Re: [Json] 2-step proposal 4627bis + I-JSON

["Martin J. Dürst" <[e-mail]>]

On 2013/07/04 9:27, John Cowan wrote:
> Tim Bray scripsit:
>
>> 2. Recharter in a way that will allow us to produce something like a
>> strawman I cooked up, I-JSON: https://www.tbray.org/tmp/i-json.html
>> Produce something like that. Second victory!
>
> This is a fine trial balloon.  I have two comments:

> 2) Stating the precision of numbers does not suffice: you ought also to
> state explicitly that the valid range is numbers whose absolute value is
> between 2^-1074 and (1 + (1 - 2^52)) * 2^1023, inclusive.  For example,
> the integer 4503599627370497 is not exactly representable as a double (it
> is 2^52+1) and ought not to be allowed in I-JSON.  So I still prefer my
> proposal of "is exactly representable as an IEEE 754:2008 64-bit binary
> floating point number".

That doesn't work very well either, because you might need quite a few 
digits after the decimal point to *exactly* represent a binary fraction 
in decimal numbers. As an example, try to write something like
(2**52+1) / 2.0**200 (** being exponentiation)

You'll need something like 50+ digits, but nobody does this. What e.g. 
Ruby does (since about version 2.0) is to produce a representation that 
has just as many digits as necessary to unambiguously have a single 
closest representation in IEEE 754:2008.

Regards,   Martin.