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

[Carsten Bormann <[e-mail]>]

On 30 May 2014, at 23:38, Tim Bray <[e-mail]> wrote:

> On Tue, May 27, 2014 at 12:17 PM, Carsten Bormann <[e-mail]> wrote:
> ​​   ➧ In particular, an I-JSON sender MUST NOT expect a receiver to treat
> ​​   an integer whose absolute value is greater than 9007199254740992 (i.e.,
> ​​   that is outside the range [-2**53, 2**53], where ** stands for exponentiation)
> ​​   as an exact value.
> 
> ​BTW, RFC7159 says: Note that when such software is used, numbers which are integers and are in the range [-(2**53)+1, (2**53)-1] are interoperable in the sense that implementations will agree exactly on their numeric values.​  So for consistency we should adjust this language to use this range and the absolute value of 9007199254740991 - right?

Consistency is good.

The new text makes use of the fact that 2**53+1 is the first integer that cannot be represented in binary64.
2**53 itself is a bit of an edge case because it can be represented exactly, but carries the uncertainty whether 2*53+1 was meant instead.
So if an implementation checks exactness only after conversion, it can only accept [-(2**53)+1, (2**53)-1].

Indeed, let’s stick with the narrower range [-(2**53)+1, (2**53)-1].

Grüße, Carsten