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

[Carsten Bormann <[e-mail]>]

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