Conversion of number to Posit8 returns NaR

[OreganeD]

Hello,
I found unexpected results when converting a normal floating point number to a Posit8, I believe a large number should return max_posit instead of NaR

julia> using SoftPosit

julia> Posit8(1e9)
NaR

Have a nice day

[milankl]

julia> Posit8(1e8)
Posit8(1.6777216e7)

julia> Posit8(1e9)
NaR

julia> Posit8(1e10)
Posit8(1.6777216e7)

So there's a "bad spot" where the conversion of x>maxpos is to NaR instead of to maxpos. Beyond that conversion returns maxpos correctly. Testing this more thoroughly

julia> for T in (Posit8,Posit16,Posit16_1,Posit32)
           for x in 5:0.1:100
               ~isfinite(T(10.0 ^ x)) && println((T,x,:overflow))
               iszero(T(10.0 ^-x)) && println((T,x,:underflow))
           end
       end
(Posit8, 8.5, :overflow)
(Posit8, 8.6, :overflow)
(Posit8, 8.7, :overflow)
(Posit8, 8.8, :overflow)
(Posit8, 8.9, :overflow)
(Posit8, 9.0, :overflow)
(Posit8, 9.1, :overflow)
(Posit8, 9.2, :overflow)
(Posit8, 9.3, :overflow)
(Posit8, 9.4, :overflow)
(Posit8, 9.5, :overflow)
(Posit8, 9.6, :overflow)
(Posit16, 18.1, :overflow)
(Posit16, 18.2, :overflow)
(Posit16, 18.3, :overflow)
(Posit16, 18.4, :overflow)
(Posit16, 18.5, :overflow)
(Posit16, 18.6, :overflow)
(Posit16, 18.7, :overflow)
(Posit16, 18.8, :overflow)
(Posit16, 18.9, :overflow)
(Posit16, 19.0, :overflow)
(Posit16, 19.1, :overflow)
(Posit16, 19.2, :overflow)
(Posit16_1, 9.1, :overflow)
(Posit16_1, 9.2, :overflow)
(Posit16_1, 9.3, :overflow)
(Posit16_1, 9.4, :overflow)
(Posit16_1, 9.5, :overflow)
(Posit16_1, 9.6, :overflow)
(Posit32, 37.4, :overflow)
(Posit32, 37.5, :overflow)
(Posit32, 37.6, :overflow)
(Posit32, 37.7, :overflow)
(Posit32, 37.8, :overflow)
(Posit32, 37.9, :overflow)
(Posit32, 38.0, :overflow)
(Posit32, 38.1, :overflow)
(Posit32, 38.2, :overflow)
(Posit32, 38.3, :overflow)
(Posit32, 38.4, :overflow)
(Posit32, 38.5, :overflow)

So each posit format with 2 exponent bits has about 1 decade of overflow, Posit16,1 has half a decade of overflow. By refining the range, it seems that overflow occurs between

(useed*maxpos,useed^2*maxpos)

With $u_{seed} = 4,16$ for $1,2$ exponent bits.
I believe this has something to do with shifting in the regime bits here

SoftPosit.jl/src/conversions.jl

Lines 109 to 111 in 73d44d7

	# combine regime, exponent, mantissa and arithmetic bitshift for 11..110em or 00..001em
	regime_exponent_mantissa = regime_bits | exponent_bits | mantissa
	regime_exponent_mantissa >>= (abs(k+1) + signbit_e) # arithmetic bitshift

Line 111 here

[milankl]

Turns out only a small change was needed to correct for this. The only test that's currently not passing is

julia> Posit32(Inf32)
Posit32(0.0)

julia> Posit32(-Inf32)
Posit32(0.0)

julia> Posit32(NaN32)
Posit32(0.0)

julia> Posit32(-NaN32)
Posit32(0.0)

So only Float32 -> Posit32 the non-finite numbers do something odd. I need to look into this.

[milankl]

Then there's apparently also this issue remaining (similar for other formats)

julia> Posit8(1f-8)
Posit8(9.536743e-7)

julia> floatmin(Posit8)
Posit8(5.9604645e-8)

Meaning that a float-value that should be converted to floatmin/minpos of posit, it actually gets converted to the next larger posit.

[milankl]

And the issue as already descriped in the issue remains

julia> Posit8(floatmin(Float32))
Posit8(0.0)

julia> Posit8(10*floatmin(Float32))
Posit8(5.9604645e-8)

floats within a multiple of floatmin underflow instead of being converted to floatmin/minpos of the posit format.