Ryu: add support for maximum significant digits

[simonbyrne]

This moves the compact truncation to the main reduction stage, which avoids problems with double rounding.

Fixes #33463

[quinnj]

Looks great! Thanks for doing this!

[simonbyrne]

The only remaining question is what to do about Float16: the easiest thing I can think of is to change it so that it switches to exponent notation for 1e3 or greater (eps(Float64(1000)) == 0.5, eps(Float16(2048)) == 2). This would be a change from earlier versions.

[quinnj]

I think that's a good idea; I feel like the previous rules were weirdly complex/inconsistent.

[simonbyrne]

Okay, this now gives

julia> Float16(999)
Float16(999.0)

julia> Float16(1000)
Float16(1.0e3)

[simonbyrne]

There are a few weird edge cases where we don't actually print the closest value in order to get a trailing 0 digit:

julia> print(nextfloat(0.0,1))
5.0e-324
julia> @printf "%.1e" nextfloat(0.0,1)
4.9e-324
julia> print(nextfloat(0.0,2))
1.0e-323
julia> @printf "%.1e" nextfloat(0.0,2)
9.9e-324

and for Float32:

julia> print(nextfloat(0f0,1))
1.0f-45
julia> @printf "%.1e" nextfloat(0f0,1)
1.4e-45
julia> print(nextfloat(0f0,2))
3.0f-45
julia> @printf "%.1e" nextfloat(0f0,2)
2.8e-45
julia> print(nextfloat(0f0,3))
4.0f-45
julia> @printf "%.1e" nextfloat(0f0,3)
4.2e-45
julia> print(nextfloat(0f0,4))
6.0f-45
julia> @printf "%.1e" nextfloat(0f0,4)
5.6e-45

The options:

1. leave as is
2. print the extra digit correctly
3. print only one digit and no decimal, e.g. 5e-324 (since these all have exponents, there is no risk of them being parsed as integers).
   • this appears to be what Python does

[simonbyrne]

Alright, I've gone for option 3 above, as I think that is the most consistent. Since this and the Float16 printing are changes from earlier versions I'll leave it for triage to decide.

Note that this will change non-subnormal values as well, e.g.

julia> 1e-30
1e-30

julia> 1e30
1e30

[simonbyrne]

Okay, it has become clear that would be a bigger change than I thought. I'll save that for a new issue.

[StefanKarpinski]

That decision seems fine to me 👍

[quinnj]

Thanks for doing this @simonbyrne; it makes me feel much better knowing someone else has done a deep dive into this code. :)