Re: [eclipse-clp-users] Con we do labeling/indomain with bigger numbers?

On 13/04/2022 16:40, Jeshan Babooa via ECLiPSe-CLP-Users wrote:
> I understood that there are certain limits concerning number ranges when using IC.
> e.g X #= 2 ^ 55, indomain(X).
> gives: out of range in indomain(X{36028797018963964 .. 36028797018963976})
> 
> This works fine in other systems like Scryer and SWI.
> 
> I was hoping to be able to label numbers of up to 2 ^ 128.
> Could this somehow work in Eclipse? hopefully in a way that doesn't need code 
> editing?
> 
> We could use several smaller integers to label them but that would meaning 
> labelling a huge number of integers.
> 
> I thought to take a look at the code and In ic.c, I saw that MAX_BITMAP_RANGE 
> could have something to do with it. When I increase it, it takes really long to 
> label just X #= 2^64.
> 
> So how should we label bigger integers?
> 
> Jeshan



Hi Jeshan,

ECLiPSe's lib(ic) constraint solver is designed for handling mixtures of real- 
and integer-valued variables and numbers. All computations in IC-constraints are 
performed using double floats to represent upper and lower bounds, and 
integrality is simply treated as an additional constraint.

Because double floats have 53 bits of precision, only integers in the range 
-9007199254740992..9007199254740992 are represented precisely. Larger integers 
are approximated by a floating point interval that encloses the true value. This 
is why your X remains uninstantiated when you exceed this range:

   ?- X #= 2 ^ 53.
   X = 9007199254740992
   Yes (0.00s cpu)

   ?- X #= 2 ^ 53 + 1.
   X = X{9007199254740991 .. 9007199254740994}
   There is 1 delayed goal.
   Yes (0.00s cpu)

It is a design decision of the IC solver to handle large numbers via this 
"fuzziness", instead of defaulting to unbounded size integer representations. 
This was done because in practice, models involving huge integer domains are 
rarely efficiently solvable, and are therefore less useful than they may seem at 
first glance.


You are not saying anything about the problem you are actually trying to solve. 
  But I suspect that your integers do not represent real world 
quantities/amounts/measurements/etc, and instead you are using them as bitmaps 
to represent arrays of booleans.   In this case I would consider modelling 
directly with boolean (0..1) variables.


-- Joachim