OpenEuphoria

Re: Big Integer Atoms

• Posted by Robert Craig <rds at RapidEuphoria.com> Jul 11, 2004
• 552 views

Kat wrote:
> On 11 Jul 2004, at 14:31, Robert Craig wrote:
> > 
> > posted by: Robert Craig <rds at RapidEuphoria.com>
> > 
> > Igor Kachan wrote:
> > > 
> > > Hi, dear Euphorians,
> > > 
> > > The EU manual says:
> > > 
> > > "... Those declared with type integer must be atoms 
> > > with integer values from -1073741824 to +1073741823
> > > inclusive. 
> > > You can perform exact calculations on larger integer
> > > values, up to about 15 decimal digits, but declare 
> > > them as atom, rather than integer ..."
> > > 
> > > This "up to about 15 decimal digits" seems to be not
> > > enough concrete thing for some cases.
> > > 
> > > Couldn't someone tell me about more precise
> > > bounds of these "larger integer values"?
> > 
> > (As I recall) with IEEE floating-point, you have 1 bit 
> > for the +/- sign, 52 bits for the mantissa, and 11 bits 
> > for the exponent.
> > 
> > When storing integers in f.p. form, 
> > at some point you are going to use up all 52 bits in 
> > the mantissa, and you won't be able to store the integers
> > exactly anymore, or get exact results from your calculations.
> > I guess you could look for the point where:
> >    x + 1 = x
> > i.e. you don't have the resolution to distinguish between
> > one huge integer and the next. There's roughly 3 decimal
> > digits per 10 binary digits, so I guess that would be
> > around 52 * 3 / 10 = 15 decimal digits, roughly.
> 
> I am guessing you cannot do something like allocate x number of 8bit 
> memory locations, repeat(poke rand(256) into them) x times, and then point 
> an Eu atom to it without warning? At least, that's what i'd do in turbo 
> pascal... i guess in Eu, to avoid the overflow, you'd use object or even 
> sequence?

Euphoria won't do anything like that automatically.
For really huge integers you can use one of the 
"big integer" math packages in the Archive. 
They let you store big integers in long sequences of digits.
All calculations use Euphoria subroutines rather than
f.p. hardware so they're pretty slow. 

e.g. a "big integer" system could store one base 10 digit per 
sequence element, or, to save memory it might store (say) 
9 digits per sequence element, and do all calculations in 
base one billion, instead of base 10.
e.g. store 123456789555555555 as:
s[1] = 123456789
s[2] = 555555555
and remember that s[1] is one billion times more significant
than s[2]. The usual math operations, add/sub/mul/div can be
implemented just like how you do them "on paper" in base 10.

Regards,
   Rob Craig
   Rapid Deployment Software
   http://www.RapidEuphoria.com