On 10/07/2013, at 02:34, Allen Wirfs-Brock wrote:

> 
> On Jul 9, 2013, at 4:14 PM, Brendan Eich wrote:
> 
>> Jeff Walden wrote:
>>> ...
>> 
>>>> Number.MAX_INTEGER == 2^53 - 1
>>>> The maximum integer value that can be stored in a number without losing precision.
>>>> (OK, so technically 2^53 can be stored, but that's an anomaly.)
>>> 
>>> Why discount the anomaly?  Looking at SpiderMonkey's source code, we have<http://mxr.mozilla.org/mozilla-central/search?string=%3C%3C%2053>  as vaguely representative of most of the places using a number like this, I think -- could be others not using the "<<  53" string, but that's probably a fair sample.  Ignore the RNG_DSCALE one, that's a red herring.  But all the others use 2**53 as the pertinent value.  (The dom/bindings/PrimitiveConversions.h hits using 2**53 -1 is a bug, I'm told, due to recent spec changes.)  So if this constant is to exist, and I think it's a fair constant to add, why would it not be 2**53?
>> 
>> I think you have a point! From http://en.wikipedia.org/wiki/Double-precision_floating-point_format,
>> 
>> "Between 2^52 =4,503,599,627,370,496 and 2^53 =9,007,199,254,740,992 the representable numbers are exactly the integers."
>> 
> 
> Isn't the anomaly (and the issue) that 2^53 (9,007,199,254,740,992) is both the upper-end of the range of integers that can be exactly represented in IEEE float64, it is is also the representation of the smallest positive integer (2^53+1) that cannot be exactly represented.
> 
> In other words, if you see the IEEE float 64 encoding of 9,007,199,254,740,992 you don't know if it is an exact representation of 2^53 or an approximate representation of 2^53+1.
> 
> 2^53-1 is the max integer value whose encoding is not also an approximation of some other integer value.

Or, in other words, the IEEE-754 doubles 9,007,199,254,740,992 and 9,007,199,254,740,993 are equal:

9007199254740992 === 9007199254740993
true
-- 
( Jorge )();

On 10/07/2013, at 02:34, Allen Wirfs-Brock wrote:

> In other words, if you see the IEEE float 64 encoding of 9,007,199,254,740,992 you don't know if it is an exact representation of 2^53 or an approximate representation of 2^53+1.
> 
> 2^53-1 is the max integer value whose encoding is not also an approximation of some other integer value.

Or, in other words, the IEEE-754 doubles 9,007,199,254,740,992 and 9,007,199,254,740,993 are equal:

```js
9007199254740992 === 9007199254740993
true
```