Correct exponent_max to conform to IEEE754-2008

[mschauer]

exponent_max was not giving the maximum exponent, but a sentinel value for Inf and NaN which is not a legal exponent. I found this error prone. Exponent exponent_max returns actual maximum exponent. As a by-product the code become somewhat more readable. ("if k is one bigger than the maximum exponent, first multiply y with 2 and then with the highest power of two representable...") I added internal docstrings to help the future readers.

[simonbyrne]

Do we need this? What's wrong with exponent(realmax(T))?

[simonbyrne]

See also #24631

[simonbyrne]

I would be in favour of renaming exponent_max to exponent_raw_max though.

[JeffreySarnoff]

Julia has been assigning exponent_max values that do not conform to IEEE754-2008,

exponent_max (Emax in the Standard) has a tabulated value for each floating point type.

#   These are the tabulated values (see Table 3.2 on page 8 of the IEEE Standard).

exponent_max(::Type{Float16}) =   15
exponent_max(::Type{Float32}) =  127
exponent_max(::Type{Float64}) = 1023

All the details are here: https://github.com/JeffreySarnoff/IEEE754-2008.md.

[mschauer]

exponent(realmax(T)) does give Emax, but there is some cognitive ballast asserting that it does to it.

[JeffreySarnoff]

As I understand the writing, Emax is one of their essential quantities. Since Emin is, by design, 1-Emax always, and that almost evenly biased exponents are used, Emax is another way of writing exponent_bias (bias). The fact that exponent(realmax(T)) also resolves as Emax(T) is more a consistency check than definitional -- I agree with your observation.

[mschauer]

Ping

[JeffreySarnoff]

It seems there are no problems with this (I dunno what Xcode failure is).

[JeffreySarnoff]

the freebsd link is to nowhere

[mschauer]

A helpful fairy fixed the tests.

[JeffreySarnoff]

super -- I await the merge!

[mschauer]

This is still good to go.

[JeffreySarnoff]

^ (any reason not to merge this)?

[simonbyrne]

I'm in favour of this. Since it is a change, should probably be documented in NEWS.md

[mschauer]

Yes. BTW pkg.julialang.com shows no use, only @JeffreySarnoff providing the functionality independently in https://github.com/JeffreySarnoff/LowLevelFloatFunctions.jl

[mschauer]

What is the right header for the NEW item?

• The unexported and previously undocumented function exponent_max now returns the actual maximum exponent according to IEEE754-2008, not the sentinel value.

[simonbyrne]

Ah, if it's not exported it probably doesn't need an item.

[simonbyrne]

Would be good to link to exponent help.

[mschauer]

Something with the CI is failing currently, I think unrelatedly to this change. I'll leave it and maybe someone with rights can trigger the tests when things run smoothly again.

[mschauer]

Ping

[musm]

Needs a rebase

[mschauer]

I am out, honestly

[JeffreySarnoff]

@admin fyi^

[musm]

@mschauer Sorry I didn't understand this comment? Do you mean you are no longer interested in rebasing this? Thanks.

[StefanKarpinski]

That was my interpretation of the comment and frankly it's pretty understandable given that it's been three years.

[JeffreySarnoff]

I concur. Would an appropriate admin rebase this, please.

[musm]

I'll try to get around to rebasing this soon. Thanks for the effort @mschauer

[musm]

#38929