[RFC] Acceptable input ranges

[kimikage]

When fixing the issue #102 (PR #131), I changed the acceptable input range for Normed as follows:

FixedPointNumbers.jl/src/normed.jl

Lines 69 to 74 in 7ad0f0c

 function _convert(::Type{U}, x::Tf) where {T, f, U <: Normed{T,f}, Tf <: Union{Float32, Float64}} 
     if T == UInt128 && f == 53 
         0 <= x <= Tf(3.777893186295717e22) || throw_converterror(U, x) 
     else 
         0 <= x <= Tf((typemax(T)-rawone(U))/rawone(U)+1) || throw_converterror(U, x) 
     end 

(typemax(T)-rawone(U))/rawone(U)+1 essentially means typemax(T)/rawone(U).

The decision is based, for example, on the idea that the range of N0f8 should be [0, 1]. In particular, regarding the lower bound, I believe that the Normeds should not accept negative inputs since the current Normeds are unsigned types.

However, the following is also true:

julia> round(UInt8, 1.0019607843137253 * 255) # typemax(UInt8)/rawone(N0f8) == 1
0xff

julia> round(UInt8, -0.00196078431372549 * 255)
0x00

So, I don't know whether the acceptable input range of Q0f7 should be [-1, 127/128] , or [-128.5/128, 127.5/128).
Accepting inputs ​​less than typemin or greater than typemax causes a bit confusing, and it is nonsense especially if the input type is not based on the binary numeral system. On the other hand, it seems to be a desirable property that the difference between the upper and lower bounds is a power of two.

[kimikage]

BTW, I do not fully understand the original intent of this test. (0.498 ≈ 127.488/256, 127/256 ≈ 0.49609375)

FixedPointNumbers.jl/test/fixed.jl

Lines 95 to 100 in 7ad0f0c

 @testset "reductions" begin 
     F8 = Fixed{Int8,8} 
     a = F8[0.498, 0.1] 
     acmp = Float64(a[1]) + Float64(a[2]) 
     @test sum(a) == acmp 
     @test sum(a, dims=1) == [acmp] 

Edit:
The test code will be changed to a = Q0f7[0.75, 0.5] by PR #159.

[kimikage]

For the time being, I decided to allow the wider range than [typemin, typemax] for Fixed types.