DouKaku?

#!/usr/local/bin/perl
use strict;
use warnings;
use bignum;
use Memoize;

no warnings 'recursion';

sub fib{
    my $n = shift;
    return 1 if $n <= 2;
    fib($n-2)+fib($n-1);
}
memoize 'fib';

sub gcd{
    my ($m, $n) = @_;
    return gcd($n, $m) if $m < $n;
    my $r = $m % $n;
    return $n unless $r;
    gcd($n, $r);
}

sub gcd_nodiv{
    my ($m, $n) = @_;
    return gcd($n, $m) if $m < $n;
    $m -= $n while $m > $n;
    return $n unless $m;
    gcd($n, $m);

}

sub gcd_regexp{
    my ($m, $n) = @_;
    return gcd($n, $m) if $m < $n;
    my $sm = 1 x $m;
    my $sn = 1 x $n;
    $sm =~ s/^$sn//g;
    return $n unless $sm;
    gcd($n, length $sm);
}

sub say { local $\="\n"; print @_ };
say gcd_regexp(fib(25), fib(24));
say gcd_nodiv(fib(1999),fib(2000));