It won't work as well, but it works well enough. My benchmark for 5000 says: 
Method 6: 14 wallclock secs (14.31 usr +  0.01 sys = 14.32 CPU)
Method 7: 15 wallclock secs (14.28 usr +  0.01 sys = 14.29 CPU)
Method 8: 14 wallclock secs (14.25 usr +  0.01 sys = 14.26 CPU)

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I got rid of the Math::BigInt call on the list of 1 then ran it a bunch of times, and there seemed to be some fluctuation. Another run gave me: 
Method 6: 14 wallclock secs (14.08 usr +  0.02 sys = 14.10 CPU)
Method 7: 14 wallclock secs (14.14 usr +  0.01 sys = 14.15 CPU)
Method 8: 15 wallclock secs (14.12 usr +  0.01 sys = 14.13 CPU)

[download]
Not bad for such a stupid approach, huh?

In truth yours is better by about as much as you lose because you used the overloading interface. If I use the overloading interface, well 

sub fact6b{
  my ($m, $n) = @_; 

  if ($m < $n) {
    my $k = int($m/2 + $n/2);
    return my $x = fact6b($m, $k) * fact6b($k+1,$n);
  }
  else {
    return Math::BigInt->new($m);
  }
}

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is very straightforward to anyone who has seen divide-and-conquer before. And recursive is only bad because Perl penalizes function calls horribly.

Of course at this point we are both slow mainly because Perl doesn't implement a good algorithm for big integer multiplication.

In reply to Re: Re^4: Factorial algorithm execution time by Anonymous Monk
in thread Factorial algorithm execution time by gri6507

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