nicolas.cellier.aka.nice at gmail.com
Mon Nov 14 15:29:51 UTC 2022
Thank you for this excellent link.
When you know that both Microsoft and Apple have a bug in ldexp in the
gradual underflow range on x64, that's a warning that tapered arithmetic
might be error prone indeed ;)
IMO, a very good property of Posits is the ease of converting to/from
increased precision (if conserving es).
I would inquire the cost/benefit of what we could get with one register
containing 1 or few extra bytes of precision filled by each elementary
IMO it would restore some good properties for TwoSum, Twoproduct, etc...
2^48 are representable on Posit64 with es=2, or up to 2^52 on Posit64 with
es=3, if I'm not mistaken...
So it does not make a great difference with Float64.
Le lun. 14 nov. 2022 à 10:22, Tony Garnock-Jones <tonyg at leastfixedpoint.com>
a écrit :
> Here's a more up-to-date criticism:
> Florent de Dinechin, Luc Forget, Jean-Michel Muller, Yohann Uguen.
> Posits: the good, the bad and the ugly. 2018. hal-01959581v2
> I still very much like the theory of posits, and their potential for use
> as a storage format. What my reading over the last few days has taught
> me, though, is that I'm not qualified to opine on their uses for
> *computation*! They still seem really promising - it seems like they're
> perhaps *usually* superior to floats for many numerical algorithms, but
> not *always* superior? And you still have to do Proper Numerical
> Analysis, just like with IEEE754. And since the standard posit formats
> have a slightly smaller range of precisely-encoded contiguous integers
> in them, maybe regular floats/doubles are better where you're doing
> something shady like using them in place of a proper integer type
> On 11/11/22 09:42, Marcel Taeumel wrote:
> > Hmm... Patrick just pointed out to me that this critique addresses Unum
> > I. "Posits" are Unum III:
> > https://en.wikipedia.org/wiki/Unum_(number_format)
> > <https://en.wikipedia.org/wiki/Unum_(number_format)>
> > Hmm...
> > Best,
> > Marcel
> >> Am 11.11.2022 04:34:31 schrieb Craig Latta <craig at blackpagedigital.com
> >> This critique was interesting also, by William Kahan, the main
> >> architect of the IEEE 754-1985 floating-point spec:
> >> https://people.eecs.berkeley.edu/~wkahan/UnumSORN.pdf
> >> -C
> >> --
> >> Craig Latta :: research computer scientist ::
> >> Black Page Digital :: Berkeley, California ::
> >> 663137D7940BF5C0AF :: C1349FB2ADA32C4D5314CE ::
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