Re: Making Lemonade (Floating-point format changes)

MitchAlsup1 wrote:

Michael S wrote:
 

On Mon, 20 May 2024 21:17:15 +0200
Terje Mathisen <terje.mathisen@tmsw.no> wrote:

>
As you note, it is only when using RoundToPlus (or Minus) Infinity
that an arbitrary small product can still produce a non-zero result.
>
Terje
>
>

 

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.

Not entirely: I was recently very surprised to learn that in non-default rounding modes, you can in fact get behavior close to but not quite what you want. I.e. if rounding would cause overflow from maximally large normal to infinity, then the rounding up is suppressed.
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"