<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">With Joseph’s approval, I’m forwarding to CFP this message from a private thread with him.<div class=""><br class=""></div><div class="">- Jim Thomas<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">Begin forwarded message:</div><br class="Apple-interchange-newline"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">From: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Jim Thomas <<a href="mailto:jaswthomas@sbcglobal.net" class="">jaswthomas@sbcglobal.net</a>><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">Subject: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class=""><b class="">Re: [SC22WG14.20798] Overflow, normalized numbers, N2805 and N2806</b><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">Date: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">November 2, 2021 at 1:19:49 PM PDT<br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">To: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Joseph Myers <<a href="mailto:joseph@codesourcery.com" class="">joseph@codesourcery.com</a>><br class=""></span></div><br class=""><div class=""><div class="">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.<br class=""><br class="">- Jim<br class=""><br class=""><blockquote type="cite" class="">On Nov 2, 2021, at 11:04 AM, Joseph Myers <<a href="mailto:joseph@codesourcery.com" class="">joseph@codesourcery.com</a>> wrote:<br class=""><br class="">On Tue, 2 Nov 2021, Jim Thomas wrote:<br class=""><br class=""><blockquote type="cite" class="">Hmm. N2806 says floating types shall be able to represent all normalized <br class="">floating-point numbers. Floating-point numbers are given by the formula <br class="">where emin <= e <= emax. N2806 says such numbers are normalized if f_1 > <br class="">0. Thus for all e such that emin <= e <= emax, the normalized <br class="">floating-point numbers include all values represented by the formula <br class="">with f_1 > 0 and without constraint on f_i, and they all must be <br class="">represented in the type. Isn’t this P(e)? Would it help to make the <br class="">absence of constraint on f_i explicit?<br class=""></blockquote></blockquote></div></div></blockquote><div><br class=""></div>[From a previous message from Joseph: I think that with the old wording, a value with exponent e is only <br class="">normalized if f_1 > 0 and e <= e_max and P(e). Where P(e) is the <br class="">proposition: all values represented by the formula (for all possible <br class="">choices of the f_i), with that value of e, are representable in the type.]</div><div><br class=""><blockquote type="cite" class=""><div class=""><div class=""><blockquote type="cite" class=""><br class="">Maybe the question here is whether the formula is saying "every number <br class="">given by this formula is a floating-point number" or "for those real <br class="">numbers representable by the type, those that can be expressed using that <br class="">formula are floating-point numbers in the sense used in the following <br class="">paragraphs". What that suggests to me is:<br class=""><br class="">* Rephrase paragraph 3 (paragraph numbers from N2731) to make the meaning <br class="">clearer.<br class=""><br class="">* Put in a separate paragraph defining which floating-point numbers are <br class="">normalized floating-point numbers; don't put that definition in the middle <br class="">of a sentence about what values shall be representable in a type.<br class=""><br class="">* Likewise, for subnormal floating-point numbers.<br class=""><br class="">* Likewise, unnormalized floating-point numbers.<br class=""><br class="">And then my concern is not so much exactly which numbers end up getting <br class="">considered normalized numbers by this definition, but rather that the <br class="">appropriate definition for (overflow, isnormal/fpclassify, LDBL_MAX_EXP) <br class="">purposes is (for the non-IEEE formats in question) one based on loss of <br class="">precision - not based on all numbers given by the formula with a given <br class="">exponent being representable.<br class=""><br class="">-- <br class="">Joseph S. Myers<br class=""><a href="mailto:joseph@codesourcery.com" class="">joseph@codesourcery.com</a><br class=""></blockquote><br class=""></div></div></blockquote></div><br class=""></div></body></html>