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From: Stefan Monnier <monnier@iro.umontreal.ca>
Newsgroups: comp.arch
Subject: Re: Making Lemonade (Floating-point format changes)
Date: Tue, 21 May 2024 15:56:47 -0400
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>> I think, we were discussing multiplication stage of FMA rather than
>> multiplication proper.
>> In case of FMA, zeroness (zeroity ?) and sign of tiny product matter in
>> all standard IEEE rounding mode except default (RNE).
> Imagine, instead, if IEEE 754 had defined positive underflow with the
> result of positive tiny, negative underflow with negative tiny,
> positive overflow with positive infinity-epsilon and negative
> overflow with negative infinity+epsilon.
> Here, the fact overflow or underflow happened is recorded in the
> result, and these results remain identifiable from real infinities
> or real zeros.
> But that ship sailed 50 years ago.

Wouldn't that just kick the problem down the street?
For example, what should `x < y` return when both `x` and `y` are
"infinity+epsilon"?


        Stefan