Mark S. Miller wrote:
FWIW, we include 2**53 as in the "contiguous range of exactly
representable natural numbers".
https://code.google.com/p/google-caja/source/browse/trunk/src/com/google/caja/ses/startSES.js#492
It's exactly representable, but its representation is not exact. If that
makes sense!
/be
On Tue, Jul 9, 2013 at 5:50 PM, Jorge Chamorro
<jo...@jorgechamorro.com <mailto:jo...@jorgechamorro.com>> wrote:
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 )();
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Cheers,
--MarkM
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