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From: Terje Mathisen <terje.mathisen@tmsw.no>
Newsgroups: comp.arch
Subject: Re: Misc: Applications of small floating point formats.
Date: Sat, 3 Aug 2024 11:40:23 +0200
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MitchAlsup1 wrote:
> On Wed, 31 Jul 2024 23:31:35 +0000, BGB wrote:
>=20
>> So, say, we have common formats:
>> =C2=A0=C2=A0 Binary64, S.E11.F52, Common Use
>> =C2=A0=C2=A0 Binary32, S.E8.F23, Common Use
>> =C2=A0=C2=A0 Binary16, S.E5.F10, Less Common Use
>>
>> But, things get funky below this:
>> =C2=A0=C2=A0 A-Law: S.E3.F4 (Bias=3D8)
>> =C2=A0=C2=A0 FP8: S.E4.F3 (Bias=3D7) (E4M3 in NVIDIA terms)
>> =C2=A0=C2=A0 FP8U: E4.F4 (Bias=3D7)
>> =C2=A0=C2=A0 FP8S: E4.F3.S (Bias=3D7)
>>
>>
>> Semi-absent in my case:
>> =C2=A0=C2=A0 BFloat16: S.E8.F7
>> =C2=A0=C2=A0=C2=A0=C2=A0 Can be faked in software in my case using Shu=
ffle ops.
>> =C2=A0=C2=A0 NVIDIA E5M2 (S.E5.F2)
>> =C2=A0=C2=A0=C2=A0=C2=A0 Could be faked using RGBA32 pack/unpack ops.
>=20
> 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=20
1:3:4 does in fact contain enough exponent and mantissa bits to be=20
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=20
zero/subnormal/normal/infinity/qnan/snan.

Afair the absolute limit is two mantissa bits in order to differentiate=20
between Inf/QNaN and SNaN, as well as two exp bits, so fp5 (1:2:2)

Terje

--=20
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"