Exact integer-valued floats

[Alister]

On Fri, 21 Sep 2012 17:29:13 +0000, Steven D'Aprano wrote:

> Python floats can represent exact integer values (e.g. 42.0), but above
> a certain value (see below), not all integers can be represented. For
> example:
> 
> py> 1e16 == 1e16 + 1  # no such float as 10000000000000001.0 True py>
> 1e16 + 3 == 1e16 + 4  # or 10000000000000003.0 True
> 
> So some integers are missing from the floats. For large enough values,
> the gap between floats is rather large, and many numbers are missing:
> 
> py> 1e200 + 1e10 == 1e200 True
> 
> The same applies for large enough negative values.
> 
> The question is, what is the largest integer number N such that every
> whole number between -N and N inclusive can be represented as a float?
> 
> If my tests are correct, that value is 9007199254740992.0 = 2**53.
> 
> Have I got this right? Is there a way to work out the gap between one
> float and the next?
> 
> (I haven't tried to exhaustively check every float because, even at one
> nanosecond per number, it will take over 200 days.)

technically this would be implementation dependant, although the other 
responses are probably accurate for most (if not all) current 
implementations :-)



-- 
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