[Cfp-interest 2259] Fwd: [SC22WG14.20798] Overflow, normalized numbers, N2805 and N2806

[Jim Thomas]

With Joseph’s approval, I’m forwarding to CFP this message from a private thread with him.

- Jim Thomas

> Begin forwarded message:
> 
> From: Jim Thomas <jaswthomas at sbcglobal.net>
> Subject: Re: [SC22WG14.20798] Overflow, normalized numbers, N2805 and N2806
> Date: November 2, 2021 at 1:19:49 PM PDT
> To: Joseph Myers <joseph at codesourcery.com>
> 
> Thanks for the clarifications and suggestions. I believe I understand your concerns now. I’ll review the CFP proposals with them in mind and think how to proceed.
> 
> - Jim
> 
>> On Nov 2, 2021, at 11:04 AM, Joseph Myers <joseph at codesourcery.com> wrote:
>> 
>> On Tue, 2 Nov 2021, Jim Thomas wrote:
>> 
>>> Hmm. N2806 says floating types shall be able to represent all normalized 
>>> floating-point numbers. Floating-point numbers are given by the formula 
>>> where emin <= e <= emax. N2806 says such numbers are normalized if f_1 > 
>>> 0. Thus for all e such that emin <= e <= emax, the normalized 
>>> floating-point numbers include all values represented by the formula 
>>> with f_1 > 0 and without constraint on f_i, and they all must be 
>>> represented in the type. Isn’t this P(e)? Would it help to make the 
>>> absence of constraint on f_i explicit?

[From a previous message from Joseph: I think that with the old wording, a value with exponent e is only 
normalized if f_1 > 0 and e <= e_max and P(e).  Where P(e) is the 
proposition: all values represented by the formula (for all possible 
choices of the f_i), with that value of e, are representable in the type.]

>> 
>> Maybe the question here is whether the formula is saying "every number 
>> given by this formula is a floating-point number" or "for those real 
>> numbers representable by the type, those that can be expressed using that 
>> formula are floating-point numbers in the sense used in the following 
>> paragraphs".  What that suggests to me is:
>> 
>> * Rephrase paragraph 3 (paragraph numbers from N2731) to make the meaning 
>> clearer.
>> 
>> * Put in a separate paragraph defining which floating-point numbers are 
>> normalized floating-point numbers; don't put that definition in the middle 
>> of a sentence about what values shall be representable in a type.
>> 
>> * Likewise, for subnormal floating-point numbers.
>> 
>> * Likewise, unnormalized floating-point numbers.
>> 
>> And then my concern is not so much exactly which numbers end up getting 
>> considered normalized numbers by this definition, but rather that the 
>> appropriate definition for (overflow, isnormal/fpclassify, LDBL_MAX_EXP) 
>> purposes is (for the non-IEEE formats in question) one based on loss of 
>> precision - not based on all numbers given by the formula with a given 
>> exponent being representable.
>> 
>> -- 
>> Joseph S. Myers
>> joseph at codesourcery.com
> 

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