For run #1, as more of an apples to apples deal, I flushed the cache after each subroutine call. The memoized version wound up about 1/2 the speed (1495/3478) of the iterative version which is a pretty impressive result considering how incredibly slow the non-memoized version is!

Then for run #2, I commented out the line with the "flush" and let fib_memo do its best. Not surprisingly the iterative version stayed the same while the memoized version sped up (4130/3516).

My curiosity is satisfied, but code is below if anybody wants to fiddle with it.

#!/usr/bin/perl -w
use strict;
use Benchmark;
use Memoize qw(flush_cache memoize);
use feature "state";

memoize ('fib_memo');

timethese (10000,

 { Normal=> 
    q{
       foreach (20..25)
       {
          #print "number $_ : fibonacci ",fibonacci($_),"\n";
          my $f = fibonacci($_);
       }
     },
         
#   Slow =>
#    q{
#        foreach (20..25)
#        {
#           #print "number $_ : fibonacci ",fibonacci_slow($_),"\n";
#           my $f = fibonacci_slow($_);
#        }
#     },
     
   Memo =>
    q{
         foreach (20..25)
         {
               #print "number $_ : fibonacci ",fib_memo($_),"\n";
               my $f = fib_memo($_);
               flush_cache('fib_memo');
         }
     },    
  } 
);

=prints
Benchmark: timing 10000 iterations of Memo, Normal...
      Memo:  7 wallclock secs ( 6.69 usr +  0.00 sys =  6.69 CPU) @ 14
+95.44/s (n=10000)
    Normal:  3 wallclock secs ( 2.88 usr +  0.00 sys =  2.88 CPU) @ 34
+78.26/s (n=10000)

Just for fun...without flush_cache('fib_memo');
Benchmark: timing 10000 iterations of Memo, Normal...
      Memo:  2 wallclock secs ( 2.42 usr +  0.00 sys =  2.42 CPU) @ 41
+30.52/s (n=10000)
    Normal:  3 wallclock secs ( 2.84 usr +  0.00 sys =  2.84 CPU) @ 35
+16.17/s (n=10000)  
=cut

sub fibonacci
{
  my $number  = shift;
  my $curnum  = 1;
  my $prevnum = 1;
  my $sum;
  
  if ($number ==1 || $number ==2){ return 1;}
  
  $number -= 2;
  while ($number--)
  {
     $sum = $curnum + $prevnum;
     $prevnum = $curnum;
     $curnum  = $sum;
  }
  
  return $sum;
}


sub fibonacci_slow
{
   my $number = shift;
   if ($number ==1 || $number ==2){ return 1;}
   
   return fibonacci_slow($number-1) + fibonacci_slow($number-2);
}

sub fib_memo {
    state $memo = { 1 => 1, 2 => 1 };
    return $memo->{ $_[0] } //= fib_memo( $_[0] - 1 ) + fib_memo( $_[0
+] - 2 );
}
[download]

You don't need to Memoize fib_memo(), the memoisation is already built in! That's what the state variable %memo is for.

Once you remove that, the real performace shows up (This is for (1..100)):

c:\test>junk21
Benchmark: timing 10000 iterations of Memo, Normal...
      Memo:  1 wallclock secs ( 0.64 usr +  0.00 sys =  0.64 CPU) @ 15
+649.45/s (n=10000)
    Normal: 15 wallclock secs (14.98 usr +  0.01 sys = 14.99 CPU) @ 66
+7.07/s (n=10000)
[download]

The difference is all the clearer with my preferred cmpthese() (why do you use timethese()?):

c:\test>junk21
          Rate Normal   Memo
Normal   669/s     --   -96%
Memo   15573/s  2229%     --
[download]

timethese() got used instead of cmpthese() because I just cut-n-pasted into some other boiler plate that I had. I also like the cmpthese() format better.

I guess you must have a 64bit processor? I can't represent fib(100) as an int without resorting to some bigger than normal integer strategy.