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Another question to Sisyphus gamo 02-11-2008
Posted by gamo on February 11, 2008, 10:44 am
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Here is a little program that compares
if m^n < n!
The problem is that it hangs out. No matter if I use bignum.
It appears related with the division of big numbers.

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

# use bignum;
$last=2;

for $m (2..1000){
for $n ($last..10000){
        $left = $m**$n;
        $rigth=1;
        for $i (2..$n){
         $rigth*=$i;
        }
        if ($left<$rigth){
         print "$m $n n/m=", $n/$m, "\n";
         $last=$n+1;
         last;
        }
}
}


__END__

PD: The n/m ratio seems to tend to 'e' number,
which is not avaible from perl like pi


--
http://www.telecable.es/personales/gamo/
perl -E 'say 111_111_111**2;'

Posted by Big and Blue on February 11, 2008, 4:11 pm
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 gamo wrote:

> PD: The n/m ratio seems to tend to 'e' number,
> which is not avaible from perl like pi

e is available directly.

[mysys]: perl -le 'print exp(1)';
2.71828182845905

--
Just because I've written it doesn't mean that
either you or I have to believe it.

Posted by gamo on February 12, 2008, 3:35 am
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On Mon, 11 Feb 2008, Big and Blue wrote:

> gamo wrote:
>
> > PD: The n/m ratio seems to tend to 'e' number,
> > which is not avaible from perl like pi
>
> e is available directly.
>
> [mysys]: perl -le 'print exp(1)';
> 2.71828182845905

Ooops! That's rigth, e^1=e
My head was out of service.

So, in the original problem the last sentence I could get is

__END__
645 1749 ...
646 1752 n/m-e=-0.00620752505347248011

and that's all... there are no more printouts

Thank you. Best regards,

>
> --
> Just because I've written it doesn't mean that
> either you or I have to believe it.
>

--
http://www.telecable.es/personales/gamo/
perl -E 'say 111_111_111**2;'

Posted by sisyphus on February 12, 2008, 8:47 am
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> On Mon, 11 Feb 2008, Big and Blue wrote:
> > gamo wrote:
>
> > > PD: The n/m ratio seems to tend to 'e' number,
> > > which is not avaible from perl like pi
>
> > =A0 =A0e is available directly.
>
> > [mysys]: perl -le 'print exp(1)';
> > 2.71828182845905
>
> Ooops! That's rigth, e^1=3De
> My head was out of service.
>
> So, in the original problem the last sentence I could get is
>
> __END__
> 645 1749 ...
> 646 1752 n/m-e=3D-0.00620752505347248011
>
> and that's all... there are no more printouts =A0
>
> Thank you. Best regards,
>
>
>
> > --
> > =A0 =A0 =A0 =A0 =A0 =A0 =A0Just because I've written it doesn't mean tha=
t
> > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 either you or I have to believe it.
>
> --http://www.telecable.es/personales/gamo/
> perl -E 'say 111_111_111**2;'

If you want to evaluate e to greater precision, I suggest (plug)
something like the following (which prints out a 10000-bit value of
e):

use warnings;
use strict;
use Math::MPFR qw(:mpfr);

my $precision =3D 10000; # bits
Rmpfr_set_default_prec($precision);

my $unity =3D Math::MPFR->new(1);
my $e =3D Math::MPFR->new();

Rmpfr_exp($e, $unity, GMP_RNDN);
print $e, "\n";

__END__

Cheers,
Rob


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