or just segfaults (because LoopVectorization doesn't understand it well).