[Cfp-interest 1816] Re: Exact subnormal results

[David Hough CFP]

> Anyway, we still need to get back to Fred's question of what to do in the 
> case of those 3 functions when the result is between [-b^emin, +b^emin], 
> i.e. the result underflows, but is exact?  Following the standard, does 
> this not mean that the underflow flag should not be set but the underflow 
> trap, if enabled, should happen. Not that I know how to achieve that.

The current 754 spec doesn't talk about traps (neither did 2008).
It talks about alternate exception handling, which can be implemented with
traps, or in other ways.     For IEEE implementations, we could say that
range error should be set whenever the underflow exception occurs.
Or we could say that range error should be set whenever the underflow
flag would be raised - a different specification, precisely in the case of exact
subnormal results.

> Does anybody have any references to (any discussion) when the POWER (PC) 
> architecture decided to provided a breakdown of the INVALID exception? Has 
> anything like that ever been considered for UNDERFLOW?

Sub-exceptions are mentioned briefly in 8.1 of 2008 and 2019 standards.
Not much is said about them - but they are listed as a topic for the future
in 

https://754r.ucbtest.org/background/future.txt

Certainly the different invalid cases constitute sub-exceptions.   I'd also
consider exact-underflow and inexact-underflow to be sub-exceptions of
underflow, but that's just my opinion.