Re: [Json] I-JSON Topic #5: Numbers

[Tim Bray <[e-mail]>]

Just to make it clear. The WG is looking at three options:

- leave it like it is in draft-i-json-01
- Add John’s paragraph: "An I-JSON sender MUST NOT expect a receiver to
treat a non-zero number whose absolute value is greater than 1e308 or less
than 1e-308 as an exact value.  Furthermore, an I-JSON sender MUST NOT
expect a receiver to treat an integer whose absolute value is greater than
9007199254740992 as an exact value."
- Add some more text; there’s been some arm-waving on the mailing list, but
no actual proposals that I could crystallize into spec text.




On Tue, May 27, 2014 at 12:27 PM, Carsten Bormann <[e-mail]> wrote:

> On 27 May 2014, at 18:45, Matt Miller <[e-mail]> wrote:
>
> > I've been told off-list that IEEE 754 (which is referenced from RFC
> > 7159, in case we've all forgotten) doesn't cover this topic at all,
> > and my own superficial review leads me to concur.
>
> IEEE Std 754-2008 describes a number of formats, and binary64 (the one
> that JavaScript and thus many JSON implementations uses) is just one of
> them.  You need to combine some basic CS knowledge with the specific
> constants for binary64 inserted into the generic formulae given before you
> can derive much meaningful information from IEEE Std 754-2008.
>
> An obvious reference (heed the title!) is
>
> David Goldberg: What Every Computer Scientist Should Know About
> Floating-Point Arithmetic, Computing Surveys, March, 1991.
>
> (reprint available from:
> http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html ).
> That does discuss binary64 (not under this name), but does not benefit
> from the recent changes to IEEE 754.
> It is also probably more accessible to CS people than to the general
> public.
>
> “95% of the folks out there are completely clueless about floating-point.”
> (James Gosling 1998-02-28, as attributed by William Kahan)
>
> We cannot fix this in this draft.
>
> What we can do is warn that the only numbers that have a good chance to be
> taken as exact numbers are the integers in [-2**53, 2**53], and that all
> numbers in many implementations are subject to the whims of floating point
> arithmetic as defined for binary64 in IEEE Std 754-2008.
> I wouldn’t try to go beyond that.  (In particular I’d not single out
> denorms, but I think I said that already.)
>
> Grüße, Carsten
>
>


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- Tim Bray (If you’d like to send me a private message, see
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