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
arithmetic op.
IMO it would restore some good properties for TwoSum, Twoproduct, etc...

Concerning languages like Javascript, please note that all integers up to
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:
>
> https://hal.inria.fr/hal-01959581v2/document
>
> 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
> (*cough cough javascript*)...
>
>
> 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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