Generic frexp

[mcabbott]

Implements roughly this idea: #148 (comment)

[codecov]

Codecov Report

Merging #150 (950cea6) into master (d4a2e48) will increase coverage by 0.11%.
The diff coverage is 85.71%.

@@            Coverage Diff             @@
##           master     #150      +/-   ##
==========================================
+ Coverage   48.75%   48.87%   +0.11%     
==========================================
  Files          63       63              
  Lines        3425     3429       +4     
==========================================
+ Hits         1670     1676       +6     
+ Misses       1755     1753       -2     

Impacted Files	Coverage Δ
src/math/prearith/prearith.jl	58.40% <85.71%> (+3.36%)	⬆️

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[JeffreySarnoff]

seems reasonable -- it is breaking though. thoughts?

[mcabbott]

I guess it's your call whether to call it a bugfix :)

No rush from me, certainly not worth 2.0.

You would have to depend on this package to be relying on the old behaviour. None of the direct packages in General seem to. What people do in private I don't know.

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From Juliahub, list of deps:
https://juliahub.com/ui/Packages/DoubleFloats/KzTCm/1.2.2?page=2
Searching the direct ones, none contain frexp

Packages which do use or define frexp include:

https://github.com/JuliaArbTypes/ArbFloats.jl/blob/9710fb9b65adff5a62336b6eff50b4d55f378f75/src/basics/IEEEfp.jl#L22-L27

https://github.com/StevenWhitaker/BlochSim.jl/blob/f5a353867c2b08c2e40b6737e97586dad8882581/src/expm.jl#L200-L212
Defines it for Dual numbers

https://github.com/JuliaPhysics/Measurements.jl/blob/b26fbff340f6a9c1432a06c8941ff9ba9a0ca34f/src/math.jl#L580-L583
Defines it to pass measurements along

https://github.com/JuliaMath/Quadmath.jl/blob/154de7bd735946b4e8dba03426c7e3e81bc3fbd1/src/Quadmath.jl#L388-L392

https://github.com/PainterQubits/Unitful.jl/blob/960e09ef518b0d3ff54747460b9c3872c08df0d7/src/quantities.jl#L467-L470
Defines it to pass units along

[mcabbott]

This is a bit of an awful name, trying to match signs. Could be more explicit like double_frexp or something.

[araujoms]

It would be great if you could merge this PR, I just had a bug because frexp, exponent, and significand don't respect the interface defined in base. With it one could define

significand(x::DoubleFloat{T}) where {T<:IEEEFloat} = frexp(x)[1] * 2

function exponent(x::DoubleFloat{T}) where {T<:IEEEFloat}
    !isfinite(x) && throw(DomainError("Cannot be NaN or Inf."))
    iszero(x) && throw(DomainError("Cannot be ±0.0."))
    return frexp(x)[2] - 1
end

and everything would work as expected.

IMHO this is a bugfix, and bugfixes are never breaking.