Re: Misc: Applications of small floating point formats.

MitchAlsup1 wrote:

On Wed, 31 Jul 2024 23:31:35 +0000, BGB wrote:
 

So, say, we have common formats:
   Binary64, S.E11.F52, Common Use
   Binary32, S.E8.F23, Common Use
   Binary16, S.E5.F10, Less Common Use
>
But, things get funky below this:
   A-Law: S.E3.F4 (Bias=8)
   FP8: S.E4.F3 (Bias=7) (E4M3 in NVIDIA terms)
   FP8U: E4.F4 (Bias=7)
   FP8S: E4.F3.S (Bias=7)
>
>
Semi-absent in my case:
   BFloat16: S.E8.F7
     Can be faked in software in my case using Shuffle ops.
   NVIDIA E5M2 (S.E5.F2)
     Could be faked using RGBA32 pack/unpack ops.

 So, you have identified the problem:: 8-bits contains insufficient
exponent and fraction widths to be considered standard format.
Thus, in order to utilize 8-bit FP one needs several incarnations.
This just points back at the problem:: FP needs at least 10 bits.

I agree that fp10 is probably the shortest sane/useful version, but 1:3:4 does in fact contain enough exponent and mantissa bits to be considered an ieee754 format.
3 exp bits means that you have 6 steps for regular/normal numbers, which is enough to give some range.
4 mantissa bits (with hidden bit of course) handles zero/subnormal/normal/infinity/qnan/snan.
Afair the absolute limit is two mantissa bits in order to differentiate between Inf/QNaN and SNaN, as well as two exp bits, so fp5 (1:2:2)
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"