OpenEuphoria

Re: File size limit

• Posted by Jason Gade <jaygade at ?a?oo.com> Jun 12, 2008
• 785 views

Fernando Bauer wrote:
> 
> Jason Gade wrote:
> > 
> [snipped]
> > 
> > > I have asked for larger file numbers too, but i don't think we will get
> > > them
> > > in Eu v4. Even if we did, we could not do basic full precision integer
> > > math
> > > on the numbers over 4gigabytes (there are such libs in the archives tho).
> > > 
> > > Kat
> > 
> > Jim Brown is working on this right now. And atoms are unique integers up to
> > (2^52) - 1 so I don't know why you can't do full precision integer math on
> > them.
> 
> The maximum contiguous integer in Eu is:
>    2^53 = power(2,53) = 9,007,199,254,740,992
> 
> Demonstrations:
> 
> 1) By decimal representation:
> 
> 2^53-5= 9007199254740987  -- ok
> 2^53-4= 9007199254740988  -- ok
> 2^53-3= 9007199254740989  -- ok
> 2^53-2= 9007199254740990  -- ok
> 2^53-1= 9007199254740991  -- ok
> 2^53+0= 9007199254740992  -- ok
> 2^53+1= 9007199254740992  -- Problem: it's equal to 2^53
> 2^53+2= 9007199254740994
> 2^53+3= 9007199254740996
> 2^53+4= 9007199254740996
> 2^53+5= 9007199254740996
> 
> 2) IEEE754 double-precision (64 bits) bit values:
> Value =|s|--exponent-|--------------------fraction------------------------|
> 2^53-5= 0 10000110011 1111111111111111111111111111111111111111111111111011
> 2^53-4= 0 10000110011 1111111111111111111111111111111111111111111111111100
> 2^53-3= 0 10000110011 1111111111111111111111111111111111111111111111111101
> 2^53-2= 0 10000110011 1111111111111111111111111111111111111111111111111110
> 2^53-1= 0 10000110011 1111111111111111111111111111111111111111111111111111
> 2^53+0= 0 10000110100 0000000000000000000000000000000000000000000000000000
> 2^53+1= 0 10000110100 0000000000000000000000000000000000000000000000000000
> 2^53+2= 0 10000110100 0000000000000000000000000000000000000000000000000001
> 2^53+3= 0 10000110100 0000000000000000000000000000000000000000000000000010
> 2^53+4= 0 10000110100 0000000000000000000000000000000000000000000000000010
> 2^53+5= 0 10000110100 0000000000000000000000000000000000000000000000000010
> 
> 3)IEEE754 double-precision normalized numbers:
>   v = (-1)^s * 2^e * (1 + fraction * 2^-52)
>     = (-1)^s * (2^e + fraction * 2^(e-52))
> 
> Note that there is NO problem when v=2^52 (e=52):
>   v = (-1)^s * (2^52 + fraction)   where 0<=fraction<=2^52-1
> 
> Note that there are problems when 2^53<v<2^54 (e=53):
>   v = (-1)^s * (2^53 + fraction * 2)   where 0<=fraction<=2^52-1
> since fraction is an integer number, it's impossible to represent 2^53+1
> exactly.
> 
> 2^53-5= +2^52 * (1 + 4503599627370491 * 2^-52)
> 2^53-4= +2^52 * (1 + 4503599627370492 * 2^-52)
> 2^53-3= +2^52 * (1 + 4503599627370493 * 2^-52)
> 2^53-2= +2^52 * (1 + 4503599627370494 * 2^-52)
> 2^53-1= +2^52 * (1 + 4503599627370495 * 2^-52)
> 2^53+0= +2^53 * (1 +                0 * 2^-52)
> 2^53+1= +2^53 * (1 +                0 * 2^-52)
> 2^53+2= +2^53 * (1 +                1 * 2^-52)
> 2^53+3= +2^53 * (1 +                2 * 2^-52)
> 2^53+4= +2^53 * (1 +                2 * 2^-52)
> 2^53+5= +2^53 * (1 +                2 * 2^-52)
> 
> 4)By measuring integer distances:
> Look at this:
> <a
> href="http://www.openeuphoria.org/cgi-bin/esearch.exu?fromMonth=1&fromYear=D&toMonth=6&toYear=D&postedBy=Fernando&keywords=NextInteger">http://www.openeuphoria.org/cgi-bin/esearch.exu?fromMonth=1&fromYear=D&toMonth=6&toYear=D&postedBy=Fernando&keywords=NextInteger</a>

Hey, thanks Fernando and Lucius. Especially for spelling it out in so much
detail, Fernando. Oh, and I do remember that previous post but I was kind of
skeptical until you proved it just now. Very nice.

I'll update limits.e

--
A complex system that works is invariably found to have evolved from a simple
system that works.
--John Gall's 15th law of Systemantics.

"Premature optimization is the root of all evil in programming."
--C.A.R. Hoare

j.