Hi,
Following tilly's posting here. I attempted to construct the code.
#!/usr/bin/perl -w
use strict;

my $h =8;
my $pure     = factorial_pure($h);
my $stirling = factorial_stirling($h);

print "PURE     : $pure\n";
print "STIRLING : $stirling\n"

#------Subroutines------------

sub factorial_stirling{
    my $n = shift;
    use constant PI => 4*atan2 (1,1);
    use constant e => exp(1);

    my $log_nfact = 
       $n * log ($n) - e* log($n) + 0.5 * (log(2*PI)+log($n));

    # Below is Tilly's suggestion, with less accuracy       
    # $n * log ($n) - ($n) + (0.5 * (log(2+ log(PI))+log($n))); 
    
    return exp($log_nfact);
}


sub factorial_pure {

     my ($n,$res) =  (shift,1);
     return undef unless $n>=0 and $n == int($n);
     $res *= $n-- while $n>1;
     return $res;

    }

[download]
Stirling method indeed gives a faster result: 
             Rate     pure stirling
pure     290034/s       --     -30%
stirling 319835/s      16%       --

[download]
With a reasonable approximation: 
PURE     : 40320
STIRLING : 417351.253768542

[download]
But when it comes to large N, e.g $h = 500. It began to fail.

I wonder if Tilly's suggestion is ever be possible,
i.e resorting to pure Perl arithmetic (no external module) yet able to handle large number in a fastway?

Regards,
Edward

In reply to Stirling Approx to N! for large Number? by monkfan

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