Re: Making Lemonade (Floating-point format changes)

BGB wrote:

On 5/20/2024 7:36 AM, Michael S wrote:

 For subnormal x subnormal you don't need result of multiplication at
all. All you need to know is if it's zero or not and what sign.
Even that is needed only in non-default rounding modes and for inexact
flag in default mode.
 

For most non-tiny formats, the seeming advantage of subnormal numbers seems small, in any case.

There is, it is called Posit (or UNUM depending).
No subnormals, wider range then IEEE, more precision than IEEE (most of the time). Whether it is better overall is still a matter of debate. It is harder to implement than IEEE but
just barely.

But, yeah, in any case I would almost prefer if there could be a separate/cheaper standard, probably mostly aimed at embedded/microcontroller style use-cases (rather than "general purpose"), and would likely relax the requirements a fair bit.

Say, likely target might be, say:
   FADD/FSUB/FMUL;
   Binary16 and Binary32 as high-priority formats;
   Binary64 as optional (but nice to have);
   Probably DAZ/FTZ;
   Potentially allow for truncate-only rounding.

Assumption being that larger or higher precision cases would fall back to software emulation.

Could optionally have some 8-bit FP formats, but 8-bit FP is a little bit too limited for general-purpose use.

Likely main candidates being:
   S.E4.F3 (Bias=7)
   S.E3.F4 (Bias=7|8, ~ Unit Range)
     More or less A-Law without the XOR.
     Though, A-Law can also be interpreted as a ~ 12 bit integer value.
     Annoyingly, exact bias depends on context for this one
       (eg: 8/7/3/0)...

I had also used:
   E4.F4
   E4.F3.S
But, this is wonky (and the possible merit of E4.F3.S is defeated once one also needs S.E4.F3 or S.E3.F4, as these are the "actually used in the wild" formats, so may have been a mistake).

I spent some of my youth trying to push against immovable objects
(i.e., standards) don't do it, it is a waste of effort and time,
similar to putting lipstick on a pig.