Re: [eclipse-clp-users] Large integers and delayed goals

From: Kish Shen <kisshen_at_...5...>
Date: Wed, 14 Mar 2012 18:23:31 +0000
Hi Sergey (and others),

Several comments:

ic does not handle large integers, i.e. it does not use the bignum 
representation of integers that ECLiPSe supports (implemented with GNU's 
GMP).

I don't think any integer finite domain solver will handle a large 
finite domain well, both because reasoning and propagating over large 
domains is expensive (e.g. many constraints have a very heavy dependency 
on the domain size(s) of its variabes (particularly if they are domain 
consistent); and also labelling variables with large domain is expensive 
(unless propagation is able to very significantly reduce the domain 
size).  In the case of ic, where a finite domain is represented as a 
bitmap (1 bit per domain value) as soon as a hole appears in the domain, 
this is particularly inefficient if you have a large domain.

Sergrey, you used labeling/1 in the code you showed, but I assume you 
must have given a finite integer interval to the variables, because you 
get an error when you try to label IC variables that do not have a 
finite integer range.

The running of the example with lib(fd) is not "correct" in the sense 
that fd correctly handles large integers in the constraint, as fd 
variables are given a default range (-10,000,000 to 10,000,000), and the 
constraint limits the range of integer range for A,B,C,D accordingly, 
and it is only these values that will be tried. If you try to give a 
variable in a constraint a value that will result in a  value that is 
outside this default range, the constraint will fail, e.g.:

:- lib(fd).

:- A*A #= B*B + C*C, A = 50000.

fails. [this is incorrect in the sense that with large enough range, the 
above does have a solution]

Thorsten: I think gfd is much slower in this example because for the 
constraint A*A*A*A + B*B*B*B +C*C*C*C #= D*D*D*D does not seem to take 
into account the default interval given to the variable, and seem to be 
reasoning assuming the variables have the full (32 bit) range  (it 
assigns a domain of 1..46340 to the variables after posting of this 
constraint, compared to 1..3162 for lib(fd)). [lib(gfd) does give a 
default interval (currently -1,000,000..1,000,000) to variables whose 
domain are not explicitly specified]

Cheers,

Kish


On 14/03/2012 07:33, Matteo Bellotto wrote:
> Dear Sergey,
>      the way numbers are managed depend on the particular solver used.
>      In your email there's a generic reference to ECLiPSe and this isn't sufficient. The only clue you gave is the use of integer constraints. So I supposed you're talking about the "IC" solver.
>
>   In this case you could read the documentation below:
>
>        http://eclipseclp.org/doc/libman/libman017.html
>
>   and
>
>        http://eclipseclp.org/doc/libman/libman019.html
>
> In general, despite the particular solver you are referring to, I think that RTFM it's a good starting point.
>
> Have a nice reading,
> Matteo.
>
>
> ________________________________
> Da: Sergey Dymchenko<kit1980@...6...>
> A: Matteo Bellotto<matteob8@...325...>
> Cc: "eclipse-clp-users@...105..."<eclipse-clp-users@...105...>
> Inviato: Marted́ 13 Marzo 2012 14:03
> Oggetto: Re: [eclipse-clp-users] Large integers and delayed goals
>
> Hi Matteo,
>
> My question was more about how ECLiPSe works with large integers, not
> about this particular problem.
> And it's clear that if we constrain our variables to be at most 100 we
> will not get rounding errors.
>
> Sergey.
>
> On Tue, Mar 13, 2012 at 2:31 PM, Matteo Bellotto<matteob8@...325...>  wrote:
>> Hi Sergey,
>>   using your code I obtained the same, wrong, result.
>> I've sligtly modified your code, defining explicitly the domain of the
>> variables, and this update has improved the search, i.e. I didn't get any
>> "wrong answer".
>> Here there the modified code:
>>
>>   :-lib(ic).
>>   test(Result):-
>>    Result=[A,B,C,D],
>>    Result:: 1..100,
>>
>>    A #>  0, B #>  0, C #>  0, D #>  0,
>>    A #=<  B, B #=<  C, C #=<  D,
>>    A*A*A*A + B*B*B*B + C*C*C*C #= D*D*D*D,
>>    labeling([A, B, C, D]).
>>
>>   ?- test(R).
>>   No (22.43s cpu)
>>
>> Please note that, increasing the domains bounds, the search will take a
>> (really) longer time.
>>
>> Bye,
>> Matteo.
>>
>> Da: Sergey Dymchenko<kit1980@...6...>
>> A: eclipse-clp-users_at_lists.sourceforge.net
>> Inviato: Venerd́ 9 Marzo 2012 18:24
>> Oggetto: [eclipse-clp-users] Large integers and delayed goals
>>
>> Hi,
>>
>> I want to find positive natural numbers A, B, C, D, such that A^4 +
>> B^4 + C^4 = D^4.
>> My program do this:
>>
>>      A #>  0, B #>  0, C #>  0, D #>  0,
>>      A #=<  B, B #=<  C, C #=<  D,
>>      A*A*A*A + B*B*B*B + C*C*C*C #= D*D*D*D,
>>      labeling([A, B, C, D])
>>
>> But I get incorrect result [1, 1, 9742, 9742] with 10 delayed goals.
>> As far as I understand, the system finds that the result is imprecise,
>> but correct enough because 9742^4 is a large number.
>> Probably floating arithmetic is used, not big integers...
>> Is there a way to force precise arithmetic for large integers?
>>
>> Sergey.
>>
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Received on Wed Mar 14 2012 - 18:23:40 CET

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