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bignum 0.22 gamo 07-04-2007
`--> Re: bignum 0.22 José Luis Pérez...07-05-2007
Posted by gamo on July 4, 2007, 9:43 am
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Hello

I found a problem related with calculating Catalan's numbers

#!/usr/local/bin/perl -w

use bignum;

while (1){
$n++;
# $Cat = (fact(2*$n))/((n+1)!n!)
$Cat = (fact(2*$n))/(($n+1)*fact($n)**2);
print "$Cat\n";
last if length $Cat > 78;
}

sub fact {
my $i = shift;
my $f = 1;
while ($i>1){
        $f *= $i;
        $i--;
}
return $f;
}

__END__

TIA

--
http://www.telecable.es/personales/gamo/
perl -e 'print 111_111_111**2,"\n";'

Posted by Sisyphus on July 5, 2007, 4:47 am
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>
> Hello
>
> I found a problem related with calculating Catalan's numbers
>

What is the problem ? (I don't see it.)

Cheers,
Rob


Posted by gamo on July 5, 2007, 5:36 am
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On Thu, 5 Jul 2007, Sisyphus wrote:

>
> >
> > Hello
> >
> > I found a problem related with calculating Catalan's numbers
> >
>
> What is the problem ? (I don't see it.)
>
> Cheers,
> Rob
>

The problem is that this output lacks precision aparently

216489185503133990863274261791925599831200000000000000000000
853702637172735926234421145556838686126800000000000000000000
3366939372774715522158184331074634818182000000000000000000000
13280705303722489004068393750349948449500000000000000000000000
52391773216519910749994580850004383791590000000000000000000000
206709359781542193322705891717290023323200000000000000000000000
815663960219058384462569194343901173113100000000000000000000000
3218959557293069695825496284821467129607000000000000000000000000
12704920022590345879098861442746675573490000000000000000000000000
50151000089172417943811295168736877263790000000000000000000000000
197987426438993719534698504405274280676200000000000000000000000000
781708976802233823680102715669100177152500000000000000000000000000
3086748267372923303762456877257472494397000000000000000000000000000
12190039767760866606383939871203238833810000000000000000000000000000
48145535217206784075634048230802707999060000000000000000000000000000
190174864107966797098754490511670696596300000000000000000000000000000
751269297881058917464501210451062751843200000000000000000000000000000
2968129521136642608343357241290264314659000000000000000000000000000000
11727731278637465915893265197293239487190000000000000000000000000000000
46343454246228695957965322150594252812290000000000000000000000000000000
183149331181095806425878953139148487114200000000000000000000000000000000
723875928001473901587997767169015449070200000000000000000000000000000000
2861304849265668492891140780463352404986000000000000000000000000000000000
11311095732253345760960290897769189975960000000000000000000000000000000000
44718285453094622775889522153971216184030000000000000000000000000000000000
176809220945312585436978572208778500912300000000000000000000000000000000000
699138751524213124094312216825551629561400000000000000000000000000000000000
2764775971936660990736598311991954171447000000000000000000000000000000000000
10934377152170553993439479038404269881060000000000000000000000000000000000000
43247909631719355347185999181748231619130000000000000000000000000000000000000
171069509209912116706646841207804116182300000000000000000000000000000000000000
676730852609799402854235298307342753721300000000000000000000000000000000000000

Cheers,

--
http://www.telecable.es/personales/gamo/
perl -e 'print 111_111_111**2,"\n";'

Posted by gamo on July 5, 2007, 6:55 am
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On Thu, 5 Jul 2007, gamo wrote:

> On Thu, 5 Jul 2007, Sisyphus wrote:
>
> >
> > >
> > > Hello
> > >
> > > I found a problem related with calculating Catalan's numbers
> > >
> >
> > What is the problem ? (I don't see it.)
> >
> > Cheers,
> > Rob
> >
>
> The problem is that this output lacks precision aparently
>
> 216489185503133990863274261791925599831200000000000000000000
> 853702637172735926234421145556838686126800000000000000000000
> 3366939372774715522158184331074634818182000000000000000000000
> 13280705303722489004068393750349948449500000000000000000000000
> 52391773216519910749994580850004383791590000000000000000000000
> 206709359781542193322705891717290023323200000000000000000000000
> 815663960219058384462569194343901173113100000000000000000000000
> 3218959557293069695825496284821467129607000000000000000000000000
> 12704920022590345879098861442746675573490000000000000000000000000
> 50151000089172417943811295168736877263790000000000000000000000000
> 197987426438993719534698504405274280676200000000000000000000000000
> 781708976802233823680102715669100177152500000000000000000000000000
> 3086748267372923303762456877257472494397000000000000000000000000000
> 12190039767760866606383939871203238833810000000000000000000000000000
> 48145535217206784075634048230802707999060000000000000000000000000000
> 190174864107966797098754490511670696596300000000000000000000000000000
> 751269297881058917464501210451062751843200000000000000000000000000000
> 2968129521136642608343357241290264314659000000000000000000000000000000
> 11727731278637465915893265197293239487190000000000000000000000000000000
> 46343454246228695957965322150594252812290000000000000000000000000000000
> 183149331181095806425878953139148487114200000000000000000000000000000000
> 723875928001473901587997767169015449070200000000000000000000000000000000
> 2861304849265668492891140780463352404986000000000000000000000000000000000
> 11311095732253345760960290897769189975960000000000000000000000000000000000
> 44718285453094622775889522153971216184030000000000000000000000000000000000
> 176809220945312585436978572208778500912300000000000000000000000000000000000
> 699138751524213124094312216825551629561400000000000000000000000000000000000
> 2764775971936660990736598311991954171447000000000000000000000000000000000000
> 10934377152170553993439479038404269881060000000000000000000000000000000000000
> 43247909631719355347185999181748231619130000000000000000000000000000000000000
> 171069509209912116706646841207804116182300000000000000000000000000000000000000
> 676730852609799402854235298307342753721300000000000000000000000000000000000000
>
> Cheers,
>
> --
> http://www.telecable.es/personales/gamo/
> perl -e 'print 111_111_111**2,"\n";'
>

The real Catalan numbers are of this form

50151000089172417943811295168736877263790538026356457136124707000
197987426438993719534698504405274280676181776208398535128701017200
781708976802233823680102715669100177152510806064194216284009188600
3086748267372923303762456877257472494397093952150920751480446539600
12190039767760866606383939871203238833805472726290924323643119385200
48145535217206784075634048230802707999063631776107012034556858076000
190174864107966797098754490511670696596301345515622697536499589400200
751269297881058917464501210451062751843240026086509499359064493663600
2968129521136642608343357241290264314659358135849980153205484311031600
11727731278637465915893265197293239487190634585553580117543620936271200
46343454246228695957965322150594252812285572152590760141906244022362000
183149331181095806425878953139148487114152581147038684080813476376374624
723875928001473901587997767169015449070222106438295751367024692344718752
2861304849265668492891140780463352404986232263244287143198790516197234752
11311095732253345760960290897769189975961199415637572612957718759342193629
44718285453094622775889522153971216184032648852520635911693306722980765510
176809220945312585436978572208778500912252165463043129681618151197016257478
699138751524213124094312216825551629561424593205010237977696200916445964684
2764775971936660990736598311991954171447451800401631395639071339987763587614
10934377152170553993439479038404269881062854488806451985760537780703486068308
43247909631719355347185999181748231619129200590055369794426007640095877732860
171069509209912116706646841207804116182333282333996796075729541331934805254424
676730852609799402854235298307342753721289013938899090358400685563095038432942
2677285562879644352897777603522480091364515660984549685943453807118230006063172

--
http://www.telecable.es/personales/gamo/
perl -e 'print 111_111_111**2,"\n";'

Posted by Mumia W. on July 5, 2007, 10:41 am
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On 07/05/2007 04:36 AM, gamo wrote:
> On Thu, 5 Jul 2007, Sisyphus wrote:
>
>>> Hello
>>>
>>> I found a problem related with calculating Catalan's numbers
>>>
>> What is the problem ? (I don't see it.)
>>
>> Cheers,
>> Rob
>>
>
> The problem is that this output lacks precision aparently
>
> 216489185503133990863274261791925599831200000000000000000000
> 853702637172735926234421145556838686126800000000000000000000
> 3366939372774715522158184331074634818182000000000000000000000
> [...]

You can set the "accuracy" of the bignum module. Read "perldoc bignum"

BTW, if you make fact() recursive and use the Memoize module, you can
get a speed improvement--a /substantial/ speed improvement :-)



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