[Cfp-interest 1815] Re: Exact subnormal results

[Damian McGuckin]

David,

On Fri, 23 Oct 2020, David Hough CFP wrote:

>> I think there was a 44-bit IEEE floating point format
>
> This might be "single extended" but I don't recall hearing of any
> implementations.

On the first point, you are correct, and on the second point, I, like you, 
have never seen any implementations thereof.

>> Aren't there some DSP's with 40-bit not-quite IEEE-754 floating point
>> still being produced.
>
> Could be, but word sizes that are not powers of two seem to have gone 
> out of style, since for most big number crunching, memory traffic is the 
> dominant factor in execution time, and there seems to be little penalty 
> for using a full 64 bits vs using 33-63 bits.

Those DSPs have a 32-bit word size but they have no 64-bit quantities or 
instructions. I have never worked with them, only ever read about them. 
Their 40bit floating point quantities are generally binary32 but with 8 
extra bits in the significand. I have no idea they get manipulated nor do 
I have any desire to learn as it looks like a nightmare.

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. But 
then again, the 'how' is not part of our remit.

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? I would have loved 
to hear the detailed discussion on the overall concept of underflow back 
in the discussions prior to IEEE754-1985 - and I do not mean the political 
intrigue about flush-to-zero that has been discussed elsewhere long ago.

Regards - Damian

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